pax_global_header00006660000000000000000000000064132340054120014504gustar00rootroot0000000000000052 comment=5d6f41a3b3aa42a19860af310fef48e46cc1d5d0 colmap-3.4/000077500000000000000000000000001323400541200126255ustar00rootroot00000000000000colmap-3.4/.appveyor.yml000066400000000000000000000010661323400541200152760ustar00rootroot00000000000000image: Visual Studio 2015 configuration: - Release cache: - build build_script: - cmd: set PATH=%APPVEYOR_BUILD_FOLDER%\build\__install__\bin\;%PATH% - cmd: set CTEST_OUTPUT_ON_FAILURE=1 - cmd: set QT_QPA_PLATFORM=offscreen - cmd: C:\Python36-x64\python.exe scripts\python\build.py --build_path %APPVEYOR_BUILD_FOLDER%\build --colmap_path . --boost_path C:\Libraries\boost_1_63_0 --qt_path C:\Qt\5.9\msvc2015_64 --build_type %CONFIGURATION% - cmd: cmake --build %APPVEYOR_BUILD_FOLDER%\build\colmap\build --config %CONFIGURATION% --target RUN_TESTS colmap-3.4/.clang-format000077500000000000000000000037221323400541200152070ustar00rootroot00000000000000--- Language: Cpp # BasedOnStyle: Google AccessModifierOffset: -1 AlignAfterOpenBracket: true AlignConsecutiveAssignments: false AlignEscapedNewlinesLeft: true AlignOperands: true AlignTrailingComments: true AllowAllParametersOfDeclarationOnNextLine: true AllowShortBlocksOnASingleLine: false AllowShortCaseLabelsOnASingleLine: false AllowShortFunctionsOnASingleLine: All AllowShortIfStatementsOnASingleLine: true AllowShortLoopsOnASingleLine: true AlwaysBreakAfterDefinitionReturnType: None AlwaysBreakBeforeMultilineStrings: true AlwaysBreakTemplateDeclarations: true BinPackArguments: true BinPackParameters: true BreakBeforeBinaryOperators: None BreakBeforeBraces: Attach BreakBeforeTernaryOperators: true BreakConstructorInitializersBeforeComma: false ColumnLimit: 80 CommentPragmas: '^ IWYU pragma:' ConstructorInitializerAllOnOneLineOrOnePerLine: true ConstructorInitializerIndentWidth: 4 ContinuationIndentWidth: 4 Cpp11BracedListStyle: true DerivePointerAlignment: false DisableFormat: false ExperimentalAutoDetectBinPacking: false ForEachMacros: [ foreach, Q_FOREACH, BOOST_FOREACH ] IndentCaseLabels: true IndentWidth: 2 IndentWrappedFunctionNames: false KeepEmptyLinesAtTheStartOfBlocks: false MacroBlockBegin: '' MacroBlockEnd: '' MaxEmptyLinesToKeep: 1 NamespaceIndentation: None ObjCBlockIndentWidth: 2 ObjCSpaceAfterProperty: false ObjCSpaceBeforeProtocolList: false PenaltyBreakBeforeFirstCallParameter: 1 PenaltyBreakComment: 300 PenaltyBreakFirstLessLess: 120 PenaltyBreakString: 1000 PenaltyExcessCharacter: 1000000 PenaltyReturnTypeOnItsOwnLine: 200 PointerAlignment: Left SpaceAfterCStyleCast: false SpaceBeforeAssignmentOperators: true SpaceBeforeParens: ControlStatements SpaceInEmptyParentheses: false SpacesBeforeTrailingComments: 2 SpacesInAngles: false SpacesInContainerLiterals: true SpacesInCStyleCastParentheses: false SpacesInParentheses: false SpacesInSquareBrackets: false Standard: Auto TabWidth: 8 UseTab: Never ... colmap-3.4/.gitignore000077500000000000000000000007021323400541200146170ustar00rootroot00000000000000# Custom files LocalConfig.cmake src/util/version.h # Custom directories .idea/ .vscode .DS_Store build/ build-debug/ build-release/ build-relwithdeb/ install-debug/ install-release/ data/ doc/_build # Compiled Object files *.slo *.lo *.o *.obj *.pyc # Precompiled Headers *.gch *.pch # Compiled Dynamic libraries *.so *.dylib *.dll # Fortran module files *.mod # Compiled Static libraries *.lai *.la *.a *.lib # Executables *.exe *.out *.app colmap-3.4/.gitmodules000066400000000000000000000001721323400541200150020ustar00rootroot00000000000000[submodule "doc/_build/html"] path = doc/_build/html url = https://github.com/colmap/colmap.github.io.git ignore = all colmap-3.4/.travis.yml000066400000000000000000000046621323400541200147460ustar00rootroot00000000000000language: cpp sudo: true dist: trusty matrix: include: - os: linux env: CMAKE_OPTIONS="-DOPENGL_ENABLED=OFF -DCeres_DIR=${TRAVIS_BUILD_DIR}/deps/ceres-solver/install/lib/cmake/Ceres -DQt5Core_DIR=/opt/qt54/lib/cmake/Qt5Core -DQt5OpenGL_DIR=/opt/qt54/lib/cmake/Qt5OpenGL" QT_QPA_PLATFORM=offscreen addons: apt: sources: - ubuntu-toolchain-r-test packages: - cmake - build-essential - libboost-program-options-dev - libboost-filesystem-dev - libboost-regex-dev - libboost-system-dev - libboost-test-dev - libeigen3-dev - libatlas-base-dev - libsuitesparse-dev - libfreeimage-dev - libgoogle-glog-dev - libgflags-dev - libglew-dev - os: osx env: CMAKE_OPTIONS="-DLTO_ENABLED=OFF -DQt5Core_DIR=/usr/local/opt/qt5/lib/cmake/Qt5Core -DQt5OpenGL_DIR=/usr/local/opt/qt5/lib/cmake/Qt5OpenGL" cache: directories: - ${TRAVIS_BUILD_DIR}/deps - ${TRAVIS_BUILD_DIR}/build before_script: - | if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then brew tap homebrew/science brew install \ cmake \ boost \ eigen \ freeimage \ glog \ gflags \ suite-sparse \ ceres-solver \ qt5 \ glew || true fi - | if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then export DISPLAY=:99.0 sh -e /etc/init.d/xvfb start sleep 3 sudo add-apt-repository --yes ppa:beineri/opt-qt542-trusty sudo apt-get update -qq sudo apt-get -y install qt54base cd ${TRAVIS_BUILD_DIR}/deps if [[ -z "$(ls -A ceres-solver)" ]]; then git clone https://ceres-solver.googlesource.com/ceres-solver fi cd ceres-solver git pull mkdir -p build install cd build cmake .. \ -DBUILD_TESTING=OFF \ -DBUILD_EXAMPLES=OFF \ -DCMAKE_INSTALL_PREFIX=../install make -j2 make install cd ${TRAVIS_BUILD_DIR} fi script: - cmake --version - cd build - | if [[ -z "$(ls -A colmap)" ]]; then git clone https://github.com/colmap/colmap.git fi - cd colmap - git checkout ${TRAVIS_BRANCH} - git pull - mkdir -p build - cd build - cmake .. -DCMAKE_BUILD_TYPE=Release -DTESTS_ENABLED=ON ${CMAKE_OPTIONS} - make -j2 - CTEST_OUTPUT_ON_FAILURE=1 make test colmap-3.4/CHANGELOG.txt000066400000000000000000000154771323400541200146730ustar00rootroot00000000000000COLMAP 3.4 (01/29/2018) ----------------------- - Unified command-line interface: The functionality of previous executables have been merged into the ``src/exe/colmap.cc`` executable. The GUI can now be started using the command ``colmap gui`` and other commands are available as ``colmap [command]``. For example, the feature extractor is now available as ``colmap feature_extractor [args]`` while all command-line arguments stay the same as before. This should result in much faster project compile times and smaller disk space usage of the program. More details about the new interface are documented at https://colmap.github.io/cli.html - More complete depth and normal maps with larger patch sizes - Faster dense stereo computation by skipping rows/columns in patch match, improved random sampling in patch match, and faster bilateral NCC - Better high DPI screen support for the graphical user interface - Improved model viewer under Windows, which now requires Qt 5.4 - Save computed two-view geometries in database - Images (keypoint/matches visualization, depth and normal maps) can now be saved from the graphical user interface - Support for PMVS format without sparse bundler file - Faster covariant feature detection - Many more bug fixes and improvements COLMAP 3.3 (11/21/2017) ----------------------- - Add DSP (Domain Size Pooling) SIFT implementation. DSP-SIFT outperforms standard SIFT in most cases, as shown in "Comparative Evaluation of Hand-Crafted and Learned Local Features", Schoenberger et al., CVPR 2017 - Improved parameters dense reconstruction of smaller models - Improved compile times due to various code optimizations - Add option to specify camera model in automatic reconstruction - Add new model orientation alignment based on upright image assumption - Improved numerical stability for generalized absolute pose solver - Support for image range specification in PMVS dense reconstruction format - Support for older Python versions in automatic build script - Fix OpenCV Fisheye camera model to exactly match OpenCV specifications COLMAP 3.2 (9/2/2017) ---------------------- - Fully automatic cross-platform build script (Windows, Mac, Linux) - Add multi-GPU feature extraction if multiple CUDA devices are available - Configurable dimension and data type for vocabulary tree implementation - Add new sequential matching mode for image sequences with high frame-rate - Add generalized relative pose solver for multi-camera systems - Add sparse least absolute deviation solver - Add CPU/GPU options to automatic reconstruction tool - Add continuous integration system under Windows, Mac, Linux through Github - Many more bug fixes and improvements COLMAP 3.1 (6/15/2017) ---------------------- - Add fast spatial verification to image retrieval module - Add binary file format for sparse models by default. Old text format still fully compatible and possible conversion in GUI and CLI - Add cross-platform little endian binary file reading and writing - Faster and less memory hungry stereo fusion by computing consistency on demand and possible limitation of image size in fusion - Simpler geometric stereo processing interface. Now geometric stereo output can be computed using a single pass - Faster and multi-architecture CUDA compilation - Add medium quality option in automatic reconstructor - Many more bug fixes and improvements COLMAP 3.0 (5/22/2017) ---------------------- - Add automatic end-to-end reconstruction tool that automatically performs sparse and dense reconstruction on a given set of images - Add multi-GPU dense stereo if multiple CUDA devices are available - Add multi-GPU feature matching if multiple CUDA devices are available - Add Manhattan-world / gravity alignment using line detection - Add CUDA-based feature extraction useful for usage on clusters - Add CPU-based feature matching for machines without GPU - Add new THIN_PRISM_FISHEYE camera model with tangential/radial correction - Add binary to triangulate existing/empty sparse reconstruction - Add binary to print summary statistics about sparse reconstruction - Add transitive feature matching to transitively complete match graph - Improved scalability of dense reconstruction by using caching - More stable GPU-based feature matching with informative warnings - Faster vocabulary tree matching using dynamic scheduling in FLANN - Faster spatial feature matching using linear index instead of kd-tree - More stable camera undistortion using numerical Newton iteration - Improved option parsing with some backwards incompatible option renaming - Faster compile times by optimizing includes and CUDA flags - More stable view selection for small baseline scenario in dense reconstruction - Many more bug fixes and improvements COLMAP 2.1 (12/7/2016) ---------------------- - Support to only index and match specific images in vocabulary tree matching - Support to perform image retrieval using vocabulary tree - Several bug fixes and improvements for multi-view stereo module - Improved Structure-from-Motion initialization strategy - Support to only reconstruct the scene using specific images in the database - Add support to merge two models using overlapping registered images - Add support to geo-register/align models using known camera locations - Support to only extract specific images in feature extraction module - Support for snapshot model export during reconstruction - Skip already undistorted images if they exist in output directory - Support to limit the number of features in image retrieval for improved speed - Miscellaneous bug fixes and improvements COLMAP 2.0 (9/8/2016) --------------------- - Implementation of dense reconstruction pipeline - Improved feature matching performance - New bundle adjuster for rigidly mounted multi-camera systems - New generalized absolute pose solver for multi-camera systems - New executable to extract colors from all images - Boost can now be linked in shared and static mode - Various bug fixes and performance improvements COLMAP 1.1 (5/19/2016) ---------------------- - Implementation of state-of-the-art image retrieval system using Hamming embedding for vocabulary tree matching. This should lead to much improved matching results as compared to the previous implementation. - Guided matching as an optional functionality. - New demo datasets for download. - Automatically switch to PBA if supported by the project. - Implementation of EPNP solver for local pose optimization in RANSAC. - Add option to extract upright SIFT features. - Saving JPEGs in superb quality by default in export. - Add option to clear matches and inlier matches in the project. - New fisheye camera models, including the FOV camera model used by Google Project Tango (Thomas Schoeps). - Extended documentation based on user feedback. - Fixed typo in documentation (Thomas Schoeps). COLMAP 1.0 (4/4/2016) --------------------- - Initial release of COLMAP. colmap-3.4/CMakeLists.txt000077500000000000000000000147501323400541200153770ustar00rootroot00000000000000cmake_minimum_required(VERSION 2.8.11) project(COLMAP) set(COLMAP_VERSION "3.4") set(COLMAP_VERSION_NUMBER "3400") ################################################################################ # Include CMake dependencies ################################################################################ set(CMAKE_MODULE_PATH ${CMAKE_SOURCE_DIR}/cmake) include(CheckCXXCompilerFlag) # Include helper macros and commands, and allow the included file to override # the CMake policies in this file include(${CMAKE_SOURCE_DIR}/cmake/CMakeHelper.cmake NO_POLICY_SCOPE) include(${CMAKE_SOURCE_DIR}/cmake/CheckSSEExtensions.cmake) if(EXISTS ${CMAKE_SOURCE_DIR}/LocalConfig.cmake) include(${CMAKE_SOURCE_DIR}/LocalConfig.cmake) endif() ################################################################################ # Options ################################################################################ option(OPENMP_ENABLED "Whether to enable OpenMP" ON) option(IPO_ENABLED "Whether to enable interprocedural optimization" ON) option(CUDA_ENABLED "Whether to enable CUDA, if available" ON) option(OPENGL_ENABLED "Whether to enable OpenGL, if available" ON) option(TESTS_ENABLED "Whether to build test binaries" OFF) option(PROFILING_ENABLED "Whether to enable google-perftools linker flags" OFF) option(BOOST_STATIC "Whether to enable static boost library linker flags" ON) option(CUDA_MULTI_ARCH "Whether to generate CUDA code for multiple architectures" OFF) if(TESTS_ENABLED) enable_testing() endif() if(BOOST_STATIC) set(Boost_USE_STATIC_LIBS ON) else() add_definitions(-DBOOST_TEST_DYN_LINK) endif() ################################################################################ # Find packages ################################################################################ if(OPENMP_ENABLED) find_package(OpenMP QUIET) endif() find_package(Boost COMPONENTS program_options filesystem regex system unit_test_framework REQUIRED) find_package(Eigen3 REQUIRED) find_package(FreeImage REQUIRED) find_package(Glog REQUIRED) find_package(Ceres REQUIRED) find_package(OpenGL REQUIRED) find_package(Glew REQUIRED) find_package(Git) set(CUDA_MIN_VERSION "7.0") if(CUDA_ENABLED) find_package(CUDA ${CUDA_MIN_VERSION} QUIET) endif() find_package(Qt5 5.4 REQUIRED) ################################################################################ # Compiler specific configuration ################################################################################ if(CMAKE_BUILD_TYPE) message(STATUS "Build type specified as ${CMAKE_BUILD_TYPE}") else() message(STATUS "Build type not specified, using Release") set(CMAKE_BUILD_TYPE Release) set(IS_DEBUG FALSE) endif() if(IS_MSVC) add_definitions("-DGLOG_NO_ABBREVIATED_SEVERITIES") add_definitions("-DGL_GLEXT_PROTOTYPES") set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc") else() set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11") endif() if(IS_GNU) # Hide incorrect warnings for uninitialized Eigen variables under GCC. set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -Wno-maybe-uninitialized") set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-maybe-uninitialized") endif() if(IS_DEBUG) add_definitions("-DEIGEN_INITIALIZE_MATRICES_BY_NAN") endif() if(OPENMP_ENABLED AND OPENMP_FOUND) message(STATUS "Enabling OpenMP support") add_definitions("-DOPENMP_ENABLED") set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} ${OpenMP_C_FLAGS}") set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}") else() message(STATUS "Disabling OpenMP support") endif() if(IPO_ENABLED AND NOT IS_DEBUG AND NOT IS_GNU) message(STATUS "Enabling interprocedural optimization") set_property(DIRECTORY PROPERTY INTERPROCEDURAL_OPTIMIZATION 1) else() message(STATUS "Disabling interprocedural optimization") endif() if(CUDA_FOUND) if(CUDA_ENABLED) add_definitions("-DCUDA_ENABLED") include(${CMAKE_SOURCE_DIR}/cmake/SelectCudaComputeArch.cmake) if(CUDA_MULTI_ARCH) CUDA_SELECT_NVCC_ARCH_FLAGS(CUDA_ARCH_FLAGS All) else() CUDA_SELECT_NVCC_ARCH_FLAGS(CUDA_ARCH_FLAGS Auto) endif() list(APPEND CUDA_NVCC_FLAGS "-Wno-deprecated-gpu-targets") list(APPEND CUDA_NVCC_FLAGS ${CUDA_ARCH_FLAGS}) message(STATUS "Enabling CUDA support (version: ${CUDA_VERSION_STRING}," " archs: ${CUDA_ARCH_FLAGS_readable})") else() set(CUDA_FOUND FALSE) message(STATUS "Disabling CUDA support") endif() else() set(CUDA_ENABLED FALSE) if(CUDA_VERSION_STRING) message(STATUS "Disabling CUDA support (found version " "${CUDA_VERSION_STRING} but >= ${CUDA_MIN_VERSION} required)") else() message(STATUS "Disabling CUDA support") endif() endif() if(OPENGL_ENABLED) add_definitions("-DOPENGL_ENABLED") message(STATUS "Enabling OpenGL support") else() message(STATUS "Disabling OpenGL support") endif() if(PROFILING_ENABLED) message(STATUS "Enabling profiling support") set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -lprofiler -ltcmalloc") set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -lprofiler -ltcmalloc") else() message(STATUS "Disabling profiling support") endif() # Qt5 was built with -reduce-relocations. if(Qt5_POSITION_INDEPENDENT_CODE) set(CMAKE_POSITION_INDEPENDENT_CODE ON) if(CUDA_ENABLED AND NOT IS_MSVC) list(APPEND CUDA_NVCC_FLAGS "--compiler-options -fPIC") endif() endif() ################################################################################ # Add sources ################################################################################ include(GenerateVersionDefinitions) add_subdirectory(src) ################################################################################ # Install/uninstall script ################################################################################ if(IS_MSVC) install(FILES "scripts/shell/COLMAP.bat" "scripts/shell/RUN_TESTS.bat" PERMISSIONS OWNER_READ OWNER_WRITE OWNER_EXECUTE GROUP_READ GROUP_EXECUTE WORLD_READ WORLD_EXECUTE DESTINATION "/") endif() configure_file("${CMAKE_SOURCE_DIR}/cmake/CMakeUninstall.cmake" "${CMAKE_CURRENT_BINARY_DIR}/CMakeUninstall.cmake" IMMEDIATE @ONLY) add_custom_target(uninstall COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_BINARY_DIR}/CMakeUninstall.cmake) set_target_properties(uninstall PROPERTIES FOLDER ${CMAKE_TARGETS_ROOT_FOLDER}) colmap-3.4/CONTRIBUTING.md000066400000000000000000000016711323400541200150630ustar00rootroot00000000000000Contributing ------------ Contributions (bug reports, bug fixes, improvements, etc.) are very welcome and should be submitted in the form of new issues and/or pull requests on GitHub. Please, adhere to the Google coding style guide: https://google.github.io/styleguide/cppguide.html by using the provided ".clang-format" file. Document functions, methods, classes, etc. with inline documentation strings describing the API, using the following format: // Short description. // // Longer description with a few sentences and multiple lines. // // @param parameter1 Description for parameter 1. // @param parameter2 Description for parameter 2. // // @return Description of optional return value. Add unit tests for all newly added code and make sure that algorithmic "improvements" generalize and actually improve the results of the pipeline on a variety of datasets. colmap-3.4/COPYING.txt000066400000000000000000001060531323400541200145030ustar00rootroot00000000000000COLMAP - Structure-from-Motion and Multi-View Stereo. Copyright (C) 2017 Johannes L. Schoenberger This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. 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Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . colmap-3.4/LocalConfigExample.cmake000077500000000000000000000025431323400541200173320ustar00rootroot00000000000000# This is an example of a LocalConfig.cmake file. This is useful on Windows # platforms, where CMake cannot find many of the libraries automatically and # it is tedious to set their paths manually in the GUI. To use this file, copy # and rename it to LocalConfig.cmake message(STATUS "NOTE: Using LocalConfig.cmake to override CMake settings in the GUI") set(Ceres_DIR "/build/install/CMake" CACHE PATH "" FORCE) set(EIGEN3_INCLUDE_DIRS "" CACHE PATH "" FORCE) set(GLOG_INCLUDE_DIR_HINTS "/src/windows" CACHE PATH "" FORCE) set(GLOG_LIBRARY_DIR_HINTS "/x64/Release" CACHE FILEPATH "" FORCE) set(BOOST_ROOT "" CACHE PATH "" FORCE) set(BOOST_LIBRARYDIR "" CACHE PATH "" FORCE) set(OPENGL_gl_LIBRARY "opengl32" CACHE STRING "" FORCE) set(OPENGL_glu_LIBRARY "glu32" CACHE STRING "" FORCE) set(GLEW_INCLUDE_DIR_HINTS "/include" CACHE PATH "" FORCE) set(GLEW_LIBRARY_DIR_HINTS "/lib/Release/x64" CACHE FILEPATH "" FORCE) set(Qt5_CMAKE_DIR "/lib/cmake" CACHE PATH "" FORCE) set(Qt5Core_DIR ${Qt5_CMAKE_DIR}/Qt5Core CACHE PATH "" FORCE) set(Qt5OpenGL_DIR ${Qt5_CMAKE_DIR}/Qt5OpenGL CACHE PATH "" FORCE) set(FREEIMAGE_INCLUDE_DIR_HINTS "/Dist/x64" CACHE PATH "" FORCE) set(FREEIMAGE_LIBRARY_DIR_HINTS "/Dist/x64" CACHE PATH "" FORCE) colmap-3.4/README.md000077500000000000000000000100471323400541200141110ustar00rootroot00000000000000COLMAP ====== About ----- COLMAP is a general-purpose Structure-from-Motion (SfM) and Multi-View Stereo (MVS) pipeline with a graphical and command-line interface. It offers a wide range of features for reconstruction of ordered and unordered image collections. The software is licensed under the GNU General Public License. If you use this project for your research, please cite: @inproceedings{schoenberger2016sfm, author = {Sch\"{o}nberger, Johannes Lutz and Frahm, Jan-Michael}, title = {Structure-from-Motion Revisited}, booktitle={IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, year={2016}, } @inproceedings{schoenberger2016mvs, author = {Sch\"{o}nberger, Johannes Lutz and Zheng, Enliang and Pollefeys, Marc and Frahm, Jan-Michael}, title = {Pixelwise View Selection for Unstructured Multi-View Stereo}, booktitle={European Conference on Computer Vision (ECCV)}, year={2016}, } If you use the image retrieval / vocabulary tree engine, please also cite: @inproceedings{schoenberger2016vote, author = {Sch\"{o}nberger, Johannes Lutz and Price, True and Sattler, Torsten and Frahm, Jan-Michael and Pollefeys, Marc}, title = {A Vote-and-Verify Strategy for Fast Spatial Verification in Image Retrieval}, booktitle={Asian Conference on Computer Vision (ACCV)}, year={2016}, } The latest source code is available at https://github.com/colmap/colmap. COLMAP builds on top of existing works and when using specific algorithms within COLMAP, please also cite the original authors, as specified in the source code. Download -------- Executables and other resources can be downloaded from https://demuc.de/colmap/. Getting Started --------------- 1. Download the pre-built binaries from https://demuc.de/colmap/ or build the library manually as described in the documentation. 2. Download one of the provided datasets at https://demuc.de/colmap/datasets/ or use your own images. 3. Use the **automatic reconstruction** to easily build models with a single click or command. 4. Watch the short introductory video at https://www.youtube.com/watch?v=P-EC0DzeVEU or read the tutorial in the documentation at https://colmap.github.io/ for more details. Documentation ------------- The documentation is available at https://colmap.github.io/. Support ------- Please, use the COLMAP Google Group at https://groups.google.com/forum/#!forum/colmap (colmap@googlegroups.com) for questions and the GitHub issue tracker at https://github.com/colmap/colmap for bug reports, feature requests/additions, etc. Acknowledgments --------------- The library was written by Johannes L. Schönberger (https://demuc.de/). Funding was provided by his PhD advisors Jan-Michael Frahm (http://frahm.web.unc.edu/) and Marc Pollefeys (https://www.inf.ethz.ch/personal/marc.pollefeys/). Contribution ------------ Contributions (bug reports, bug fixes, improvements, etc.) are very welcome and should be submitted in the form of new issues and/or pull requests on GitHub. License ------- The software is licensed under the GNU General Public License v3 or later. If you are interested in licensing the software for commercial purposes, without disclosing your modifications, please contact the authors. COLMAP - Structure-from-Motion and Multi-View Stereo. Copyright (C) 2017 Johannes L. Schoenberger This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . colmap-3.4/cmake/000077500000000000000000000000001323400541200137055ustar00rootroot00000000000000colmap-3.4/cmake/CMakeHelper.cmake000066400000000000000000000221301323400541200170250ustar00rootroot00000000000000if(POLICY CMP0043) cmake_policy(SET CMP0043 OLD) endif() if(POLICY CMP0054) cmake_policy(SET CMP0054 OLD) endif() if("${CMAKE_CXX_COMPILER_ID}" STREQUAL "MSVC") set(IS_MSVC TRUE) endif() if("${CMAKE_CXX_COMPILER_ID}" STREQUAL "GNU") set(IS_GNU TRUE) endif() if("${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang") set(IS_CLANG TRUE) endif() string(TOLOWER "${CMAKE_BUILD_TYPE}" CMAKE_BUILD_TYPE_LOWER) if(CMAKE_BUILD_TYPE_LOWER STREQUAL "debug" OR CMAKE_BUILD_TYPE_LOWER STREQUAL "relwithdebinfo") set(IS_DEBUG TRUE) endif() # Enable solution folders set_property(GLOBAL PROPERTY USE_FOLDERS ON) set(CMAKE_TARGETS_ROOT_FOLDER "cmake") set_property(GLOBAL PROPERTY PREDEFINED_TARGETS_FOLDER ${CMAKE_TARGETS_ROOT_FOLDER}) set(COLMAP_TARGETS_ROOT_FOLDER "colmap_targets") set(COLMAP_SRC_ROOT_FOLDER "colmap_src") # Remove the default warning level set by CMake so that later code can allow # the user to specify a custom warning level. set(REMOVED_WARNING_LEVEL FALSE) if(IS_MSVC) # CXX Flags if(CMAKE_CXX_FLAGS MATCHES "/W[0-4]") string(REGEX REPLACE "/W[0-4]" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") set(REMOVED_WARNING_LEVEL TRUE) elseif(CMAKE_CXX_FLAGS MATCHES "/Wall") string(REGEX REPLACE "/Wall" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") set(REMOVED_WARNING_LEVEL TRUE) endif() # C Flags if(CMAKE_C_FLAGS MATCHES "/W[0-4]") string(REGEX REPLACE "/W[0-4]" "" CMAKE_C_FLAGS "${CMAKE_C_FLAGS}") set(REMOVED_WARNING_LEVEL TRUE) elseif(CMAKE_C_FLAGS MATCHES "/Wall") string(REGEX REPLACE "/Wall" "" CMAKE_C_FLAGS "${CMAKE_C_FLAGS}") set(REMOVED_WARNING_LEVEL TRUE) endif() elseif(IS_GNU OR IS_CLANG) # CXX Flags if(CMAKE_CXX_FLAGS MATCHES "-Wall") string(REGEX REPLACE "-Wall" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") set(REMOVED_WARNING_LEVEL TRUE) endif() # C Flags if(CMAKE_C_FLAGS MATCHES "-Wall") string(REGEX REPLACE "-Wall" "" CMAKE_C_FLAGS "${CMAKE_C_FLAGS}") set(REMOVED_WARNING_LEVEL TRUE) endif() else() message(WARNING "Unsupported compiler. Please update CMakeLists.txt") endif() if(REMOVED_WARNING_LEVEL) message("Removed warning level from default CMAKE_CXX_FLAGS.") set(CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS} CACHE STRING "Flags used by the compiler during all build types." FORCE) set(CMAKE_C_FLAGS ${CMAKE_C_FLAGS} CACHE STRING "Flags used by the compiler during all build types." FORCE) endif() # Construct a list of the possible warning levels that the user can set. set(COMPILER_DEFAULT_WARNING_LEVEL "") if(IS_MSVC) set(WARNING_LEVEL_OPTIONS ${COMPILER_DEFAULT_WARNING_LEVEL} /W0 /W1 /W2 /W3 /W4 /Wall) elseif(IS_GNU OR IS_CLANG) set(WARNING_LEVEL_OPTIONS ${COMPILER_DEFAULT_WARNING_LEVEL} -w -Wall "-Wall -pedantic" "-Wall -pedantic -Wextra -Wno-long-long") else() message(WARNING "Unsupported compiler. Please update CMakeLists.txt") endif() # Set the default warning level. if(IS_MSVC) set(COLMAP_WARNING_LEVEL "/W3" CACHE STRING "Default compiler warning level.") elseif(IS_GNU OR IS_CLANG) set(COLMAP_WARNING_LEVEL "-Wall -pedantic" CACHE STRING "Default compiler warning level.") else() message(WARNING "Unsupported compiler. Please update CMakeLists.txt") endif() # Allow the user to change the default warning level using a drop-down list in # the CMake GUI. set_property(CACHE COLMAP_WARNING_LEVEL PROPERTY STRINGS ${WARNING_LEVEL_OPTIONS}) # Set the default warning level for 3rd-party targets. if(IS_MSVC) set(COLMAP_WARNING_LEVEL_THIRD_PARTY "/W0" CACHE STRING "Default compiler warning level for 3rd-party targets.") elseif(IS_GNU OR IS_CLANG) set(COLMAP_WARNING_LEVEL_THIRD_PARTY "-w" CACHE STRING "Default compiler warning level for 3rd-party targets.") else() message(WARNING "Unsupported compiler. Please update CMakeLists.txt") endif() # Allow the user to change the default warning level for 3rd-party targets # using a drop-down list in the CMake GUI. set_property(CACHE COLMAP_WARNING_LEVEL_THIRD_PARTY PROPERTY STRINGS ${WARNING_LEVEL_OPTIONS}) # Macro used to define that all following targets should be treated as # 3rd-party targets. macro(COLMAP_SET_THIRD_PARTY_FOLDER) set(COLMAP_THIRD_PARTY_FOLDER TRUE) endmacro(COLMAP_SET_THIRD_PARTY_FOLDER) # Macro used to define that all following targets should not be treated as # 3rd-party targets. macro(COLMAP_UNSET_THIRD_PARTY_FOLDER) set(COLMAP_THIRD_PARTY_FOLDER FALSE) endmacro(COLMAP_UNSET_THIRD_PARTY_FOLDER) # Macro to help provide replacements to the normal add_library(), # add_executable(), etc. commands. macro(COLMAP_ADD_TARGET_HELPER TARGET_NAME) # Set the name of the folder that will contain this target in the GUI. # It is assumed that FOLDER_NAME has already been defined. set_target_properties(${TARGET_NAME} PROPERTIES FOLDER ${COLMAP_TARGETS_ROOT_FOLDER}/${FOLDER_NAME}) # Get the warning level to use for this target. if(COLMAP_THIRD_PARTY_FOLDER) set(CURRENT_WARNING_LEVEL ${COLMAP_WARNING_LEVEL_THIRD_PARTY}) else() set(CURRENT_WARNING_LEVEL ${COLMAP_WARNING_LEVEL}) endif() # Only update the target's compile options if a valid warning level has # been selected. if(NOT ${CURRENT_WARNING_LEVEL} STREQUAL ${COMPILER_DEFAULT_WARNING_LEVEL}) # Get the current compile options. get_target_property(CURRENT_COMPILE_OPTIONS ${TARGET_NAME} COMPILE_OPTIONS) # If compile options have not already been set for this target, set them to # a default value. if(NOT CURRENT_COMPILE_OPTIONS) set(CURRENT_COMPILE_OPTIONS "") endif() separate_arguments(CURRENT_WARNING_LEVEL) # If the warning level consists of multiple tokens, add each token to the # current list of compile options. foreach(WARNING_LEVEL ${CURRENT_WARNING_LEVEL}) list(APPEND CURRENT_COMPILE_OPTIONS ${WARNING_LEVEL}) endforeach() unset(WARNING_LEVEL) unset(CURRENT_WARNING_LEVEL) # Set the target's updated compile options. set_target_properties(${TARGET_NAME} PROPERTIES COMPILE_OPTIONS "${CURRENT_COMPILE_OPTIONS}") unset(CURRENT_COMPILE_OPTIONS) endif() endmacro(COLMAP_ADD_TARGET_HELPER) # Replacement for the normal add_library() command. The syntax remains the same # in that the first argument is the target name, and the following arguments # are the source files to use when building the target. macro(COLMAP_ADD_LIBRARY TARGET_NAME) # ${ARGN} will store the list of source files passed to this function. add_library(${TARGET_NAME} ${ARGN}) qt5_use_modules(${TARGET_NAME} ${COLMAP_QT_MODULES}) COLMAP_ADD_TARGET_HELPER(${TARGET_NAME}) endmacro(COLMAP_ADD_LIBRARY) # Replacement for the normal cuda_add_library() command. The syntax remains the # same in that the first argument is the target name, and the following # arguments are the source files to use when building the target. macro(COLMAP_CUDA_ADD_LIBRARY TARGET_NAME) # ${ARGN} will store the list of source files passed to this function. cuda_add_library(${TARGET_NAME} ${ARGN}) COLMAP_ADD_TARGET_HELPER(${TARGET_NAME}) endmacro(COLMAP_CUDA_ADD_LIBRARY) # Replacement for the normal add_executable() command. The syntax remains the # same in that the first argument is the target name, and the following # arguments are the source files to use when building the target. macro(COLMAP_ADD_EXECUTABLE TARGET_NAME) # ${ARGN} will store the list of source files passed to this function. add_executable(${TARGET_NAME} ${ARGN}) target_link_libraries(${TARGET_NAME} ${COLMAP_LIBRARIES}) qt5_use_modules(${TARGET_NAME} ${COLMAP_QT_MODULES}) COLMAP_ADD_TARGET_HELPER(${TARGET_NAME}) install(TARGETS ${TARGET_NAME} DESTINATION bin/) endmacro(COLMAP_ADD_EXECUTABLE) # Wrapper for test executables macro(COLMAP_ADD_TEST TARGET_NAME) if(TESTS_ENABLED) # ${ARGN} will store the list of source files passed to this function. add_executable(${TARGET_NAME} ${ARGN}) target_link_libraries(${TARGET_NAME} ${COLMAP_LIBRARIES} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY}) COLMAP_ADD_TARGET_HELPER(${TARGET_NAME}) add_test("${FOLDER_NAME}/${TARGET_NAME}" ${TARGET_NAME}) if(IS_MSVC) install(TARGETS ${TARGET_NAME} DESTINATION bin/) endif() endif() endmacro(COLMAP_ADD_TEST) # Wrapper for CUDA test executables macro(COLMAP_CUDA_ADD_TEST TARGET_NAME) if(TESTS_ENABLED) # ${ARGN} will store the list of source files passed to this function. cuda_add_executable(${TARGET_NAME} ${ARGN}) target_link_libraries(${TARGET_NAME} ${COLMAP_LIBRARIES} ${Boost_UNIT_TEST_FRAMEWORK_LIBRARY}) COLMAP_ADD_TARGET_HELPER(${TARGET_NAME}) add_test("${FOLDER_NAME}/${TARGET_NAME}" ${TARGET_NAME}) if(IS_MSVC) install(TARGETS ${TARGET_NAME} DESTINATION bin/) endif() endif() endmacro(COLMAP_CUDA_ADD_TEST) colmap-3.4/cmake/CMakeUninstall.cmake000066400000000000000000000015331323400541200175630ustar00rootroot00000000000000if(NOT EXISTS "@CMAKE_CURRENT_BINARY_DIR@/install_manifest.txt") message(FATAL_ERROR "Cannot find install manifest: @CMAKE_CURRENT_BINARY_DIR@/install_manifest.txt") endif() file(READ "@CMAKE_CURRENT_BINARY_DIR@/install_manifest.txt" files) string(REGEX REPLACE "\n" ";" files "${files}") foreach(file ${files}) message(STATUS "Uninstalling $ENV{DESTDIR}${file}") if(IS_SYMLINK "$ENV{DESTDIR}${file}" OR EXISTS "$ENV{DESTDIR}${file}") exec_program("@CMAKE_COMMAND@" ARGS "-E remove \"$ENV{DESTDIR}${file}\"" OUTPUT_VARIABLE rm_out RETURN_VALUE rm_retval) if(NOT "${rm_retval}" STREQUAL 0) message(FATAL_ERROR "Problem when removing $ENV{DESTDIR}${file}") endif() else() message(STATUS "File $ENV{DESTDIR}${file} does not exist.") endif() endforeach() colmap-3.4/cmake/CheckSSEExtensions.cmake000066400000000000000000000107331323400541200203630ustar00rootroot00000000000000include(CheckCXXSourceRuns) ################################################################################ # SSE ################################################################################ if(IS_GNU OR IS_CLANG) set(CMAKE_REQUIRED_FLAGS "-msse") endif() CHECK_CXX_SOURCE_RUNS(" #include int main() { __m128 a, b; float vals[4] = {0}; a = _mm_loadu_ps(vals); b = a; b = _mm_add_ps(a, b); _mm_storeu_ps(vals, b); return 0; }" HAS_SSE_EXTENSION) ################################################################################ # SSE 2 ################################################################################ if(IS_GNU OR IS_CLANG) set(CMAKE_REQUIRED_FLAGS "-msse2") endif() CHECK_CXX_SOURCE_RUNS(" #include int main() { __m128d a, b; double vals[2] = {0}; a = _mm_loadu_pd(vals); b = _mm_add_pd(a, a); _mm_storeu_pd(vals, b); return 0; }" HAS_SSE2_EXTENSION) ################################################################################ # SSE 3 ################################################################################ if(IS_GNU OR IS_CLANG) set(CMAKE_REQUIRED_FLAGS "-msse3") endif() CHECK_CXX_SOURCE_RUNS(" #include int main() { __m128d a, b; double vals[2] = {0}; a = _mm_loadu_pd(vals); b = _mm_hadd_pd(a, a); _mm_storeu_pd(vals, b); return 0; }" HAS_SSE3_EXTENSION) ################################################################################ # SSE 4.1 ################################################################################ if(IS_GNU OR IS_CLANG) set(CMAKE_REQUIRED_FLAGS "-msse4.1") endif() CHECK_CXX_SOURCE_RUNS(" #include int main() { __m128 a, b; float vals[4] = {1, 2, 3, 4}; const int mask = 123; a = _mm_loadu_ps(vals); b = a; b = _mm_dp_ps(a, a, mask); _mm_storeu_ps(vals, b); return 0; }" HAS_SSE41_EXTENSION) ################################################################################ # SSE 4.2 ################################################################################ if(IS_GNU OR IS_CLANG) set(CMAKE_REQUIRED_FLAGS "-msse4.2") endif() CHECK_CXX_SOURCE_RUNS(" #include #include int main() { long long a[2] = { 1, 2}; long long b[2] = {-1, 3}; long long c[2]; __m128i va = _mm_loadu_si128((__m128i*)a); __m128i vb = _mm_loadu_si128((__m128i*)b); __m128i vc = _mm_cmpgt_epi64(va, vb); _mm_storeu_si128((__m128i*)c, vc); if (c[0] == -1LL && c[1] == 0LL) return 0; else return 1; }" HAS_SSE42_EXTENSION) ################################################################################ # AVX ################################################################################ if(IS_GNU OR IS_CLANG) set(CMAKE_REQUIRED_FLAGS "-mavx") endif() CHECK_CXX_SOURCE_RUNS(" #include #include int main() { __m256 a = _mm256_set_ps(2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0); __m256 b = _mm256_set_ps(1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 13.0, 15.0); __m256 c = _mm256_sub_ps(a, b); float* f = (float*)&c; return 0; }" HAS_AVX_EXTENSION) ################################################################################ # Setup the compile flags ################################################################################ # Clear the set flags from above. set(CMAKE_REQUIRED_FLAGS) # Set the compile flags for the supported extensions. set(SSE_FLAGS) if(IS_GNU OR IS_CLANG) if(HAS_SSE_EXTENSION) set(SSE_FLAGS "${SSE_FLAGS} -msse") endif() if(HAS_SSE2_EXTENSION) set(SSE_FLAGS "${SSE_FLAGS} -msse2") endif() if(HAS_SSE3_EXTENSION) set(SSE_FLAGS "${SSE_FLAGS} -msse3") endif() if(HAS_SSE41_EXTENSION) set(SSE_FLAGS "${SSE_FLAGS} -msse4.1") endif() if(HAS_SSE41_EXTENSION) set(SSE_FLAGS "${SSE_FLAGS} -msse4.2") endif() if(HAS_AVX_EXTENSION) set(SSE_FLAGS "${SSE_FLAGS} -mavx") endif() endif() colmap-3.4/cmake/FindEigen3.cmake000077500000000000000000000055101323400541200166260ustar00rootroot00000000000000# Sets: # EIGEN3_FOUND - TRUE if System has Eigen library with correct version. # EIGEN3_INCLUDE_DIRS - The Eigen include directory. # EIGEN3_VERSION - Eigen version. # # The following variables control the behavior of this module: # # EIGEN3_INCLUDE_DIR_HINTS: List of additional directories in which to # search for Eigen includes. set(EIGEN3_INCLUDE_DIR_HINTS "" CACHE PATH "Eigen include directory") if(NOT Eigen3_FIND_VERSION) if(NOT Eigen3_FIND_VERSION_MAJOR) set(Eigen3_FIND_VERSION_MAJOR 2) endif() if(NOT Eigen3_FIND_VERSION_MINOR) set(Eigen3_FIND_VERSION_MINOR 91) endif() if(NOT Eigen3_FIND_VERSION_PATCH) set(Eigen3_FIND_VERSION_PATCH 0) endif() set(Eigen3_FIND_VERSION "${Eigen3_FIND_VERSION_MAJOR}.${Eigen3_FIND_VERSION_MINOR}.${Eigen3_FIND_VERSION_PATCH}") endif() macro(_eigen3_check_version) file(READ "${EIGEN3_INCLUDE_DIRS}/Eigen/src/Core/util/Macros.h" _eigen3_version_header) string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen3_world_version_match "${_eigen3_version_header}") set(EIGEN3_WORLD_VERSION "${CMAKE_MATCH_1}") string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen3_major_version_match "${_eigen3_version_header}") set(EIGEN3_MAJOR_VERSION "${CMAKE_MATCH_1}") string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen3_minor_version_match "${_eigen3_version_header}") set(EIGEN3_MINOR_VERSION "${CMAKE_MATCH_1}") set(EIGEN3_VERSION ${EIGEN3_WORLD_VERSION}.${EIGEN3_MAJOR_VERSION}.${EIGEN3_MINOR_VERSION}) if(${EIGEN3_VERSION} VERSION_LESS ${Eigen3_FIND_VERSION}) set(EIGEN3_VERSION_OK FALSE) else() set(EIGEN3_VERSION_OK TRUE) endif() if(NOT EIGEN3_VERSION_OK) message(STATUS "Eigen3 version ${EIGEN3_VERSION} found in ${EIGEN3_INCLUDE_DIRS}, " "but at least version ${Eigen3_FIND_VERSION} is required.") endif() endmacro() if(EIGEN3_INCLUDE_DIRS) _eigen3_check_version() set(EIGEN3_FOUND ${EIGEN3_VERSION_OK}) else() find_path(EIGEN3_INCLUDE_DIRS NAMES signature_of_eigen3_matrix_library PATHS ${EIGEN3_INCLUDE_DIR_HINTS} /usr/include /usr/local/include /opt/include /opt/local/include PATH_SUFFIXES eigen3 eigen ) if(EIGEN3_INCLUDE_DIRS) _eigen3_check_version() endif() include(FindPackageHandleStandardArgs) find_package_handle_standard_args(Eigen3 DEFAULT_MSG EIGEN3_INCLUDE_DIRS EIGEN3_VERSION_OK) mark_as_advanced(EIGEN3_INCLUDE_DIRS) endif() if(EIGEN3_FOUND) message(STATUS "Found Eigen3") message(STATUS " Includes : ${EIGEN3_INCLUDE_DIRS}") else() if(Eigen3_FIND_REQUIRED) message(FATAL_ERROR "Could not find Eigen3") endif() endif() colmap-3.4/cmake/FindFreeImage.cmake000077500000000000000000000030471323400541200173430ustar00rootroot00000000000000# Sets: # FREEIMAGE_FOUND: TRUE if FreeImage is found. # FREEIMAGE_INCLUDE_DIRS: Include directories for FreeImage. # FREEIMAGE_LIBRARIES: Libraries required to link FreeImage. # # The following variables control the behavior of this module: # # FREEIMAGE_INCLUDE_DIR_HINTS: List of additional directories in which to # search for FreeImage includes. # FREEIMAGE_LIBRARY_DIR_HINTS: List of additional directories in which to # search for FreeImage libraries. set(FREEIMAGE_INCLUDE_DIR_HINTS "" CACHE PATH "FreeImage include directory") set(FREEIMAGE_LIBRARY_DIR_HINTS "" CACHE PATH "FreeImage library directory") list(APPEND FREEIMAGE_CHECK_INCLUDE_DIRS ${FREEIMAGE_INCLUDE_DIR_HINTS} /usr/include /usr/local/include /opt/include /opt/local/include ) list(APPEND FREEIMAGE_CHECK_LIBRARY_DIRS ${FREEIMAGE_LIBRARY_DIR_HINTS} /usr/lib /usr/local/lib /opt/lib /opt/local/lib ) find_path(FREEIMAGE_INCLUDE_DIRS NAMES FreeImage.h PATHS ${FREEIMAGE_CHECK_INCLUDE_DIRS}) find_library(FREEIMAGE_LIBRARIES NAMES freeimage PATHS ${FREEIMAGE_CHECK_LIBRARY_DIRS}) if(FREEIMAGE_INCLUDE_DIRS AND FREEIMAGE_LIBRARIES) set(FREEIMAGE_FOUND TRUE) endif() if(FREEIMAGE_FOUND) message(STATUS "Found FreeImage") message(STATUS " Includes : ${FREEIMAGE_INCLUDE_DIRS}") message(STATUS " Libraries : ${FREEIMAGE_LIBRARIES}") else() if(FreeImage_FIND_REQUIRED) message(FATAL_ERROR "Could not find FreeImage") endif() endif() colmap-3.4/cmake/FindGlew.cmake000077500000000000000000000025161323400541200164150ustar00rootroot00000000000000# Sets: # GLEW_FOUND: TRUE if Glew is found. # GLEW_INCLUDE_DIRS: Include directories for Glew. # GLEW_LIBRARIES: Libraries required to link Glew. # # The following variables control the behavior of this module: # # GLEW_INCLUDE_DIR_HINTS: List of additional directories in which to # search for Glew includes. # GLEW_LIBRARY_DIR_HINTS: List of additional directories in which to # search for Glew libraries. set(GLEW_INCLUDE_DIR_HINTS "" CACHE PATH "Glew include directory") set(GLEW_LIBRARY_DIR_HINTS "" CACHE PATH "Glew library directory") find_path(GLEW_INCLUDE_DIRS NAMES GL/glew.h PATHS ${GLEW_INCLUDE_DIR_HINTS} /usr/include /usr/local/include /sw/include /opt/include /opt/local/include) find_library(GLEW_LIBRARIES NAMES GLEW Glew glew glew32 PATHS ${GLEW_LIBRARY_DIR_HINTS} /usr/lib64 /usr/lib /usr/local/lib64 /usr/local/lib /sw/lib /opt/lib /opt/local/lib) if(GLEW_INCLUDE_DIRS AND GLEW_LIBRARIES) set(GLEW_FOUND TRUE) message(STATUS "Found Glew") message(STATUS " Includes : ${GLEW_INCLUDE_DIRS}") message(STATUS " Libraries : ${GLEW_LIBRARIES}") else() set(GLEW_FOUND FALSE) if(Glew_FIND_REQUIRED) message(FATAL_ERROR "Could not find Glew") endif() endif() colmap-3.4/cmake/FindGlog.cmake000077500000000000000000000034541323400541200164110ustar00rootroot00000000000000# Sets: # GLOG_FOUND: TRUE if Glog is found. # GLOG_INCLUDE_DIRS: Include directories for Glog. # GLOG_LIBRARIES: Libraries required to link Glog. # # The following variables control the behavior of this module: # # GLOG_INCLUDE_DIR_HINTS: List of additional directories in which to # search for Glog includes. # GLOG_LIBRARY_DIR_HINTS: List of additional directories in which to # search for Glog libraries. set(GLOG_INCLUDE_DIR_HINTS "" CACHE PATH "Glog include directory") set(GLOG_LIBRARY_DIR_HINTS "" CACHE PATH "Glog library directory") include(FindPackageHandleStandardArgs) list(APPEND GLOG_CHECK_INCLUDE_DIRS /usr/local/include /usr/local/homebrew/include /opt/local/var/macports/software /opt/local/include /usr/include) list(APPEND GLOG_CHECK_PATH_SUFFIXES glog/include glog/Include Glog/include Glog/Include src/windows) list(APPEND GLOG_CHECK_LIBRARY_DIRS /usr/local/lib /usr/local/homebrew/lib /opt/local/lib /usr/lib) list(APPEND GLOG_CHECK_LIBRARY_SUFFIXES glog/lib glog/Lib Glog/lib Glog/Lib x64/Release) find_path(GLOG_INCLUDE_DIRS NAMES glog/logging.h PATHS ${GLOG_INCLUDE_DIR_HINTS} ${GLOG_CHECK_INCLUDE_DIRS} PATH_SUFFIXES ${GLOG_CHECK_PATH_SUFFIXES}) find_library(GLOG_LIBRARIES NAMES glog libglog PATHS ${GLOG_LIBRARY_DIR_HINTS} ${GLOG_CHECK_LIBRARY_DIRS} PATH_SUFFIXES ${GLOG_CHECK_LIBRARY_SUFFIXES}) if (GLOG_INCLUDE_DIRS AND GLOG_LIBRARIES) set(GLOG_FOUND TRUE) message(STATUS "Found Glog") message(STATUS " Includes : ${GLOG_INCLUDE_DIRS}") message(STATUS " Libraries : ${GLOG_LIBRARIES}") else() if(Glog_FIND_REQUIRED) message(FATAL_ERROR "Could not find Glog") endif() endif() colmap-3.4/cmake/FindQt5.cmake000066400000000000000000000024531323400541200161650ustar00rootroot00000000000000# Sets: # Qt5_FOUND: TRUE if Qt5 is found. # Qt5_INCLUDE_DIRS: Include directories for Qt5. # Qt5_LIBRARIES: Libraries required to link Qt5. find_package(Qt5Core QUIET) find_package(Qt5OpenGL QUIET) if(Qt5Core_FOUND AND Qt5OpenGL_FOUND) set(Qt5_FOUND TRUE) set(Qt5_INCLUDE_DIRS "${Qt5Core_INCLUDE_DIRS} ${Qt5OpenGL_INCLUDE_DIRS}") set(Qt5_LIBRARIES "${Qt5Core_LIBRARIES} ${Qt5OpenGL_LIBRARIES}") endif() if(Qt5_FOUND) if(Qt5Core_VERSION VERSION_LESS Qt5_FIND_VERSION) message(FATAL_ERROR "Qt5 version ${Qt5_FIND_VERSION} or newer needed, " "but only found ${Qt5Core_VERSION}") else() message(STATUS "Found Qt ${Qt5Core_VERSION_STRING}") endif() else() if(Qt5_FIND_REQUIRED) set(Qt5_ERROR_MESSAGE "Could not find Qt5:") if(NOT Qt5Core_FOUND) set(Qt5_ERROR_MESSAGE "${Qt5_ERROR_MESSAGE} Qt5Core") endif() if(NOT Qt5OpenGL_FOUND) set(Qt5_ERROR_MESSAGE "${Qt5_ERROR_MESSAGE} Qt5OpenGL") endif() set(Qt5_ERROR_MESSAGE "${Qt5_ERROR_MESSAGE} not found, try " "setting -DQt5Core_DIR and -DQt5OpenGL_DIR to the directories " "containing Qt5CoreConfig.cmake and Qt5OpenGLConfig.cmake") message(FATAL_ERROR ${Qt5_ERROR_MESSAGE}) endif() endif() colmap-3.4/cmake/GenerateVersionDefinitions.cmake000066400000000000000000000012771323400541200222120ustar00rootroot00000000000000if(Git_FOUND AND EXISTS "${CMAKE_SOURCE_DIR}/.git") execute_process(COMMAND "${GIT_EXECUTABLE}" rev-parse --short HEAD WORKING_DIRECTORY "${CMAKE_SOURCE_DIR}" OUTPUT_VARIABLE GIT_COMMIT_ID ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE) execute_process(COMMAND "${GIT_EXECUTABLE}" log -1 --format=%ad --date=short WORKING_DIRECTORY "${CMAKE_SOURCE_DIR}" OUTPUT_VARIABLE GIT_COMMIT_DATE ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE) else() set(GIT_COMMIT_ID "Unknown") set(GIT_COMMIT_DATE "Unknown") endif() configure_file("${CMAKE_SOURCE_DIR}/src/util/version.h.in" "${CMAKE_SOURCE_DIR}/src/util/version.h") colmap-3.4/cmake/SelectCudaComputeArch.cmake000066400000000000000000000224551323400541200210660ustar00rootroot00000000000000# CMake - Cross Platform Makefile Generator # Copyright 2000-2017 Kitware, Inc. and Contributors # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # * Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # * Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # * Neither the name of Kitware, Inc. nor the names of Contributors # may be used to endorse or promote products derived from this # software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR # A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT # HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, # SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT # LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, # DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY # THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT # (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. # Synopsis: # CUDA_SELECT_NVCC_ARCH_FLAGS(out_variable [target_CUDA_architectures]) # -- Selects GPU arch flags for nvcc based on target_CUDA_architectures # target_CUDA_architectures : Auto | Common | All | LIST(ARCH_AND_PTX ...) # - "Auto" detects local machine GPU compute arch at runtime. # - "Common" and "All" cover common and entire subsets of architectures # ARCH_AND_PTX : NAME | NUM.NUM | NUM.NUM(NUM.NUM) | NUM.NUM+PTX # NAME: Fermi Kepler Maxwell Kepler+Tegra Kepler+Tesla Maxwell+Tegra Pascal # NUM: Any number. Only those pairs are currently accepted by NVCC though: # 2.0 2.1 3.0 3.2 3.5 3.7 5.0 5.2 5.3 6.0 6.2 # Returns LIST of flags to be added to CUDA_NVCC_FLAGS in ${out_variable} # Additionally, sets ${out_variable}_readable to the resulting numeric list # Example: # CUDA_SELECT_NVCC_ARCH_FLAGS(ARCH_FLAGS 3.0 3.5+PTX 5.2(5.0) Maxwell) # LIST(APPEND CUDA_NVCC_FLAGS ${ARCH_FLAGS}) # # More info on CUDA architectures: https://en.wikipedia.org/wiki/CUDA # # This list will be used for CUDA_ARCH_NAME = All option set(CUDA_KNOWN_GPU_ARCHITECTURES "Fermi" "Kepler" "Maxwell") # This list will be used for CUDA_ARCH_NAME = Common option (enabled by default) set(CUDA_COMMON_GPU_ARCHITECTURES "3.0" "3.5" "5.0") if (CUDA_VERSION VERSION_GREATER "6.5") list(APPEND CUDA_KNOWN_GPU_ARCHITECTURES "Kepler+Tegra" "Kepler+Tesla" "Maxwell+Tegra") list(APPEND CUDA_COMMON_GPU_ARCHITECTURES "5.2") endif () if (CUDA_VERSION VERSION_GREATER "7.5") list(APPEND CUDA_KNOWN_GPU_ARCHITECTURES "Pascal") list(APPEND CUDA_COMMON_GPU_ARCHITECTURES "6.0" "6.1") else() list(APPEND CUDA_COMMON_GPU_ARCHITECTURES "5.2+PTX") endif () if (CUDA_VERSION VERSION_GREATER "8.5") list(APPEND CUDA_KNOWN_GPU_ARCHITECTURES "Volta") list(APPEND CUDA_COMMON_GPU_ARCHITECTURES "7.0" "7.0+PTX") else() list(APPEND CUDA_COMMON_GPU_ARCHITECTURES "6.1+PTX") endif() ################################################################################################ # A function for automatic detection of GPUs installed (if autodetection is enabled) # Usage: # CUDA_DETECT_INSTALLED_GPUS(OUT_VARIABLE) # function(CUDA_DETECT_INSTALLED_GPUS OUT_VARIABLE) if(NOT CUDA_GPU_DETECT_OUTPUT) set(file ${PROJECT_BINARY_DIR}/detect_cuda_compute_capabilities.cpp) file(WRITE ${file} "" "#include \n" "#include \n" "int main()\n" "{\n" " int count = 0;\n" " if (cudaSuccess != cudaGetDeviceCount(&count)) return -1;\n" " if (count == 0) return -1;\n" " for (int device = 0; device < count; ++device)\n" " {\n" " cudaDeviceProp prop;\n" " if (cudaSuccess == cudaGetDeviceProperties(&prop, device))\n" " std::printf(\"%d.%d \", prop.major, prop.minor);\n" " }\n" " return 0;\n" "}\n") try_run(run_result compile_result ${PROJECT_BINARY_DIR} ${file} CMAKE_FLAGS "-DINCLUDE_DIRECTORIES=${CUDA_INCLUDE_DIRS}" LINK_LIBRARIES ${CUDA_LIBRARIES} RUN_OUTPUT_VARIABLE compute_capabilities) if(run_result EQUAL 0) string(REPLACE "2.1" "2.1(2.0)" compute_capabilities "${compute_capabilities}") set(CUDA_GPU_DETECT_OUTPUT ${compute_capabilities} CACHE INTERNAL "Returned GPU architectures from detect_gpus tool" FORCE) endif() endif() if(NOT CUDA_GPU_DETECT_OUTPUT) message(STATUS "Automatic GPU detection failed. Building for common architectures.") set(${OUT_VARIABLE} ${CUDA_COMMON_GPU_ARCHITECTURES} PARENT_SCOPE) else() set(${OUT_VARIABLE} ${CUDA_GPU_DETECT_OUTPUT} PARENT_SCOPE) endif() endfunction() ################################################################################################ # Function for selecting GPU arch flags for nvcc based on CUDA architectures from parameter list # Usage: # SELECT_NVCC_ARCH_FLAGS(out_variable [list of CUDA compute archs]) function(CUDA_SELECT_NVCC_ARCH_FLAGS out_variable) set(CUDA_ARCH_LIST "${ARGN}") if("X${CUDA_ARCH_LIST}" STREQUAL "X" ) set(CUDA_ARCH_LIST "Auto") endif() set(cuda_arch_bin) set(cuda_arch_ptx) if("${CUDA_ARCH_LIST}" STREQUAL "All") set(CUDA_ARCH_LIST ${CUDA_KNOWN_GPU_ARCHITECTURES}) elseif("${CUDA_ARCH_LIST}" STREQUAL "Common") set(CUDA_ARCH_LIST ${CUDA_COMMON_GPU_ARCHITECTURES}) elseif("${CUDA_ARCH_LIST}" STREQUAL "Auto") CUDA_DETECT_INSTALLED_GPUS(CUDA_ARCH_LIST) message(STATUS "Autodetected CUDA architecture(s): ${CUDA_ARCH_LIST}") endif() # Now process the list and look for names string(REGEX REPLACE "[ \t]+" ";" CUDA_ARCH_LIST "${CUDA_ARCH_LIST}") list(REMOVE_DUPLICATES CUDA_ARCH_LIST) foreach(arch_name ${CUDA_ARCH_LIST}) set(arch_bin) set(arch_ptx) set(add_ptx FALSE) # Check to see if we are compiling PTX if(arch_name MATCHES "(.*)\\+PTX$") set(add_ptx TRUE) set(arch_name ${CMAKE_MATCH_1}) endif() if(arch_name MATCHES "^([0-9]\\.[0-9](\\([0-9]\\.[0-9]\\))?)$") set(arch_bin ${CMAKE_MATCH_1}) set(arch_ptx ${arch_bin}) else() # Look for it in our list of known architectures if(${arch_name} STREQUAL "Fermi") set(arch_bin 2.0 "2.1(2.0)") elseif(${arch_name} STREQUAL "Kepler+Tegra") set(arch_bin 3.2) elseif(${arch_name} STREQUAL "Kepler+Tesla") set(arch_bin 3.7) elseif(${arch_name} STREQUAL "Kepler") set(arch_bin 3.0 3.5) set(arch_ptx 3.5) elseif(${arch_name} STREQUAL "Maxwell+Tegra") set(arch_bin 5.3) elseif(${arch_name} STREQUAL "Maxwell") set(arch_bin 5.0 5.2) set(arch_ptx 5.2) elseif(${arch_name} STREQUAL "Pascal") set(arch_bin 6.0 6.1) set(arch_ptx 6.1) elseif(${arch_name} STREQUAL "Volta") set(arch_bin 7.0 7.0) set(arch_ptx 7.0) else() message(SEND_ERROR "Unknown CUDA Architecture Name ${arch_name} in CUDA_SELECT_NVCC_ARCH_FLAGS") endif() endif() if(NOT arch_bin) message(SEND_ERROR "arch_bin wasn't set for some reason") endif() list(APPEND cuda_arch_bin ${arch_bin}) if(add_ptx) if (NOT arch_ptx) set(arch_ptx ${arch_bin}) endif() list(APPEND cuda_arch_ptx ${arch_ptx}) endif() endforeach() # remove dots and convert to lists string(REGEX REPLACE "\\." "" cuda_arch_bin "${cuda_arch_bin}") string(REGEX REPLACE "\\." "" cuda_arch_ptx "${cuda_arch_ptx}") string(REGEX MATCHALL "[0-9()]+" cuda_arch_bin "${cuda_arch_bin}") string(REGEX MATCHALL "[0-9]+" cuda_arch_ptx "${cuda_arch_ptx}") if(cuda_arch_bin) list(REMOVE_DUPLICATES cuda_arch_bin) endif() if(cuda_arch_ptx) list(REMOVE_DUPLICATES cuda_arch_ptx) endif() set(nvcc_flags "") set(nvcc_archs_readable "") # Tell NVCC to add binaries for the specified GPUs foreach(arch ${cuda_arch_bin}) if(arch MATCHES "([0-9]+)\\(([0-9]+)\\)") # User explicitly specified ARCH for the concrete CODE list(APPEND nvcc_flags -gencode arch=compute_${CMAKE_MATCH_2},code=sm_${CMAKE_MATCH_1}) list(APPEND nvcc_archs_readable sm_${CMAKE_MATCH_1}) else() # User didn't explicitly specify ARCH for the concrete CODE, we assume ARCH=CODE list(APPEND nvcc_flags -gencode arch=compute_${arch},code=sm_${arch}) list(APPEND nvcc_archs_readable sm_${arch}) endif() endforeach() # Tell NVCC to add PTX intermediate code for the specified architectures foreach(arch ${cuda_arch_ptx}) list(APPEND nvcc_flags -gencode arch=compute_${arch},code=compute_${arch}) list(APPEND nvcc_archs_readable compute_${arch}) endforeach() string(REPLACE ";" " " nvcc_archs_readable "${nvcc_archs_readable}") set(${out_variable} ${nvcc_flags} PARENT_SCOPE) set(${out_variable}_readable ${nvcc_archs_readable} PARENT_SCOPE) endfunction() colmap-3.4/doc/000077500000000000000000000000001323400541200133725ustar00rootroot00000000000000colmap-3.4/doc/Makefile000077500000000000000000000151521323400541200150410ustar00rootroot00000000000000# Makefile for Sphinx documentation # # You can set these variables from the command line. 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The pseudo-XML files are in $(BUILDDIR)/pseudoxml." colmap-3.4/doc/_build/000077500000000000000000000000001323400541200146305ustar00rootroot00000000000000colmap-3.4/doc/_build/html/000077500000000000000000000000001323400541200155745ustar00rootroot00000000000000colmap-3.4/doc/bibliography.rst000077500000000000000000000036371323400541200166130ustar00rootroot00000000000000Bibliography ============ .. [ceres] Agarwal, Sameer and Mierle, Keir and Others. "Ceres Solver". http://ceres-solver.org .. [furukawa10] Furukawa, Yasutaka, and Jean Ponce. "Accurate, dense, and robust multiview stereopsis." Transactions on Pattern Analysis and Machine Intelligence, 2010. .. [hofer16] Hofer, M., Maurer, M., and Bischof, H. Efficient 3D Scene Abstraction Using Line Segments, Computer Vision and Image Understanding, 2016. .. [jancosek11] Jancosek, Michal, and Tomás Pajdla. "Multi-view reconstruction preserving weakly-supported surfaces." Conference on Computer Vision and Pattern Recognition, 2011. .. [kazhdan2013] Kazhdan, Michael and Hoppe, Hugues "Screened poisson surface reconstruction." ACM Transactions on Graphics (TOG), 2013. .. [schoenberger16sfm] Schönberger, Johannes Lutz and Frahm, Jan-Michael. "Structure-from-Motion Revisited." Conference on Computer Vision and Pattern Recognition, 2016. .. [schoenberger16mvs] Schönberger, Johannes Lutz and Zheng, Enliang and Pollefeys, Marc and Frahm, Jan-Michael. "Pixelwise View Selection for Unstructured Multi-View Stereo." European Conference on Computer Vision, 2016. .. [schoenberger16vote] Schönberger, Johannes Lutz and Price, True and Sattler, Torsten and Frahm, Jan-Michael and Pollefeys, Marc "A Vote­-and­-Verify Strategy for Fast Spatial Verification in Image Retrieval." Asian Conference on Computer Vision, 2016. .. [lowe04] Lowe, David G. "Distinctive image features from scale-invariant keypoints". International journal of computer vision 60.2 (2004): 91-110. .. [wu11] Wu, Changchang, Sameer Agarwal, Brian Curless, and Steven M. Seitz. "Multicore bundle adjustment." Conference on Computer Vision and Pattern Recognition, 2011. .. [wu13] Wu, Changchang. "Towards linear-time incremental structure from motion." International Conference 3D Vision, 2013. colmap-3.4/doc/cameras.rst000066400000000000000000000051261323400541200155430ustar00rootroot00000000000000Camera Models ============= COLMAP implements different camera models of varying complexity. If no intrinsic parameters are known a priori, it is generally best to use the simplest camera model that is complex enough to model the distortion effects: - ``SIMPLE_PINHOLE``, ``PINHOLE``: Use these camera models, if your images are undistorted a priori. Note that even in the case of undistorted images, COLMAP could try to improve the intrinsics with a more complex camera model. - ``SIMPLE_RADIAL``, ``RADIAL``: This should be the camera model of choice, if the intrinsics are unknown and every image has a different camera calibration, e.g., in the case of Internet photos. Both models are simplified versions of the ``OPENCV`` model only modeling radial distortion effects with one and two parameters, respectively. - ``OPENCV``, ``FULL_OPENCV``: Use these camera models, if you know the calibration parameters a priori. You can also try to let COLMAP estimate the parameters, if you share the intrinsics for multiple images. Note that the automatic estimation of parameters will most likely fail, if every image has a separate set of intrinsic parameters. - ``SIMPLE_RADIAL_FISHEYE``, ``RADIAL_FISHEYE``, ``OPENCV_FISHEYE``, ``FOV``, ``THIN_PRISM_FISHEYE``: Use these camera models for fisheye lenses and note that all other models are not really capable of modeling the distortion effects of fisheye lenses. The ``FOV`` model is used by Google Project Tango (make sure to not initialize `omega` to zero). You can inspect the estimated intrinsic parameters by double-clicking specific images in the model viewer or by exporting the model and opening the `cameras.txt` file. To achieve optimal reconstruction results, you might have to try different camera models for your problem. Generally, when the reconstruction fails and the estimated focal length values / distortion coefficients are grossly wrong, it is a sign of using a too complex camera model. Contrary, if COLMAP uses many iterative local and global bundle adjustments, it is a sign of using a too simple camera model that is not able to fully model the distortion effects. You can also share intrinsics between multiple images to obtain more reliable results (see :ref:`Share intrinsic camera parameters `) or you can fix the intrinsic parameters during the reconstruction (see :ref:`Fix intrinsic camera parameters `). Please, refer to the camera models header file for information on the parameters of the different camera models: https://github.com/colmap/colmap/blob/master/src/base/camera_models.h colmap-3.4/doc/changelog.rst000066400000000000000000000001031323400541200160450ustar00rootroot00000000000000.. _changelog: Changelog ========= .. include:: ../CHANGELOG.txt colmap-3.4/doc/cli.rst000066400000000000000000000237171323400541200147050ustar00rootroot00000000000000.. _cli: Command-line Interface ====================== The command-line interface provides access to all of COLMAP's functionality for automated scripting. Each core functionality is implemented as a command to the ``colmap`` executable. Run ``colmap -h`` to list the available commands (or ``COLMAP.bat -h`` under Windows). Note that if you run COLMAP from the CMake build folder, the executable is located at ``./src/exe/colmap``. To start the graphical user interface, run ``colmap gui``. Example ------- Assuming you stored the images of your project in the following structure:: /path/to/project/... +── images │   +── image1.jpg │   +── image2.jpg │   +── ... │   +── imageN.jpg The command for the automatic reconstruction tool would be:: # The project folder must contain a folder "images" with all the images. $ DATASET_PATH=/path/to/project $ colmap automatic_reconstructor \ --workspace_path $DATASET_PATH \ --image_path $DATASET_PATH/images Note that any command lists all available options using the ``-h,--help`` command-line argument. In case you need more control over the individual parameters of the reconstruction process, you can execute the following sequence of commands as an alternative to the automatic reconstruction command:: # The project folder must contain a folder "images" with all the images. $ DATASET_PATH=/path/to/dataset $ colmap feature_extractor \ --database_path $DATASET_PATH/database.db \ --image_path $DATASET_PATH/images $ colmap exhaustive_matcher \ --database_path $DATASET_PATH/database.db $ mkdir $DATASET_PATH/sparse $ colmap mapper \ --database_path $DATASET_PATH/database.db \ --image_path $DATASET_PATH/images \ --export_path $DATASET_PATH/sparse $ mkdir $DATASET_PATH/dense $ colmap image_undistorter \ --image_path $DATASET_PATH/images \ --input_path $DATASET_PATH/sparse/0 \ --output_path $DATASET_PATH/dense \ --output_type COLMAP \ --max_image_size 2000 $ colmap dense_stereo \ --workspace_path $DATASET_PATH/dense \ --workspace_format COLMAP \ --DenseStereo.geom_consistency true $ colmap dense_fuser \ --workspace_path $DATASET_PATH/dense \ --workspace_format COLMAP \ --input_type geometric \ --output_path $DATASET_PATH/dense/fused.ply $ colmap dense_mesher \ --input_path $DATASET_PATH/dense/fused.ply \ --output_path $DATASET_PATH/dense/meshed.ply If you want to run COLMAP on a computer without an attached display (e.g., cluster or cloud service), COLMAP automatically switches to use CUDA if supported by your system. If no CUDA enabled device is available, you can manually select to use CPU-based feature extraction and matching by setting the ``--SiftExtraction.use_gpu 0`` and ``--SiftMatching.use_gpu 0`` options. Help ---- The available commands can be listed using the command:: $ colmap help Usage: colmap [command] [options] Documentation: https://colmap.github.io/ Example usage: colmap help [ -h, --help ] colmap gui colmap gui -h [ --help ] colmap automatic_reconstructor -h [ --help ] colmap automatic_reconstructor --image_path IMAGES --workspace_path WORKSPACE colmap feature_extractor --image_path IMAGES --database_path DATABASE colmap exhaustive_matcher --database_path DATABASE colmap mapper --image_path IMAGES --database_path DATABASE --export_path EXPORT ... Available commands: help gui automatic_reconstructor bundle_adjuster color_extractor database_creator dense_fuser dense_mesher dense_stereo exhaustive_matcher feature_extractor feature_importer image_rectifier image_registrator image_undistorter mapper matches_importer model_aligner model_analyzer model_converter model_merger model_orientation_aligner point_triangulator rig_bundle_adjuster sequential_matcher spatial_matcher transitive_matcher vocab_tree_builder vocab_tree_matcher vocab_tree_retriever And each command has a ``-h,--help`` command-line argument to show the usage and the available options, e.g.:: $ colmap feature_extractor -h Options can either be specified via command-line or by defining them in a .ini project file passed to `--project_path`. -h [ --help ] --project_path arg --database_path arg --image_path arg --image_list_path arg --ImageReader.camera_model arg (=SIMPLE_RADIAL) --ImageReader.single_camera arg (=0) --ImageReader.camera_params arg --ImageReader.default_focal_length_factor arg (=1.2) --SiftExtraction.num_threads arg (=-1) --SiftExtraction.use_gpu arg (=1) --SiftExtraction.gpu_index arg (=-1) --SiftExtraction.max_image_size arg (=3200) --SiftExtraction.max_num_features arg (=8192) --SiftExtraction.first_octave arg (=-1) --SiftExtraction.num_octaves arg (=4) --SiftExtraction.octave_resolution arg (=3) --SiftExtraction.peak_threshold arg (=0.0066666666666666671) --SiftExtraction.edge_threshold arg (=10) --SiftExtraction.estimate_affine_shape arg (=0) --SiftExtraction.max_num_orientations arg (=2) --SiftExtraction.upright arg (=0) --SiftExtraction.domain_size_pooling arg (=0) --SiftExtraction.dsp_min_scale arg (=0.16666666666666666) --SiftExtraction.dsp_max_scale arg (=3) --SiftExtraction.dsp_num_scales arg (=10) The available options can either be provided directly from the command-line or through a `.ini` file provided to ``--project_path``. Commands -------- The following list briefly documents the functionality of each command, that is available as ``colmap [command]``: - ``gui``: The graphical user interface, see :ref:`Graphical User Interface ` for more information. - ``automatic_reconstruction``: Automatically reconstruct sparse and dense model for a set of input images. - ``feature_extractor``, ``feature_importer``: Perform feature extraction or import features for a set of images. - ``exhaustive_matcher``, ``vocab_tree_matcher``, ``sequential_matcher``, ``spatial_matcher``, ``transitive_matcher``, ``matches_importer``: Perform feature matching after performing feature extraction. - ``mapper``: Sparse 3D reconstruction / mapping of the dataset using SfM after performing feature extraction and matching. - ``image_undistorter``: Undistort images and/or export them for MVS or to external dense reconstruction software, such as CMVS/PMVS. - ``image_rectifier``: Stereo rectify cameras and undistort images for stereo disparity estimation. - ``dense_stereo``: Dense 3D reconstruction / mapping using MVS after running the ``image_undistorter`` to initialize the workspace. - ``dense_fuser``: Fusion of MVS depth and normal maps to a colored point cloud. - ``dense_mesher``: Meshing of the fused point cloud using Poisson surface reconstruction. - ``image_registrator``: Register new images in the database against an existing model, e.g., when extracting features and matching newly added images in a database after running ``mapper``. Note that no bundle adjustment or triangulation is performed. - ``point_triangulator``: Triangulate all observations of registered images in an existing model using the feature matches in a database. - ``bundle_adjuster``: Run global bundle adjustment on a reconstructed scene, e.g., when a refinement of the intrinsics is needed or after running the ``image_registrator``. - ``database_creator``: Create an empty COLMAP SQLite database with the necessary database schema information. - ``model_analyzer``: Print statistics about reconstructions. - ``model_aligner``: Align/geo-register model to coordinate system of given camera centers. - ``model_orientation_aligner``: Align the coordinate axis of a model using a Manhattan world assumption. - ``model_converter``: Convert the COLMAP export format to another format, such as PLY or NVM. - ``model_merger``: Attempt to merge two disconnected reconstructions, if they have common registered images. - ``color_extractor``: Extract mean colors for all 3D points of a model. - ``vocab_tree_builder``: Create a vocabulary tree from a database with extracted images. This is an offline procedure and can be run once, while the same vocabulary tree can be reused for other datasets. Note that, as a rule of thumb, you should use at least 10-100 times more features than visual words. Pre-trained trees can be downloaded from https://demuc.de/colmap/. This is useful if you want to build a custom tree with a different trade-off in terms of precision/recall vs. speed. - ``vocab_tree_retriever``: Perform vocabulary tree based image retrieval. Visualization ------------- If you want to quickly visualize the outputs of the sparse or dense reconstruction pipelines, COLMAP offers you the following possibilities: - The sparse point cloud obtained with the ``mapper`` can be visualized via the COLMAP GUI by importing the following files: choose ``File > Import Model`` and select the folder where the three files, ``cameras.txt``,``images.txt``, and ``points3d.txt`` are located. - The dense point cloud obtained with the ``dense_fuser`` can be visualized via the COLMAP GUI by importing ``fused.ply``: choose ``File > Import Model from...`` and then select the file ``fused.ply``. - The dense mesh model ``meshed.ply`` obtained with the ``dense_mesher`` can currently not be visualized with COLMAP, instead you can, e.g., use Meshlab. colmap-3.4/doc/colmap.1000066400000000000000000000021021323400541200147220ustar00rootroot00000000000000.TH colmap 1 "January 4 2018" .SH NAME colmap \- Structure-from-Motion and Multi-View Stereo .SH SYNOPSIS .B colmap .RI "[command] [options]" .SH DESCRIPTION This manual page documents briefly the .B colmap command. .PP COLMAP is a general-purpose Structure-from-Motion (SfM) and Multi-View Stereo (MVS) pipeline with a graphical and command-line interface. It offers a wide range of features for reconstruction of ordered and unordered image collections. .SH OPTIONS This program offers a graphical and command-line interface. Each command offers summary of all available options. .TP .B help [ \-h, \-\-help ] Show summary of all options. .TP .B gui Start graphical interface. .TP .B gui \-h [ \-\-help ] Show summary of graphical interface options. .TP .B feature_extractor \-h [ \-\-help ] Show summary of feature extractor options. .TP .B feature_extractor \-\-image_path IMAGES \-\-database_path DATABASE Extract features for images in the given folder and store them in the database. .br .TP .B ... .br .SH ONLINE DOCUMENTATION The program is documented at https://colmap.github.io/ colmap-3.4/doc/conf.py000077500000000000000000000200551323400541200146760ustar00rootroot00000000000000# -*- coding: utf-8 -*- # # COLMAP documentation build configuration file, created by # sphinx-quickstart on Wed Jan 28 09:31:25 2015. # # This file is execfile()d with the current directory set to its # containing dir. # # Note that not all possible configuration values are present in this # autogenerated file. # # All configuration values have a default; values that are commented out # serve to show the default. import sys import os # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. #sys.path.insert(0, os.path.abspath('.')) # -- General configuration ------------------------------------------------ # If your documentation needs a minimal Sphinx version, state it here. #needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ 'sphinx.ext.mathjax', ] # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] # The suffix of source filenames. source_suffix = '.rst' # The encoding of source files. #source_encoding = 'utf-8-sig' # The master toctree document. master_doc = 'index' # General information about the project. project = u'COLMAP' copyright = u'2018, Johannes L. Schoenberger' # The version info for the project you're documenting, acts as replacement for # |version| and |release|, also used in various other places throughout the # built documents. # # The short X.Y version. version = '3.4' # The full version, including alpha/beta/rc tags. release = version # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. #language = None # There are two options for replacing |today|: either, you set today to some # non-false value, then it is used: #today = '' # Else, today_fmt is used as the format for a strftime call. #today_fmt = '%B %d, %Y' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. exclude_patterns = ['_build'] # The reST default role (used for this markup: `text`) to use for all # documents. #default_role = None # If true, '()' will be appended to :func: etc. cross-reference text. #add_function_parentheses = True # If true, the current module name will be prepended to all description # unit titles (such as .. function::). #add_module_names = True # If true, sectionauthor and moduleauthor directives will be shown in the # output. They are ignored by default. #show_authors = False # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # A list of ignored prefixes for module index sorting. #modindex_common_prefix = [] # If true, keep warnings as "system message" paragraphs in the built documents. #keep_warnings = False # -- Options for HTML output ---------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. html_theme = 'sphinx_rtd_theme' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. html_theme_options = {} # Add any paths that contain custom themes here, relative to this directory. html_theme_path = ["_themes"] # The name for this set of Sphinx documents. If None, it defaults to # " v documentation". #html_title = None # A shorter title for the navigation bar. Default is the same as html_title. #html_short_title = None # The name of an image file (relative to this directory) to place at the top # of the sidebar. #html_logo = None # The name of an image file (within the static path) to use as favicon of the # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 # pixels large. #html_favicon = None # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". #html_static_path = ['_static'] # Add any extra paths that contain custom files (such as robots.txt or # .htaccess) here, relative to this directory. These files are copied # directly to the root of the documentation. #html_extra_path = [] # If not '', a 'Last updated on:' timestamp is inserted at every page bottom, # using the given strftime format. #html_last_updated_fmt = '%b %d, %Y' # If true, SmartyPants will be used to convert quotes and dashes to # typographically correct entities. #html_use_smartypants = True # Custom sidebar templates, maps document names to template names. #html_sidebars = {} # Additional templates that should be rendered to pages, maps page names to # template names. #html_additional_pages = {} # If false, no module index is generated. #html_domain_indices = True # If false, no index is generated. #html_use_index = True # If true, the index is split into individual pages for each letter. #html_split_index = False # If true, links to the reST sources are added to the pages. #html_show_sourcelink = True # If true, "Created using Sphinx" is shown in the HTML footer. Default is True. #html_show_sphinx = True # If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. #html_show_copyright = True # If true, an OpenSearch description file will be output, and all pages will # contain a tag referring to it. The value of this option must be the # base URL from which the finished HTML is served. #html_use_opensearch = '' # This is the file name suffix for HTML files (e.g. ".xhtml"). #html_file_suffix = None # Output file base name for HTML help builder. htmlhelp_basename = 'COLMAPdoc' # -- Options for LaTeX output --------------------------------------------- latex_elements = { # The paper size ('letterpaper' or 'a4paper'). # 'papersize': 'a4paper', # The font size ('10pt', '11pt' or '12pt'). # 'pointsize': '10pt', # Additional stuff for the LaTeX preamble. #'preamble': '', } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, # author, documentclass [howto, manual, or own class]). latex_documents = [ ('index', 'COLMAP.tex', u'COLMAP Documentation', u'Johannes L. Schoenberger', 'manual'), ] # The name of an image file (relative to this directory) to place at the top of # the title page. #latex_logo = None # For "manual" documents, if this is true, then toplevel headings are parts, # not chapters. #latex_use_parts = False # If true, show page references after internal links. latex_show_pagerefs = True # If true, show URL addresses after external links. latex_show_urls = 'footnote' # Documents to append as an appendix to all manuals. #latex_appendices = [] # If false, no module index is generated. latex_domain_indices = False # -- Options for manual page output --------------------------------------- # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ ('index', 'colmap', u'COLMAP Documentation', [u'Johannes L. Schoenberger'], 1) ] # If true, show URL addresses after external links. #man_show_urls = False # -- Options for Texinfo output ------------------------------------------- # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ ('index', 'COLMAP', u'COLMAP Documentation', u'Johannes L. Schoenberger', 'COLMAP', 'Structure-from-Motion.', 'Miscellaneous'), ] # Documents to append as an appendix to all manuals. #texinfo_appendices = [] # If false, no module index is generated. #texinfo_domain_indices = True # How to display URL addresses: 'footnote', 'no', or 'inline'. #texinfo_show_urls = 'footnote' # If true, do not generate a @detailmenu in the "Top" node's menu. #texinfo_no_detailmenu = False colmap-3.4/doc/contribution.rst000066400000000000000000000016731323400541200166520ustar00rootroot00000000000000Contribution ============ Contributions (bug reports, bug fixes, improvements, etc.) are very welcome and should be submitted in the form of new issues and/or pull requests on GitHub. Please, adhere to the Google coding style guide:: https://google.github.io/styleguide/cppguide.html by using the provided ".clang-format" file. Document functions, methods, classes, etc. with inline documentation strings describing the API, using the following format:: // Short description. // // Longer description with a few sentences and multiple lines. // // @param parameter1 Description for parameter 1. // @param parameter2 Description for parameter 2. // // @return Description of optional return value. Add unit tests for all newly added code and make sure that algorithmic "improvements" generalize and actually improve the results of the pipeline on a variety of datasets. colmap-3.4/doc/database.rst000077500000000000000000000107361323400541200157020ustar00rootroot00000000000000.. _database-format: Database Format =============== COLMAP stores all extracted information in a single SQLite database file. The database can be accessed with the database management toolkit in the COLMAP GUI, the provided C++ database API (see ``src/base/database.h``), or with a scripting language of your choice (see ``scripts/python/*`` for examples). The database contains the following tables: - cameras - images - keypoints - descriptors - matches - inlier_matches To initialize an empty SQLite database file with the required schema, you can either create a new project in the GUI or execute `src/exe/database_create.cc`. Cameras and Images ------------------ The relation between cameras and images is 1-to-N. This has important implications for Structure-from-Motion, since one camera shares the same intrinsic parameters (focal length, principal point, distortion, etc.), while every image has separate extrinsic parameters (orientation and location). The intrinsic parameters of cameras are stored as contiguous binary blobs in `float64`, ordered as specified in ``src/base/camera_models.h``. COLMAP only uses cameras that are referenced by images, all other cameras are ignored. The ``name`` column in the images table is the unique relative path in the image folder. As such, the database file and image folder can be moved to different locations, as long as the relative folder structure is preserved. When manually inserting images and cameras into the database, make sure that all identifiers are positive and non-zero, i.e. ``image_id > 0`` and ``camera_id > 0``. Keypoints and Descriptors ------------------------- The detected keypoints are stored as row-major `float32` binary blobs, where the first two columns are the X and Y locations in the image, respectively. COLMAP uses the convention that the upper left image corner has coordinate `(0, 0)` and the center of the upper left most pixel has coordinate `(0.5, 0.5)`. If the keypoints have 4 columns, then the feature geometry is a similarity and the third column is the scale and the fourth column the orientation of the feature (according to SIFT conventions). If the keypoints have 6 columns, then the feature geometry is an affinity and the last 4 columns encode its affine shape (see ``src/feature/types.h`` for details). The extracted descriptors are stored as row-major `uint8` binary blobs, where each row describes the feature appearance of the corresponding entry in the keypoints table. Note that COLMAP only supports 128-D descriptors for now, i.e. the `cols` column must be 128. In both tables, the `rows` table specifies the number of detected features per image, while `rows=0` means that an image has no features. For feature matching and geometric verification, every image must have a corresponding keypoints and descriptors entry. Note that only vocabulary tree matching with fast spatial verification requires meaningful values for the local feature geometry, i.e., only X and Y must be provided and the other keypoint columns can be set to zero. The rest of the reconstruction pipeline only uses the keypoint locations. Matches ------- Feature matching stores its output in the `matches` table and geometric verification in the `inlier_matches` table. COLMAP only uses the data in `inlier_matches` for reconstruction. Every entry in the two tables stores the feature matches between two unique images, where the `pair_id` is the row-major, linear index in the upper-triangular match matrix, generated as follows:: def image_ids_to_pair_id(image_id1, image_id2): if image_id1 > image_id2: return 2147483647 * image_id2 + image_id1 else: return 2147483647 * image_id1 + image_id2 and image identifiers can be uniquely determined from the `pair_id` as:: def pair_id_to_image_ids(pair_id): image_id2 = pair_id % 2147483647 image_id1 = (pair_id - image_id2) / 2147483647 return image_id1, image_id2 The `pair_id` enables efficient database queries, as the matches tables may contain several hundred millions of entries. This scheme limits the maximum number of images in a database to 2147483647 (maximum value of signed 32-bit integers), i.e. `image_id` must be smaller than 2147483647. The binary blobs in the matches tables are row-major `uint32` matrices, where the left column are zero-based indices into the features of `image_id1` and the second column into the features of `image_id2`. The column `cols` must be 2 and the `rows` column specifies the number of feature matches. colmap-3.4/doc/datasets.rst000066400000000000000000000023011323400541200157300ustar00rootroot00000000000000.. _datasets: Datasets ======== A number of different datasets are available for download at: https://demuc.de/colmap/datasets/ - **Gerrard Hall**: 100 high-resolution images of the "Gerrard" hall at UNC Chapel Hill, which is the building right next to the "South" building. The images are taken with the same camera but different focus using a wide-angle lens. - **Graham Hall**: 1273 high-resolution images of the interior and exterior of "Graham" memorial hall at UNC Chapel Hill. The images are taken with the same camera but different focus using a wide-angle lens. - **Person Hall**: 330 high-resolution images of the "Person" hall at UNC Chapel Hill. The images are taken with the same camera using a wide-angle lens. - **South Building**: 128 images of the "South" building at UNC Chapel Hill. The images are taken with the same camera, kindly provided by Christopher Zach. A number of sample reconstructions produced by COLMAP can be viewed here: **Sparse reconstructions**: - https://www.youtube.com/watch?v=Gb086k7b0wg - https://www.youtube.com/watch?v=DIv1aGKqSIk - https://www.youtube.com/watch?v=xu-nWgjWKI0 **Dense reconstructions**: - https://www.youtube.com/watch?v=GRW2APWn9wY colmap-3.4/doc/faq.rst000066400000000000000000000424241323400541200147010ustar00rootroot00000000000000Frequently Asked Questions ========================== Extending COLMAP ---------------- If you need to simply analyze the produced sparse or dense reconstructions from COLMAP, you can load the sparse models in Python and Matlab using the provided scripts in ``scripts/python`` and ``scripts/matlab``. If you want to write a C/C++ executable that builds on top of COLMAP, the easiest approach is to start from the ``src/tools/example.cc`` code template and implement the desired functionality in a new binary. .. _faq-share-intrinsics: Share intrinsics ---------------- COLMAP supports shared intrinsics for arbitrary groups of images and camera models. Images share the same intrinsics, if they refer to the same camera, as specified by the `camera_id` property in the database. You can add new cameras and set shared intrinsics in the database management tool. Please, refer to :ref:`Database Management ` for more information. .. _faq-fix-intrinsics: Fix intrinsics -------------- By default, COLMAP tries to refine the intrinsic camera parameters (except principal point) automatically during the reconstruction. Usually, if there are enough images in the dataset and you share the intrinsics between multiple images, the estimated intrinsic camera parameters in SfM should be better than parameters manually obtained with a calibration pattern. However, sometimes COLMAP's self-calibration routine might converge in degenerate parameters, especially in case of the more complex camera models with many distortion parameters. If you know the calibration parameters a priori, you can fix different parameter groups during the reconstruction. Choose ``Reconstruction > Reconstruction options > Bundle Adj. > refine_*`` and check which parameter group to refine or to keep constant. Even if you keep the parameters constant during the reconstruction, you can refine the parameters in a final global bundle adjustment by setting ``Reconstruction > Bundle adj. options > refine_*`` and then running ``Reconstruction > Bundle adjustment``. Principal point refinement -------------------------- By default, COLMAP keeps the principal point constant during the reconstruction, as principal point estimation is an ill-posed problem in general. Once all images are reconstructed, the problem is most often constrained enough that you can try to refine the principal point in global bundle adjustment, especially when sharing intrinsic parameters between multiple images. Please, refer to :ref:`Fix intrinsics ` for more information. Increase number of sparse 3D points ----------------------------------- By default, COLMAP ignores two-view feature tracks in triangulation, resulting in fewer 3D points than possible. Triangulation of two-view tracks can in rare cases improve the stability of sparse image collections by providing additional constraints in bundle adjustment. To also triangulate two-view tracks, unselect the option ``Reconstruction > Reconstruction options > Triangulation > ignore_two_view_tracks``. If your images are taken from far distance with respect to the scene, you can try to reduce the minimum triangulation angle. .. _faq-merge-models: Merge disconnected models ------------------------- Sometimes COLMAP fails to reconstruct all images into the same model and hence produces multiple sub-models. If those sub-models have common registered images, they can be merged into a single model as post-processing step:: colmap model_merger \ --input_path1 /path/to/sub-model1 \ --input_path2 /path/to/sub-model2 \ --output_path /path/to/merged-model To improve the quality of the alignment between the two sub-models, it is recommended to run another global bundle adjustment after the merge:: colmap bundle_adjuster \ --input_path /path/to/merged-model \ --output_path /path/to/refined-merged-model Geo-registration ---------------- Geo-registration of models is possible by providing the 3D locations for the camera centers of a subset or all registered images. The 3D similarity transformation between the reconstructed model and the target coordinate frame of the geo-registration is determined from these correspondences. The geo-registered 3D coordinates of the camera centers for images must be specified in a text-file with the following format:: image_name1.jpg X1 Y1 Z1 image_name2.jpg X2 Y2 Z2 image_name3.jpg X3 Y3 Z3 ... Note that at least 3 images must be specified to estimate a 3D similarity transformation. Then, the model can be geo-registered using:: colmap model_aligner \ --input_path /path/to/model \ --output_path /path/to/geo-registered-model \ --ref_images_path /path/to/text-file Manhattan world alignment ------------------------- COLMAP has functionality to align the coordinate axes of a reconstruction using a Manhattan world assumption, i.e. COLMAP can automatically determine the gravity axis and the major horizontal axis of the Manhattan world through vanishing point detection in the images. Please, refer to the ``model_orientation_aligner`` for more details. Register/localize new images into an existing reconstruction ------------------------------------------------------------ If you have an existing reconstruction of images and want to register/localize new images within this reconstruction, you can follow these steps:: colmap feature_extractor \ --database_path $PROJECT_PATH/database.db \ --image_path $PROJECT_PATH/images \ --image_list_path /path/to/image-list.txt colmap vocab_tree_matcher \ --database_path $PROJECT_PATH/database.db \ --VocabTreeMatching.vocab_tree_path /path/to/vocab-tree.bin \ --VocabTreeMatching.match_list_path /path/to/image-list.txt colmap image_registrator \ --database_path $PROJECT_PATH/database.db \ --image_path $PROJECT_PATH/images \ --import_path /path/to/existing-model \ --export_path /path/to/model-with-new-images colmap bundle_adjuster \ --input_path /path/to/model-with-new-images \ --output_path /path/to/model-with-new-images Note that this first extracts features for the new images, then matches them to the existing images in the database, and finally registers them into the model. The image list text file contains a list of images to extract and match, specified as one image file name per line. The bundle adjustment is optional. If you need a more accurate image registration with triangulation, then you should restart or continue the reconstruction process rather than just registering the images to the model. Instead of running the ``image_registrator``, you should run the ``mapper`` to continue the reconstruction process from the existing model:: colmap mapper \ --database_path $PROJECT_PATH/database.db \ --image_path $PROJECT_PATH/images \ --import_path /path/to/existing-model \ --export_path /path/to/model-with-new-images Or, alternatively, you can start the reconstruction from scratch:: colmap mapper \ --database_path $PROJECT_PATH/database.db \ --image_path $PROJECT_PATH/images \ --export_path /path/to/model-with-new-images Note that dense reconstruction must be re-run from scratch after adding new images, as the coordinate frame of the model is changed. Available functionality without GPU/CUDA ---------------------------------------- If you do not have a CUDA-enabled GPU but some other GPU, you can use all COLMAP functionality except the dense reconstruction part. However, you can use external dense reconstruction software as an alternative, as described in the :ref:`Tutorial `. If you have a GPU with low compute power or you want to execute COLMAP on a machine without an attached display and without CUDA support, you can run all steps on the CPU by specifying the appropriate options (e.g., ``--SiftExtraction.use_gpu=false`` for the feature extraction step). But not that this might result in a significant slow-down of the reconstruction pipeline. Multi-GPU support in feature extraction/matching ------------------------------------------------ You can run feature extraction/matching on multiple GPUs by specifying multiple indices for CUDA-enabled GPUs, e.g., ``--SiftExtraction.gpu_index=0,1,2,3`` and ``--SiftMatching.gpu_index=0,1,2,3`` runs the feature extraction/matching on 4 GPUs in parallel. Note that you can only run one thread per GPU and this typically also gives the best performance. By default, COLMAP runs one feature extraction/matching thread per CUDA-enabled GPU and this usually gives the best performance as compared to running multiple threads on the same GPU. Feature matching fails due to illegal memory access --------------------------------------------------- If you encounter the following error message:: MultiplyDescriptor: an illegal memory access was encountered or the following: ERROR: Feature matching failed. This probably caused by insufficient GPU memory. Consider reducing the maximum number of features. during feature matching, your GPU runs out of memory. Try decreasing the option ``--SiftMatching.max_num_matches`` until the error disappears. Note that this might lead to inferior feature matching results, since the lower-scale input features will be clamped in order to fit them into GPU memory. Alternatively, you could change to CPU-based feature matching, but this can become very slow, or you use a GPU with more memory. Trading off completeness and accuracy in dense reconstruction ------------------------------------------------------------- If the dense point cloud contains too many outliers and too much noise, try to increase the value of option ``--DenseFusion.min_num_pixels``. If the reconstructed dense surface mesh model contains no surface or there are too many outlier surfaces, you should reduce the value of option ``--DenseMeshing.trim`` to decrease the surface are and vice versa to increase it. Also consider to try the reduce the outliers or increase the completeness in the fusion stage, as described above. Improving dense reconstruction results for weakly textured surfaces ------------------------------------------------------------------- For scenes with weakly textured surfaces it can help to have a high resolution of the input images (``--DenseStereo.max_image_size``) and a large patch window radius (``--DenseStereo.window_radius``). You may also want to reduce the filtering threshold for the photometric consistency cost (``--DenseStereo.filter_min_ncc``). Speedup dense reconstruction ---------------------------- The dense reconstruction can be speeded up in multiple ways: - Put more GPUs in your system as the dense reconstruction can make use of multiple GPUs during the stereo reconstruction step. Put more RAM into your system and increase the ``--DenseStereo.cache_size``, ``--DenseFusion.cache_size`` to the largest possible value in order to speed up the dense fusion step. - Do not perform geometric dense stereo reconstruction ``--DenseStereo.geom_consistency false``. Make sure to also enable ``--DenseStereo.filter true`` in this case. - Reduce the ``--DenseStereo.max_image_size``, ``--DenseFusion.max_image_size`` values to perform dense reconstruction on a maximum image resolution. - Reduce the number of source images per reference image to be considered, as described :ref:`here `. - Reduce the patch window radius ``--DenseStereo.window_radius``. - Reduce the number of patch match iterations ``--DenseStereo.num_iterations``. - Reduce the number of sampled views ``--DenseStereo.num_samples``. - To speedup the dense stereo and fusion step for very large reconstructions, you can use CMVS to partition your scene into multiple clusters and to prune redundant images, as described :ref:`here `. Note that apart from upgrading your hardware, the proposed changes might degrade the quality of the dense reconstruction results. When canceling the stereo reconstruction process and restarting it later, the previous progress is not lost and any already processed views will be skipped. .. _faq-dense-memory: Reduce memory usage during dense reconstruction ----------------------------------------------- If you run out of GPU memory during patch match stereo, you can either reduce the maximum image size by setting the option ``--DenseStereo.max_image_size`` or reduce the number of source images in the ``stereo/patch-match.cfg`` file from e.g. ``__auto__, 30`` to ``__auto__, 10``. Note that enabling the ``geom_consistency`` option increases the required GPU memory. If you run out of CPU memory during stereo or fusion, you can reduce the ``--DenseStereo.cache_size`` or ``--DenseFusion.cache_size`` specified in gigabytes or you can reduce ``--DenseStereo.max_image_size`` or ``--DenseFusion.max_image_size``. Note that a too low value might lead to very slow processing and heavy load on the hard disk. For large-scale reconstructions of several thousands of images, you should consider splitting your sparse reconstruction into more manageable clusters of images using e.g. CMVS [furukawa10]_. In addition, CMVS allows to prune redundant images observing the same scene elements. Note that, for this use case, COLMAP's dense reconstruction pipeline also supports the PMVS/CMVS folder structure when executed from the command-line. Please, refer to the workspace folder for example shell scripts. Since CMVS produces highly overlapping clusters, it is recommended to increase the default value of 100 images per cluster to as high as possible according to your available system resources and speed requirements. To change the number of images using CMVS, you must modify the shell scripts accordingly. For example, ``cmvs pmvs/ 500`` to limit each cluster to 500 images. If you want to use CMVS to prune redundant images but not to cluster the scene, you can simply set this number to a very large value. Manual specification of source images during dense reconstruction ----------------------------------------------------------------- You can change the number of source images in the ``stereo/patch-match.cfg`` file from e.g. ``__auto__, 30`` to ``__auto__, 10``. This selects the images with the most visual overlap automatically as source images. Alternatively, you can manually specify images with their name, for example:: image1.jpg image2.jpg, image3.jpg image2.jpg image1.jpg, image3.jpg image3.jpg image1.jpg, image2.jpg Here, ``image2.jpg`` and ``image3.jpg`` are used as source images for ``image1.jpg``, etc. Multi-GPU support in dense reconstruction ----------------------------------------- You can run dense reconstruction on multiple GPUs by specifying multiple indices for CUDA-enabled GPUs, e.g., ``--DenseStereo.gpu_index=0,1,2,3`` runs the dense reconstruction on 4 GPUs in parallel. You can also run multiple dense reconstruction threads on the same GPU by specifying the same GPU index twice, e.g., ``--DenseStereo.gpu_index=0,0,1,1,2,3``. By default, COLMAP runs one dense reconstruction thread per CUDA-enabled GPU. .. _faq-dense-timeout: Fix GPU freezes and timeouts during dense reconstruction -------------------------------------------------------- The stereo reconstruction pipeline runs on the GPU using CUDA and puts the GPU under heavy load. You might experience a display freeze or even a program crash during the reconstruction. As a solution to this problem, you could use a secondary GPU in your system, that is not connected to your display by setting the GPU indices explicitly (usually index 0 corresponds to the card that the display is attached to). Alternatively, you can increase the GPU timeouts of your system, as detailed in the following. By default, the Windows operating system detects response problems from the GPU, and recovers to a functional desktop by resetting the card and aborting the stereo reconstruction process. The solution is to increase the so-called "Timeout Detection & Recovery" (TDR) delay to a larger value. Please, refer to the `NVIDIA Nsight documentation `_ or to the `Microsoft documentation `_ on how to increase the delay time under Windows. You can increase the delay using the following Windows Registry entries:: [HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\GraphicsDrivers] "TdrLevel"=dword:00000001 "TdrDelay"=dword:00000120 To set the registry entries, execute the following commands using administrator privileges (e.g., in ``cmd.exe`` or ``powershell.exe``):: reg add HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\GraphicsDrivers /v TdrLevel /t REG_DWORD /d 00000001 reg add HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\GraphicsDrivers /v TdrDelay /t REG_DWORD /d 00000120 and restart your machine afterwards to make the changes effective. The X window system under Linux/Unix has a similar feature and detects response problems of the GPU. The easiest solution to avoid timeout problems under the X window system is to shut it down and run the stereo reconstruction from the command-line. Under Ubuntu, you could first stop X using:: sudo service lightdm stop And then run the dense reconstruction code from the command-line:: colmap dense_stereo ... Finally, you can restart your desktop environment with the following command:: sudo service lightdm start colmap-3.4/doc/format.rst000066400000000000000000000220571323400541200154220ustar00rootroot00000000000000.. _output-format: Output Format ============= ================== Binary File Format ================== Note that all binary data is stored using little endian byte ordering. All x86 processors are little endian and thus no special care has to be taken when reading COLMAP binary data on most platforms. ======================= Indices and Identifiers ======================= Any variable name ending with ``*_idx`` should be considered as an ordered, contiguous zero-based index. In general, any variable name ending with ``*_id`` should be considered as an unordered, non-contiguous identifier. For example, the unique identifiers of cameras (`CAMERA_ID`), images (`IMAGE_ID`), and 3D points (`POINT3D_ID`) are unordered and are most likely not contiguous. This also means that the maximum `POINT3D_ID` does not necessarily correspond to the number 3D points, since some `POINT3D_ID`'s are missing due to filtering during the reconstruction, etc. ===================== Sparse Reconstruction ===================== By default, COLMAP uses a binary file format (machine-readable, fast) for storing sparse models. In addition, COLMAP provides the option to store the sparse models as text files (human-readable, slow). In both cases, the information is split into three files for the information about `cameras`, `images`, and `points`. Any directory containing those three files constitutes a sparse model. The binary files have the file extension `.bin` and the text files the file extension `.txt`. Note that when loading a model from a directory which contains both binary and text files, COLMAP prefers the binary format. To export the currently selected model in the GUI, choose ``File > Export model``. To export all reconstructed models in the current dataset, choose ``File > Export all``. The selected folder then contains the three files, and for convenience, the current project configuration for importing the model to COLMAP. To import the exported models, e.g., for visualization or to resume the reconstruction, choose ``File > Import model`` and select the folder containing the `cameras`, `images`, and `points3D` files. To convert between the binary and text format in the GUI, you can load the model using ``File > Import model`` and then export the model in the desired output format using ``File > Export model`` (binary) or ``File > Export model as text`` (text). In addition, you can export sparse models to other formats, such as VisualSfM's NVM, Bundler files, PLY, VRML, etc., using ``File > Export as...``. To convert between various formats from the CLI, use the ``model_converter`` executable. There are two source files to conveniently read the sparse reconstructions using Python (``scripts/python/read_model.py`` supporting binary and text) and Matlab (``scripts/matlab/read_model.m`` supporting text). ----------- Text Format ----------- COLMAP exports the following three text files for every reconstructed model: `cameras.txt`, `images.txt`, and `points3D.txt`. Comments start with a leading "#" character and are ignored. The first comment lines briefly describe the format of the text files, as described in more detailed on this page. cameras.txt ----------- This file contains the intrinsic parameters of all reconstructed cameras in the dataset using one line per camera, e.g.:: # Camera list with one line of data per camera: # CAMERA_ID, MODEL, WIDTH, HEIGHT, PARAMS[] # Number of cameras: 3 1 SIMPLE_PINHOLE 3072 2304 2559.81 1536 1152 2 PINHOLE 3072 2304 2560.56 2560.56 1536 1152 3 SIMPLE_RADIAL 3072 2304 2559.69 1536 1152 -0.0218531 Here, the dataset contains 3 cameras based using different distortion models with the same sensor dimensions (width: 3072, height: 2304). The length of parameters is variable and depends on the camera model. For the first camera, there are 3 parameters with a single focal length of 2559.81 pixels and a principal point at pixel location `(1536, 1152)`. The intrinsic parameters of a camera can be shared by multiple images, which refer to cameras using the unique identifier `CAMERA_ID`. images.txt ---------- This file contains the pose and keypoints of all reconstructed images in the dataset using two lines per image, e.g.:: # Image list with two lines of data per image: # IMAGE_ID, QW, QX, QY, QZ, TX, TY, TZ, CAMERA_ID, NAME # POINTS2D[] as (X, Y, POINT3D_ID) # Number of images: 2, mean observations per image: 2 1 0.851773 0.0165051 0.503764 -0.142941 -0.737434 1.02973 3.74354 1 P1180141.JPG 2362.39 248.498 58396 1784.7 268.254 59027 1784.7 268.254 -1 2 0.851773 0.0165051 0.503764 -0.142941 -0.737434 1.02973 3.74354 1 P1180142.JPG 1190.83 663.957 23056 1258.77 640.354 59070 Here, the first two lines define the information of the first image, and so on. The reconstructed pose of an image is specified as the projection from world to image coordinate system using a quaternion (QW, QX, QY, QZ) and a translation vector (TX, TY, TZ). The quaternion is defined using the Hamilton convention, which is, for example, also used by the Eigen library. The coordinates of the projection center are given by ``-R^t * T``, where ``R^t`` is the inverse/transpose of the 3x3 rotation matrix composed from the quaternion and ``T`` is the translation vector. Both images use the same camera model and share intrinsics (`CAMERA_ID = 1`). The image name is relative to the selected base image folder of the project. The first image has 3 keypoints and the second image has 2 keypoints, while the location of the keypoints is specified in pixel coordinates. Both images observe 2 3D points and note that the last keypoint of the first image does not observe a 3D point in the reconstruction as the 3D point identifier is -1. points3D.txt ------------ This file contains the information of all reconstructed 3D points in the dataset using one line per point, e.g.:: # 3D point list with one line of data per point: # POINT3D_ID, X, Y, Z, R, G, B, ERROR, TRACK[] as (IMAGE_ID, POINT2D_IDX) # Number of points: 3, mean track length: 3.3334 63390 1.67241 0.292931 0.609726 115 121 122 1.33927 16 6542 15 7345 6 6714 14 7227 63376 2.01848 0.108877 -0.0260841 102 209 250 1.73449 16 6519 15 7322 14 7212 8 3991 63371 1.71102 0.28566 0.53475 245 251 249 0.612829 118 4140 117 4473 Here, there are three reconstructed 3D points, where `POINT2D_IDX` defines the zero-based index of the keypoint in the `images.txt` file. The error is given in pixels of reprojection error and is only updated after global bundle adjustment. ==================== Dense Reconstruction ==================== COLMAP uses the following workspace folder structure:: +── images │   +── image1.jpg │   +── image2.jpg │   +── ... +── sparse │   +── cameras.txt │   +── images.txt │   +── points3D.txt +── stereo │   +── consistency_graphs │   │   +── image1.jpg.photometric.bin │   │   +── image2.jpg.photometric.bin │   │   +── ... │   +── depth_maps │   │   +── image1.jpg.photometric.bin │   │   +── image2.jpg.photometric.bin │   │   +── ... │   +── normal_maps │   │   +── image1.jpg.photometric.bin │   │   +── image2.jpg.photometric.bin │   │   +── ... │   +── patch-match.cfg │   +── fusion.cfg +── fused.ply +── meshed.ply +── run-colmap-geometric.sh +── run-colmap-photometric.sh Here, the `images` folder contains the undistorted images, the `sparse` folder contains the sparse reconstruction with undistorted cameras, the `stereo` folder contains the stereo reconstruction results, `point-cloud.ply` and `mesh.ply` are the results of the fusion and meshing procedure, and `run-colmap-geometric.sh` and `run-colmap-photometric.sh` contain example command-line usage to perform the dense reconstruction. --------------------- Depth and Normal Maps --------------------- The depth maps are stored as mixed text and binary files. The text header defines the dimensions of the image in the format ``with&height&channels&`` followed by row-major `float32` binary data. For depth maps ``channels=1`` and for normal maps ``channels=3``. The depth and normal maps can be conveniently read with Python using the functions in ``scripts/python/read_dense.py`` and with Matlab using the functions in ``scripts/matlab/read_depth_map.m`` and ``scripts/matlab/read_normal_map.m``. ------------------ Consistency Graphs ------------------ The consistency graph defines, for all pixels in an image, the source images a pixel is consistent with. The graph is stored as a mixed text and binary file, while the text part is equivalent to the depth and normal maps and the binary part is a continuous list of `int32` values in the format ``...``. Here, ``(row, col)`` defines the location of the pixel in the image followed by a list of ``N`` image indices. The indices are specified w.r.t. the ordering in the ``images.txt`` file. colmap-3.4/doc/gui.rst000066400000000000000000000060001323400541200147040ustar00rootroot00000000000000.. _gui: Graphical User Interface ======================== The graphical user interface of COLMAP provides access to most of the available functionality and visualizes the reconstruction process in "real-time". To start the GUI, you can run the pre-built packages (Windows: `COLMAP.bat`, Mac: `COLMAP.app`), execute ``colmap gui`` if you installed COLMAP or execute ``./src/exe/colmap gui`` from the CMake build folder. The GUI application requires an attached display with at least OpenGL 3.2 support. Registered images are visualized in red and reconstructed points in their average point color extracted from the images. The viewer can also visualize dense point clouds produced from Multi-View Stereo. Model Viewer Controls --------------------- - **Rotate model**: Left-click and drag. - **Shift model**: Right-click or -click (-click) and drag. - **Zoom model**: Scroll. - **Change point size**: -scroll (-scroll). - **Change camera size**: -scroll. - **Adjust clipping plane**: -scroll. - **Select point**: Double-left-click point (change point size if too small). The green lines visualize the projections into the images that see the point. The opening window shows the projected locations of the point in all images. - **Select camera**: Double-left-click camera (change camera size if too small). The purple lines visualize images that see at least one common point with the selected image. The opening window shows a few statistics of the image. - **Reset view**: To reset all viewing settings, choose ``Render > Reset view``. Render Options -------------- The model viewer allows you to render the model with different settings, projections, colormaps, etc. Please, choose ``Render > Render options``. Create Screenshots ------------------ To create screenshots of the current viewpoint (without coordinate axes), choose ``Extras > Grab image`` and save the image in the format of your choice. Create Screencast ----------------- To create a video screen capture of the reconstructed model, choose ``Extras > Grab movie``. This dialog allows you to set individual control viewpoints by choosing ``Add``. COLMAP generates a fixed number of frames per second between each control viewpoint by smoothly interpolating the linear trajectory, and to interpolate the configured point and the camera sizes at the time of clicking ``Add``. To change the number of frames between two viewpoints or to reorder individual viewpoints, modify the time of the viewpoint by double-clicking the respective cell in the table. Note that the video capture requires to set the perspective projection model in the render options. You can review the trajectory in the viewer, which is rendered in light blue. Choose ``Assemble movie``, if you are done creating the trajectory. The output directory then contains the individual frames of the video capture, which can be assembled to a movie using `FFMPEG `_ with the following command:: ffmpeg -i frame%06d.png -r 30 -vf scale=1680:1050 movie.mp4 colmap-3.4/doc/images/000077500000000000000000000000001323400541200146375ustar00rootroot00000000000000colmap-3.4/doc/images/dense.png000066400000000000000000034071551323400541200164620ustar00rootroot00000000000000‰PNG  IHDRÐ#jîšôgAMA± üa cHRMz&€„ú€èu0ê`:˜pœºQ< pHYs"š"š¾Ýû*YiTXtXML:com.adobe.xmp 1 LÂ'Y@IDATxì½W·Ùu¦7wÎù䀜P@¡PÅP¤DQjSÒh·G»/zxxøøÎ?Ä¿À—ö¥}å¡vÕ¶F7Õ’%Cå€xrÜ9'?ïÜÉ–È"KU…B×Î9;|ß ïZëÛß\ï|çŒìŸÖç€@@ ð\   rä¹hIhD@ €@@ €@@ ðeE`>Ÿ["‘°Ë‹sûŸÿ§ÿѪ•eëŽ'öúßµõ•»þÒ+–HÅmmcÝV–«ÖﵬÓ<²û¼cãþØ¢ñ˜½ñÆ»–ŠçìÎkhkW¶ì+w®ÛêÊ’½÷á;xüÐRÓ®%b#›²ãÙi7­ÝéØÞá¡ýÝ÷¾oýþȲٜEÙ UY³ÙÌŒ6Ígs›ú&iÔ"}µÉhds‹Z,ÆO”cx>Žø(nãùÔbüÓ¹ãÙÄâј%Ói΋plÔÆ“?ÎsÌÌŠ¥’uº]ÎY±˜³élê8Ähc¿×ç§KýsK&á˜Éhb]Ú½²ºd¹t¼.-–HY«Û·r®b¿ÿW-OXg0°N§gÓ±Úe–¥ åBÎr¹ mY´/—ÍZ„ö¦qKSÖ˜.Çiçt:³J1o ι·wh³y„c’–ŒGm4èY2•¶ápl#p–‘XŠzÆ´­o Ú9rèf6ôm>y}3ÊŒG„!Ýæœ 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:figclass: align-center Sparse model of central Rome using 21K photos produced by COLMAP's SfM pipeline. .. figure:: images/dense.png :alt: Dense reconstruction of landmarks. :figclass: align-center Dense models of several landmarks produced by COLMAP's MVS pipeline. About ----- COLMAP is a general-purpose Structure-from-Motion (SfM) and Multi-View Stereo (MVS) pipeline with a graphical and command-line interface. It offers a wide range of features for reconstruction of ordered and unordered image collections. The software is licensed under the GNU General Public License. If you use this project for your research, please cite:: @inproceedings{schoenberger2016sfm, author = {Sch\"{o}nberger, Johannes Lutz and Frahm, Jan-Michael}, title = {Structure-from-Motion Revisited}, booktitle={IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, year={2016}, } @inproceedings{schoenberger2016mvs, author = {Sch\"{o}nberger, Johannes Lutz and Zheng, Enliang and Pollefeys, Marc and Frahm, Jan-Michael}, title = {Pixelwise View Selection for Unstructured Multi-View Stereo}, booktitle={European Conference on Computer Vision (ECCV)}, year={2016}, } If you use the image retrieval / vocabulary tree engine, please also cite:: @inproceedings{schoenberger2016vote, author = {Sch\"{o}nberger, Johannes Lutz and Price, True and Sattler, Torsten and Frahm, Jan-Michael and Pollefeys, Marc}, title = {A Vote-and-Verify Strategy for Fast Spatial Verification in Image Retrieval}, booktitle={Asian Conference on Computer Vision (ACCV)}, year={2016}, } The latest source code is available at `GitHub `_. COLMAP builds on top of existing works and when using specific algorithms within COLMAP, please also cite the original authors, as specified in the source code. Download -------- Executables and other resources can be downloaded from https://demuc.de/colmap/. Getting Started --------------- 1. Download the `pre-built binaries `_ or build the library manually from `source `_ (see :ref:`Installation `). 2. Download one of the provided datasets (see :ref:`Datasets `) or use your own images. 3. Use the **automatic reconstruction** to easily build models with a single click (see :ref:`Quickstart `). 4. Watch the short introductory video at `YouTube `_ or read the :ref:`Tutorial ` for more details. Support ------- Please, use the `Google Group `_ (colmap@googlegroups.com) for questions and the `GitHub issue tracker `_ for bug reports, feature requests/additions, etc. Acknowledgments --------------- The library was written by `Johannes L. Schönberger `_. Funding was provided by his PhD advisors `Jan-Michael Frahm `_ and `Marc Pollefeys `_. .. toctree:: :hidden: :maxdepth: 2 install tutorial database cameras format datasets gui cli faq changelog contribution license bibliography colmap-3.4/doc/install.rst000077500000000000000000000140221323400541200155740ustar00rootroot00000000000000.. _installation: Installation ============ You can either download one of the pre-built binaries from https://demuc.de/colmap/ or build the source code manually. ------------------ Pre-built Binaries ------------------ Windows ------- For convenience, the pre-built binaries for Windows contain both the graphical and command-line interface executables. To start the COLMAP GUI, you can simply double-click the ``COLMAP.bat`` batch script or alternatively run it from the Windows command shell or Powershell. The command-line interface is also accessible through this batch script, which automatically sets the necessary library paths. To list the available COLMAP commands, run ``COLMAP.bat -h`` in the command shell ``cmd.exe`` or in Powershell. Mac --- The pre-built application package for Mac contains both the GUI and command-line version of COLMAP. To open the GUI, simply open the application and note that COLMAP is shipped as an unsigned application, i.e., when your first open the application, you have to right-click the application and select *Open* and then accept to trust the application. In the future, you can then simply double-click the application to open COLMAP. The command-line interface is accessible by running the packaged binary ``COLMAP.app/Contents/MacOS/colmap``. To list the available COLMAP commands, run ``COLMAP.app/Contents/MacOS/colmap -h``. ----------------- Build from Source ----------------- COLMAP builds on all major platforms (Linux, Mac, Windows) with little effort. First, checkout the latest source code:: git clone https://github.com/colmap/colmap The latest stable version lives in the ``master`` branch and the latest development version lives in the ``dev`` branch. On Linux and Mac it is generally recommended to follow the installation instructions below, which use the system package managers to install the required dependencies. Alternatively, there is a Python build script that builds COLMAP and its dependencies locally. This script is useful under Windows and on a (cluster) system if you do not have root access under Linux or Mac. Linux ----- *Recommended dependencies:* CUDA. Dependencies from default Ubuntu repositories:: sudo apt-get install \ cmake \ build-essential \ libboost-all-dev \ libeigen3-dev \ libsuitesparse-dev \ libfreeimage-dev \ libgoogle-glog-dev \ libgflags-dev \ libglew-dev \ qtbase5-dev \ libqt5opengl5-dev Install `Ceres Solver `_:: sudo apt-get install libatlas-base-dev libsuitesparse-dev git clone https://ceres-solver.googlesource.com/ceres-solver cd ceres-solver mkdir build cd build cmake .. -DBUILD_TESTING=OFF -DBUILD_EXAMPLES=OFF make sudo make install Configure and compile COLMAP:: cd path/to/colmap mkdir build cd build cmake .. make sudo make install Run COLMAP:: colmap -h colmap gui Mac --- *Recommended dependencies:* CUDA. Dependencies from `Homebrew `_:: brew tap homebrew/science brew install \ cmake \ boost \ eigen \ freeimage \ glog \ gflags \ suite-sparse \ ceres-solver \ qt5 \ glew Create the file ``LocalConfig.cmake`` in the COLMAP base directory and then insert the following lines into it:: set(Qt5_CMAKE_DIR "/usr/local/opt/qt5/lib/cmake") set(Qt5Core_DIR ${Qt5_CMAKE_DIR}/Qt5Core) set(Qt5OpenGL_DIR ${Qt5_CMAKE_DIR}/Qt5OpenGL) Configure and compile COLMAP:: cd path/to/colmap mkdir build cd build cmake .. make Run COLMAP:: colmap -h colmap gui Windows ------- *Recommended dependencies:* CUDA. On Windows it is recommended to use the Python build script. Please follow the instructions in the next section. Alternatively, you can install the dependencies manually. To make the process of configuring CMake less painful, please have a look at ``LocalConfigExample.config``. MSVC12 (Microsoft Visual Studio 2013) and newer are confirmed to compile COLMAP without any issues. Build Script ------------ COLMAP ships with an automated Python build script. The build script installs COLMAP and its dependencies locally under Windows, Mac, and Linux. Note that under Mac and Linux, it is usually easier and faster to use the available package managers for the dependencies (see above). However, if you are on a (cluster) system without root access, this script might be useful. This script downloads the necessary dependencies automatically from the Internet. It assumes that CMake, Boost, Qt5, and CUDA (optional) are already installed on the system. E.g., under Windows you must specify the location of these libraries as:: python scripts/python/build.py \ --build_path path/to/colmap/build \ --colmap_path path/to/colmap \ --boost_path "C:/local/boost_1_64_0/lib64-msvc-14.0" \ --qt_path "C:/Qt/5.9.3/msvc2015_64" \ --cuda_path "C:/Program Files/NVIDIA GPU Computing Toolkit/CUDA/v8.0" Note that under Windows you must use forward slashes for specifying the paths here. If you want to compile COLMAP using a specific Visual Studio version, you can for example specify ``--cmake_generator "Visual Studio 14"`` for Visual Studio 2015. If you want to open the COLMAP source code in Visual Studio, you can open the solution file in ``path/to/colmap/build/colmap/build``. If you use Homebrew under Mac, you can use the following command:: python scripts/python/build.py \ --build_path path/to/colmap/build \ --colmap_path path/to/colmap \ --qt5_path /usr/local/opt/qt/ To see the full list of command-line options, pass the ``--help`` argument. ------------- Documentation ------------- You need Python and Sphinx to build the HTML documentation:: cd path/to/colmap/doc sudo apt-get install python pip install sphinx make html open _build/html/index.html Alternatively, you can build the documentation as PDF, EPUB, etc.:: make latexpdf open _build/pdf/COLMAP.pdf colmap-3.4/doc/license.rst000066400000000000000000000020151323400541200155440ustar00rootroot00000000000000License ======= The software is licensed under the GNU General Public License v3 or later. If you are interested in licensing the software for commercial purposes, without disclosing your modifications, please contact the authors. .. code-block:: text COLMAP - Structure-from-Motion and Multi-View Stereo. Copyright (C) 2017 Johannes L. Schoenberger This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . colmap-3.4/doc/make.bat000077500000000000000000000144731323400541200150130ustar00rootroot00000000000000@ECHO OFF REM Command file for Sphinx documentation if "%SPHINXBUILD%" == "" ( set SPHINXBUILD=sphinx-build ) set BUILDDIR=_build set ALLSPHINXOPTS=-d %BUILDDIR%/doctrees %SPHINXOPTS% . set I18NSPHINXOPTS=%SPHINXOPTS% . if NOT "%PAPER%" == "" ( set ALLSPHINXOPTS=-D latex_paper_size=%PAPER% %ALLSPHINXOPTS% set I18NSPHINXOPTS=-D latex_paper_size=%PAPER% %I18NSPHINXOPTS% ) if "%1" == "" goto help if "%1" == "help" ( :help echo.Please use `make ^` where ^ is one of echo. html to make standalone HTML files echo. dirhtml to make HTML files named index.html in directories echo. singlehtml to make a single large HTML file echo. pickle to make pickle files echo. json to make JSON files echo. htmlhelp to make HTML files and a HTML help project echo. qthelp to make HTML files and a qthelp project echo. devhelp to make HTML files and a Devhelp project echo. epub to make an epub echo. latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter echo. text to make text files echo. man to make manual pages echo. texinfo to make Texinfo files echo. gettext to make PO message catalogs echo. changes to make an overview over all changed/added/deprecated items echo. xml to make Docutils-native XML files echo. pseudoxml to make pseudoxml-XML files for display purposes echo. linkcheck to check all external links for integrity echo. doctest to run all doctests embedded in the documentation if enabled goto end ) if "%1" == "clean" ( for /d %%i in (%BUILDDIR%\*) do rmdir /q /s %%i del /q /s %BUILDDIR%\* goto end ) %SPHINXBUILD% 2> nul if errorlevel 9009 ( echo. echo.The 'sphinx-build' command was not found. Make sure you have Sphinx echo.installed, then set the SPHINXBUILD environment variable to point echo.to the full path of the 'sphinx-build' executable. Alternatively you echo.may add the Sphinx directory to PATH. echo. echo.If you don't have Sphinx installed, grab it from echo.http://sphinx-doc.org/ exit /b 1 ) if "%1" == "html" ( %SPHINXBUILD% -b html %ALLSPHINXOPTS% %BUILDDIR%/html if errorlevel 1 exit /b 1 echo. echo.Build finished. The HTML pages are in %BUILDDIR%/html. goto end ) if "%1" == "dirhtml" ( %SPHINXBUILD% -b dirhtml %ALLSPHINXOPTS% %BUILDDIR%/dirhtml if errorlevel 1 exit /b 1 echo. echo.Build finished. The HTML pages are in %BUILDDIR%/dirhtml. goto end ) if "%1" == "singlehtml" ( %SPHINXBUILD% -b singlehtml %ALLSPHINXOPTS% %BUILDDIR%/singlehtml if errorlevel 1 exit /b 1 echo. echo.Build finished. The HTML pages are in %BUILDDIR%/singlehtml. goto end ) if "%1" == "pickle" ( %SPHINXBUILD% -b pickle %ALLSPHINXOPTS% %BUILDDIR%/pickle if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can process the pickle files. goto end ) if "%1" == "json" ( %SPHINXBUILD% -b json %ALLSPHINXOPTS% %BUILDDIR%/json if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can process the JSON files. goto end ) if "%1" == "htmlhelp" ( %SPHINXBUILD% -b htmlhelp %ALLSPHINXOPTS% %BUILDDIR%/htmlhelp if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can run HTML Help Workshop with the ^ .hhp project file in %BUILDDIR%/htmlhelp. goto end ) if "%1" == "qthelp" ( %SPHINXBUILD% -b qthelp %ALLSPHINXOPTS% %BUILDDIR%/qthelp if errorlevel 1 exit /b 1 echo. echo.Build finished; now you can run "qcollectiongenerator" with the ^ .qhcp project file in %BUILDDIR%/qthelp, like this: echo.^> qcollectiongenerator %BUILDDIR%\qthelp\COLMAP.qhcp echo.To view the help file: echo.^> assistant -collectionFile %BUILDDIR%\qthelp\COLMAP.ghc goto end ) if "%1" == "devhelp" ( %SPHINXBUILD% -b devhelp %ALLSPHINXOPTS% %BUILDDIR%/devhelp if errorlevel 1 exit /b 1 echo. echo.Build finished. goto end ) if "%1" == "epub" ( %SPHINXBUILD% -b epub %ALLSPHINXOPTS% %BUILDDIR%/epub if errorlevel 1 exit /b 1 echo. echo.Build finished. The epub file is in %BUILDDIR%/epub. goto end ) if "%1" == "latex" ( %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex if errorlevel 1 exit /b 1 echo. echo.Build finished; the LaTeX files are in %BUILDDIR%/latex. goto end ) if "%1" == "latexpdf" ( %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex cd %BUILDDIR%/latex make all-pdf cd %BUILDDIR%/.. echo. echo.Build finished; the PDF files are in %BUILDDIR%/latex. goto end ) if "%1" == "latexpdfja" ( %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex cd %BUILDDIR%/latex make all-pdf-ja cd %BUILDDIR%/.. echo. echo.Build finished; the PDF files are in %BUILDDIR%/latex. goto end ) if "%1" == "text" ( %SPHINXBUILD% -b text %ALLSPHINXOPTS% %BUILDDIR%/text if errorlevel 1 exit /b 1 echo. echo.Build finished. The text files are in %BUILDDIR%/text. goto end ) if "%1" == "man" ( %SPHINXBUILD% -b man %ALLSPHINXOPTS% %BUILDDIR%/man if errorlevel 1 exit /b 1 echo. echo.Build finished. The manual pages are in %BUILDDIR%/man. goto end ) if "%1" == "texinfo" ( %SPHINXBUILD% -b texinfo %ALLSPHINXOPTS% %BUILDDIR%/texinfo if errorlevel 1 exit /b 1 echo. echo.Build finished. The Texinfo files are in %BUILDDIR%/texinfo. goto end ) if "%1" == "gettext" ( %SPHINXBUILD% -b gettext %I18NSPHINXOPTS% %BUILDDIR%/locale if errorlevel 1 exit /b 1 echo. echo.Build finished. The message catalogs are in %BUILDDIR%/locale. goto end ) if "%1" == "changes" ( %SPHINXBUILD% -b changes %ALLSPHINXOPTS% %BUILDDIR%/changes if errorlevel 1 exit /b 1 echo. echo.The overview file is in %BUILDDIR%/changes. goto end ) if "%1" == "linkcheck" ( %SPHINXBUILD% -b linkcheck %ALLSPHINXOPTS% %BUILDDIR%/linkcheck if errorlevel 1 exit /b 1 echo. echo.Link check complete; look for any errors in the above output ^ or in %BUILDDIR%/linkcheck/output.txt. goto end ) if "%1" == "doctest" ( %SPHINXBUILD% -b doctest %ALLSPHINXOPTS% %BUILDDIR%/doctest if errorlevel 1 exit /b 1 echo. echo.Testing of doctests in the sources finished, look at the ^ results in %BUILDDIR%/doctest/output.txt. goto end ) if "%1" == "xml" ( %SPHINXBUILD% -b xml %ALLSPHINXOPTS% %BUILDDIR%/xml if errorlevel 1 exit /b 1 echo. echo.Build finished. The XML files are in %BUILDDIR%/xml. goto end ) if "%1" == "pseudoxml" ( %SPHINXBUILD% -b pseudoxml %ALLSPHINXOPTS% %BUILDDIR%/pseudoxml if errorlevel 1 exit /b 1 echo. echo.Build finished. The pseudo-XML files are in %BUILDDIR%/pseudoxml. goto end ) :end colmap-3.4/doc/tutorial.rst000077500000000000000000000635031323400541200160010ustar00rootroot00000000000000.. _tutorial: Tutorial ======== 3D reconstruction from images traditionally first recovers a sparse representation of the scene and the camera poses of the input images using Structure-from-Motion. This output then serves as the input to Multi-View Stereo to recover a dense representation of the scene. .. _quick-start: Quickstart ---------- First, start the graphical user interface of COLMAP, as described :ref:`here `. COLMAP provides an automatic reconstruction tool that simply takes a folder of input images and produces a sparse and dense reconstruction in a workspace folder. Click ``Reconstruction > Automatic Reconstruction`` in the GUI and specify the relevant options. The output is written to the workspace folder. For example, if your images are located in ``path/to/project/images``, you could select ``path/to/project`` as a workspace folder and after running the automatic reconstruction tool, the folder would look similar to this:: +── images │   +── image1.jpg │   +── image2.jpg │   +── ... +── sparse │   +── 0 │   │ +── cameras.bin │   │ +── images.bin │   │ +── points3D.bin │ +── ... +── dense │   +── 0 │   │ +── images │   │ +── sparse │   │ +── stereo │   │ +── fused.ply │   │ +── meshed.ply │ +── ... +── database.db Here, the ``path/to/project/sparse`` contains the sparse models for all reconstructed components, while ``path/to/project/dense`` contains their corresponding dense models. The dense point cloud ``fused.ply`` can be imported in COLMAP using ``File > Import model from ...``, while the dense mesh must be visualized with an external viewer such as Meshlab. The following sections give general recommendations and describe the reconstruction process in more detail, if you need more control over the reconstruction process/parameters or if you are interested in the underlying technology in COLMAP. Structure-from-Motion --------------------- .. figure:: images/incremental-sfm.png :alt: Incremental Structure-from-Motion pipeline :figclass: align-center COLMAP's incremental Structure-from-Motion pipeline. Structure-from-Motion (SfM) is the process of reconstructing 3D structure from its projections into a series of images. The input is a set of overlapping images of the same object, taken from different viewpoints. The output is a 3-D reconstruction of the object, and the reconstructed intrinsic and extrinsic camera parameters of all images. Typically, Structure-from-Motion systems divide this process into three stages: 1) Feature detection and extraction 2) Feature matching and geometric verification 3) Structure and motion reconstruction COLMAP reflects these stages in different modules, that can be combined depending on the application. More information on Structure-from-Motion in general and the algorithms in COLMAP can be found in [schoenberger16sfm]_ and [schoenberger16mvs]_. If you have control over the picture capture process, please follow these guidelines for optimal reconstruction results: - Capture images with **good texture**. Avoid completely texture-less images (e.g., a white wall or empty desk). If the scene does not contain enough texture itself, you could place additional background objects, such as posters, etc. - Capture images at **similar illumination** conditions. Avoid high dynamic range scenes (e.g., pictures against the sun with shadows or pictures through doors/windows). Avoid specularities on shiny surfaces. - Capture images with **high visual overlap**. Make sure that each object is seen in at least 3 images -- the more images the better. - Capture images from **different viewpoints**. Do not take images from the same location by only rotating the camera, e.g., make a few steps after each shot. At the same time, try to have enough images from a relatively similar viewpoint. Note that more images is not necessarily better and might lead to a slow reconstruction process. If you use a video as input, consider down-sampling the frame rate. Multi-View Stereo ----------------- Multi-View Stereo (MVS) takes the output of SfM to compute depth and/or normal information for every pixel in an image. Fusion of the depth and normal maps of multiple images in 3D then produces a dense point cloud of the scene. Using the depth and normal information of the fused point cloud, algorithms such as the (screened) Poisson surface reconstruction [kazhdan2013]_ can then recover the 3D surface geometry of the scene. More information on Multi-View Stereo in general and the algorithms in COLMAP can be found in [schoenberger16mvs]_. Preface ------- COLMAP requires only few steps to do a standard reconstruction for a general user. For more experienced users, the program exposes many different parameters, only some of which are intuitive to a beginner. The program should usually work without the need to modify any parameters. The defaults are chosen as a trade- off between reconstruction robustness/quality and speed. You can set "optimal" options for different reconstruction scenarios by choosing ``Extras > Set options for ... data``. If in doubt what settings to choose, stick to the defaults. The source code contains more documentation about all parameters. COLMAP is research software and in rare cases it may exit ungracefully if some constraints are not fulfilled. In this case, the program prints a traceback to stdout. To see this traceback or more debug information, it is recommended to run the executables (including the GUI) from the command-line, where you can define various levels of logging verbosity. Terminology ----------- The term **camera** is associated with the physical object of a camera using the same zoom-factor and lens. A camera defines the intrinsic projection model in COLMAP. A single camera can take multiple images with the same resolution, intrinsic parameters, and distortion characteristics. The term **image** is associated with a bitmap file, e.g., a JPEG or PNG file on disk. COLMAP detects **keypoints** in each image whose appearance is described by numerical **descriptors**. Pure appearance-based correspondences between keypoints/descriptors are defined by **matches**, while **inlier matches** are geometrically verified and used for the reconstruction procedure. Data Structure -------------- COLMAP assumes that all input images are in one input directory with potentially nested sub-directories. It recursively considers all images stored in this directory, and it supports various different image formats (see `FreeImage `_). Other files are automatically ignored. If high performance is a requirement, then you should separate any files that are not images. Images are identified uniquely by their relative file path. For lather processing, such as image undistortion or dense reconstruction, the relative folder structure should be preserved. COLMAP does not modify the input images or directory and all extracted data is stored in a single, self-contained SQLite database file (see :doc:`database`). The first step is to start the graphical user interface of COLMAP by running the pre-built binaries (Windows: `COLMAP.bat`, Mac: `COLMAP.app`) or by executing ``./src/exe/colmap gui`` from the CMake build folder. Next, create a new project by choosing ``File > New project``. In this dialog, you must select where to store the database and the folder that contains the input images. For convenience, you can save the entire project settings to a configuration file by choosing ``File > Save project``. The project configuration stores the absolute path information of the database and image folder in addition to any other parameter settings. If you decide to move the database or image folder, you must change the paths accordingly by creating a new project. Alternatively, the resulting `.ini` configuration file can be directly modified in a text editor of your choice. To reopen an existing project, you can simply open the configuration file by choosing ``File > Open project`` and all parameter settings should be recovered. Note that all COLMAP executables can be started from the command-line by either specifying individual settings as command-line arguments or by providing the path to the project configuration file (see :ref:`Interface `). An example folder structure could look like this:: /path/to/project/... +── images │   +── image1.jpg │   +── image2.jpg │   +── ... │   +── imageN.jpg +── database.db +── project.ini In this example, you would select `/path/to/project/images` as the image folder path, `/path/to/project/database.db` as the database file path, and save the project configuration to `/path/to/project/project.ini`. Feature Detection and Extraction -------------------------------- In the first step, feature detection/extraction finds sparse feature points in the image and describes their appearance using a numerical descriptor. COLMAP imports images and performs feature detection/extraction in one step in order to only load images from disk once. Next, choose ``Processing > Extract features``. In this dialog, you must first decide on the employed intrinsic camera model. You can either automatically extract focal length information from the embedded EXIF information or manually specify intrinsic parameters, e.g., as obtained in a lab calibration. If an image has partial EXIF information, COLMAP tries to find the missing camera specifications in a large database of camera models automatically. If all your images were captured by the same physical camera with identical zoom factor, it is recommended to share intrinsics between all images. Note that the program will exit ungracefully if the same camera model is shared among all images but not all images have the same size or EXIF focal length. If you have several groups of images that share the same intrinsic camera parameters, you can easily modify the camera models at a later point as well (see :ref:`Database Management `). If in doubt what to choose in this step, simply stick to the default parameters. You can either detect and extract new features from the images or import existing features from text files. COLMAP extracts SIFT [lowe04]_ features either on the GPU or the CPU. The GPU version requires an attached display, while the CPU version is recommended for use on a server. In general, the GPU version is favorable as it has a customized feature detection mode that often produces higher quality features in the case of high contrast images. If you import existing features, every image must have a text file next to it (e.g., `/path/to/image1.jpg` and `/path/to/image1.jpg.txt`) in the following format:: NUM_FEATURES 128 X Y SCALE ORIENTATION D_1 D_2 D_3 ... D_128 ... X Y SCALE ORIENTATION D_1 D_2 D_3 ... D_128 where `X, Y, SCALE, ORIENTATION` are floating point numbers and `D_1...D_128` values in the range `0...255`. The file should have `NUM_FEATURES` lines with one line per feature. For example, if an image has 4 features, then the text file should look something like this:: 4 128 1.2 2.3 0.1 0.3 1 2 3 4 ... 21 2.2 3.3 1.1 0.3 3 2 3 2 ... 32 0.2 1.3 1.1 0.3 3 2 3 2 ... 2 1.2 2.3 1.1 0.3 3 2 3 2 ... 3 Note that by convention the upper left corner of an image has coordinate `(0, 0)` and the center of the upper left most pixel has coordinate `(0.5, 0.5)`. If you must import features for large image collections, it is much more efficient to directly access the database with your favorite scripting language (see :ref:`Database Format `). If you are done setting all options, choose ``Extract`` and wait for the extraction to finish or cancel. If you cancel during the extraction process, the next time you start extracting images for the same project, COLMAP automatically continues where it left off. This also allows you to add images to an existing project/reconstruction. In this case, be sure to verify the camera parameters when using shared intrinsics. All extracted data will be stored in the database file and can be reviewed/managed in the database management tool (see :ref:`Database Management `) or, for experts, directly modified using SQLite (see :ref:`Database Format `). Feature Matching and Geometric Verification ------------------------------------------- In the second step, feature matching and geometric verification finds correspondences between the feature points in different images. Please, choose ``Processing > Match features`` and select one of the provided matching modes, that are intended for different input scenarios: - **Exhaustive Matching**: If the number of images in your dataset is relatively low (up to several hundreds), this matching mode should be fast enough and leads to the best reconstruction results. Here, every image is matched against every other image, while the block size determines how many images are loaded from disk into memory at the same time. - **Sequential Matching**: This mode is useful if the images are acquired in sequential order, e.g., by a video camera. In this case, consecutive frames have visual overlap and there is no need to match all image pairs exhaustively. Instead, consecutively captured images are matched against each other. This matching mode has built-in loop detection based on a vocabulary tree, where every N-th image (`loop_detection_period`) is matched against its visually most similar images (`loop_detection_num_images`). Note that image file names must be ordered sequentially (e.g., `image0001.jpg`, `image0002.jpg`, etc.). You can verify the correct order in the database management tool (see :ref:`Database Format `). Note that loop detection requires a pre-trained vocabulary tree, that can be downloaded from https://demuc.de/colmap/. - **Vocabulary Tree Matching**: In this matching mode [schoenberger16vote]_, every image is matched against its visual nearest neighbors using a vocabulary tree with spatial re-ranking. This is the recommended matching mode for large image collections (several thousands). This requires a pre-trained vocabulary tree, that can be downloaded from https://demuc.de/colmap/. - **Spatial Matching**: This matching mode matches every image against its spatial nearest neighbors. Spatial locations can be manually set in the database management. By default, COLMAP also extracts GPS information from EXIF and uses it for spatial nearest neighbor search. If accurate prior location information is available, this is the recommended matching mode. - **Transitive Matching**: This matching mode uses the transitive relations of already existing feature matches to produce a more complete matching graph. If an image A matches to an image B and B matches to C, then this matcher attempts to match A to C directly. - **Custom Matching**: This mode allows to specify individual image pairs for matching or to import individual feature matches. To specify image pairs, you have to provide a text file with one image pair per line:: image1.jpg image2.jpg image1.jpg image3.jpg ... where `image1.jpg` is the relative path in the image folder. You have two options to import individual feature matches. Either raw feature matches, which are not geometrically verified or already geometrically verified feature matches. In both cases, the expected format is:: image1.jpg image2.jpg 0 1 1 2 3 4 image1.jpg image3.jpg 0 1 1 2 3 4 4 5 ... where `image1.jpg` is the relative path in the image folder and the pairs of numbers are zero-based feature indices in the respective images. If you must import many matches for large image collections, it is more efficient to directly access the database with a scripting language of your choice. If you are done setting all options, choose ``Match`` and wait for the matching to finish or cancel in between. Note that this step can take a significant amount of time depending on the number of images, the number of features per image, and the chosen matching mode. Expected times for exhaustive matching are from a few minutes for tens of images to a few hours for hundreds of images to days or weeks for thousands of images. If you cancel the matching process or import new images after matching, COLMAP only matches image pairs that have not been matched previously. The overhead of skipping already matched image pairs is low. This also enables to match additional images imported after an initial matching and it enables to combine different matching modes for the same dataset. All extracted data will be stored in the database file and can be reviewed/managed in the database management tool (see :ref:`Database Management `) or, for experts, directly modified using SQLite (see :ref:`Database Format `). Note that feature matching requires a GPU and that the display performance of your computer might degrade significantly during the matching process. If your system has multiple CUDA-enabled GPUs, you can select specific GPUs with the `gpu_index` option. Sparse Reconstruction --------------------- After producing the scene graph in the previous two steps, you can start the incremental reconstruction process by choosing ``Reconstruction > Start``. COLMAP first loads all extracted data from the database into memory and seeds the reconstruction from an initial image pair. Then, the scene is incrementally extended by registering new images and triangulating new points. The results are visualized in "real-time" during this reconstruction process. Refer to the :ref:`Graphical User Interface ` section for more details about the available controls. COLMAP attempts to reconstruct multiple models if not all images are registered into the same model. The different models can be selected from the drop-down menu in the toolbar. If the different models have common registered images, you can use the ``model_converter`` executable to merge them into a single reconstruction (see :ref:`FAQ ` for details). If all your images use the `SIMPLE_RADIAL` camera model (default) without shared intrinsics, you can use PBA [wu11]_ instead of Ceres Solver [ceres]_ for fast bundle adjustment, which can be activated in the reconstruction options under the bundle adjustment section (`use_pba=true`). Ideally, the reconstruction works fine and all images are registered. If this is not the case, it is recommended to: - Perform additional matching. For best results, use exhaustive matching, enable guided matching, increase the number of nearest neighbors in vocabulary tree matching, or increase the overlap in sequential matching, etc. - Manually choose an initial image pair, if COLMAP fails to initialize. Choose ``Reconstruction > Reconstruction options > Init`` and set images from the database management tool that have enough matches from different viewpoints. Importing and Exporting ----------------------- COLMAP provides several export options for further processing. For full flexibility, it is recommended to export the reconstruction in COLMAP's data format by choosing ``File > Export`` to export the currently viewed model or ``File > Export all`` to export all reconstructed models. The model is exported in the selected folder using separate text files for the reconstructed cameras, images, and points. When exporting in COLMAP's data format, you can re- import the reconstruction for later visualization, image undistortion, or to continue an existing reconstruction from where it left off (e.g., after importing and matching new images). To import a model, choose ``File > Import`` and select the export folder path. Alternatively, you can also export the model in various other formats, such as Bundler, VisualSfM [#f1]_, PLY, or VRML by choosing ``File > Export as...``. COLMAP can visualize plain PLY point cloud files with RGB information by choosing ``File > Import From...``. Further information about the format of the exported models can be found :ref:`here `. .. _dense-reconstruction: Dense Reconstruction -------------------- After reconstructing a sparse representation of the scene and the camera poses of the input images, MVS can now recover denser scene geometry. COLMAP has an integrated dense reconstruction pipeline to produce depth and normal maps for all registered images, to fuse the depth and normal maps into a dense point cloud with normal information, and to finally estimate a dense surface from the fused point cloud using Poisson reconstruction [kazhdan2013]_. To get started, import your sparse 3D model into COLMAP (or select the reconstructed model after finishing the previous sparse reconstruction steps). Then, choose ``Reconstruction > Multi-view stereo`` and select an empty or existing workspace folder, which is used for the output and of all dense reconstruction results. The first step is to ``undistort`` the images, second to compute the depth and normal maps using ``stereo``, third to ``fuse`` the depth and normals maps to a point cloud, followed by a final, optional point cloud ``meshing`` step. During the stereo reconstruction process, the display might freeze due to heavy compute load and, if your GPU does not have enough memory, the reconstruction process might ungracefully crash. Please, refer to the FAQ (:ref:`freeze ` and :ref:`memory `) for information on how to avoid these problems. Note that the reconstructed normals of the point cloud cannot be directly visualized in COLMAP, but e.g. in Meshlab by enabling ``Render > Show Normal/Curvature``. Similarly, the reconstructed dense surface mesh model must be visualized with external software. Note that COLMAP requires a CUDA-enabled GPU, so in addition to the internal dense reconstruction functionality, COLMAP exports to several other dense reconstruction libraries, such as CMVS/PMVS [furukawa10]_ or CMP-MVS [jancosek11]_. Please choose ``Extras > Undistort images`` and select the appropriate format. The output folders contain the reconstruction and the undistorted images. In addition, the folders contain sample shell scripts to perform the dense reconstruction. To run PMVS2, execute the following commands:: ./path/to/pmvs2 /path/to/undistortion/folder/pmvs/ option-all where `/path/to/undistortion/folder` is the folder selected in the undistortion dialog. Make sure not to forget the trailing slash in `/path/to/undistortion/folder/pmvs/` in the above command-line arguments. For large datasets, you probably want to first run CMVS to cluster the scene into more manageable parts and then run COLMAP or PMVS2. Please, refer to the sample shell scripts in the undistortion output folder on how to run CMVS in combination with COLMAP or PMVS2. Moreover, there are a number of external libraries that support COLMAP's output: - `CMVS/PMVS `_ [furukawa10]_ - `CMP-MVS `_ [jancosek11]_ - `Line3D++ `_ [hofer16]_. .. _database-management: Database Management ------------------- You can review and manage the imported cameras, images, and feature matches in the database management tool. Choose ``Processing > Manage database``. In the opening dialog, you can see the list of imported images and cameras. You can view the features and matches for each image by clicking ``Show image`` and ``Show matches``. Individual entries in the database tables can be modified by double clicking specific cells. Note that any changes to the database are only effective after clicking ``Save``. To share intrinsic camera parameters between arbitrary groups of images, select a single or multiple images, choose ``Set camera`` and set the `camera_id`, which corresponds to the unique `camera_id` column in the cameras table. You can also add new cameras with specific parameters. By setting the `prior_focal_length` flag to 0 or 1, you can give a hint whether the reconstruction algorithm should trust the focal length value. In case of a prior lab calibration, you want to set this value to 1. Without prior knowledge about the focal length, it is recommended to set this value to `1.25 * max(width_in_px, height_in_px)`. The database management tool has only limited functionality and, for full control over the data, you must directly modify the SQLite database (see :ref:`Database Format `). By accessing the database directly, you can use COLMAP only for feature extraction and matching or you can import your own features and matches to only use COLMAP's incremental reconstruction algorithm. .. _interface: Graphical and Command-line Interface ------------------------------------ Most of COLMAP's features are accessible from both the graphical and the command-line interface, which are both embedded in the same executable. You can provide the options directly as command-line arguments or you can provide a `.ini` project configuration file containing the options using the ``--project_path path/to/project.ini`` argument. To start the GUI application, please execute ``colmap gui`` or directly specify a project configuration as ``colmap gui --project_path path/to/project.ini`` to avoid tedious selection in the GUI. To list the different commands available from the command-line, execute ``colmap help``. For example, to run feature extraction from the command-line, you must execute ``colmap feature_extractor``. The :ref:`Graphical User Interface ` and :ref:`Command- line Interface ` sections provide more details about the available commands. .. rubric:: Footnotes .. [#f1] VisualSfM's [wu13]_ projection model applies the distortion to the measurements and COLMAP to the projection, hence the exported NVM file is not fully compatible with VisualSfM. colmap-3.4/scripts/000077500000000000000000000000001323400541200143145ustar00rootroot00000000000000colmap-3.4/scripts/matlab/000077500000000000000000000000001323400541200155545ustar00rootroot00000000000000colmap-3.4/scripts/matlab/cmap2rgb.m000066400000000000000000000021241323400541200174260ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function rgb = cmap2rgb(image, cmap, varargin) if length(varargin) == 1 clim = varargin{1}; image(image <= clim(1)) = clim(1); image(image > clim(2)) = clim(2); end image_min = min(image(:)); image_max = max(image(:)); image = (image - image_min) / (image_max - image_min) * size(cmap, 1); rgb = ind2rgb(uint32(image), cmap); end colmap-3.4/scripts/matlab/plot_model.m000077500000000000000000000030631323400541200200750ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function plot_model(cameras, images, points) % Visualize COLMAP model. keys = images.keys; camera_centers = zeros(images.length, 3); view_dirs = zeros(3 * images.length, 3); for i = 1:images.length image_id = keys{i}; image = images(image_id); camera_centers(i,:) = -image.R' * image.t; view_dirs(3 * i - 2,:) = camera_centers(i,:); view_dirs(3 * i - 1,:) = camera_centers(i,:)' + image.R' * [0; 0; 0.3]; view_dirs(3 * i,:) = nan; end keys = points.keys; xyz = zeros(points.length, 3); for i = 1:points.length point_id = keys{i}; point = points(point_id); xyz(i,:) = point.xyz; end hold on; plot3(camera_centers(:,1), camera_centers(:,2), camera_centers(:,3), 'xr'); plot3(view_dirs(:,1), view_dirs(:,2), view_dirs(:,3), '-b'); plot3(xyz(:,1), xyz(:,2), xyz(:,3), '.k'); hold off; end colmap-3.4/scripts/matlab/quat2rotmat.m000077500000000000000000000024521323400541200202230ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function rotmat = quat2rotmat(qvec) rotmat = [1 - 2 * qvec(3).^2 - 2 * qvec(4).^2, ... 2 * qvec(2) * qvec(3) - 2 * qvec(1) * qvec(4), ... 2 * qvec(4) * qvec(2) + 2 * qvec(1) * qvec(3); ... 2 * qvec(2) * qvec(3) + 2 * qvec(1) * qvec(4), ... 1 - 2 * qvec(2).^2 - 2 * qvec(4).^2, ... 2 * qvec(3) * qvec(4) - 2 * qvec(1) * qvec(2); ... 2 * qvec(4) * qvec(2) - 2 * qvec(1) * qvec(3), ... 2 * qvec(3) * qvec(4) + 2 * qvec(1) * qvec(2), ... 1 - 2 * qvec(2).^2 - 2 * qvec(3).^2]; end colmap-3.4/scripts/matlab/read_array.m000066400000000000000000000022631323400541200200460ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function array = read_array(path, varargin) if length(varargin) == 1 dtype = varargin{1}; else dtype = 'single'; end fid = fopen(path); line = fscanf(fid, '%d&%d&%d&', [1, 3]); width = line(1); height = line(2); channels = line(3); num = width * height * channels; array = fread(fid, num, dtype); array = reshape(array, [width, height, channels]); array = permute(array, [2 1 3]); array = cast(array, dtype); fclose(fid); end colmap-3.4/scripts/matlab/read_depth_map.m000066400000000000000000000017751323400541200207000ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function [depth_map, depth_map_rgb] = read_depth_map(path) depth_map = read_array(path); depth_range = prctile(depth_map(depth_map(:) > 0), [2, 98]); depth_map(depth_map<=0) = nan; depth_map_rgb = cmap2rgb(depth_map, [0 0 0; jet(2^15)], depth_range); end colmap-3.4/scripts/matlab/read_model.m000077500000000000000000000074451323400541200200420ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function [cameras, images, points3D] = read_model(path) % Read COLMAP model from folder, which contains a % cameras.txt, images.txt, and points3D.txt. if numel(path) > 0 && path(end) ~= '/' path = [path '/']; end cameras = read_cameras([path 'cameras.txt']); images = read_images([path 'images.txt']); points3D = read_points3D([path 'points3D.txt']); end function cameras = read_cameras(path) cameras = containers.Map('KeyType', 'int64', 'ValueType', 'any'); fid = fopen(path); tline = fgets(fid); while ischar(tline) elems = strsplit(tline); if numel(elems) < 4 || strcmp(elems(1), '#') tline = fgets(fid); continue end if mod(cameras.Count, 10) == 0 fprintf('Reading camera %d\n', cameras.length); end camera = struct; camera.camera_id = str2num(elems{1}); camera.model = elems{2}; camera.width = str2num(elems{3}); camera.height = str2num(elems{4}); camera.params = zeros(numel(elems) - 5, 1); for i = 5:numel(elems) - 1 camera.params(i - 4) = str2double(elems{i}); end cameras(camera.camera_id) = camera; tline = fgets(fid); end fclose(fid); end function images = read_images(path) images = containers.Map('KeyType', 'int64', 'ValueType', 'any'); fid = fopen(path); tline = fgets(fid); while ischar(tline) elems = strsplit(tline); if numel(elems) < 4 || strcmp(elems(1), '#') tline = fgets(fid); continue end if mod(images.Count, 10) == 0 fprintf('Reading image %d\n', images.length); end image = struct; image.image_id = str2num(elems{1}); qw = str2double(elems{2}); qx = str2double(elems{3}); qy = str2double(elems{4}); qz = str2double(elems{5}); image.R = quat2rotmat([qw, qx, qy, qz]); tx = str2double(elems{6}); ty = str2double(elems{7}); tz = str2double(elems{8}); image.t = [tx; ty; tz]; image.camera_id = str2num(elems{9}); image.name = elems{10}; tline = fgets(fid); elems = sscanf(tline, '%f'); elems = reshape(elems, [3, numel(elems) / 3]); image.xys = elems(1:2,:)'; image.point3D_ids = elems(3,:)'; images(image.image_id) = image; tline = fgets(fid); end fclose(fid); end function points3D = read_points3D(path) points3D = containers.Map('KeyType', 'int64', 'ValueType', 'any'); fid = fopen(path); tline = fgets(fid); while ischar(tline) if numel(tline) == 0 || strcmp(tline(1), '#') tline = fgets(fid); continue; end elems = sscanf(tline, '%f'); if numel(elems) == 0 tline = fgets(fid); continue; end if mod(points3D.Count, 1000) == 0 fprintf('Reading point %d\n', points3D.length); end point = struct; point.point3D_id = int64(elems(1)); point.xyz = elems(2:4); point.rgb = int8(elems(5:7)); point.error = elems(8); point.track = int64(elems(9:end)); point.track = reshape(point.track, [2, numel(point.track) / 2])'; point.track(:,2) = point.track(:,2) + 1; points3D(point.point3D_id) = point; tline = fgets(fid); end fclose(fid); end colmap-3.4/scripts/matlab/read_normal_map.m000066400000000000000000000023701323400541200210540ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function [normal_map, normal_map_rgb] = read_normal_map(path, varargin) normal_map = read_array(path); normal_map_rgb = -[normal_map(:,:,1) normal_map(:,:,2) ... 2 * normal_map(:,:,3) + 1]; normal_map_rgb = reshape(normal_map_rgb, ... size(normal_map,1), size(normal_map,2), 3); normal_map_rgb = uint8(((normal_map_rgb + 1) ./ 2) .* 255); if length(varargin) == 1 depth_map = varargin{1}; normal_map_rgb(repmat(isnan(depth_map), [1, 1, 3])) = 0; end end colmap-3.4/scripts/matlab/read_ply.m000077500000000000000000000027101323400541200175340ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function [xyz, normals, rgb] = read_ply(path) % Read point cloud from PLY text file. file = fopen(path, 'r'); type = fscanf(file, '%s', 1); format = fscanf(file, '%s', 3); data = fscanf(file, '%s', 2); num_points = fscanf(file, '%d', 1); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 3); fscanf(file, '%s', 1); points_data = textscan(file, '%f %f %f %f %f %f %f %f %f', num_points); xyz = [points_data{1}, points_data{2}, points_data{3}]; rgb = [points_data{7}, points_data{8}, points_data{9}]; normals = [points_data{4}, points_data{5}, points_data{6}]; end colmap-3.4/scripts/matlab/write_array.m000066400000000000000000000017251323400541200202670ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function write_array(path, array) fid = fopen(path, 'w'); fprintf(fid, '%d&%d&%d&', size(array, 2), size(array, 1), size(array, 3)); array = permute(array, [2 1 3]); fwrite(fid, array, class(array)); fclose(fid); end colmap-3.4/scripts/matlab/write_ply.m000077500000000000000000000031331323400541200177530ustar00rootroot00000000000000% COLMAP - Structure-from-Motion and Multi-View Stereo. % Copyright (C) 2017 Johannes L. Schoenberger % % This program is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with this program. If not, see . function write_ply(path, xyz, normals, rgb) % Write point cloud to PLY text file. file = fopen(path, 'W'); fprintf(file,'ply\n'); fprintf(file,'format ascii 1.0\n'); fprintf(file,'element vertex %d\n',size(xyz,1)); fprintf(file,'property float x\n'); fprintf(file,'property float y\n'); fprintf(file,'property float z\n'); fprintf(file,'property float nx\n'); fprintf(file,'property float ny\n'); fprintf(file,'property float nz\n'); fprintf(file,'property uchar diffuse_red\n'); fprintf(file,'property uchar diffuse_green\n'); fprintf(file,'property uchar diffuse_blue\n'); fprintf(file,'end_header\n'); for i = 1:size(xyz, 1) fprintf(file, '%f %f %f %f %f %f %d %d %d\n', ... xyz(i,1), xyz(i,2), xyz(i,3), ... normals(i,1), normals(i,2), normals(i,3), ... uint8(rgb(i,1)), uint8(rgb(i,2)), uint8(rgb(i,3))); end fclose(file); end colmap-3.4/scripts/python/000077500000000000000000000000001323400541200156355ustar00rootroot00000000000000colmap-3.4/scripts/python/build.py000066400000000000000000000452051323400541200173140ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . import os import sys import glob import shutil import fileinput import platform import argparse import zipfile import hashlib import urllib.request import subprocess import multiprocessing PLATFORM_IS_WINDOWS = platform.system() == "Windows" PLATFORM_IS_LINUX = platform.system() == "Linux" PLATFORM_IS_MAC = platform.system() == "Darwin" def parse_args(): parser = argparse.ArgumentParser( description="Build COLMAP and its dependencies locally under Windows, " "Mac, and Linux. Note that under Mac and Linux, it is " "usually easier and faster to use the available package " "managers for the dependencies (see documentation). " "However, if you are on a (cluster) system without root " "access, this script might be useful. This script " "downloads the necessary dependencies automatically from " "the Internet. It assumes that CMake, Boost, Qt5, and CUDA " "(optional) are already installed on the system. Under " "Windows you must specify the location of these libraries.") parser.add_argument("--build_path", required=True) parser.add_argument("--colmap_path", required=True, help="The path to the top COLMAP source folder, which " "contains src/, scripts/, CMakeLists.txt, etc." ) parser.add_argument("--qt_path", default="", required=PLATFORM_IS_WINDOWS or PLATFORM_IS_MAC, help="The path to the folder containing Qt, " "e.g., under Windows: C:/Qt/5.9.1/msvc2013_64/ " "or under Mac: /usr/local/opt/qt/") parser.add_argument("--boost_path", default="", required=PLATFORM_IS_WINDOWS, help="The path to the folder containing Boost, " "e.g., under Windows: " "C:/local/boost_1_64_0/lib64-msvc-12.0") parser.add_argument("--cuda_path", default="", help="The path to the folder containing CUDA, " "e.g., under Windows: C:/Program Files/NVIDIA GPU " "Computing Toolkit/CUDA/v8.0") parser.add_argument("--cuda_multi_arch", dest="cuda_multi_arch", action="store_true",) parser.add_argument("--no_cuda_multi_arch", dest="cuda_multi_arch", action="store_false", help="Whether to compile CUDA code for " "multiple GPU architectures (default no)") parser.add_argument("--with_suite_sparse", dest="with_suite_sparse", action="store_true") parser.add_argument("--without_suite_sparse", dest="with_suite_sparse", action="store_false", help="Whether to use SuiteSparse as a sparse solver " "(default with SuiteSparse)") parser.add_argument("--with_tests", dest="with_tests", action="store_true") parser.add_argument("--without_tests", dest="with_tests", action="store_false", help="Whether to build unit tests") parser.add_argument("--build_type", default="Release", help="Build type, e.g., Debug, Release, RelWithDebInfo") parser.add_argument("--cmake_generator", default="", help="CMake generator, e.g., Visual Studio 14") parser.set_defaults(cuda_multi_arch=False) parser.set_defaults(with_suite_sparse=True) parser.set_defaults(with_tests=True) args = parser.parse_args() args.build_path = os.path.abspath(args.build_path) args.download_path = os.path.join(args.build_path, "__download__") args.install_path = os.path.join(args.build_path, "__install__") args.cmake_config_args = [] args.cmake_config_args.append( "-DCMAKE_BUILD_TYPE={}".format(args.build_type)) args.cmake_config_args.append( "-DCMAKE_PREFIX_PATH={}".format(args.install_path)) args.cmake_config_args.append( "-DCMAKE_INSTALL_PREFIX={}".format(args.install_path)) if args.cmake_generator: args.cmake_config_args.extend(["-G", args.cmake_generator]) if PLATFORM_IS_WINDOWS: args.cmake_config_args.append( "-DCMAKE_GENERATOR_PLATFORM=x64") args.cmake_build_args = ["--"] if PLATFORM_IS_WINDOWS: # Assuming that the build system is MSVC. args.cmake_build_args.append( "/maxcpucount:{}".format(multiprocessing.cpu_count())) else: # Assuming that the build system is Make. args.cmake_build_args.append( "-j{}".format(multiprocessing.cpu_count())) return args def mkdir_if_not_exists(path): assert os.path.exists(os.path.dirname(os.path.abspath(path))) if not os.path.exists(path): os.makedirs(path) def copy_file_if_not_exists(source, destination): if os.path.exists(destination): return shutil.copyfile(source, destination) def check_md5_hash(path, md5_hash): computed_md5_hash = hashlib.md5() with open(path, "rb") as f: for chunk in iter(lambda: f.read(4096), b""): computed_md5_hash.update(chunk) computed_md5_hash = computed_md5_hash.hexdigest() if md5_hash != computed_md5_hash: print("MD5 mismatch for {}: {} == {}".format( path, md5_hash, computed_md5_hash)) sys.exit(1) def download_zipfile(url, archive_path, unzip_path, md5_hash): if not os.path.exists(archive_path): urllib.request.urlretrieve(url, archive_path) check_md5_hash(archive_path, md5_hash) with zipfile.ZipFile(archive_path, "r") as fid: fid.extractall(unzip_path) def build_cmake_project(args, path, extra_config_args=[], extra_build_args=[], cmakelists_path=".."): mkdir_if_not_exists(path) cmake_command = ["cmake"] \ + args.cmake_config_args \ + extra_config_args \ + [cmakelists_path] return_code = subprocess.call(cmake_command, cwd=path) if return_code != 0: print("Command failed:", " ".join(cmake_command)) sys.exit(1) cmake_command = ["cmake", "--build", ".", "--target", "install", "--config", args.build_type] \ + args.cmake_build_args \ + extra_build_args return_code = subprocess.call(cmake_command, cwd=path) if return_code != 0: print("Command failed:", " ".join(cmake_command)) sys.exit(1) def build_eigen(args): path = os.path.join(args.build_path, "eigen") if os.path.exists(path): return url = "https://github.com/RLovelett/eigen/archive/3.3.4.zip" archive_path = os.path.join(args.download_path, "eigen.zip") download_zipfile(url, archive_path, args.build_path, "5e6c210a4cd6821f6147c96fd3aab8a7") shutil.move(os.path.join(args.build_path, "eigen-3.3.4"), path) build_cmake_project(args, os.path.join(path, "build")) def build_freeimage(args): path = os.path.join(args.build_path, "freeimage") if os.path.exists(path): return if PLATFORM_IS_WINDOWS: url = "https://kent.dl.sourceforge.net/project/freeimage/" \ "Binary%20Distribution/3.17.0/FreeImage3170Win32Win64.zip" archive_path = os.path.join(args.download_path, "freeimage.zip") download_zipfile(url, archive_path, args.build_path, "a7e6f2f261e72260ec5b91c2a0f4bde3") shutil.move(os.path.join(args.build_path, "FreeImage"), path) copy_file_if_not_exists( os.path.join(path, "Dist/x64/FreeImage.h"), os.path.join(args.install_path, "include/FreeImage.h")) copy_file_if_not_exists( os.path.join(path, "Dist/x64/FreeImage.lib"), os.path.join(args.install_path, "lib/FreeImage.lib")) copy_file_if_not_exists( os.path.join(path, "Dist/x64/FreeImage.dll"), os.path.join(args.install_path, "lib/FreeImage.dll")) else: url = "https://kent.dl.sourceforge.net/project/freeimage/" \ "Source%20Distribution/3.17.0/FreeImage3170.zip" archive_path = os.path.join(args.download_path, "freeimage.zip") download_zipfile(url, archive_path, args.build_path) shutil.move(os.path.join(args.build_path, "FreeImage"), path) if PLATFORM_IS_MAC: with fileinput.FileInput(os.path.join(path, "Makefile.gnu"), inplace=True, backup=".bak") as fid: for line in fid: if "cp *.so Dist/" in line: continue if "FreeImage: $(STATICLIB) $(SHAREDLIB)" in line: line = "FreeImage: $(STATICLIB)" print(line, end="") elif PLATFORM_IS_LINUX: with fileinput.FileInput( os.path.join(path, "Source/LibWebP/src/dsp/" "dsp.upsampling_mips_dsp_r2.c"), inplace=True, backup=".bak") as fid: for i, line in enumerate(fid): if i >= 36 and i <= 44: line = line.replace("%[\"", "%[\" ") line = line.replace("\"],", " \"],") print(line, end="") with fileinput.FileInput( os.path.join(path, "Source/LibWebP/src/dsp/" "dsp.yuv_mips_dsp_r2.c"), inplace=True, backup=".bak") as fid: for i, line in enumerate(fid): if i >= 56 and i <= 58: line = line.replace("\"#", "\"# ") line = line.replace("\"(%", " \"(%") print(line, end="") subprocess.call(["make", "-f", "Makefile.gnu", "-j{}".format(multiprocessing.cpu_count())], cwd=path) copy_file_if_not_exists( os.path.join(path, "Source/FreeImage.h"), os.path.join(args.install_path, "include/FreeImage.h")) copy_file_if_not_exists( os.path.join(path, "libfreeimage.a"), os.path.join(args.install_path, "lib/libfreeimage.a")) def build_glew(args): path = os.path.join(args.build_path, "glew") if os.path.exists(path): return url = "https://kent.dl.sourceforge.net/project/glew/" \ "glew/2.1.0/glew-2.1.0.zip" archive_path = os.path.join(args.download_path, "glew.zip") download_zipfile(url, archive_path, args.build_path, "dff2939fd404d054c1036cc0409d19f1") shutil.move(os.path.join(args.build_path, "glew-2.1.0"), path) build_cmake_project(args, os.path.join(path, "build/cmake/build")) if PLATFORM_IS_WINDOWS: shutil.move(os.path.join(args.install_path, "bin/glew32.dll"), os.path.join(args.install_path, "lib/glew32.dll")) os.remove(os.path.join(args.install_path, "bin/glewinfo.exe")) os.remove(os.path.join(args.install_path, "bin/visualinfo.exe")) def build_gflags(args): path = os.path.join(args.build_path, "gflags") if os.path.exists(path): return url = "https://github.com/gflags/gflags/archive/v2.2.1.zip" archive_path = os.path.join(args.download_path, "gflags.zip") download_zipfile(url, archive_path, args.build_path, "2d988ef0b50939fb50ada965dafce96b") shutil.move(os.path.join(args.build_path, "gflags-2.2.1"), path) os.remove(os.path.join(path, "BUILD")) build_cmake_project(args, os.path.join(path, "build")) def build_glog(args): path = os.path.join(args.build_path, "glog") if os.path.exists(path): return url = "https://github.com/google/glog/archive/v0.3.5.zip" archive_path = os.path.join(args.download_path, "glog.zip") download_zipfile(url, archive_path, args.build_path, "454766d0124951091c95bad33dafeacd") shutil.move(os.path.join(args.build_path, "glog-0.3.5"), path) build_cmake_project(args, os.path.join(path, "build")) def build_suite_sparse(args): if not args.with_suite_sparse: return path = os.path.join(args.build_path, "suite-sparse") if os.path.exists(path): return url = "https://codeload.github.com/jlblancoc/" \ "suitesparse-metis-for-windows/zip/" \ "7bc503bfa2c4f1be9176147d36daf9e18340780a" archive_path = os.path.join(args.download_path, "suite-sparse.zip") download_zipfile(url, archive_path, args.build_path, "e7c27075e8e0afc9d2cf188630090946") shutil.move(os.path.join(args.build_path, "suitesparse-metis-for-windows-master"), path) build_cmake_project(args, os.path.join(path, "build")) if PLATFORM_IS_WINDOWS: lapack_blas_path = os.path.join(args.install_path, "lib64/lapack_blas_windows/*.dll") for library_path in glob.glob(lapack_blas_path): copy_file_if_not_exists( library_path, os.path.join(args.install_path, "lib", os.path.basename(library_path))) def build_ceres_solver(args): path = os.path.join(args.build_path, "ceres-solver") if os.path.exists(path): return url = "https://github.com/ceres-solver/ceres-solver/archive/1.13.0.zip" archive_path = os.path.join(args.download_path, "ceres-solver.zip") download_zipfile(url, archive_path, args.build_path, "f32e5b222205ad0f5cf34624f4ea59df") shutil.move(os.path.join(args.build_path, "ceres-solver-1.13.0"), path) extra_config_args = [ "-DBUILD_TESTING=OFF", "-DBUILD_EXAMPLES=OFF", ] if args.with_suite_sparse: extra_config_args.extend([ "-DLAPACK=ON", "-DSUITESPARSE=ON", ]) if PLATFORM_IS_WINDOWS: extra_config_args.extend([ "-DLAPACK_LIBRARIES={}".format( os.path.join(args.install_path, "lib64/lapack_blas_windows/liblapack.lib")), "-DBLAS_LIBRARIES={}".format( os.path.join(args.install_path, "lib64/lapack_blas_windows/libblas.lib")), ]) if PLATFORM_IS_WINDOWS: extra_config_args.append("-DCMAKE_CXX_FLAGS=/DGOOGLE_GLOG_DLL_DECL=") build_cmake_project(args, os.path.join(path, "build"), extra_config_args=extra_config_args) def build_colmap(args): extra_config_args = [] if args.qt_path != "": extra_config_args.append("-DQt5Core_DIR={}".format( os.path.join(args.qt_path, "lib/cmake/Qt5Core"))) extra_config_args.append("-DQt5OpenGL_DIR={}".format( os.path.join(args.qt_path, "lib/cmake/Qt5OpenGL"))) if args.boost_path != "": extra_config_args.append( "-DBOOST_ROOT={}".format(args.boost_path)) extra_config_args.append( "-DBOOST_LIBRARYDIR={}".format(args.boost_path)) if args.cuda_path != "": extra_config_args.append( "-DCUDA_TOOLKIT_ROOT_DIR={}".format(args.cuda_path)) if args.cuda_multi_arch: extra_config_args.append("-DCUDA_MULTI_ARCH=ON") else: extra_config_args.append("-DCUDA_MULTI_ARCH=OFF") if args.with_tests: extra_config_args.append("-DTESTS_ENABLED=ON") else: extra_config_args.append("-DTESTS_ENABLED=OFF") if PLATFORM_IS_WINDOWS: extra_config_args.append("-DCMAKE_CXX_FLAGS=/DGOOGLE_GLOG_DLL_DECL=") mkdir_if_not_exists(os.path.join(args.build_path, "colmap")) build_cmake_project(args, os.path.join(args.build_path, "colmap/build"), extra_config_args=extra_config_args, cmakelists_path=os.path.abspath(args.colmap_path)) def build_post_process(args): if PLATFORM_IS_WINDOWS: if args.qt_path: copy_file_if_not_exists( os.path.join(args.qt_path, "bin/Qt5Core.dll"), os.path.join(args.install_path, "lib/Qt5Core.dll")) copy_file_if_not_exists( os.path.join(args.qt_path, "bin/Qt5Gui.dll"), os.path.join(args.install_path, "lib/Qt5Gui.dll")) copy_file_if_not_exists( os.path.join(args.qt_path, "bin/Qt5Widgets.dll"), os.path.join(args.install_path, "lib/Qt5Widgets.dll")) mkdir_if_not_exists( os.path.join(args.install_path, "bin/platforms")) copy_file_if_not_exists( os.path.join(args.qt_path, "plugins/platforms/qwindows.dll"), os.path.join(args.install_path, "bin/platforms/qwindows.dll")) def main(): args = parse_args() mkdir_if_not_exists(args.build_path) mkdir_if_not_exists(args.download_path) mkdir_if_not_exists(args.install_path) mkdir_if_not_exists(os.path.join(args.install_path, "include")) mkdir_if_not_exists(os.path.join(args.install_path, "bin")) mkdir_if_not_exists(os.path.join(args.install_path, "lib")) mkdir_if_not_exists(os.path.join(args.install_path, "share")) build_eigen(args) build_freeimage(args) build_glew(args) build_gflags(args) build_glog(args) build_suite_sparse(args) build_ceres_solver(args) build_colmap(args) build_post_process(args) print() print() print("Successfully installed COLMAP in: {}".format(args.install_path)) if PLATFORM_IS_WINDOWS: print(" To run COLMAP, navigate to {} and run COLMAP.bat".format( args.install_path)) else: print(" To run COLMAP, execute LD_LIBRARY_PATH={} {}".format( os.path.join(args.install_path, "lib"), os.path.join(args.install_path, "colmap"))) if __name__ == "__main__": main() colmap-3.4/scripts/python/bundler_to_ply.py000077500000000000000000000074751323400541200212500ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script converts a Bundler reconstruction file to a PLY point cloud. import argparse import numpy as np def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--bundler_path", required=True) parser.add_argument("--ply_path", required=True) parser.add_argument("--normalize", type=bool, default=True) parser.add_argument("--normalize_p0", type=float, default=0.2) parser.add_argument("--normalize_p1", type=float, default=0.8) parser.add_argument("--min_track_length", type=int, default=3) args = parser.parse_args() return args def main(): args = parse_args() with open(args.bundler_path, "r") as fid: line = fid.readline() line = fid.readline() num_images, num_points = map(int, line.split()) for i in range(5 * num_images): fid.readline() xyz = np.zeros((num_points, 3), dtype=np.float64) rgb = np.zeros((num_points, 3), dtype=np.uint16) track_lengths = np.zeros((num_points,), dtype=np.uint32) for i in range(num_points): if i % 1000 == 0: print "Reading point", i, "/", num_points xyz[i] = map(float, fid.readline().split()) rgb[i] = map(int, fid.readline().split()) track_lengths[i] = int(fid.readline().split()[0]) mask = track_lengths >= args.min_track_length xyz = xyz[mask] rgb = rgb[mask] if args.normalize: sorted_x = np.sort(xyz[:, 0]) sorted_y = np.sort(xyz[:, 1]) sorted_z = np.sort(xyz[:, 2]) num_coords = sorted_x.size min_coord = int(args.normalize_p0 * num_coords) max_coord = int(args.normalize_p1 * num_coords) mean_coords = xyz.mean(0) bbox_min = np.array([sorted_x[min_coord], sorted_y[min_coord], sorted_z[min_coord]]) bbox_max = np.array([sorted_x[max_coord], sorted_y[max_coord], sorted_z[max_coord]]) extent = np.linalg.norm(bbox_max - bbox_min) scale = 10.0 / extent xyz -= mean_coords xyz *= scale xyz[:, 2] *= -1 with open(args.ply_path, "w") as fid: fid.write("ply\n") fid.write("format ascii 1.0\n") fid.write("element vertex %d\n" % xyz.shape[0]) fid.write("property float x\n") fid.write("property float y\n") fid.write("property float z\n") fid.write("property float nx\n") fid.write("property float ny\n") fid.write("property float nz\n") fid.write("property uchar diffuse_red\n") fid.write("property uchar diffuse_green\n") fid.write("property uchar diffuse_blue\n") fid.write("end_header\n") for i in range(xyz.shape[0]): if i % 1000 == 0: print "Writing point", i, "/", xyz.shape[0] fid.write("%f %f %f 0 0 0 %d %d %d\n" % (xyz[i, 0], xyz[i, 1], xyz[i, 2], rgb[i, 0], rgb[i, 1], rgb[i, 2])) if __name__ == "__main__": main() colmap-3.4/scripts/python/clang_format_code.py000077500000000000000000000033161323400541200216430ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . import os import string import argparse import subprocess def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--path", required=True) parser.add_argument("--exts", default=".h,.cc") parser.add_argument("--style", default="File") args = parser.parse_args() return args def main(): args = parse_args() exts = map(string.lower, args.exts.split(",")) for root, subdirs, files in os.walk(args.path): for f in files: name, ext = os.path.splitext(f) if ext.lower() in exts: file_path = os.path.join(root, f) proc = subprocess.Popen(["clang-format", "--style", args.style, file_path], stdout=subprocess.PIPE) text = "".join(proc.stdout) with open(file_path, "w") as fd: fd.write(text) if __name__ == "__main__": main() colmap-3.4/scripts/python/crawl_camera_specs.py000077500000000000000000000107011323400541200220260ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . import re import argparse import requests from lxml.html import soupparser MAX_REQUEST_TRIALS = 10 def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--lib_path", required=True) args = parser.parse_args() return args def request_trial(func, *args, **kwargs): for i in range(MAX_REQUEST_TRIALS): try: response = func(*args, **kwargs) except: continue else: return response raise SystemError def main(): args = parse_args() ########################################################################## # Header file ########################################################################## with open(args.lib_path + ".h", "w") as f: f.write("#include \n") f.write("#include \n") f.write("#include \n\n") f.write("// { make1 : ({ model1 : sensor-width in mm }, ...), ... }\n") f.write("typedef std::vector> make_specs_t;\n") f.write("typedef std::unordered_map camera_specs_t;;\n\n") f.write("camera_specs_t InitializeCameraSpecs();\n\n") ########################################################################## # Source file ########################################################################## makes_response = requests.get("http://www.digicamdb.com") makes_tree = soupparser.fromstring(makes_response.text) makes_node = makes_tree.find(".//select[@id=\"select_brand\"]") makes = [b.attrib["value"] for b in makes_node.iter("option")] with open(args.lib_path + ".cc", "w") as f: f.write("camera_specs_t InitializeCameraSpecs() {\n") f.write(" camera_specs_t specs;\n\n") for make in makes: f.write(" {\n") f.write(" auto& make_specs = specs[\"%s\"];\n" % make.lower().replace(" ", "")) models_response = request_trial( requests.post, "http://www.digicamdb.com/inc/ajax.php", data={"b": make, "role": "header_search"}) models_tree = soupparser.fromstring(models_response.text) models_code = "" num_models = 0 for model_node in models_tree.iter("option"): model = model_node.attrib.get("value") model_name = model_node.text if model is None: continue url = "http://www.digicamdb.com/specs/{0}_{1}" \ .format(make, model) specs_response = request_trial(requests.get, url) specs_tree = soupparser.fromstring(specs_response.text) for spec in specs_tree.findall(".//td[@class=\"info_key\"]"): if spec.text.strip() == "Sensor:": sensor_text = spec.find("..").find("./td[@class=\"bold\"]") sensor_text = sensor_text.text.strip() m = re.match(".*?([\d.]+) x ([\d.]+).*?", sensor_text) sensor_width = m.group(1) data = (model_name.lower().replace(" ", ""), float(sensor_width.replace(" ", ""))) models_code += " make_specs.emplace_back(\"%s\", %.4ff);\n" % data print make, model_name print " ", sensor_text num_models += 1 f.write(" make_specs.reserve(%d);\n" % num_models) f.write(models_code) f.write(" }\n\n") f.write(" return specs;\n") f.write("}\n") if __name__ == "__main__": main() colmap-3.4/scripts/python/export_inlier_matches.py000077500000000000000000000047311323400541200226060ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script exports inlier matches from a COLMAP database to a text file. import os import argparse import sqlite3 import numpy as np def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--database_path", required=True) parser.add_argument("--output_path", required=True) parser.add_argument("--min_num_matches", type=int, default=15) args = parser.parse_args() return args def pair_id_to_image_ids(pair_id): image_id2 = pair_id % 2147483647 image_id1 = (pair_id - image_id2) / 2147483647 return image_id1, image_id2 def main(): args = parse_args() connection = sqlite3.connect(args.database_path) cursor = connection.cursor() images = {} cursor.execute("SELECT image_id, camera_id, name FROM images;") for row in cursor: image_id = row[0] image_name = row[2] images[image_id] = image_name with open(os.path.join(args.output_path), "w") as fid: cursor.execute("SELECT pair_id, data FROM inlier_matches WHERE rows>=?;", (args.min_num_matches,)) for row in cursor: pair_id = row[0] inlier_matches = np.fromstring(row[1], dtype=np.uint32).reshape(-1, 2) image_id1, image_id2 = pair_id_to_image_ids(pair_id) image_name1 = images[image_id1] image_name2 = images[image_id2] fid.write("%s %s %d\n" % (image_name1, image_name2, inlier_matches.shape[0])) for i in range(inlier_matches.shape[0]): fid.write("%d %d\n" % tuple(inlier_matches[i])) cursor.close() connection.close() if __name__ == "__main__": main() colmap-3.4/scripts/python/export_inlier_pairs.py000077500000000000000000000044251323400541200223000ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script exports inlier image pairs from a COLMAP database to a text file. import sqlite3 import argparse def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--database_path", required=True) parser.add_argument("--match_list_path", required=True) parser.add_argument("--min_num_matches", type=int, default=15) args = parser.parse_args() return args def pair_id_to_image_ids(pair_id): image_id2 = pair_id % 2147483647 image_id1 = (pair_id - image_id2) / 2147483647 return image_id1, image_id2 def main(): args = parse_args() connection = sqlite3.connect(args.database_path) cursor = connection.cursor() # Get a mapping between image ids and image names image_id_to_name = dict() cursor.execute('SELECT image_id, name FROM images;') for row in cursor: image_id = row[0] name = row[1] image_id_to_name[image_id] = name # Iterate over entries in the inlier_matches table output = open(args.match_list_path, 'w') cursor.execute('SELECT pair_id, rows FROM inlier_matches;') for row in cursor: pair_id = row[0] rows = row[1] if rows < args.min_num_matches: continue image_id1, image_id2 = pair_id_to_image_ids(pair_id) image_name1 = image_id_to_name[image_id1] image_name2 = image_id_to_name[image_id2] output.write("%s %s\n" % (image_name1, image_name2)) output.close() cursor.close() connection.close() if __name__ == "__main__": main() colmap-3.4/scripts/python/export_to_bundler.py000077500000000000000000000127461323400541200217620ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script exports a COLMAP database to the file structure to run Bundler. import os import argparse import sqlite3 import shutil import gzip import numpy as np def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--database_path", required=True) parser.add_argument("--image_path", required=True) parser.add_argument("--output_path", required=True) parser.add_argument("--min_num_matches", type=int, default=15) args = parser.parse_args() return args def pair_id_to_image_ids(pair_id): image_id2 = pair_id % 2147483647 image_id1 = (pair_id - image_id2) / 2147483647 return image_id1, image_id2 def main(): args = parse_args() connection = sqlite3.connect(args.database_path) cursor = connection.cursor() try: os.makedirs(args.output_path) except: pass cameras = {} cursor.execute("SELECT camera_id, params FROM cameras;") for row in cursor: camera_id = row[0] params = np.fromstring(row[1], dtype=np.double) cameras[camera_id] = params images = {} with open(os.path.join(args.output_path, "list.txt"), "w") as fid: cursor.execute("SELECT image_id, camera_id, name FROM images;") for row in cursor: image_id = row[0] camera_id = row[1] image_name = row[2] print "Copying image", image_name images[image_id] = (len(images), image_name) fid.write("./%s 0 %f\n" % (image_name, cameras[camera_id][0])) if not os.path.exists(os.path.join(args.output_path, image_name)): shutil.copyfile(os.path.join(args.image_path, image_name), os.path.join(args.output_path, image_name)) for image_id, (image_idx, image_name) in images.iteritems(): print "Exporting key file for", image_name base_name, ext = os.path.splitext(image_name) key_file_name = os.path.join(args.output_path, base_name + ".key") key_file_name_gz = key_file_name + ".gz" if os.path.exists(key_file_name_gz): continue cursor.execute("SELECT data FROM keypoints WHERE image_id=?;", (image_id,)) row = next(cursor) keypoints = np.fromstring(row[0], dtype=np.float32).reshape(-1, 4) cursor.execute("SELECT data FROM descriptors WHERE image_id=?;", (image_id,)) row = next(cursor) descriptors = np.fromstring(row[0], dtype=np.uint8).reshape(-1, 128) with open(key_file_name, "w") as fid: fid.write("%d %d\n" % (keypoints.shape[0], descriptors.shape[1])) for r in range(keypoints.shape[0]): fid.write("%f %f %f %f\n" % (keypoints[r, 1], keypoints[r, 0], keypoints[r, 2], keypoints[r, 3])) for i in range(0, 128, 20): desc_block = descriptors[r, i:i+20] fid.write(" ".join(map(str, desc_block.ravel().tolist()))) fid.write("\n") with open(key_file_name, "rb") as fid_in: with gzip.open(key_file_name + ".gz", "wb") as fid_out: fid_out.writelines(fid_in) os.remove(key_file_name) with open(os.path.join(args.output_path, "matches.init.txt"), "w") as fid: cursor.execute("SELECT pair_id, data FROM inlier_matches " "WHERE rows>=?;", (args.min_num_matches,)) for row in cursor: pair_id = row[0] inlier_matches = np.fromstring(row[1], dtype=np.uint32).reshape(-1, 2) image_id1, image_id2 = pair_id_to_image_ids(pair_id) image_idx1 = images[image_id1][0] image_idx2 = images[image_id2][0] fid.write("%d %d\n%d\n" % (image_idx1, image_idx2, inlier_matches.shape[0])) for i in range(inlier_matches.shape[0]): fid.write("%d %d\n" % (inlier_matches[i, 0], inlier_matches[i, 1])) with open(os.path.join(args.output_path, "run_bundler.sh"), "w") as fid: fid.write("bin/Bundler list.txt \\\n") fid.write("--run_bundle \\\n") fid.write("--use_focal_estimate \\\n") fid.write("--output_all bundle_ \\\n") fid.write("--constrain_focal \\\n") fid.write("--estimate_distortion \\\n") fid.write("--match_table matches.init.txt \\\n") fid.write("--variable_focal_length \\\n") fid.write("--output_dir bundle \\\n") fid.write("--output bundle.out \\\n") fid.write("--constrain_focal_weight 0.0001 \\\n") cursor.close() connection.close() if __name__ == "__main__": main() colmap-3.4/scripts/python/export_to_visualsfm.py000077500000000000000000000112221323400541200223240ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script exports a COLMAP database to the file structure to run VisualSfM. import os import sys import argparse import sqlite3 import shutil import gzip import numpy as np def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--database_path", required=True) parser.add_argument("--image_path", required=True) parser.add_argument("--output_path", required=True) parser.add_argument("--min_num_matches", type=int, default=15) args = parser.parse_args() return args def pair_id_to_image_ids(pair_id): image_id2 = pair_id % 2147483647 image_id1 = (pair_id - image_id2) / 2147483647 return image_id1, image_id2 def main(): args = parse_args() connection = sqlite3.connect(args.database_path) cursor = connection.cursor() try: os.makedirs(args.output_path) except: pass cameras = {} cursor.execute("SELECT camera_id, params FROM cameras;") for row in cursor: camera_id = row[0] params = np.fromstring(row[1], dtype=np.double) cameras[camera_id] = params images = {} cursor.execute("SELECT image_id, camera_id, name FROM images;") for row in cursor: image_id = row[0] camera_id = row[1] image_name = row[2] print "Copying image", image_name images[image_id] = (len(images), image_name) if not os.path.exists(os.path.join(args.output_path, image_name)): shutil.copyfile(os.path.join(args.image_path, image_name), os.path.join(args.output_path, image_name)) for image_id, (image_idx, image_name) in images.iteritems(): print "Exporting key file for", image_name base_name, ext = os.path.splitext(image_name) key_file_name = os.path.join(args.output_path, base_name + ".sift") if os.path.exists(key_file_name): continue cursor.execute("SELECT data FROM keypoints WHERE image_id=?;", (image_id,)) row = next(cursor) if row[0] is None: keypoints = np.zeros((0, 4), dtype=np.float32) descriptors = np.zeros((0, 128), dtype=np.uint8) else: keypoints = np.fromstring(row[0], dtype=np.float32).reshape(-1, 4) cursor.execute("SELECT data FROM descriptors WHERE image_id=?;", (image_id,)) row = next(cursor) descriptors = np.fromstring(row[0], dtype=np.uint8).reshape(-1, 128) with open(key_file_name, "w") as fid: fid.write("%d %d\n" % (keypoints.shape[0], descriptors.shape[1])) for r in range(keypoints.shape[0]): fid.write("%f %f %f %f " % (keypoints[r, 0], keypoints[r, 1], keypoints[r, 2], keypoints[r, 3])) fid.write(" ".join(map(str, descriptors[r].ravel().tolist()))) fid.write("\n") with open(os.path.join(args.output_path, "matches.txt"), "w") as fid: cursor.execute("SELECT pair_id, data FROM inlier_matches " "WHERE rows>=?;", (args.min_num_matches,)) for row in cursor: pair_id = row[0] inlier_matches = np.fromstring(row[1], dtype=np.uint32).reshape(-1, 2) image_id1, image_id2 = pair_id_to_image_ids(pair_id) image_name1 = images[image_id1][1] image_name2 = images[image_id2][1] fid.write("%s %s %d\n" % (image_name1, image_name2, inlier_matches.shape[0])) line1 = "" line2 = "" for i in range(inlier_matches.shape[0]): line1 += "%d " % inlier_matches[i, 0] line2 += "%d " % inlier_matches[i, 1] fid.write(line1 + "\n") fid.write(line2 + "\n") cursor.close() connection.close() if __name__ == "__main__": main() colmap-3.4/scripts/python/flickr_downloader.py000077500000000000000000000124731323400541200217110ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # Filip Radenovic # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script downloads images from Flickr for a given search query, ordered # from most recent to older images. If the downloader does not find images for # more than `max_days_without_image` in a row, it exits to avoid an infinite # loop. Note that too many parallel download processes may lead to being banned # from Flickr for a certain time. import os import time import datetime import urllib import urllib2 import socket import argparse import multiprocessing import xml.etree.ElementTree as ElementTree PER_PAGE = 500 SORT = "date-posted-desc" URL = "https://api.flickr.com/services/rest/?method=flickr.photos.search&" \ "api_key=%s&text=%s&sort=%s&per_page=%d&page=%d&min_upload_date=%s&" \ "max_upload_date=%s&format=rest&extras=url_o,url_l,url_c,url_z,url_n" MAX_PAGE_REQUESTS = 5 MAX_PAGE_TIMEOUT = 20 MAX_IMAGE_REQUESTS = 3 TIME_SKIP = 24 * 60 * 60 MAX_DATE = time.time() MIN_DATE = MAX_DATE - TIME_SKIP def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--search_text", required=True) parser.add_argument("--api_key", required=True) parser.add_argument("--image_path", required=True) parser.add_argument("--num_procs", type=int, default=10) parser.add_argument("--max_days_without_image", type=int, default=365) args = parser.parse_args() return args def compose_url(page, api_key, text, min_date, max_date): return URL % (api_key, text, SORT, PER_PAGE, page, str(min_date), str(max_date)) def parse_page(page, api_key, text, min_date, max_date): f = None for _ in range(MAX_PAGE_REQUESTS): try: f = urllib2.urlopen(compose_url(page, api_key, text, min_date, max_date), timeout=MAX_PAGE_TIMEOUT) except socket.timeout: continue else: break if f is None: return {'pages': '0', 'total': '0', 'page': '0', 'perpage': '0'}, tuple() response = f.read() root = ElementTree.fromstring(response) if root.attrib["stat"] != "ok": raise IOError photos = [] for photo in root.iter("photo"): photos.append(photo.attrib) return root.find("photos").attrib, photos class PhotoDownloader(object): def __init__(self, image_path): self.image_path = image_path def __call__(self, photo): image_name = "%s_%s.jpg" % (photo["id"], photo["secret"]) path = os.path.join(self.image_path, image_name) if not os.path.exists(path): url = None for url_suffix in ("o", "l", "k", "h", "b", "c", "z"): url_attr = "url_%s" % url_suffix if photo.get(url_attr) is not None: url = photo.get(url_attr) break if url is not None: print url for _ in range(MAX_IMAGE_REQUESTS): try: urllib.urlretrieve(url, path) except urllib.ContentTooShortError: continue else: break def main(): args = parse_args() downloader = PhotoDownloader(args.image_path) pool = multiprocessing.Pool(processes=args.num_procs) num_pages = float("inf") page = 0 min_date = MIN_DATE max_date = MAX_DATE days_in_row = 0; search_text = args.search_text.replace(" ", "-") while num_pages > page: page += 1 metadata, photos = parse_page(page, args.api_key, search_text, min_date, max_date) num_pages = int(metadata["pages"]) print 78 * "=" print "Page:\t\t", page, "of", num_pages print "Min-Date:\t", datetime.datetime.fromtimestamp(min_date) print "Max-Date:\t", datetime.datetime.fromtimestamp(max_date) print "Num-Photos:\t", len(photos) print 78 * "=" try: pool.map_async(downloader, photos).get(1e10) except KeyboardInterrupt: pool.wait() break if page >= num_pages: max_date -= TIME_SKIP min_date -= TIME_SKIP page = 0 if num_pages == 0: days_in_row = days_in_row + 1 num_pages = float("inf") print " No images in", days_in_row, "days in a row" if days_in_row == args.max_days_without_image: break else: days_in_row = 0 if __name__ == "__main__": main() colmap-3.4/scripts/python/merge_ply_files.py000077500000000000000000000033731323400541200213650ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script merges multiple homogeneous PLY files into a single PLY file. import os import glob import argparse import numpy as np import plyfile def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--folder_path", required=True) parser.add_argument("--merged_path", required=True) args = parser.parse_args() return args def main(): args = parse_args() files = [] for file_name in os.listdir(args.folder_path): if len(file_name) < 4 or file_name[-4:].lower() != ".ply": continue print "Reading file", file_name file = plyfile.PlyData.read(os.path.join(args.folder_path, file_name)) for element in file.elements: files.append(element.data) print "Merging files" merged_file = np.concatenate(files, -1) merged_el = plyfile.PlyElement.describe(merged_file, 'vertex') print "Writing merged file" plyfile.PlyData([merged_el]).write(args.merged_path) if __name__ == '__main__': main() colmap-3.4/scripts/python/nvm_to_ply.py000077500000000000000000000075111323400541200204040ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script converts a VisualSfM reconstruction file to a PLY point cloud. import os import argparse import numpy as np def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--nvm_path", required=True) parser.add_argument("--ply_path", required=True) parser.add_argument("--normalize", type=bool, default=True) parser.add_argument("--normalize_p0", type=float, default=0.2) parser.add_argument("--normalize_p1", type=float, default=0.8) parser.add_argument("--min_track_length", type=int, default=3) args = parser.parse_args() return args def main(): args = parse_args() with open(args.nvm_path, "r") as fid: line = fid.readline() line = fid.readline() num_images = int(fid.readline()) for i in range(num_images + 1): fid.readline() num_points = int(fid.readline()) xyz = np.zeros((num_points, 3), dtype=np.float64) rgb = np.zeros((num_points, 3), dtype=np.uint16) track_lengths = np.zeros((num_points,), dtype=np.uint32) for i in range(num_points): if i % 1000 == 0: print "Reading point", i, "/", num_points elems = fid.readline().split() xyz[i] = map(float, elems[0:3]) rgb[i] = map(int, elems[3:6]) track_lengths[i] = int(elems[6]) mask = track_lengths >= args.min_track_length xyz = xyz[mask] rgb = rgb[mask] if args.normalize: sorted_x = np.sort(xyz[:, 0]) sorted_y = np.sort(xyz[:, 1]) sorted_z = np.sort(xyz[:, 2]) num_coords = sorted_x.size min_coord = int(args.normalize_p0 * num_coords) max_coord = int(args.normalize_p1 * num_coords) mean_coords = xyz.mean(0) bbox_min = np.array([sorted_x[min_coord], sorted_y[min_coord], sorted_z[min_coord]]) bbox_max = np.array([sorted_x[max_coord], sorted_y[max_coord], sorted_z[max_coord]]) extent = np.linalg.norm(bbox_max - bbox_min) scale = 10.0 / extent xyz -= mean_coords xyz *= scale with open(args.ply_path, "w") as fid: fid.write("ply\n") fid.write("format ascii 1.0\n") fid.write("element vertex %d\n" % xyz.shape[0]) fid.write("property float x\n") fid.write("property float y\n") fid.write("property float z\n") fid.write("property float nx\n") fid.write("property float ny\n") fid.write("property float nz\n") fid.write("property uchar diffuse_red\n") fid.write("property uchar diffuse_green\n") fid.write("property uchar diffuse_blue\n") fid.write("end_header\n") for i in range(xyz.shape[0]): if i % 1000 == 0: print "Writing point", i, "/", xyz.shape[0] fid.write("%f %f %f 0 0 0 %d %d %d\n" % (xyz[i, 0], xyz[i, 1], xyz[i, 2], rgb[i, 0], rgb[i, 1], rgb[i, 2])) if __name__ == "__main__": main() colmap-3.4/scripts/python/plyfile.py000077500000000000000000000631321323400541200176630ustar00rootroot00000000000000# Copyright 2014 Darsh Ranjan # # This file is part of python-plyfile. # # python-plyfile is free software: you can redistribute it and/or # modify it under the terms of the GNU General Public License as # published by the Free Software Foundation, either version 3 of the # License, or (at your option) any later version. # # python-plyfile is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # You should have received a copy of the GNU General Public License # along with python-plyfile. If not, see # . from itertools import islice as _islice import numpy as _np from sys import byteorder as _byteorder try: _range = xrange except NameError: _range = range # Many-many relation _data_type_relation = [ ('int8', 'i1'), ('char', 'i1'), ('uint8', 'u1'), ('uchar', 'b1'), ('uchar', 'u1'), ('int16', 'i2'), ('short', 'i2'), ('uint16', 'u2'), ('ushort', 'u2'), ('int32', 'i4'), ('int', 'i4'), ('uint32', 'u4'), ('uint', 'u4'), ('float32', 'f4'), ('float', 'f4'), ('float64', 'f8'), ('double', 'f8') ] _data_types = dict(_data_type_relation) _data_type_reverse = dict((b, a) for (a, b) in _data_type_relation) _types_list = [] _types_set = set() for (_a, _b) in _data_type_relation: if _a not in _types_set: _types_list.append(_a) _types_set.add(_a) if _b not in _types_set: _types_list.append(_b) _types_set.add(_b) _byte_order_map = { 'ascii': '=', 'binary_little_endian': '<', 'binary_big_endian': '>' } _byte_order_reverse = { '<': 'binary_little_endian', '>': 'binary_big_endian' } _native_byte_order = {'little': '<', 'big': '>'}[_byteorder] def _lookup_type(type_str): if type_str not in _data_type_reverse: try: type_str = _data_types[type_str] except KeyError: raise ValueError("field type %r not in %r" % (type_str, _types_list)) return _data_type_reverse[type_str] def _split_line(line, n): fields = line.split(None, n) if len(fields) == n: fields.append('') assert len(fields) == n + 1 return fields def make2d(array, cols=None, dtype=None): ''' Make a 2D array from an array of arrays. The `cols' and `dtype' arguments can be omitted if the array is not empty. ''' if (cols is None or dtype is None) and not len(array): raise RuntimeError("cols and dtype must be specified for empty " "array") if cols is None: cols = len(array[0]) if dtype is None: dtype = array[0].dtype return _np.fromiter(array, [('_', dtype, (cols,))], count=len(array))['_'] class PlyParseError(Exception): ''' Raised when a PLY file cannot be parsed. The attributes `element', `row', `property', and `message' give additional information. ''' def __init__(self, message, element=None, row=None, prop=None): self.message = message self.element = element self.row = row self.prop = prop s = '' if self.element: s += 'element %r: ' % self.element.name if self.row is not None: s += 'row %d: ' % self.row if self.prop: s += 'property %r: ' % self.prop.name s += self.message Exception.__init__(self, s) def __repr__(self): return ('PlyParseError(%r, element=%r, row=%r, prop=%r)' % self.message, self.element, self.row, self.prop) class PlyData(object): ''' PLY file header and data. A PlyData instance is created in one of two ways: by the static method PlyData.read (to read a PLY file), or directly from __init__ given a sequence of elements (which can then be written to a PLY file). ''' def __init__(self, elements=[], text=False, byte_order='=', comments=[], obj_info=[]): ''' elements: sequence of PlyElement instances. text: whether the resulting PLY file will be text (True) or binary (False). byte_order: '<' for little-endian, '>' for big-endian, or '=' for native. This is only relevant if `text' is False. comments: sequence of strings that will be placed in the header between the 'ply' and 'format ...' lines. obj_info: like comments, but will be placed in the header with "obj_info ..." instead of "comment ...". ''' if byte_order == '=' and not text: byte_order = _native_byte_order self.byte_order = byte_order self.text = text self.comments = list(comments) self.obj_info = list(obj_info) self.elements = elements def _get_elements(self): return self._elements def _set_elements(self, elements): self._elements = tuple(elements) self._index() elements = property(_get_elements, _set_elements) def _get_byte_order(self): return self._byte_order def _set_byte_order(self, byte_order): if byte_order not in ['<', '>', '=']: raise ValueError("byte order must be '<', '>', or '='") self._byte_order = byte_order byte_order = property(_get_byte_order, _set_byte_order) def _index(self): self._element_lookup = dict((elt.name, elt) for elt in self._elements) if len(self._element_lookup) != len(self._elements): raise ValueError("two elements with same name") @staticmethod def _parse_header(stream): ''' Parse a PLY header from a readable file-like stream. ''' lines = [] comments = {'comment': [], 'obj_info': []} while True: line = stream.readline().decode('ascii').strip() fields = _split_line(line, 1) if fields[0] == 'end_header': break elif fields[0] in comments.keys(): lines.append(fields) else: lines.append(line.split()) a = 0 if lines[a] != ['ply']: raise PlyParseError("expected 'ply'") a += 1 while lines[a][0] in comments.keys(): comments[lines[a][0]].append(lines[a][1]) a += 1 if lines[a][0] != 'format': raise PlyParseError("expected 'format'") if lines[a][2] != '1.0': raise PlyParseError("expected version '1.0'") if len(lines[a]) != 3: raise PlyParseError("too many fields after 'format'") fmt = lines[a][1] if fmt not in _byte_order_map: raise PlyParseError("don't understand format %r" % fmt) byte_order = _byte_order_map[fmt] text = fmt == 'ascii' a += 1 while a < len(lines) and lines[a][0] in comments.keys(): comments[lines[a][0]].append(lines[a][1]) a += 1 return PlyData(PlyElement._parse_multi(lines[a:]), text, byte_order, comments['comment'], comments['obj_info']) @staticmethod def read(stream): ''' Read PLY data from a readable file-like object or filename. ''' must_close = False try: if isinstance(stream, str): stream = open(stream, 'rb') must_close = True data = PlyData._parse_header(stream) for elt in data: elt._read(stream, data.text, data.byte_order) finally: if must_close: stream.close() return data def write(self, stream): ''' Write PLY data to a writeable file-like object or filename. ''' must_close = False try: if isinstance(stream, str): stream = open(stream, 'wb') must_close = True stream.write(self.header.encode('ascii')) stream.write(b'\r\n') for elt in self: elt._write(stream, self.text, self.byte_order) finally: if must_close: stream.close() @property def header(self): ''' Provide PLY-formatted metadata for the instance. ''' lines = ['ply'] if self.text: lines.append('format ascii 1.0') else: lines.append('format ' + _byte_order_reverse[self.byte_order] + ' 1.0') # Some information is lost here, since all comments are placed # between the 'format' line and the first element. for c in self.comments: lines.append('comment ' + c) for c in self.obj_info: lines.append('obj_info ' + c) lines.extend(elt.header for elt in self.elements) lines.append('end_header') return '\r\n'.join(lines) def __iter__(self): return iter(self.elements) def __len__(self): return len(self.elements) def __contains__(self, name): return name in self._element_lookup def __getitem__(self, name): return self._element_lookup[name] def __str__(self): return self.header def __repr__(self): return ('PlyData(%r, text=%r, byte_order=%r, ' 'comments=%r, obj_info=%r)' % (self.elements, self.text, self.byte_order, self.comments, self.obj_info)) class PlyElement(object): ''' PLY file element. A client of this library doesn't normally need to instantiate this directly, so the following is only for the sake of documenting the internals. Creating a PlyElement instance is generally done in one of two ways: as a byproduct of PlyData.read (when reading a PLY file) and by PlyElement.describe (before writing a PLY file). ''' def __init__(self, name, properties, count, comments=[]): ''' This is not part of the public interface. The preferred methods of obtaining PlyElement instances are PlyData.read (to read from a file) and PlyElement.describe (to construct from a numpy array). ''' self._name = str(name) self._check_name() self._count = count self._properties = tuple(properties) self._index() self.comments = list(comments) self._have_list = any(isinstance(p, PlyListProperty) for p in self.properties) @property def count(self): return self._count def _get_data(self): return self._data def _set_data(self, data): self._data = data self._count = len(data) self._check_sanity() data = property(_get_data, _set_data) def _check_sanity(self): for prop in self.properties: if prop.name not in self._data.dtype.fields: raise ValueError("dangling property %r" % prop.name) def _get_properties(self): return self._properties def _set_properties(self, properties): self._properties = tuple(properties) self._check_sanity() self._index() properties = property(_get_properties, _set_properties) def _index(self): self._property_lookup = dict((prop.name, prop) for prop in self._properties) if len(self._property_lookup) != len(self._properties): raise ValueError("two properties with same name") def ply_property(self, name): return self._property_lookup[name] @property def name(self): return self._name def _check_name(self): if any(c.isspace() for c in self._name): msg = "element name %r contains spaces" % self._name raise ValueError(msg) def dtype(self, byte_order='='): ''' Return the numpy dtype of the in-memory representation of the data. (If there are no list properties, and the PLY format is binary, then this also accurately describes the on-disk representation of the element.) ''' return [(prop.name, prop.dtype(byte_order)) for prop in self.properties] @staticmethod def _parse_multi(header_lines): ''' Parse a list of PLY element definitions. ''' elements = [] while header_lines: (elt, header_lines) = PlyElement._parse_one(header_lines) elements.append(elt) return elements @staticmethod def _parse_one(lines): ''' Consume one element definition. The unconsumed input is returned along with a PlyElement instance. ''' a = 0 line = lines[a] if line[0] != 'element': raise PlyParseError("expected 'element'") if len(line) > 3: raise PlyParseError("too many fields after 'element'") if len(line) < 3: raise PlyParseError("too few fields after 'element'") (name, count) = (line[1], int(line[2])) comments = [] properties = [] while True: a += 1 if a >= len(lines): break if lines[a][0] == 'comment': comments.append(lines[a][1]) elif lines[a][0] == 'property': properties.append(PlyProperty._parse_one(lines[a])) else: break return (PlyElement(name, properties, count, comments), lines[a:]) @staticmethod def describe(data, name, len_types={}, val_types={}, comments=[]): ''' Construct a PlyElement from an array's metadata. len_types and val_types can be given as mappings from list property names to type strings (like 'u1', 'f4', etc., or 'int8', 'float32', etc.). These can be used to define the length and value types of list properties. List property lengths always default to type 'u1' (8-bit unsigned integer), and value types default to 'i4' (32-bit integer). ''' if not isinstance(data, _np.ndarray): raise TypeError("only numpy arrays are supported") if len(data.shape) != 1: raise ValueError("only one-dimensional arrays are " "supported") count = len(data) properties = [] descr = data.dtype.descr for t in descr: if not isinstance(t[1], str): raise ValueError("nested records not supported") if not t[0]: raise ValueError("field with empty name") if len(t) != 2 or t[1][1] == 'O': # non-scalar field, which corresponds to a list # property in PLY. if t[1][1] == 'O': if len(t) != 2: raise ValueError("non-scalar object fields not " "supported") len_str = _data_type_reverse[len_types.get(t[0], 'u1')] if t[1][1] == 'O': val_type = val_types.get(t[0], 'i4') val_str = _lookup_type(val_type) else: val_str = _lookup_type(t[1][1:]) prop = PlyListProperty(t[0], len_str, val_str) else: val_str = _lookup_type(t[1][1:]) prop = PlyProperty(t[0], val_str) properties.append(prop) elt = PlyElement(name, properties, count, comments) elt.data = data return elt def _read(self, stream, text, byte_order): ''' Read the actual data from a PLY file. ''' if text: self._read_txt(stream) else: if self._have_list: # There are list properties, so a simple load is # impossible. self._read_bin(stream, byte_order) else: # There are no list properties, so loading the data is # much more straightforward. self._data = _np.fromfile(stream, self.dtype(byte_order), self.count) if len(self._data) < self.count: k = len(self._data) del self._data raise PlyParseError("early end-of-file", self, k) self._check_sanity() def _write(self, stream, text, byte_order): ''' Write the data to a PLY file. ''' if text: self._write_txt(stream) else: if self._have_list: # There are list properties, so serialization is # slightly complicated. self._write_bin(stream, byte_order) else: # no list properties, so serialization is # straightforward. self.data.astype(self.dtype(byte_order), copy=False).tofile(stream) def _read_txt(self, stream): ''' Load a PLY element from an ASCII-format PLY file. The element may contain list properties. ''' self._data = _np.empty(self.count, dtype=self.dtype()) k = 0 for line in _islice(iter(stream.readline, b''), self.count): fields = iter(line.strip().split()) for prop in self.properties: try: self._data[prop.name][k] = prop._from_fields(fields) except StopIteration: raise PlyParseError("early end-of-line", self, k, prop) except ValueError: raise PlyParseError("malformed input", self, k, prop) try: next(fields) except StopIteration: pass else: raise PlyParseError("expected end-of-line", self, k) k += 1 if k < self.count: del self._data raise PlyParseError("early end-of-file", self, k) def _write_txt(self, stream): ''' Save a PLY element to an ASCII-format PLY file. The element may contain list properties. ''' for rec in self.data: fields = [] for prop in self.properties: fields.extend(prop._to_fields(rec[prop.name])) _np.savetxt(stream, [fields], '%.18g', newline='\r\n') def _read_bin(self, stream, byte_order): ''' Load a PLY element from a binary PLY file. The element may contain list properties. ''' self._data = _np.empty(self.count, dtype=self.dtype(byte_order)) for k in _range(self.count): for prop in self.properties: try: self._data[prop.name][k] = \ prop._read_bin(stream, byte_order) except StopIteration: raise PlyParseError("early end-of-file", self, k, prop) def _write_bin(self, stream, byte_order): ''' Save a PLY element to a binary PLY file. The element may contain list properties. ''' for rec in self.data: for prop in self.properties: prop._write_bin(rec[prop.name], stream, byte_order) @property def header(self): ''' Format this element's metadata as it would appear in a PLY header. ''' lines = ['element %s %d' % (self.name, self.count)] # Some information is lost here, since all comments are placed # between the 'element' line and the first property definition. for c in self.comments: lines.append('comment ' + c) lines.extend(list(map(str, self.properties))) return '\r\n'.join(lines) def __getitem__(self, key): return self.data[key] def __setitem__(self, key, value): self.data[key] = value def __str__(self): return self.header def __repr__(self): return ('PlyElement(%r, %r, count=%d, comments=%r)' % (self.name, self.properties, self.count, self.comments)) class PlyProperty(object): ''' PLY property description. This class is pure metadata; the data itself is contained in PlyElement instances. ''' def __init__(self, name, val_dtype): self._name = str(name) self._check_name() self.val_dtype = val_dtype def _get_val_dtype(self): return self._val_dtype def _set_val_dtype(self, val_dtype): self._val_dtype = _data_types[_lookup_type(val_dtype)] val_dtype = property(_get_val_dtype, _set_val_dtype) @property def name(self): return self._name def _check_name(self): if any(c.isspace() for c in self._name): msg = "Error: property name %r contains spaces" % self._name raise RuntimeError(msg) @staticmethod def _parse_one(line): assert line[0] == 'property' if line[1] == 'list': if len(line) > 5: raise PlyParseError("too many fields after " "'property list'") if len(line) < 5: raise PlyParseError("too few fields after " "'property list'") return PlyListProperty(line[4], line[2], line[3]) else: if len(line) > 3: raise PlyParseError("too many fields after " "'property'") if len(line) < 3: raise PlyParseError("too few fields after " "'property'") return PlyProperty(line[2], line[1]) def dtype(self, byte_order='='): ''' Return the numpy dtype description for this property (as a tuple of strings). ''' return byte_order + self.val_dtype def _from_fields(self, fields): ''' Parse from generator. Raise StopIteration if the property could not be read. ''' return _np.dtype(self.dtype()).type(next(fields)) def _to_fields(self, data): ''' Return generator over one item. ''' yield _np.dtype(self.dtype()).type(data) def _read_bin(self, stream, byte_order): ''' Read data from a binary stream. Raise StopIteration if the property could not be read. ''' try: return _np.fromfile(stream, self.dtype(byte_order), 1)[0] except IndexError: raise StopIteration def _write_bin(self, data, stream, byte_order): ''' Write data to a binary stream. ''' _np.dtype(self.dtype(byte_order)).type(data).tofile(stream) def __str__(self): val_str = _data_type_reverse[self.val_dtype] return 'property %s %s' % (val_str, self.name) def __repr__(self): return 'PlyProperty(%r, %r)' % (self.name, _lookup_type(self.val_dtype)) class PlyListProperty(PlyProperty): ''' PLY list property description. ''' def __init__(self, name, len_dtype, val_dtype): PlyProperty.__init__(self, name, val_dtype) self.len_dtype = len_dtype def _get_len_dtype(self): return self._len_dtype def _set_len_dtype(self, len_dtype): self._len_dtype = _data_types[_lookup_type(len_dtype)] len_dtype = property(_get_len_dtype, _set_len_dtype) def dtype(self, byte_order='='): ''' List properties always have a numpy dtype of "object". ''' return '|O' def list_dtype(self, byte_order='='): ''' Return the pair (len_dtype, val_dtype) (both numpy-friendly strings). ''' return (byte_order + self.len_dtype, byte_order + self.val_dtype) def _from_fields(self, fields): (len_t, val_t) = self.list_dtype() n = int(_np.dtype(len_t).type(next(fields))) data = _np.loadtxt(list(_islice(fields, n)), val_t, ndmin=1) if len(data) < n: raise StopIteration return data def _to_fields(self, data): ''' Return generator over the (numerical) PLY representation of the list data (length followed by actual data). ''' (len_t, val_t) = self.list_dtype() data = _np.asarray(data, dtype=val_t).ravel() yield _np.dtype(len_t).type(data.size) for x in data: yield x def _read_bin(self, stream, byte_order): (len_t, val_t) = self.list_dtype(byte_order) try: n = _np.fromfile(stream, len_t, 1)[0] except IndexError: raise StopIteration data = _np.fromfile(stream, val_t, n) if len(data) < n: raise StopIteration return data def _write_bin(self, data, stream, byte_order): ''' Write data to a binary stream. ''' (len_t, val_t) = self.list_dtype(byte_order) data = _np.asarray(data, dtype=val_t).ravel() _np.array(data.size, dtype=len_t).tofile(stream) data.tofile(stream) def __str__(self): len_str = _data_type_reverse[self.len_dtype] val_str = _data_type_reverse[self.val_dtype] return 'property list %s %s %s' % (len_str, val_str, self.name) def __repr__(self): return ('PlyListProperty(%r, %r, %r)' % (self.name, _lookup_type(self.len_dtype), _lookup_type(self.val_dtype))) colmap-3.4/scripts/python/read_dense.py000066400000000000000000000036751323400541200203130ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . import numpy as np import pylab as plt def read_array(path): with open(path, "rb") as fid: width, height, channels = np.genfromtxt(fid, delimiter="&", max_rows=1, usecols=(0, 1, 2), dtype=int) fid.seek(0) num_delimiter = 0 byte = fid.read(1) while True: if byte == b"&": num_delimiter += 1 if num_delimiter >= 3: break byte = fid.read(1) array = np.fromfile(fid, np.float32) array = array.reshape((width, height, channels), order="F") return np.transpose(array, (1, 0, 2)).squeeze() def main(): # Read depth and normal maps corresponding to the same image. depth_map = read_array( "path/to/dense/stereo/depth_maps/image1.jpg.photometric.bin") normal_map = read_array( "path/to/dense/stereo/normal_maps/image1.jpg.photometric.bin") # Visualize the depth map. min_depth, max_depth = np.percentile(depth_map, [5, 95]) depth_map[depth_map < min_depth] = min_depth depth_map[depth_map > max_depth] = max_depth plt.imshow(depth_map) plt.show() if __name__ == "__main__": main() colmap-3.4/scripts/python/read_model.py000077500000000000000000000301241323400541200203050ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . import os import sys import collections import numpy as np import struct CameraModel = collections.namedtuple( "CameraModel", ["model_id", "model_name", "num_params"]) Camera = collections.namedtuple( "Camera", ["id", "model", "width", "height", "params"]) BaseImage = collections.namedtuple( "Image", ["id", "qvec", "tvec", "camera_id", "name", "xys", "point3D_ids"]) Point3D = collections.namedtuple( "Point3D", ["id", "xyz", "rgb", "error", "image_ids", "point2D_idxs"]) class Image(BaseImage): def qvec2rotmat(self): return qvec2rotmat(self.qvec) CAMERA_MODELS = { CameraModel(model_id=0, model_name="SIMPLE_PINHOLE", num_params=3), CameraModel(model_id=1, model_name="PINHOLE", num_params=4), CameraModel(model_id=2, model_name="SIMPLE_RADIAL", num_params=4), CameraModel(model_id=3, model_name="RADIAL", num_params=5), CameraModel(model_id=4, model_name="OPENCV", num_params=8), CameraModel(model_id=5, model_name="OPENCV_FISHEYE", num_params=8), CameraModel(model_id=6, model_name="FULL_OPENCV", num_params=12), CameraModel(model_id=7, model_name="FOV", num_params=5), CameraModel(model_id=8, model_name="SIMPLE_RADIAL_FISHEYE", num_params=4), CameraModel(model_id=9, model_name="RADIAL_FISHEYE", num_params=5), CameraModel(model_id=10, model_name="THIN_PRISM_FISHEYE", num_params=12) } CAMERA_MODEL_IDS = dict([(camera_model.model_id, camera_model) \ for camera_model in CAMERA_MODELS]) def read_next_bytes(fid, num_bytes, format_char_sequence, endian_character="<"): """Read and unpack the next bytes from a binary file. :param fid: :param num_bytes: Sum of combination of {2, 4, 8}, e.g. 2, 6, 16, 30, etc. :param format_char_sequence: List of {c, e, f, d, h, H, i, I, l, L, q, Q}. :param endian_character: Any of {@, =, <, >, !} :return: Tuple of read and unpacked values. """ data = fid.read(num_bytes) return struct.unpack(endian_character + format_char_sequence, data) def read_cameras_text(path): """ see: src/base/reconstruction.cc void Reconstruction::WriteCamerasText(const std::string& path) void Reconstruction::ReadCamerasText(const std::string& path) """ cameras = {} with open(path, "r") as fid: while True: line = fid.readline() if not line: break line = line.strip() if len(line) > 0 and line[0] != "#": elems = line.split() camera_id = int(elems[0]) model = elems[1] width = int(elems[2]) height = int(elems[3]) params = np.array(tuple(map(float, elems[4:]))) cameras[camera_id] = Camera(id=camera_id, model=model, width=width, height=height, params=params) return cameras def read_cameras_binary(path_to_model_file): """ see: src/base/reconstruction.cc void Reconstruction::WriteCamerasBinary(const std::string& path) void Reconstruction::ReadCamerasBinary(const std::string& path) """ cameras = {} with open(path_to_model_file, "rb") as fid: num_cameras = read_next_bytes(fid, 8, "Q")[0] for camera_line_index in range(num_cameras): camera_properties = read_next_bytes( fid, num_bytes=24, format_char_sequence="iiQQ") camera_id = camera_properties[0] model_id = camera_properties[1] model_name = CAMERA_MODEL_IDS[camera_properties[1]].model_name width = camera_properties[2] height = camera_properties[3] num_params = CAMERA_MODEL_IDS[model_id].num_params params = read_next_bytes(fid, num_bytes=8*num_params, format_char_sequence="d"*num_params) cameras[camera_id] = Camera(id=camera_id, model=model_name, width=width, height=height, params=np.array(params)) assert len(cameras) == num_cameras return cameras def read_images_text(path): """ see: src/base/reconstruction.cc void Reconstruction::ReadImagesText(const std::string& path) void Reconstruction::WriteImagesText(const std::string& path) """ images = {} with open(path, "r") as fid: while True: line = fid.readline() if not line: break line = line.strip() if len(line) > 0 and line[0] != "#": elems = line.split() image_id = int(elems[0]) qvec = np.array(tuple(map(float, elems[1:5]))) tvec = np.array(tuple(map(float, elems[5:8]))) camera_id = int(elems[8]) image_name = elems[9] elems = fid.readline().split() xys = np.column_stack([tuple(map(float, elems[0::3])), tuple(map(float, elems[1::3]))]) point3D_ids = np.array(tuple(map(int, elems[2::3]))) images[image_id] = Image( id=image_id, qvec=qvec, tvec=tvec, camera_id=camera_id, name=image_name, xys=xys, point3D_ids=point3D_ids) return images def read_images_binary(path_to_model_file): """ see: src/base/reconstruction.cc void Reconstruction::ReadImagesBinary(const std::string& path) void Reconstruction::WriteImagesBinary(const std::string& path) """ images = {} with open(path_to_model_file, "rb") as fid: num_reg_images = read_next_bytes(fid, 8, "Q")[0] for image_index in range(num_reg_images): binary_image_properties = read_next_bytes( fid, num_bytes=64, format_char_sequence="idddddddi") image_id = binary_image_properties[0] qvec = np.array(binary_image_properties[1:5]) tvec = np.array(binary_image_properties[5:8]) camera_id = binary_image_properties[8] image_name = "" current_char = read_next_bytes(fid, 1, "c")[0] while current_char != b"\x00": # look for the ASCII 0 entry image_name += current_char.decode("utf-8") current_char = read_next_bytes(fid, 1, "c")[0] num_points2D = read_next_bytes(fid, num_bytes=8, format_char_sequence="Q")[0] x_y_id_s = read_next_bytes(fid, num_bytes=24*num_points2D, format_char_sequence="ddq"*num_points2D) xys = np.column_stack([tuple(map(float, x_y_id_s[0::3])), tuple(map(float, x_y_id_s[1::3]))]) point3D_ids = np.array(tuple(map(int, x_y_id_s[2::3]))) images[image_id] = Image( id=image_id, qvec=qvec, tvec=tvec, camera_id=camera_id, name=image_name, xys=xys, point3D_ids=point3D_ids) return images def read_points3D_text(path): """ see: src/base/reconstruction.cc void Reconstruction::ReadPoints3DText(const std::string& path) void Reconstruction::WritePoints3DText(const std::string& path) """ points3D = {} with open(path, "r") as fid: while True: line = fid.readline() if not line: break line = line.strip() if len(line) > 0 and line[0] != "#": elems = line.split() point3D_id = int(elems[0]) xyz = np.array(tuple(map(float, elems[1:4]))) rgb = np.array(tuple(map(int, elems[4:7]))) error = float(elems[7]) image_ids = np.array(tuple(map(int, elems[8::2]))) point2D_idxs = np.array(tuple(map(int, elems[9::2]))) points3D[point3D_id] = Point3D(id=point3D_id, xyz=xyz, rgb=rgb, error=error, image_ids=image_ids, point2D_idxs=point2D_idxs) return points3D def read_points3d_binary(path_to_model_file): """ see: src/base/reconstruction.cc void Reconstruction::ReadPoints3DBinary(const std::string& path) void Reconstruction::WritePoints3DBinary(const std::string& path) """ points3D = {} with open(path_to_model_file, "rb") as fid: num_points = read_next_bytes(fid, 8, "Q")[0] for point_line_index in range(num_points): binary_point_line_properties = read_next_bytes( fid, num_bytes=43, format_char_sequence="QdddBBBd") point3D_id = binary_point_line_properties[0] xyz = np.array(binary_point_line_properties[1:4]) rgb = np.array(binary_point_line_properties[4:7]) error = np.array(binary_point_line_properties[7]) track_length = read_next_bytes( fid, num_bytes=8, format_char_sequence="Q")[0] track_elems = read_next_bytes( fid, num_bytes=8*track_length, format_char_sequence="ii"*track_length) image_ids = np.array(tuple(map(int, track_elems[0::2]))) point2D_idxs = np.array(tuple(map(int, track_elems[1::2]))) points3D[point3D_id] = Point3D( id=point3D_id, xyz=xyz, rgb=rgb, error=error, image_ids=image_ids, point2D_idxs=point2D_idxs) return points3D def read_model(path, ext): if ext == ".txt": cameras = read_cameras_text(os.path.join(path, "cameras" + ext)) images = read_images_text(os.path.join(path, "images" + ext)) points3D = read_points3D_text(os.path.join(path, "points3D") + ext) else: cameras = read_cameras_binary(os.path.join(path, "cameras" + ext)) images = read_images_binary(os.path.join(path, "images" + ext)) points3D = read_points3d_binary(os.path.join(path, "points3D") + ext) return cameras, images, points3D def qvec2rotmat(qvec): return np.array([ [1 - 2 * qvec[2]**2 - 2 * qvec[3]**2, 2 * qvec[1] * qvec[2] - 2 * qvec[0] * qvec[3], 2 * qvec[3] * qvec[1] + 2 * qvec[0] * qvec[2]], [2 * qvec[1] * qvec[2] + 2 * qvec[0] * qvec[3], 1 - 2 * qvec[1]**2 - 2 * qvec[3]**2, 2 * qvec[2] * qvec[3] - 2 * qvec[0] * qvec[1]], [2 * qvec[3] * qvec[1] - 2 * qvec[0] * qvec[2], 2 * qvec[2] * qvec[3] + 2 * qvec[0] * qvec[1], 1 - 2 * qvec[1]**2 - 2 * qvec[2]**2]]) def rotmat2qvec(R): Rxx, Ryx, Rzx, Rxy, Ryy, Rzy, Rxz, Ryz, Rzz = R.flat K = np.array([ [Rxx - Ryy - Rzz, 0, 0, 0], [Ryx + Rxy, Ryy - Rxx - Rzz, 0, 0], [Rzx + Rxz, Rzy + Ryz, Rzz - Rxx - Ryy, 0], [Ryz - Rzy, Rzx - Rxz, Rxy - Ryx, Rxx + Ryy + Rzz]]) / 3.0 eigvals, eigvecs = np.linalg.eigh(K) qvec = eigvecs[[3, 0, 1, 2], np.argmax(eigvals)] if qvec[0] < 0: qvec *= -1 return qvec def main(): if len(sys.argv) != 3: print("Usage: python read_model.py path/to/model/folder [.txt,.bin]") return cameras, images, points3D = read_model(path=sys.argv[1], ext=sys.argv[2]) print("num_cameras:", len(cameras)) print("num_images:", len(images)) print("num_points3D:", len(points3D)) if __name__ == "__main__": main() colmap-3.4/scripts/python/test_read_model.py000077500000000000000000000043231323400541200213460ustar00rootroot00000000000000import numpy as np from read_model import read_model def compare_cameras(cameras1, cameras2): assert len(cameras1) == len(cameras2) for camera_id1 in cameras1: camera1 = cameras1[camera_id1] camera2 = cameras2[camera_id1] assert camera1.id == camera2.id assert camera1.width == camera2.width assert camera1.height == camera2.height assert np.allclose(camera1.params, camera2.params) def compare_images(images1, images2): assert len(images1) == len(images2) for image_id1 in images1: image1 = images1[image_id1] image2 = images2[image_id1] assert image1.id == image2.id assert np.allclose(image1.qvec, image2.qvec) assert np.allclose(image1.tvec, image2.tvec) assert image1.camera_id == image2.camera_id assert image1.name == image2.name assert np.allclose(image1.xys, image2.xys) assert np.array_equal(image1.point3D_ids, image2.point3D_ids) def compare_points(points3D1, points3D2): for point3D_id1 in points3D1: point3D1 = points3D1[point3D_id1] point3D2 = points3D2[point3D_id1] assert point3D1.id == point3D2.id assert np.allclose(point3D1.xyz, point3D1.xyz) assert np.array_equal(point3D1.rgb, point3D1.rgb) assert np.allclose(point3D1.error, point3D2.error) assert np.array_equal(point3D1.image_ids, point3D1.image_ids) assert np.array_equal(point3D1.point2D_idxs, point3D1.point2D_idxs) def main(): import sys if len(sys.argv) != 3: print("Usage: python read_model.py " "path/to/model/folder/txt path/to/model/folder/bin") return print("Comparing text and binary models ...") path_to_model_txt_folder = sys.argv[1] path_to_model_bin_folder = sys.argv[2] cameras_txt, images_txt, points3D_txt = \ read_model(path_to_model_txt_folder, ext=".txt") cameras_bin, images_bin, points3D_bin = \ read_model(path_to_model_bin_folder, ext=".bin") compare_cameras(cameras_txt, cameras_bin) compare_images(images_txt, images_bin) compare_points(points3D_txt, points3D_bin) print("... text and binary models are equal.") if __name__ == "__main__": main() colmap-3.4/scripts/shell/000077500000000000000000000000001323400541200154235ustar00rootroot00000000000000colmap-3.4/scripts/shell/build_mac_app.sh000077500000000000000000000045371323400541200205520ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # This script creates a deployable package of COLMAP for Mac OS X. BIN_PATH="." echo "Creating bundle directory" mkdir -p "$BIN_PATH/COLMAP.app/Contents/MacOS" echo "Copying binary" cp "$BIN_PATH/colmap" "$BIN_PATH/COLMAP.app/Contents/MacOS/colmap" echo "Writing Info.plist" cat <"$BIN_PATH/COLMAP.app/Contents/Info.plist" CFBundlePackageType APPL CFBundleExecutable colmap CFBundleIdentifier COLMAP CFBundleName COLMAP CFBundleDisplayName COLMAP NSHighResolutionCapable NSAppSleepDisabled EOM install_name_tool -change @rpath/libtbb.dylib /usr/local/lib/libtbb.dylib $BIN_PATH/COLMAP.app/Contents/MacOS/COLMAP install_name_tool -change @rpath/libtbbmalloc.dylib /usr/local/lib/libtbbmalloc.dylib $BIN_PATH/COLMAP.app/Contents/MacOS/COLMAP echo "Linking dynamic libraries" /usr/local/opt/qt5/bin/macdeployqt "$BIN_PATH/COLMAP.app" echo "Wrapping binary" cat <"$BIN_PATH/COLMAP.app/Contents/MacOS/colmap_gui.sh" #!/bin/bash script_path="\$(cd "\$(dirname "\${BASH_SOURCE[0]}")" && pwd)" \$script_path/colmap gui EOM chmod +x $BIN_PATH/COLMAP.app/Contents/MacOS/colmap_gui.sh sed -i '' 's#colmap#colmap_gui.sh#g' $BIN_PATH/COLMAP.app/Contents/Info.plist colmap-3.4/scripts/shell/colmap.bat000066400000000000000000000006241323400541200173700ustar00rootroot00000000000000@echo off set SCRIPT_PATH=%~dp0 set PATH=%SCRIPT_PATH%\lib;%PATH% set QT_PLUGIN_PATH=%SCRIPT_PATH%\lib;%QT_PLUGIN_PATH% set COMMAND=%1 set ARGUMENTS= shift :extract_argument_loop if "%1"=="" goto after_extract_argument_loop set ARGUMENTS=%ARGUMENTS% %1 shift goto extract_argument_loop :after_extract_argument_loop if "%COMMAND%"=="" set COMMAND=gui "%SCRIPT_PATH%\bin\colmap" %COMMAND% %ARGUMENTS% colmap-3.4/scripts/shell/images_to_video.sh000077500000000000000000000016031323400541200211170ustar00rootroot00000000000000# COLMAP - Structure-from-Motion and Multi-View Stereo. # Copyright (C) 2017 Johannes L. Schoenberger # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see . # Command to produce video from images produced by COLMAP movie grabber tool. ffmpeg -i frame%06d.png -r 30 -vf scale=1680:1050 out.mp4 colmap-3.4/scripts/shell/restore_git_submodules.sh000066400000000000000000000004211323400541200225440ustar00rootroot00000000000000set -e git config -f .gitmodules --get-regexp '^submodule\..*\.path$' | while read path_key path do url_key=$(echo $path_key | sed 's/\.path/.url/') url=$(git config -f .gitmodules --get "$url_key") git submodule add -f $url $path done colmap-3.4/scripts/shell/run_tests.bat000066400000000000000000000003301323400541200201350ustar00rootroot00000000000000set SCRIPT_PATH=%~dp0 set PATH=%SCRIPT_PATH%\lib;%PATH% set QT_PLUGIN_PATH=%SCRIPT_PATH%\lib;%QT_PLUGIN_PATH% for %%i in (%SCRIPT_PATH%\bin\*_test.exe) do ( %%i if %errorlevel% neq 0 goto end ) :end pause colmap-3.4/src/000077500000000000000000000000001323400541200134145ustar00rootroot00000000000000colmap-3.4/src/CMakeLists.txt000077500000000000000000000102051323400541200161550ustar00rootroot00000000000000include_directories( . ${Boost_INCLUDE_DIRS} ${EIGEN3_INCLUDE_DIRS} ${GLOG_INCLUDE_DIRS} ${FREEIMAGE_INCLUDE_DIRS} ${CERES_INCLUDE_DIRS} ${GLEW_INCLUDE_DIRS} ${Qt5_INCLUDE_DIRS} ) link_directories( ${Boost_LIBRARY_DIRS} ) set(COLMAP_LIBRARIES mvs sfm controllers base feature ui util controllers mvs sfm estimators base feature ui util estimators optim retrieval estimators base util flann graclus lsd pba poisson_recon sqlite3 sift_gpu vlfeat ${CMAKE_DL_LIBS} ${Boost_FILESYSTEM_LIBRARY} ${Boost_PROGRAM_OPTIONS_LIBRARY} ${Boost_REGEX_LIBRARY} ${Boost_SYSTEM_LIBRARY} ${GLOG_LIBRARIES} ${FREEIMAGE_LIBRARIES} ${CERES_LIBRARIES} ${OPENGL_gl_LIBRARY} ${OPENGL_glu_LIBRARY}) if(CUDA_ENABLED) set(COLMAP_LIBRARIES mvs mvs_cuda util_cuda ${COLMAP_LIBRARIES} mvs mvs_cuda mvs util_cuda) endif() if(UNIX) set(COLMAP_LIBRARIES ${COLMAP_LIBRARIES} pthread) endif() set(COLMAP_QT_MODULES Core Widgets OpenGL) add_subdirectory(base) add_subdirectory(controllers) add_subdirectory(estimators) add_subdirectory(exe) add_subdirectory(ext) add_subdirectory(feature) add_subdirectory(mvs) add_subdirectory(optim) add_subdirectory(retrieval) add_subdirectory(sfm) add_subdirectory(tools) add_subdirectory(ui) add_subdirectory(util) # This macro will search for source files in a given directory, will add them # to a source group (folder within a project), and will then return paths to # each of the found files. The usage of the macro is as follows: # ADD_SOURCE_DIR( # # # ) macro(ADD_SOURCE_DIR SRC_DIR SRC_VAR) # Create the list of expressions to be used in the search. set(GLOB_EXPRESSIONS "") foreach(ARG ${ARGN}) list(APPEND GLOB_EXPRESSIONS ${SRC_DIR}/${ARG}) endforeach() # Perform the search for the source files. file(GLOB ${SRC_VAR} RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ${GLOB_EXPRESSIONS}) # Create the source group. string(REPLACE "/" "\\" GROUP_NAME ${SRC_DIR}) source_group(${GROUP_NAME} FILES ${${SRC_VAR}}) # Clean-up. unset(GLOB_EXPRESSIONS) unset(ARG) unset(GROUP_NAME) endmacro(ADD_SOURCE_DIR) ADD_SOURCE_DIR(base BASE_SRC *.h *.cc) ADD_SOURCE_DIR(controllers CONTROLLERS_SRC *.h *.cc) ADD_SOURCE_DIR(estimators ESTIMATORS_SRC *.h *.cc) ADD_SOURCE_DIR(exe EXE_SRC *.h *.cc) ADD_SOURCE_DIR(ext/FLANN EXT_FLANN_SRC *.h *.cpp *.hpp *.cu) ADD_SOURCE_DIR(ext/Graclus EXT_GRACLUS_SRC *.h *.c) ADD_SOURCE_DIR(ext/LSD EXT_LSD_SRC *.h *.c) ADD_SOURCE_DIR(ext/PBA EXT_PBA_SRC *.h *.cpp *.cu) ADD_SOURCE_DIR(ext/PoissonRecon EXT_POISSON_RECON_SRC *.h *.cpp *.inl) ADD_SOURCE_DIR(ext/SiftGPU EXT_SIFT_GPU_SRC *.h *.cpp *.cu) ADD_SOURCE_DIR(ext/SQLite EXT_SQLITE_SRC *.h *.c) ADD_SOURCE_DIR(ext/VLFeat EXT_VLFEAT_SRC *.h *.c *.tc) ADD_SOURCE_DIR(feature FEATURE_SRC *.h *.cc) ADD_SOURCE_DIR(mvs MVS_SRC *.h *.cc *.cu) ADD_SOURCE_DIR(optim OPTIM_SRC *.h *.cc) ADD_SOURCE_DIR(retrieval RETRIEVAL_SRC *.h *.cc) ADD_SOURCE_DIR(sfm SFM_SRC *.h *.cc) ADD_SOURCE_DIR(tools TOOLS_SRC *.h *.cc) ADD_SOURCE_DIR(ui UI_SRC *.h *.cc) ADD_SOURCE_DIR(util UTIL_SRC *.h *.cc) # Add all of the source files to a regular library target, as using a custom # target does not allow us to set its C++ include directories (and thus # intellisense can't find any of the included files). add_library( ${COLMAP_SRC_ROOT_FOLDER} ${BASE_SRC} ${CONTROLLERS_SRC} ${ESTIMATORS_SRC} ${EXE_SRC} ${EXT_FLANN_SRC} ${EXT_GRACLUS_SRC} ${EXT_LSD_SRC} ${EXT_PBA_SRC} ${EXT_POISSON_RECON_SRC} ${EXT_SIFT_GPU_SRC} ${EXT_SQLITE_SRC} ${EXT_VLFEAT_SRC} ${FEATURE_SRC} ${MVS_SRC} ${OPTIM_SRC} ${RETRIEVAL_SRC} ${SFM_SRC} ${TOOLS_SRC} ${UI_SRC} ${UTIL_SRC}) # Prevent the library from being compiled automatically. set_target_properties( ${COLMAP_SRC_ROOT_FOLDER} PROPERTIES EXCLUDE_FROM_ALL 1 EXCLUDE_FROM_DEFAULT_BUILD 1) colmap-3.4/src/base/000077500000000000000000000000001323400541200143265ustar00rootroot00000000000000colmap-3.4/src/base/CMakeLists.txt000077500000000000000000000046741323400541200171040ustar00rootroot00000000000000set(FOLDER_NAME "base") COLMAP_ADD_LIBRARY(base camera.h camera.cc camera_database.h camera_database.cc camera_models.h camera_models.cc camera_rig.h camera_rig.cc database.h database.cc database_cache.h database_cache.cc essential_matrix.h essential_matrix.cc gps.h gps.cc graph_cut.h graph_cut.cc homography_matrix.h homography_matrix.cc image.h image.cc image_reader.h image_reader.cc line.h line.cc point2d.h point2d.cc point3d.h point3d.cc polynomial.h polynomial.cc pose.h pose.cc projection.h projection.cc reconstruction.h reconstruction.cc reconstruction_manager.h reconstruction_manager.cc scene_clustering.h scene_clustering.cc scene_graph.h scene_graph.cc similarity_transform.h similarity_transform.cc track.h track.cc triangulation.h triangulation.cc undistortion.h undistortion.cc visibility_pyramid.h visibility_pyramid.cc warp.h warp.cc ) COLMAP_ADD_TEST(camera_database_test camera_database_test.cc) COLMAP_ADD_TEST(camera_models_test camera_models_test.cc) COLMAP_ADD_TEST(camera_rig_test camera_rig_test.cc) COLMAP_ADD_TEST(camera_test camera_test.cc) COLMAP_ADD_TEST(cost_functions_test cost_functions_test.cc) COLMAP_ADD_TEST(database_cache_test database_cache_test.cc) COLMAP_ADD_TEST(database_test database_test.cc) COLMAP_ADD_TEST(essential_matrix_utils_test essential_matrix_test.cc) COLMAP_ADD_TEST(gps_test gps_test.cc) COLMAP_ADD_TEST(graph_cut_test graph_cut_test.cc) COLMAP_ADD_TEST(homography_matrix_utils_test homography_matrix_test.cc) COLMAP_ADD_TEST(image_test image_test.cc) COLMAP_ADD_TEST(line_test line_test.cc) COLMAP_ADD_TEST(point2d_test point2d_test.cc) COLMAP_ADD_TEST(point3d_test point3d_test.cc) COLMAP_ADD_TEST(polynomial_test polynomial_test.cc) COLMAP_ADD_TEST(pose_test pose_test.cc) COLMAP_ADD_TEST(projection_test projection_test.cc) COLMAP_ADD_TEST(reconstruction_test reconstruction_test.cc) COLMAP_ADD_TEST(reconstruction_manager_test reconstruction_manager_test.cc) COLMAP_ADD_TEST(scene_clustering_test scene_clustering_test.cc) COLMAP_ADD_TEST(scene_graph_test scene_graph_test.cc) COLMAP_ADD_TEST(similarity_transform_test similarity_transform_test.cc) COLMAP_ADD_TEST(track_test track_test.cc) COLMAP_ADD_TEST(triangulation_test triangulation_test.cc) COLMAP_ADD_TEST(undistortion_test undistortion_test.cc) COLMAP_ADD_TEST(visibility_pyramid_test visibility_pyramid_test.cc) COLMAP_ADD_TEST(warp_test warp_test.cc) colmap-3.4/src/base/camera.cc000077500000000000000000000161661323400541200161020ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/camera.h" #include #include "util/logging.h" #include "util/misc.h" namespace colmap { Camera::Camera() : camera_id_(kInvalidCameraId), model_id_(kInvalidCameraModelId), width_(0), height_(0), prior_focal_length_(false) {} std::string Camera::ModelName() const { return CameraModelIdToName(model_id_); } void Camera::SetModelId(const int model_id) { CHECK(ExistsCameraModelWithId(model_id)); model_id_ = model_id; params_.resize(CameraModelNumParams(model_id_), 0); } void Camera::SetModelIdFromName(const std::string& model_name) { CHECK(ExistsCameraModelWithName(model_name)); model_id_ = CameraModelNameToId(model_name); params_.resize(CameraModelNumParams(model_id_), 0); } const std::vector& Camera::FocalLengthIdxs() const { return CameraModelFocalLengthIdxs(model_id_); } const std::vector& Camera::PrincipalPointIdxs() const { return CameraModelPrincipalPointIdxs(model_id_); } const std::vector& Camera::ExtraParamsIdxs() const { return CameraModelExtraParamsIdxs(model_id_); } Eigen::Matrix3d Camera::CalibrationMatrix() const { Eigen::Matrix3d K = Eigen::Matrix3d::Identity(); const std::vector& idxs = FocalLengthIdxs(); if (idxs.size() == 1) { K(0, 0) = params_[idxs[0]]; K(1, 1) = params_[idxs[0]]; } else if (idxs.size() == 2) { K(0, 0) = params_[idxs[0]]; K(1, 1) = params_[idxs[1]]; } else { LOG(FATAL) << "Camera model must either have 1 or 2 focal length parameters."; } K(0, 2) = PrincipalPointX(); K(1, 2) = PrincipalPointY(); return K; } std::string Camera::ParamsInfo() const { return CameraModelParamsInfo(model_id_); } double Camera::MeanFocalLength() const { const auto& focal_length_idxs = FocalLengthIdxs(); double focal_length = 0; for (const auto idx : focal_length_idxs) { focal_length += params_[idx]; } return focal_length / focal_length_idxs.size(); } double Camera::FocalLength() const { const std::vector& idxs = FocalLengthIdxs(); CHECK_EQ(idxs.size(), 1); return params_[idxs[0]]; } double Camera::FocalLengthX() const { const std::vector& idxs = FocalLengthIdxs(); CHECK_EQ(idxs.size(), 2); return params_[idxs[0]]; } double Camera::FocalLengthY() const { const std::vector& idxs = FocalLengthIdxs(); CHECK_EQ(idxs.size(), 2); return params_[idxs[1]]; } void Camera::SetFocalLength(const double focal_length) { const std::vector& idxs = FocalLengthIdxs(); for (const auto idx : idxs) { params_[idx] = focal_length; } } void Camera::SetFocalLengthX(const double focal_length_x) { const std::vector& idxs = FocalLengthIdxs(); CHECK_EQ(idxs.size(), 2); params_[idxs[0]] = focal_length_x; } void Camera::SetFocalLengthY(const double focal_length_y) { const std::vector& idxs = FocalLengthIdxs(); CHECK_EQ(idxs.size(), 2); params_[idxs[1]] = focal_length_y; } double Camera::PrincipalPointX() const { const std::vector& idxs = PrincipalPointIdxs(); CHECK_EQ(idxs.size(), 2); return params_[idxs[0]]; } double Camera::PrincipalPointY() const { const std::vector& idxs = PrincipalPointIdxs(); CHECK_EQ(idxs.size(), 2); return params_[idxs[1]]; } void Camera::SetPrincipalPointX(const double ppx) { const std::vector& idxs = PrincipalPointIdxs(); CHECK_EQ(idxs.size(), 2); params_[idxs[0]] = ppx; } void Camera::SetPrincipalPointY(const double ppy) { const std::vector& idxs = PrincipalPointIdxs(); CHECK_EQ(idxs.size(), 2); params_[idxs[1]] = ppy; } std::string Camera::ParamsToString() const { return VectorToCSV(params_); } bool Camera::SetParamsFromString(const std::string& string) { params_ = CSVToVector(string); return VerifyParams(); } bool Camera::VerifyParams() const { return CameraModelVerifyParams(model_id_, params_); } bool Camera::HasBogusParams(const double min_focal_length_ratio, const double max_focal_length_ratio, const double max_extra_param) const { return CameraModelHasBogusParams(model_id_, params_, width_, height_, min_focal_length_ratio, max_focal_length_ratio, max_extra_param); } void Camera::InitializeWithId(const int model_id, const double focal_length, const size_t width, const size_t height) { CHECK(ExistsCameraModelWithId(model_id)); model_id_ = model_id; width_ = width; height_ = height; params_ = CameraModelInitializeParams(model_id, focal_length, width, height); } void Camera::InitializeWithName(const std::string& model_name, const double focal_length, const size_t width, const size_t height) { InitializeWithId(CameraModelNameToId(model_name), focal_length, width, height); } Eigen::Vector2d Camera::ImageToWorld(const Eigen::Vector2d& image_point) const { Eigen::Vector2d world_point; CameraModelImageToWorld(model_id_, params_, image_point(0), image_point(1), &world_point(0), &world_point(1)); return world_point; } double Camera::ImageToWorldThreshold(const double threshold) const { return CameraModelImageToWorldThreshold(model_id_, params_, threshold); } Eigen::Vector2d Camera::WorldToImage(const Eigen::Vector2d& world_point) const { Eigen::Vector2d image_point; CameraModelWorldToImage(model_id_, params_, world_point(0), world_point(1), &image_point(0), &image_point(1)); return image_point; } void Camera::Rescale(const double scale) { CHECK_GT(scale, 0.0); const double scale_x = std::round(scale * width_) / static_cast(width_); const double scale_y = std::round(scale * height_) / static_cast(height_); width_ = static_cast(std::round(scale * width_)); height_ = static_cast(std::round(scale * height_)); SetPrincipalPointX(scale_x * PrincipalPointX()); SetPrincipalPointY(scale_y * PrincipalPointY()); if (FocalLengthIdxs().size() == 1) { SetFocalLength((scale_x + scale_y) / 2.0 * FocalLength()); } else if (FocalLengthIdxs().size() == 2) { SetFocalLengthX(scale_x * FocalLengthX()); SetFocalLengthY(scale_y * FocalLengthY()); } else { LOG(FATAL) << "Camera model must either have 1 or 2 focal length parameters."; } } } // namespace colmap colmap-3.4/src/base/camera.h000077500000000000000000000156141323400541200157410ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_CAMERA_H_ #define COLMAP_SRC_BASE_CAMERA_H_ #include #include "base/camera_models.h" #include "util/types.h" namespace colmap { // Camera class that holds the intrinsic parameters. Cameras may be shared // between multiple images, e.g., if the same "physical" camera took multiple // pictures with the exact same lens and intrinsics (focal length, etc.). // This class has a specific distortion model defined by a camera model class. class Camera { public: Camera(); // Access the unique identifier of the camera. inline camera_t CameraId() const; inline void SetCameraId(const camera_t camera_id); // Access the camera model. inline int ModelId() const; std::string ModelName() const; void SetModelId(const int model_id); void SetModelIdFromName(const std::string& model_name); // Access dimensions of the camera sensor. inline size_t Width() const; inline size_t Height() const; inline void SetWidth(const size_t width); inline void SetHeight(const size_t height); // Access focal length parameters. double MeanFocalLength() const; double FocalLength() const; double FocalLengthX() const; double FocalLengthY() const; void SetFocalLength(const double focal_length); void SetFocalLengthX(const double focal_length_x); void SetFocalLengthY(const double focal_length_y); // Check if camera has prior focal length. inline bool HasPriorFocalLength() const; inline void SetPriorFocalLength(const bool prior); // Access principal point parameters. Only works if there are two // principal point parameters. double PrincipalPointX() const; double PrincipalPointY() const; void SetPrincipalPointX(const double ppx); void SetPrincipalPointY(const double ppy); // Get the indices of the parameter groups in the parameter vector. const std::vector& FocalLengthIdxs() const; const std::vector& PrincipalPointIdxs() const; const std::vector& ExtraParamsIdxs() const; // Get intrinsic calibration matrix composed from focal length and principal // point parameters, excluding distortion parameters. Eigen::Matrix3d CalibrationMatrix() const; // Get human-readable information about the parameter vector ordering. std::string ParamsInfo() const; // Access the raw parameter vector. inline size_t NumParams() const; inline const std::vector& Params() const; inline std::vector& Params(); inline double Params(const size_t idx) const; inline double& Params(const size_t idx); inline const double* ParamsData() const; inline double* ParamsData(); inline void SetParams(const std::vector& params); // Concatenate parameters as comma-separated list. std::string ParamsToString() const; // Set camera parameters from comma-separated list. bool SetParamsFromString(const std::string& string); // Check whether parameters are valid, i.e. the parameter vector has // the correct dimensions that match the specified camera model. bool VerifyParams() const; // Check whether camera has bogus parameters. bool HasBogusParams(const double min_focal_length_ratio, const double max_focal_length_ratio, const double max_extra_param) const; // Initialize parameters for given camera model and focal length, and set // the principal point to be the image center. void InitializeWithId(const int model_id, const double focal_length, const size_t width, const size_t height); void InitializeWithName(const std::string& model_name, const double focal_length, const size_t width, const size_t height); // Project point in image plane to world / infinity. Eigen::Vector2d ImageToWorld(const Eigen::Vector2d& image_point) const; // Convert pixel threshold in image plane to world space. double ImageToWorldThreshold(const double threshold) const; // Project point from world / infinity to image plane. Eigen::Vector2d WorldToImage(const Eigen::Vector2d& world_point) const; // Rescale camera dimensions and accordingly the focal length and // and the principal point. void Rescale(const double scale); private: // The unique identifier of the camera. If the identifier is not specified // it is set to `kInvalidCameraId`. camera_t camera_id_; // The identifier of the camera model. If the camera model is not specified // the identifier is `kInvalidCameraModelId`. int model_id_; // The dimensions of the image, 0 if not initialized. size_t width_; size_t height_; // The focal length, principal point, and extra parameters. If the camera // model is not specified, this vector is empty. std::vector params_; // Whether there is a safe prior for the focal length, // e.g. manually provided or extracted from EXIF bool prior_focal_length_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// camera_t Camera::CameraId() const { return camera_id_; } void Camera::SetCameraId(const camera_t camera_id) { camera_id_ = camera_id; } int Camera::ModelId() const { return model_id_; } size_t Camera::Width() const { return width_; } size_t Camera::Height() const { return height_; } void Camera::SetWidth(const size_t width) { width_ = width; } void Camera::SetHeight(const size_t height) { height_ = height; } bool Camera::HasPriorFocalLength() const { return prior_focal_length_; } void Camera::SetPriorFocalLength(const bool prior) { prior_focal_length_ = prior; } size_t Camera::NumParams() const { return params_.size(); } const std::vector& Camera::Params() const { return params_; } std::vector& Camera::Params() { return params_; } double Camera::Params(const size_t idx) const { return params_[idx]; } double& Camera::Params(const size_t idx) { return params_[idx]; } const double* Camera::ParamsData() const { return params_.data(); } double* Camera::ParamsData() { return params_.data(); } void Camera::SetParams(const std::vector& params) { params_ = params; } } // namespace colmap #endif // COLMAP_SRC_BASE_CAMERA_H_ colmap-3.4/src/base/camera_database.cc000077500000000000000000000047521323400541200177240ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/camera_database.h" #include "util/string.h" namespace colmap { const camera_specs_t CameraDatabase::specs_ = InitializeCameraSpecs(); CameraDatabase::CameraDatabase() {} bool CameraDatabase::QuerySensorWidth(const std::string& make, const std::string& model, double* sensor_width) { // Clean the strings from all separators. std::string cleaned_make = make; std::string cleaned_model = model; StringReplace(cleaned_make, " ", ""); StringReplace(cleaned_model, " ", ""); StringReplace(cleaned_make, "-", ""); StringReplace(cleaned_model, "-", ""); StringToLower(&cleaned_make); StringToLower(&cleaned_model); // Make sure that make name is not duplicated. cleaned_model = StringReplace(cleaned_model, cleaned_make, ""); // Check if cleaned_make exists in database: Test whether EXIF string is // substring of database entry and vice versa. size_t spec_matches = 0; for (const auto& make_elem : specs_) { if (StringContains(cleaned_make, make_elem.first) || StringContains(make_elem.first, cleaned_make)) { for (const auto& model_elem : make_elem.second) { if (StringContains(cleaned_model, model_elem.first) || StringContains(model_elem.first, cleaned_model)) { *sensor_width = model_elem.second; if (cleaned_model == model_elem.first) { // Model exactly matches, return immediately. return true; } spec_matches += 1; if (spec_matches > 1) { break; } } } } } // Only return unique results, if model does not exactly match. return spec_matches == 1; } } // namespace colmap colmap-3.4/src/base/camera_database.h000077500000000000000000000026421323400541200175620ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_CAMERA_DATABASE_H_ #define COLMAP_SRC_BASE_CAMERA_DATABASE_H_ #include #include "util/camera_specs.h" namespace colmap { // Database that contains sensor widths for many cameras, which is useful // to automatically extract the focal length if EXIF information is incomplete. class CameraDatabase { public: CameraDatabase(); size_t NumEntries() const { return specs_.size(); } bool QuerySensorWidth(const std::string& make, const std::string& model, double* sensor_width); private: static const camera_specs_t specs_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_CAMERA_DATABASE_H_ colmap-3.4/src/base/camera_database_test.cc000077500000000000000000000030071323400541200207530ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/camera_database" #include "util/testing.h" #include "base/camera_database.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestInitialization) { CameraDatabase database; camera_specs_t specs = InitializeCameraSpecs(); BOOST_CHECK_EQUAL(database.NumEntries(), specs.size()); } BOOST_AUTO_TEST_CASE(TestExactMatch) { CameraDatabase database; double sensor_width; BOOST_CHECK( database.QuerySensorWidth("canon", "digitalixus100is", &sensor_width)); BOOST_CHECK_EQUAL(sensor_width, 6.1600f); } BOOST_AUTO_TEST_CASE(TestAmbiguousMatch) { CameraDatabase database; double sensor_width; BOOST_CHECK( !database.QuerySensorWidth("canon", "digitalixus", &sensor_width)); BOOST_CHECK_EQUAL(sensor_width, 6.1600f); } colmap-3.4/src/base/camera_models.cc000077500000000000000000000164501323400541200174410ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/camera_models.h" #include #include namespace colmap { // Initialize params_info, focal_length_idxs, principal_point_idxs, // extra_params_idxs #define CAMERA_MODEL_CASE(CameraModel) \ const int CameraModel::model_id = InitializeModelId(); \ const std::string CameraModel::model_name = \ CameraModel::InitializeModelName(); \ const size_t CameraModel::num_params = InitializeNumParams(); \ const std::string CameraModel::params_info = \ CameraModel::InitializeParamsInfo(); \ const std::vector CameraModel::focal_length_idxs = \ CameraModel::InitializeFocalLengthIdxs(); \ const std::vector CameraModel::principal_point_idxs = \ CameraModel::InitializePrincipalPointIdxs(); \ const std::vector CameraModel::extra_params_idxs = \ CameraModel::InitializeExtraParamsIdxs(); CAMERA_MODEL_CASES #undef CAMERA_MODEL_CASE std::unordered_map InitialzeCameraModelNameToId() { std::unordered_map camera_model_name_to_id; #define CAMERA_MODEL_CASE(CameraModel) \ camera_model_name_to_id.emplace(CameraModel::model_name, \ CameraModel::model_id); CAMERA_MODEL_CASES #undef CAMERA_MODEL_CASE return camera_model_name_to_id; } std::unordered_map InitialzeCameraModelIdToName() { std::unordered_map camera_model_id_to_name; #define CAMERA_MODEL_CASE(CameraModel) \ camera_model_id_to_name.emplace(CameraModel::model_id, \ CameraModel::model_name); CAMERA_MODEL_CASES #undef CAMERA_MODEL_CASE return camera_model_id_to_name; } static const std::unordered_map CAMERA_MODEL_NAME_TO_ID = InitialzeCameraModelNameToId(); static const std::unordered_map CAMERA_MODEL_ID_TO_NAME = InitialzeCameraModelIdToName(); bool ExistsCameraModelWithName(const std::string& model_name) { return CAMERA_MODEL_NAME_TO_ID.count(model_name) > 0; } bool ExistsCameraModelWithId(const int model_id) { return CAMERA_MODEL_ID_TO_NAME.count(model_id) > 0; } int CameraModelNameToId(const std::string& model_name) { const auto it = CAMERA_MODEL_NAME_TO_ID.find(model_name); if (it == CAMERA_MODEL_NAME_TO_ID.end()) { return kInvalidCameraModelId; } else { return it->second; } } std::string CameraModelIdToName(const int model_id) { const auto it = CAMERA_MODEL_ID_TO_NAME.find(model_id); if (it == CAMERA_MODEL_ID_TO_NAME.end()) { return ""; } else { return it->second; } } std::vector CameraModelInitializeParams(const int model_id, const double focal_length, const size_t width, const size_t height) { // Assuming that image measurements are within [0, dim], i.e. that the // upper left corner is the (0, 0) coordinate (rather than the center of // the upper left pixel). This complies with the default SiftGPU convention. switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::InitializeParams(focal_length, width, height); \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } } std::string CameraModelParamsInfo(const int model_id) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::params_info; \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return "Camera model does not exist"; } static const std::vector EMPTY_IDXS; const std::vector& CameraModelFocalLengthIdxs(const int model_id) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::focal_length_idxs; \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return EMPTY_IDXS; } const std::vector& CameraModelPrincipalPointIdxs(const int model_id) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::principal_point_idxs; \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return EMPTY_IDXS; } const std::vector& CameraModelExtraParamsIdxs(const int model_id) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::extra_params_idxs; \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return EMPTY_IDXS; } size_t CameraModelNumParams(const int model_id) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::num_params; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return 0; } bool CameraModelVerifyParams(const int model_id, const std::vector& params) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ if (params.size() == CameraModel::num_params) { \ return true; \ } \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return false; } bool CameraModelHasBogusParams(const int model_id, const std::vector& params, const size_t width, const size_t height, const double min_focal_length_ratio, const double max_focal_length_ratio, const double max_extra_param) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::HasBogusParams( \ params, width, height, min_focal_length_ratio, max_focal_length_ratio, \ max_extra_param); \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return false; } } // namespace colmap colmap-3.4/src/base/camera_models.h000077500000000000000000001402671323400541200173070ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_CAMERA_MODELS_H_ #define COLMAP_SRC_BASE_CAMERA_MODELS_H_ #include #include #include #include #include #include namespace colmap { // This file defines several different camera models and arbitrary new camera // models can be added by the following steps: // // 1. Add a new struct in this file which implements all the necessary methods. // 2. Define an unique model_name and model_id for the camera model. // 3. Add camera model to `CAMERA_MODEL_CASES` macro in this file. // 4. Add new template specialization of test case for camera model to // `camera_models_test.cc`. // // A camera model can have three different types of camera parameters: focal // length, principal point, extra parameters (distortion parameters). The // parameter array is split into different groups, so that we can enable or // disable the refinement of the individual groups during bundle adjustment. It // is up to the camera model to access the parameters correctly (it is free to // do so in an arbitrary manner) - the parameters are not accessed from outside. // // A camera model must have the following methods: // // - `WorldToImage`: transform normalized camera coordinates to image // coordinates (the inverse of `ImageToWorld`). Assumes that the world // coordinates are given as (u, v, 1). // - `ImageToWorld`: transform image coordinates to normalized camera // coordinates (the inverse of `WorldToImage`). Produces world coordinates // as (u, v, 1). // - `ImageToWorldThreshold`: transform a threshold given in pixels to // normalized units (e.g. useful for reprojection error thresholds). // // Whenever you specify the camera parameters in a list, they must appear // exactly in the order as they are accessed in the defined model struct. // // The camera models follow the convention that the upper left image corner has // the coordinate (0, 0), the lower right corner (width, height), i.e. that // the upper left pixel center has coordinate (0.5, 0.5) and the lower right // pixel center has the coordinate (width - 0.5, height - 0.5). static const int kInvalidCameraModelId = -1; #ifndef CAMERA_MODEL_DEFINITIONS #define CAMERA_MODEL_DEFINITIONS(model_id_value, model_name_value, \ num_params_value) \ static const int kModelId = model_id_value; \ static const size_t kNumParams = num_params_value; \ static const int model_id; \ static const std::string model_name; \ static const size_t num_params; \ static const std::string params_info; \ static const std::vector focal_length_idxs; \ static const std::vector principal_point_idxs; \ static const std::vector extra_params_idxs; \ \ static inline int InitializeModelId() { return model_id_value; }; \ static inline std::string InitializeModelName() { \ return model_name_value; \ }; \ static inline size_t InitializeNumParams() { return num_params_value; }; \ static inline std::string InitializeParamsInfo(); \ static inline std::vector InitializeFocalLengthIdxs(); \ static inline std::vector InitializePrincipalPointIdxs(); \ static inline std::vector InitializeExtraParamsIdxs(); \ static inline std::vector InitializeParams( \ const double focal_length, const size_t width, const size_t height); \ \ template \ static void WorldToImage(const T* params, const T u, const T v, T* x, T* y); \ template \ static void ImageToWorld(const T* params, const T x, const T y, T* u, T* v); \ template \ static void Distortion(const T* extra_params, const T u, const T v, T* du, \ T* dv); #endif #ifndef CAMERA_MODEL_CASES #define CAMERA_MODEL_CASES \ CAMERA_MODEL_CASE(SimplePinholeCameraModel) \ CAMERA_MODEL_CASE(PinholeCameraModel) \ CAMERA_MODEL_CASE(SimpleRadialCameraModel) \ CAMERA_MODEL_CASE(SimpleRadialFisheyeCameraModel) \ CAMERA_MODEL_CASE(RadialCameraModel) \ CAMERA_MODEL_CASE(RadialFisheyeCameraModel) \ CAMERA_MODEL_CASE(OpenCVCameraModel) \ CAMERA_MODEL_CASE(OpenCVFisheyeCameraModel) \ CAMERA_MODEL_CASE(FullOpenCVCameraModel) \ CAMERA_MODEL_CASE(FOVCameraModel) \ CAMERA_MODEL_CASE(ThinPrismFisheyeCameraModel) #endif #ifndef CAMERA_MODEL_SWITCH_CASES #define CAMERA_MODEL_SWITCH_CASES \ CAMERA_MODEL_CASES \ default: \ CAMERA_MODEL_DOES_NOT_EXIST_EXCEPTION \ break; #endif #define CAMERA_MODEL_DOES_NOT_EXIST_EXCEPTION \ throw std::domain_error("Camera model does not exist"); // The "Curiously Recurring Template Pattern" (CRTP) is used here, so that we // can reuse some shared functionality between all camera models - // defined in the BaseCameraModel. template struct BaseCameraModel { template static inline bool HasBogusParams(const std::vector& params, const size_t width, const size_t height, const T min_focal_length_ratio, const T max_focal_length_ratio, const T max_extra_param); template static inline bool HasBogusFocalLength(const std::vector& params, const size_t width, const size_t height, const T min_focal_length_ratio, const T max_focal_length_ratio); template static inline bool HasBogusPrincipalPoint(const std::vector& params, const size_t width, const size_t height); template static inline bool HasBogusExtraParams(const std::vector& params, const T max_extra_param); template static inline T ImageToWorldThreshold(const T* params, const T threshold); template static inline void IterativeUndistortion(const T* params, T* u, T* v); }; // Simple Pinhole camera model. // // No Distortion is assumed. Only focal length and principal point is modeled. // // Parameter list is expected in the following order: // // f, cx, cy // // See https://en.wikipedia.org/wiki/Pinhole_camera_model struct SimplePinholeCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(0, "SIMPLE_PINHOLE", 3) }; // Pinhole camera model. // // No Distortion is assumed. Only focal length and principal point is modeled. // // Parameter list is expected in the following order: // // fx, fy, cx, cy // // See https://en.wikipedia.org/wiki/Pinhole_camera_model struct PinholeCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(1, "PINHOLE", 4) }; // Simple camera model with one focal length and one radial distortion // parameter. // // This model is similar to the camera model that VisualSfM uses with the // difference that the distortion here is applied to the projections and // not to the measurements. // // Parameter list is expected in the following order: // // f, cx, cy, k // struct SimpleRadialCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(2, "SIMPLE_RADIAL", 4) }; // Simple camera model with one focal length and two radial distortion // parameters. // // This model is equivalent to the camera model that Bundler uses // (except for an inverse z-axis in the camera coordinate system). // // Parameter list is expected in the following order: // // f, cx, cy, k1, k2 // struct RadialCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(3, "RADIAL", 5) }; // OpenCV camera model. // // Based on the pinhole camera model. Additionally models radial and // tangential distortion (up to 2nd degree of coefficients). Not suitable for // large radial distortions of fish-eye cameras. // // Parameter list is expected in the following order: // // fx, fy, cx, cy, k1, k2, p1, p2 // // See // http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html struct OpenCVCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(4, "OPENCV", 8) }; // OpenCV fish-eye camera model. // // Based on the pinhole camera model. Additionally models radial and // tangential Distortion (up to 2nd degree of coefficients). Suitable for // large radial distortions of fish-eye cameras. // // Parameter list is expected in the following order: // // fx, fy, cx, cy, k1, k2, k3, k4 // // See // http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html struct OpenCVFisheyeCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(5, "OPENCV_FISHEYE", 8) }; // Full OpenCV camera model. // // Based on the pinhole camera model. Additionally models radial and // tangential Distortion. // // Parameter list is expected in the following order: // // fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, k5, k6 // // See // http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html struct FullOpenCVCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(6, "FULL_OPENCV", 12) }; // FOV camera model. // // Based on the pinhole camera model. Additionally models radial distortion. // This model is for example used by Project Tango for its equidistant // calibration type. // // Parameter list is expected in the following order: // // fx, fy, cx, cy, omega // // See: // Frederic Devernay, Olivier Faugeras. Straight lines have to be straight: // Automatic calibration and removal of distortion from scenes of structured // environments. Machine vision and applications, 2001. struct FOVCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(7, "FOV", 5) template static void Undistortion(const T* extra_params, const T u, const T v, T* du, T* dv); }; // Simple camera model with one focal length and one radial distortion // parameter, suitable for fish-eye cameras. // // This model is equivalent to the OpenCVFisheyeCameraModel but has only one // radial distortion coefficient. // // Parameter list is expected in the following order: // // f, cx, cy, k // struct SimpleRadialFisheyeCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(8, "SIMPLE_RADIAL_FISHEYE", 4) }; // Simple camera model with one focal length and two radial distortion // parameters, suitable for fish-eye cameras. // // This model is equivalent to the OpenCVFisheyeCameraModel but has only two // radial distortion coefficients. // // Parameter list is expected in the following order: // // f, cx, cy, k1, k2 // struct RadialFisheyeCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(9, "RADIAL_FISHEYE", 5) }; // Camera model with radial and tangential distortion coefficients and // additional coefficients accounting for thin-prism distortion. // // This camera model is described in // // "Camera Calibration with Distortion Models and Accuracy Evaluation", // J Weng et al., TPAMI, 1992. // // Parameter list is expected in the following order: // // fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, sx1, sy1 // struct ThinPrismFisheyeCameraModel : public BaseCameraModel { CAMERA_MODEL_DEFINITIONS(10, "THIN_PRISM_FISHEYE", 12) }; // Check whether camera model with given name or identifier exists. bool ExistsCameraModelWithName(const std::string& model_name); bool ExistsCameraModelWithId(const int model_id); // Convert camera name to unique camera model identifier. // // @param name Unique name of camera model. // // @return Unique identifier of camera model. int CameraModelNameToId(const std::string& model_name); // Convert camera model identifier to unique camera model name. // // @param model_id Unique identifier of camera model. // // @return Unique name of camera model. std::string CameraModelIdToName(const int model_id); // Initialize camera parameters using given image properties. // // Initializes all focal length parameters to the same given focal length and // sets the principal point to the image center. // // @param model_id Unique identifier of camera model. // @param focal_length Focal length, equal for all focal length parameters. // @param width Sensor width of the camera. // @param height Sensor height of the camera. std::vector CameraModelInitializeParams(const int model_id, const double focal_length, const size_t width, const size_t height); // Get human-readable information about the parameter vector order. // // @param model_id Unique identifier of camera model. std::string CameraModelParamsInfo(const int model_id); // Get the indices of the parameter groups in the parameter vector. // // @param model_id Unique identifier of camera model. const std::vector& CameraModelFocalLengthIdxs(const int model_id); const std::vector& CameraModelPrincipalPointIdxs(const int model_id); const std::vector& CameraModelExtraParamsIdxs(const int model_id); // Get the total number of parameters of a camera model. size_t CameraModelNumParams(const int model_id); // Check whether parameters are valid, i.e. the parameter vector has // the correct dimensions that match the specified camera model. // // @param model_id Unique identifier of camera model. // @param params Array of camera parameters. bool CameraModelVerifyParams(const int model_id, const std::vector& params); // Check whether camera has bogus parameters. // // @param model_id Unique identifier of camera model. // @param params Array of camera parameters. // @param width Sensor width of the camera. // @param height Sensor height of the camera. // @param min_focal_length_ratio Minimum ratio of focal length over // maximum sensor dimension. // @param min_focal_length_ratio Maximum ratio of focal length over // maximum sensor dimension. // @param max_extra_param Maximum magnitude of each extra parameter. bool CameraModelHasBogusParams(const int model_id, const std::vector& params, const size_t width, const size_t height, const double min_focal_length_ratio, const double max_focal_length_ratio, const double max_extra_param); // Transform world coordinates in camera coordinate system to image coordinates. // // This is the inverse of `CameraModelImageToWorld`. // // @param model_id Unique model_id of camera model as defined in // `CAMERA_MODEL_NAME_TO_CODE`. // @param params Array of camera parameters. // @param u, v Coordinates in camera system as (u, v, 1). // @param x, y Output image coordinates in pixels. inline void CameraModelWorldToImage(const int model_id, const std::vector& params, const double u, const double v, double* x, double* y); // Transform image coordinates to world coordinates in camera coordinate system. // // This is the inverse of `CameraModelWorldToImage`. // // @param model_id Unique identifier of camera model. // @param params Array of camera parameters. // @param x, y Image coordinates in pixels. // @param v, u Output Coordinates in camera system as (u, v, 1). inline void CameraModelImageToWorld(const int model_id, const std::vector& params, const double x, const double y, double* u, double* v); // Convert pixel threshold in image plane to world space by dividing // the threshold through the mean focal length. // // @param model_id Unique identifier of camera model. // @param params Array of camera parameters. // @param threshold Image space threshold in pixels. // // @ return World space threshold. inline double CameraModelImageToWorldThreshold( const int model_id, const std::vector& params, const double threshold); //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // BaseCameraModel template template bool BaseCameraModel::HasBogusParams( const std::vector& params, const size_t width, const size_t height, const T min_focal_length_ratio, const T max_focal_length_ratio, const T max_extra_param) { if (HasBogusPrincipalPoint(params, width, height)) { return true; } if (HasBogusFocalLength(params, width, height, min_focal_length_ratio, max_focal_length_ratio)) { return true; } if (HasBogusExtraParams(params, max_extra_param)) { return true; } return false; } template template bool BaseCameraModel::HasBogusFocalLength( const std::vector& params, const size_t width, const size_t height, const T min_focal_length_ratio, const T max_focal_length_ratio) { const size_t max_size = std::max(width, height); for (const auto& idx : CameraModel::focal_length_idxs) { const T focal_length_ratio = params[idx] / max_size; if (focal_length_ratio < min_focal_length_ratio || focal_length_ratio > max_focal_length_ratio) { return true; } } return false; } template template bool BaseCameraModel::HasBogusPrincipalPoint( const std::vector& params, const size_t width, const size_t height) { const T cx = params[CameraModel::principal_point_idxs[0]]; const T cy = params[CameraModel::principal_point_idxs[1]]; return cx < 0 || cx > width || cy < 0 || cy > height; } template template bool BaseCameraModel::HasBogusExtraParams( const std::vector& params, const T max_extra_param) { for (const auto& idx : CameraModel::extra_params_idxs) { if (std::abs(params[idx]) > max_extra_param) { return true; } } return false; } template template T BaseCameraModel::ImageToWorldThreshold(const T* params, const T threshold) { T mean_focal_length = 0; for (const auto& idx : CameraModel::focal_length_idxs) { mean_focal_length += params[idx]; } mean_focal_length /= CameraModel::focal_length_idxs.size(); return threshold / mean_focal_length; } template template void BaseCameraModel::IterativeUndistortion(const T* params, T* u, T* v) { // Parameters for Newton iteration using numerical differentiation with // central differences, 100 iterations should be enough even for complex // camera models with higher order terms. const size_t kNumIterations = 100; const double kMaxStepNorm = 1e-10; const double kRelStepSize = 1e-6; Eigen::Matrix2d J; const Eigen::Vector2d x0(*u, *v); Eigen::Vector2d x(*u, *v); Eigen::Vector2d dx; Eigen::Vector2d dx_0b; Eigen::Vector2d dx_0f; Eigen::Vector2d dx_1b; Eigen::Vector2d dx_1f; for (size_t i = 0; i < kNumIterations; ++i) { const double step0 = std::max(std::numeric_limits::epsilon(), std::abs(kRelStepSize * x(0))); const double step1 = std::max(std::numeric_limits::epsilon(), std::abs(kRelStepSize * x(1))); CameraModel::Distortion(params, x(0), x(1), &dx(0), &dx(1)); CameraModel::Distortion(params, x(0) - step0, x(1), &dx_0b(0), &dx_0b(1)); CameraModel::Distortion(params, x(0) + step0, x(1), &dx_0f(0), &dx_0f(1)); CameraModel::Distortion(params, x(0), x(1) - step1, &dx_1b(0), &dx_1b(1)); CameraModel::Distortion(params, x(0), x(1) + step1, &dx_1f(0), &dx_1f(1)); J(0, 0) = 1 + (dx_0f(0) - dx_0b(0)) / (2 * step0); J(0, 1) = (dx_1f(0) - dx_1b(0)) / (2 * step1); J(1, 0) = (dx_0f(1) - dx_0b(1)) / (2 * step0); J(1, 1) = 1 + (dx_1f(1) - dx_1b(1)) / (2 * step1); const Eigen::Vector2d step_x = J.inverse() * (x + dx - x0); x -= step_x; if (step_x.squaredNorm() < kMaxStepNorm) { break; } } *u = x(0); *v = x(1); } //////////////////////////////////////////////////////////////////////////////// // SimplePinholeCameraModel std::string SimplePinholeCameraModel::InitializeParamsInfo() { return "f, cx, cy"; } std::vector SimplePinholeCameraModel::InitializeFocalLengthIdxs() { return {0}; } std::vector SimplePinholeCameraModel::InitializePrincipalPointIdxs() { return {1, 2}; } std::vector SimplePinholeCameraModel::InitializeExtraParamsIdxs() { return {}; } std::vector SimplePinholeCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, width / 2.0, height / 2.0}; } template void SimplePinholeCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // No Distortion // Transform to image coordinates *x = f * u + c1; *y = f * v + c2; } template void SimplePinholeCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; *u = (x - c1) / f; *v = (y - c2) / f; } //////////////////////////////////////////////////////////////////////////////// // PinholeCameraModel std::string PinholeCameraModel::InitializeParamsInfo() { return "fx, fy, cx, cy"; } std::vector PinholeCameraModel::InitializeFocalLengthIdxs() { return {0, 1}; } std::vector PinholeCameraModel::InitializePrincipalPointIdxs() { return {2, 3}; } std::vector PinholeCameraModel::InitializeExtraParamsIdxs() { return {}; } std::vector PinholeCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, focal_length, width / 2.0, height / 2.0}; } template void PinholeCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // No Distortion // Transform to image coordinates *x = f1 * u + c1; *y = f2 * v + c2; } template void PinholeCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; *u = (x - c1) / f1; *v = (y - c2) / f2; } //////////////////////////////////////////////////////////////////////////////// // SimpleRadialCameraModel std::string SimpleRadialCameraModel::InitializeParamsInfo() { return "f, cx, cy, k"; } std::vector SimpleRadialCameraModel::InitializeFocalLengthIdxs() { return {0}; } std::vector SimpleRadialCameraModel::InitializePrincipalPointIdxs() { return {1, 2}; } std::vector SimpleRadialCameraModel::InitializeExtraParamsIdxs() { return {3}; } std::vector SimpleRadialCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, width / 2.0, height / 2.0, 0}; } template void SimpleRadialCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Distortion T du, dv; Distortion(¶ms[3], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f * *x + c1; *y = f * *y + c2; } template void SimpleRadialCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Lift points to normalized plane *u = (x - c1) / f; *v = (y - c2) / f; IterativeUndistortion(¶ms[3], u, v); } template void SimpleRadialCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k = extra_params[0]; const T u2 = u * u; const T v2 = v * v; const T r2 = u2 + v2; const T radial = k * r2; *du = u * radial; *dv = v * radial; } //////////////////////////////////////////////////////////////////////////////// // RadialCameraModel std::string RadialCameraModel::InitializeParamsInfo() { return "f, cx, cy, k1, k2"; } std::vector RadialCameraModel::InitializeFocalLengthIdxs() { return {0}; } std::vector RadialCameraModel::InitializePrincipalPointIdxs() { return {1, 2}; } std::vector RadialCameraModel::InitializeExtraParamsIdxs() { return {3, 4}; } std::vector RadialCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, width / 2.0, height / 2.0, 0, 0}; } template void RadialCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Distortion T du, dv; Distortion(¶ms[3], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f * *x + c1; *y = f * *y + c2; } template void RadialCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Lift points to normalized plane *u = (x - c1) / f; *v = (y - c2) / f; IterativeUndistortion(¶ms[3], u, v); } template void RadialCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k1 = extra_params[0]; const T k2 = extra_params[1]; const T u2 = u * u; const T v2 = v * v; const T r2 = u2 + v2; const T radial = k1 * r2 + k2 * r2 * r2; *du = u * radial; *dv = v * radial; } //////////////////////////////////////////////////////////////////////////////// // OpenCVCameraModel std::string OpenCVCameraModel::InitializeParamsInfo() { return "fx, fy, cx, cy, k1, k2, p1, p2"; } std::vector OpenCVCameraModel::InitializeFocalLengthIdxs() { return {0, 1}; } std::vector OpenCVCameraModel::InitializePrincipalPointIdxs() { return {2, 3}; } std::vector OpenCVCameraModel::InitializeExtraParamsIdxs() { return {4, 5, 6, 7}; } std::vector OpenCVCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, focal_length, width / 2.0, height / 2.0, 0, 0, 0, 0}; } template void OpenCVCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Distortion T du, dv; Distortion(¶ms[4], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f1 * *x + c1; *y = f2 * *y + c2; } template void OpenCVCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Lift points to normalized plane *u = (x - c1) / f1; *v = (y - c2) / f2; IterativeUndistortion(¶ms[4], u, v); } template void OpenCVCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k1 = extra_params[0]; const T k2 = extra_params[1]; const T p1 = extra_params[2]; const T p2 = extra_params[3]; const T u2 = u * u; const T uv = u * v; const T v2 = v * v; const T r2 = u2 + v2; const T radial = k1 * r2 + k2 * r2 * r2; *du = u * radial + T(2) * p1 * uv + p2 * (r2 + T(2) * u2); *dv = v * radial + T(2) * p2 * uv + p1 * (r2 + T(2) * v2); } //////////////////////////////////////////////////////////////////////////////// // OpenCVFisheyeCameraModel std::string OpenCVFisheyeCameraModel::InitializeParamsInfo() { return "fx, fy, cx, cy, k1, k2, k3, k4"; } std::vector OpenCVFisheyeCameraModel::InitializeFocalLengthIdxs() { return {0, 1}; } std::vector OpenCVFisheyeCameraModel::InitializePrincipalPointIdxs() { return {2, 3}; } std::vector OpenCVFisheyeCameraModel::InitializeExtraParamsIdxs() { return {4, 5, 6, 7}; } std::vector OpenCVFisheyeCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, focal_length, width / 2.0, height / 2.0, 0, 0, 0, 0}; } template void OpenCVFisheyeCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Distortion T du, dv; Distortion(¶ms[4], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f1 * *x + c1; *y = f2 * *y + c2; } template void OpenCVFisheyeCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Lift points to normalized plane *u = (x - c1) / f1; *v = (y - c2) / f2; IterativeUndistortion(¶ms[4], u, v); } template void OpenCVFisheyeCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k1 = extra_params[0]; const T k2 = extra_params[1]; const T k3 = extra_params[2]; const T k4 = extra_params[3]; const T r = ceres::sqrt(u * u + v * v); if (r > T(std::numeric_limits::epsilon())) { const T theta = ceres::atan(r); const T theta2 = theta * theta; const T theta4 = theta2 * theta2; const T theta6 = theta4 * theta2; const T theta8 = theta4 * theta4; const T thetad = theta * (T(1) + k1 * theta2 + k2 * theta4 + k3 * theta6 + k4 * theta8); *du = u * thetad / r - u; *dv = v * thetad / r - v; } else { *du = T(0); *dv = T(0); } } //////////////////////////////////////////////////////////////////////////////// // FullOpenCVCameraModel std::string FullOpenCVCameraModel::InitializeParamsInfo() { return "fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, k5, k6"; } std::vector FullOpenCVCameraModel::InitializeFocalLengthIdxs() { return {0, 1}; } std::vector FullOpenCVCameraModel::InitializePrincipalPointIdxs() { return {2, 3}; } std::vector FullOpenCVCameraModel::InitializeExtraParamsIdxs() { return {4, 5, 6, 7, 8, 9, 10, 11}; } std::vector FullOpenCVCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, focal_length, width / 2.0, height / 2.0, 0, 0, 0, 0, 0, 0, 0, 0}; } template void FullOpenCVCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Distortion T du, dv; Distortion(¶ms[4], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f1 * *x + c1; *y = f2 * *y + c2; } template void FullOpenCVCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Lift points to normalized plane *u = (x - c1) / f1; *v = (y - c2) / f2; IterativeUndistortion(¶ms[4], u, v); } template void FullOpenCVCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k1 = extra_params[0]; const T k2 = extra_params[1]; const T p1 = extra_params[2]; const T p2 = extra_params[3]; const T k3 = extra_params[4]; const T k4 = extra_params[5]; const T k5 = extra_params[6]; const T k6 = extra_params[7]; const T u2 = u * u; const T uv = u * v; const T v2 = v * v; const T r2 = u2 + v2; const T r4 = r2 * r2; const T r6 = r4 * r2; const T radial = (T(1) + k1 * r2 + k2 * r4 + k3 * r6) / (T(1) + k4 * r2 + k5 * r4 + k6 * r6); *du = u * radial + T(2) * p1 * uv + p2 * (r2 + T(2) * u2) - u; *dv = v * radial + T(2) * p2 * uv + p1 * (r2 + T(2) * v2) - v; } //////////////////////////////////////////////////////////////////////////////// // FOVCameraModel std::string FOVCameraModel::InitializeParamsInfo() { return "fx, fy, cx, cy, omega"; } std::vector FOVCameraModel::InitializeFocalLengthIdxs() { return {0, 1}; } std::vector FOVCameraModel::InitializePrincipalPointIdxs() { return {2, 3}; } std::vector FOVCameraModel::InitializeExtraParamsIdxs() { return {4}; } std::vector FOVCameraModel::InitializeParams(const double focal_length, const size_t width, const size_t height) { return {focal_length, focal_length, width / 2.0, height / 2.0, 1e-2}; } template void FOVCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Distortion Distortion(¶ms[4], u, v, x, y); // Transform to image coordinates *x = f1 * *x + c1; *y = f2 * *y + c2; } template void FOVCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Lift points to normalized plane const T uu = (x - c1) / f1; const T vv = (y - c2) / f2; // Undistortion Undistortion(¶ms[4], uu, vv, u, v); } template void FOVCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T omega = extra_params[0]; // Chosen arbitrarily. const T kEpsilon = T(1e-4); const T radius2 = u * u + v * v; const T omega2 = omega * omega; T factor; if (omega2 < kEpsilon) { // Derivation of this case with Matlab: // syms radius omega; // factor(radius) = atan(radius * 2 * tan(omega / 2)) / ... // (radius * omega); // simplify(taylor(factor, omega, 'order', 3)) factor = (omega2 * radius2) / T(3) - omega2 / T(12) + T(1); } else if (radius2 < kEpsilon) { // Derivation of this case with Matlab: // syms radius omega; // factor(radius) = atan(radius * 2 * tan(omega / 2)) / ... // (radius * omega); // simplify(taylor(factor, radius, 'order', 3)) const T tan_half_omega = ceres::tan(omega / T(2)); factor = (T(-2) * tan_half_omega * (T(4) * radius2 * tan_half_omega * tan_half_omega - T(3))) / (T(3) * omega); } else { const T radius = ceres::sqrt(radius2); const T numerator = ceres::atan(radius * T(2) * ceres::tan(omega / T(2))); factor = numerator / (radius * omega); } *du = u * factor; *dv = v * factor; } template void FOVCameraModel::Undistortion(const T* extra_params, const T u, const T v, T* du, T* dv) { T omega = extra_params[0]; // Chosen arbitrarily. const T kEpsilon = T(1e-4); const T radius2 = u * u + v * v; const T omega2 = omega * omega; T factor; if (omega2 < kEpsilon) { // Derivation of this case with Matlab: // syms radius omega; // factor(radius) = tan(radius * omega) / ... // (radius * 2*tan(omega/2)); // simplify(taylor(factor, omega, 'order', 3)) factor = (omega2 * radius2) / T(3) - omega2 / T(12) + T(1); } else if (radius2 < kEpsilon) { // Derivation of this case with Matlab: // syms radius omega; // factor(radius) = tan(radius * omega) / ... // (radius * 2*tan(omega/2)); // simplify(taylor(factor, radius, 'order', 3)) factor = (omega * (omega * omega * radius2 + T(3))) / (T(6) * ceres::tan(omega / T(2))); } else { const T radius = ceres::sqrt(radius2); const T numerator = ceres::tan(radius * omega); factor = numerator / (radius * T(2) * ceres::tan(omega / T(2))); } *du = u * factor; *dv = v * factor; } //////////////////////////////////////////////////////////////////////////////// // SimpleRadialFisheyeCameraModel std::string SimpleRadialFisheyeCameraModel::InitializeParamsInfo() { return "f, cx, cy, k"; } std::vector SimpleRadialFisheyeCameraModel::InitializeFocalLengthIdxs() { return {0}; } std::vector SimpleRadialFisheyeCameraModel::InitializePrincipalPointIdxs() { return {1, 2}; } std::vector SimpleRadialFisheyeCameraModel::InitializeExtraParamsIdxs() { return {3}; } std::vector SimpleRadialFisheyeCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, width / 2.0, height / 2.0, 0}; } template void SimpleRadialFisheyeCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Distortion T du, dv; Distortion(¶ms[3], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f * *x + c1; *y = f * *y + c2; } template void SimpleRadialFisheyeCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Lift points to normalized plane *u = (x - c1) / f; *v = (y - c2) / f; IterativeUndistortion(¶ms[3], u, v); } template void SimpleRadialFisheyeCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k = extra_params[0]; const T r = ceres::sqrt(u * u + v * v); if (r > T(std::numeric_limits::epsilon())) { const T theta = ceres::atan(r); const T theta2 = theta * theta; const T thetad = theta * (T(1) + k * theta2); *du = u * thetad / r - u; *dv = v * thetad / r - v; } else { *du = T(0); *dv = T(0); } } //////////////////////////////////////////////////////////////////////////////// // RadialFisheyeCameraModel std::string RadialFisheyeCameraModel::InitializeParamsInfo() { return "f, cx, cy, k1, k2"; } std::vector RadialFisheyeCameraModel::InitializeFocalLengthIdxs() { return {0}; } std::vector RadialFisheyeCameraModel::InitializePrincipalPointIdxs() { return {1, 2}; } std::vector RadialFisheyeCameraModel::InitializeExtraParamsIdxs() { return {3, 4}; } std::vector RadialFisheyeCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, width / 2.0, height / 2.0, 0, 0}; } template void RadialFisheyeCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Distortion T du, dv; Distortion(¶ms[3], u, v, &du, &dv); *x = u + du; *y = v + dv; // Transform to image coordinates *x = f * *x + c1; *y = f * *y + c2; } template void RadialFisheyeCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f = params[0]; const T c1 = params[1]; const T c2 = params[2]; // Lift points to normalized plane *u = (x - c1) / f; *v = (y - c2) / f; IterativeUndistortion(¶ms[3], u, v); } template void RadialFisheyeCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k1 = extra_params[0]; const T k2 = extra_params[1]; const T r = ceres::sqrt(u * u + v * v); if (r > T(std::numeric_limits::epsilon())) { const T theta = ceres::atan(r); const T theta2 = theta * theta; const T theta4 = theta2 * theta2; const T thetad = theta * (T(1) + k1 * theta2 + k2 * theta4); *du = u * thetad / r - u; *dv = v * thetad / r - v; } else { *du = T(0); *dv = T(0); } } //////////////////////////////////////////////////////////////////////////////// // ThinPrismFisheyeCameraModel std::string ThinPrismFisheyeCameraModel::InitializeParamsInfo() { return "fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, sx1, sy1"; } std::vector ThinPrismFisheyeCameraModel::InitializeFocalLengthIdxs() { return {0, 1}; } std::vector ThinPrismFisheyeCameraModel::InitializePrincipalPointIdxs() { return {2, 3}; } std::vector ThinPrismFisheyeCameraModel::InitializeExtraParamsIdxs() { return {4, 5, 6, 7, 8, 9, 10, 11}; } std::vector ThinPrismFisheyeCameraModel::InitializeParams( const double focal_length, const size_t width, const size_t height) { return {focal_length, focal_length, width / 2.0, height / 2.0, 0, 0, 0, 0, 0, 0, 0, 0}; } template void ThinPrismFisheyeCameraModel::WorldToImage(const T* params, const T u, const T v, T* x, T* y) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; const T r = ceres::sqrt(u * u + v * v); T uu, vv; if (r > T(std::numeric_limits::epsilon())) { const T theta = ceres::atan(r); uu = theta * u / r; vv = theta * v / r; } else { uu = u; vv = v; } // Distortion T du, dv; Distortion(¶ms[4], uu, vv, &du, &dv); *x = uu + du; *y = vv + dv; // Transform to image coordinates *x = f1 * *x + c1; *y = f2 * *y + c2; } template void ThinPrismFisheyeCameraModel::ImageToWorld(const T* params, const T x, const T y, T* u, T* v) { const T f1 = params[0]; const T f2 = params[1]; const T c1 = params[2]; const T c2 = params[3]; // Lift points to normalized plane *u = (x - c1) / f1; *v = (y - c2) / f2; IterativeUndistortion(¶ms[4], u, v); const T theta = ceres::sqrt(*u * *u + *v * *v); const T theta_cos_theta = theta * ceres::cos(theta); if (theta_cos_theta > T(std::numeric_limits::epsilon())) { const T scale = ceres::sin(theta) / theta_cos_theta; *u *= scale; *v *= scale; } } template void ThinPrismFisheyeCameraModel::Distortion(const T* extra_params, const T u, const T v, T* du, T* dv) { const T k1 = extra_params[0]; const T k2 = extra_params[1]; const T p1 = extra_params[2]; const T p2 = extra_params[3]; const T k3 = extra_params[4]; const T k4 = extra_params[5]; const T sx1 = extra_params[6]; const T sy1 = extra_params[7]; const T u2 = u * u; const T uv = u * v; const T v2 = v * v; const T r2 = u2 + v2; const T r4 = r2 * r2; const T r6 = r4 * r2; const T r8 = r6 * r2; const T radial = k1 * r2 + k2 * r4 + k3 * r6 + k4 * r8; *du = u * radial + T(2) * p1 * uv + p2 * (r2 + T(2) * u2) + sx1 * r2; *dv = v * radial + T(2) * p2 * uv + p1 * (r2 + T(2) * v2) + sy1 * r2; } //////////////////////////////////////////////////////////////////////////////// void CameraModelWorldToImage(const int model_id, const std::vector& params, const double u, const double v, double* x, double* y) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ CameraModel::WorldToImage(params.data(), u, v, x, y); \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } } void CameraModelImageToWorld(const int model_id, const std::vector& params, const double x, const double y, double* u, double* v) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ CameraModel::ImageToWorld(params.data(), x, y, u, v); \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } } double CameraModelImageToWorldThreshold(const int model_id, const std::vector& params, const double threshold) { switch (model_id) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ return CameraModel::ImageToWorldThreshold(params.data(), threshold); \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } return -1; } } // namespace colmap #endif // COLMAP_SRC_BASE_CAMERA_MODELS_H_ colmap-3.4/src/base/camera_models_test.cc000077500000000000000000000173251323400541200205020ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/camera_models" #include "util/testing.h" #include "base/camera_models.h" using namespace colmap; template void TestWorldToImageToWorld(const std::vector params, const double u0, const double v0) { double u, v, x, y, xx, yy; CameraModel::WorldToImage(params.data(), u0, v0, &x, &y); CameraModelWorldToImage(CameraModel::model_id, params, u0, v0, &xx, &yy); BOOST_CHECK_EQUAL(x, xx); BOOST_CHECK_EQUAL(y, yy); CameraModel::ImageToWorld(params.data(), x, y, &u, &v); BOOST_CHECK_LT(std::abs(u - u0), 1e-6); BOOST_CHECK_LT(std::abs(v - v0), 1e-6); } template void TestImageToWorldToImage(const std::vector params, const double x0, const double y0) { double u, v, x, y, uu, vv; CameraModel::ImageToWorld(params.data(), x0, y0, &u, &v); CameraModelImageToWorld(CameraModel::model_id, params, x0, y0, &uu, &vv); BOOST_CHECK_EQUAL(u, uu); BOOST_CHECK_EQUAL(v, vv); CameraModel::WorldToImage(params.data(), u, v, &x, &y); BOOST_CHECK_LT(std::abs(x - x0), 1e-6); BOOST_CHECK_LT(std::abs(y - y0), 1e-6); } template void TestModel(const std::vector& params) { BOOST_CHECK(CameraModelVerifyParams(CameraModel::model_id, params)); const std::vector default_params = CameraModelInitializeParams(CameraModel::model_id, 100, 100, 100); BOOST_CHECK(CameraModelVerifyParams(CameraModel::model_id, default_params)); BOOST_CHECK_EQUAL(CameraModelParamsInfo(CameraModel::model_id), CameraModel::params_info); BOOST_CHECK_EQUAL(&CameraModelFocalLengthIdxs(CameraModel::model_id), &CameraModel::focal_length_idxs); BOOST_CHECK_EQUAL(&CameraModelPrincipalPointIdxs(CameraModel::model_id), &CameraModel::principal_point_idxs); BOOST_CHECK_EQUAL(&CameraModelExtraParamsIdxs(CameraModel::model_id), &CameraModel::extra_params_idxs); BOOST_CHECK_EQUAL(CameraModelNumParams(CameraModel::model_id), CameraModel::num_params); BOOST_CHECK(!CameraModelHasBogusParams(CameraModel::model_id, default_params, 100, 100, 0.1, 2.0, 1.0)); BOOST_CHECK(CameraModelHasBogusParams(CameraModel::model_id, default_params, 100, 100, 0.1, 0.5, 1.0)); BOOST_CHECK(CameraModelHasBogusParams(CameraModel::model_id, default_params, 100, 100, 1.5, 2.0, 1.0)); if (CameraModel::extra_params_idxs.size() > 0) { BOOST_CHECK(CameraModelHasBogusParams(CameraModel::model_id, default_params, 100, 100, 0.1, 2.0, -0.1)); } BOOST_CHECK_EQUAL( CameraModelImageToWorldThreshold(CameraModel::model_id, params, 0), 0); BOOST_CHECK_GT( CameraModelImageToWorldThreshold(CameraModel::model_id, params, 1), 0); BOOST_CHECK_EQUAL(CameraModelImageToWorldThreshold(CameraModel::model_id, default_params, 1), 1.0 / 100.0); BOOST_CHECK(ExistsCameraModelWithName(CameraModel::model_name)); BOOST_CHECK(!ExistsCameraModelWithName(CameraModel::model_name + "FOO")); BOOST_CHECK(ExistsCameraModelWithId(CameraModel::model_id)); BOOST_CHECK(!ExistsCameraModelWithId(CameraModel::model_id + 123456789)); BOOST_CHECK_EQUAL( CameraModelNameToId(CameraModelIdToName(CameraModel::model_id)), CameraModel::model_id); BOOST_CHECK_EQUAL( CameraModelIdToName(CameraModelNameToId(CameraModel::model_name)), CameraModel::model_name); for (double u = -0.5; u <= 0.5; u += 0.1) { for (double v = -0.5; v <= 0.5; v += 0.1) { TestWorldToImageToWorld(params, u, v); } } for (double x = 0; x <= 800; x += 50) { for (double y = 0; y <= 800; y += 50) { TestImageToWorldToImage(params, x, y); } } const auto pp_idxs = CameraModel::principal_point_idxs; TestImageToWorldToImage(params, params[pp_idxs.at(0)], params[pp_idxs.at(1)]); } BOOST_AUTO_TEST_CASE(TestSimplePinhole) { std::vector params = {655.123, 386.123, 511.123}; TestModel(params); } BOOST_AUTO_TEST_CASE(TestPinhole) { std::vector params = {651.123, 655.123, 386.123, 511.123}; TestModel(params); } BOOST_AUTO_TEST_CASE(TestSimpleRadial) { std::vector params = {651.123, 386.123, 511.123, 0}; TestModel(params); params[3] = 0.1; TestModel(params); } BOOST_AUTO_TEST_CASE(TestRadial) { std::vector params = {651.123, 386.123, 511.123, 0, 0}; TestModel(params); params[3] = 0.1; TestModel(params); params[3] = 0.05; TestModel(params); params[4] = 0.03; TestModel(params); } BOOST_AUTO_TEST_CASE(TestOpenCV) { std::vector params = {651.123, 655.123, 386.123, 511.123, -0.471, 0.223, -0.001, 0.001}; TestModel(params); } BOOST_AUTO_TEST_CASE(TestOpenCVFisheye) { std::vector params = {651.123, 655.123, 386.123, 511.123, -0.471, 0.223, -0.001, 0.001}; TestModel(params); } BOOST_AUTO_TEST_CASE(TestFullOpenCV) { std::vector params = {651.123, 655.123, 386.123, 511.123, -0.471, 0.223, -0.001, 0.001, 0.001, 0.02, -0.02, 0.001}; TestModel(params); } BOOST_AUTO_TEST_CASE(TestFOV) { std::vector params = {651.123, 655.123, 386.123, 511.123, 0.9}; TestModel(params); params[4] = 0; TestModel(params); params[4] = 1e-6; TestModel(params); params[4] = 1e-2; TestModel(params); BOOST_CHECK_EQUAL( CameraModelInitializeParams(FOVCameraModel::model_id, 100, 100, 100) .back(), 1e-2); } BOOST_AUTO_TEST_CASE(TestSimpleRadialFisheye) { std::vector params = {651.123, 386.123, 511.123, 0}; TestModel(params); params[3] = 0.1; TestModel(params); } BOOST_AUTO_TEST_CASE(TestRadialFisheye) { std::vector params = {651.123, 386.123, 511.123, 0, 0}; TestModel(params); params[3] = 0.1; TestModel(params); params[3] = 0.05; TestModel(params); params[4] = 0.03; TestModel(params); } BOOST_AUTO_TEST_CASE(TestThinPrismFisheye) { std::vector params = {651.123, 655.123, 386.123, 511.123, -0.471, 0.223, -0.001, 0.001, 0.001, 0.02, -0.02, 0.001}; TestModel(params); } colmap-3.4/src/base/camera_rig.cc000066400000000000000000000202361323400541200167310ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/camera_rig.h" #include "util/misc.h" namespace colmap { CameraRig::CameraRig() {} size_t CameraRig::NumCameras() const { return rig_cameras_.size(); } size_t CameraRig::NumSnapshots() const { return snapshots_.size(); } bool CameraRig::HasCamera(const camera_t camera_id) const { return rig_cameras_.count(camera_id); } camera_t CameraRig::RefCameraId() const { return ref_camera_id_; } void CameraRig::SetRefCameraId(const camera_t camera_id) { CHECK(HasCamera(camera_id)); ref_camera_id_ = camera_id; } std::vector CameraRig::GetCameraIds() const { std::vector rig_camera_ids; rig_camera_ids.reserve(NumCameras()); for (const auto& rig_camera : rig_cameras_) { rig_camera_ids.push_back(rig_camera.first); } return rig_camera_ids; } const std::vector>& CameraRig::Snapshots() const { return snapshots_; } void CameraRig::AddCamera(const camera_t camera_id, const Eigen::Vector4d& rel_qvec, const Eigen::Vector3d& rel_tvec) { CHECK(!HasCamera(camera_id)); CHECK_EQ(NumSnapshots(), 0); RigCamera rig_camera; rig_camera.rel_qvec = rel_qvec; rig_camera.rel_tvec = rel_tvec; rig_cameras_.emplace(camera_id, rig_camera); } void CameraRig::AddSnapshot(const std::vector& image_ids) { CHECK(!image_ids.empty()); CHECK_LE(image_ids.size(), NumCameras()); CHECK(!VectorContainsDuplicateValues(image_ids)); snapshots_.push_back(image_ids); } void CameraRig::Check(const Reconstruction& reconstruction) const { CHECK(HasCamera(ref_camera_id_)); for (const auto& rig_camera : rig_cameras_) { CHECK(reconstruction.ExistsCamera(rig_camera.first)); } std::unordered_set all_image_ids; for (const auto& snapshot : snapshots_) { CHECK(!snapshot.empty()); CHECK_LE(snapshot.size(), NumCameras()); bool has_ref_camera = false; for (const auto image_id : snapshot) { CHECK(reconstruction.ExistsImage(image_id)); CHECK_EQ(all_image_ids.count(image_id), 0); all_image_ids.insert(image_id); const auto& image = reconstruction.Image(image_id); CHECK(HasCamera(image.CameraId())); if (image.CameraId() == ref_camera_id_) { has_ref_camera = true; } } CHECK(has_ref_camera); } } Eigen::Vector4d& CameraRig::RelativeQvec(const camera_t camera_id) { return rig_cameras_.at(camera_id).rel_qvec; } const Eigen::Vector4d& CameraRig::RelativeQvec(const camera_t camera_id) const { return rig_cameras_.at(camera_id).rel_qvec; } Eigen::Vector3d& CameraRig::RelativeTvec(const camera_t camera_id) { return rig_cameras_.at(camera_id).rel_tvec; } const Eigen::Vector3d& CameraRig::RelativeTvec(const camera_t camera_id) const { return rig_cameras_.at(camera_id).rel_tvec; } double CameraRig::ComputeScale(const Reconstruction& reconstruction) const { CHECK_GT(NumSnapshots(), 0); CHECK_GT(NumCameras(), 0); double scaling_factor = 0; size_t num_dists = 0; std::vector rel_proj_centers(NumCameras()); std::vector abs_proj_centers(NumCameras()); for (const auto& snapshot : snapshots_) { // Compute the projection relative and absolute projection centers. for (size_t i = 0; i < NumCameras(); ++i) { const auto& image = reconstruction.Image(snapshot[i]); rel_proj_centers[i] = ProjectionCenterFromParameters( RelativeQvec(image.CameraId()), RelativeTvec(image.CameraId())); abs_proj_centers[i] = image.ProjectionCenter(); } // Accumulate the scaling factor for all pairs of camera distances. for (size_t i = 0; i < NumCameras(); ++i) { for (size_t j = 0; j < i; ++j) { const double rel_dist = (rel_proj_centers[i] - rel_proj_centers[j]).norm(); const double abs_dist = (abs_proj_centers[i] - abs_proj_centers[j]).norm(); const double kMinDist = 1e-6; if (rel_dist > kMinDist && abs_dist > kMinDist) { scaling_factor += rel_dist / abs_dist; num_dists += 1; } } } } if (num_dists == 0) { return std::numeric_limits::quiet_NaN(); } return scaling_factor / num_dists; } void CameraRig::ComputeRelativePoses(const Reconstruction& reconstruction) { CHECK_GT(NumSnapshots(), 0); CHECK_NE(ref_camera_id_, kInvalidCameraId); for (auto& rig_camera : rig_cameras_) { rig_camera.second.rel_tvec = Eigen::Vector3d::Zero(); } EIGEN_STL_UMAP(camera_t, std::vector) rel_qvecs; for (const auto& snapshot : snapshots_) { // Find the image of the reference camera in the current snapshot. const Image* ref_image = nullptr; for (const auto image_id : snapshot) { const auto& image = reconstruction.Image(image_id); if (image.CameraId() == ref_camera_id_) { ref_image = ℑ } } CHECK_NOTNULL(ref_image); // Compute the relative poses from all cameras in the current snapshot to // the reference camera. for (const auto image_id : snapshot) { const auto& image = reconstruction.Image(image_id); if (image.CameraId() != ref_camera_id_) { Eigen::Vector4d rel_qvec; Eigen::Vector3d rel_tvec; ComputeRelativePose(ref_image->Qvec(), ref_image->Tvec(), image.Qvec(), image.Tvec(), &rel_qvec, &rel_tvec); rel_qvecs[image.CameraId()].push_back(rel_qvec); RelativeTvec(image.CameraId()) += rel_tvec; } } } RelativeQvec(ref_camera_id_) = ComposeIdentityQuaternion(); RelativeTvec(ref_camera_id_) = Eigen::Vector3d(0, 0, 0); // Compute the average relative poses. for (auto& rig_camera : rig_cameras_) { if (rig_camera.first != ref_camera_id_) { CHECK_GT(rel_qvecs.count(rig_camera.first), 0) << "Need at least one snapshot with an image of camera " << rig_camera.first << " and the reference camera " << ref_camera_id_ << " to compute its relative pose in the camera rig"; const std::vector& camera_rel_qvecs = rel_qvecs.at(rig_camera.first); const std::vector rel_qvec_weights(camera_rel_qvecs.size(), 1.0); rig_camera.second.rel_qvec = AverageQuaternions(camera_rel_qvecs, rel_qvec_weights); rig_camera.second.rel_tvec /= camera_rel_qvecs.size(); } } } void CameraRig::ComputeAbsolutePose(const size_t snapshot_idx, const Reconstruction& reconstruction, Eigen::Vector4d* abs_qvec, Eigen::Vector3d* abs_tvec) const { const auto& snapshot = snapshots_.at(snapshot_idx); std::vector abs_qvecs; *abs_tvec = Eigen::Vector3d::Zero(); for (const auto image_id : snapshot) { const auto& image = reconstruction.Image(image_id); Eigen::Vector4d inv_rel_qvec; Eigen::Vector3d inv_rel_tvec; InvertPose(RelativeQvec(image.CameraId()), RelativeTvec(image.CameraId()), &inv_rel_qvec, &inv_rel_tvec); const Eigen::Vector4d qvec = ConcatenateQuaternions(image.Qvec(), inv_rel_qvec); const Eigen::Vector3d tvec = QuaternionRotatePoint( inv_rel_qvec, image.Tvec() - RelativeTvec(image.CameraId())); abs_qvecs.push_back(qvec); *abs_tvec += tvec; } const std::vector abs_qvec_weights(snapshot.size(), 1); *abs_qvec = AverageQuaternions(abs_qvecs, abs_qvec_weights); *abs_tvec /= snapshot.size(); } } // namespace colmap colmap-3.4/src/base/camera_rig.h000066400000000000000000000110371323400541200165720ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_CAMERA_RIG_H_ #define COLMAP_SRC_BASE_CAMERA_RIG_H_ #include #include #include "base/camera.h" #include "base/pose.h" #include "base/reconstruction.h" #include "util/alignment.h" #include "util/types.h" namespace colmap { // This class holds information about the relative configuration of camera rigs. // Camera rigs are composed of multiple cameras with a rigid relative extrinsic // configuration over multiple snapshots. Snapshots are defined as the // collection of images captured simultaneously by all cameras in the rig. class CameraRig { public: CameraRig(); // The number of cameras in the rig. size_t NumCameras() const; // The number of snapshots captured by this rig. size_t NumSnapshots() const; // Check whether the given camera is part of the rig. bool HasCamera(const camera_t camera_id) const; // Access the reference camera. camera_t RefCameraId() const; void SetRefCameraId(const camera_t camera_id); // Get the identifiers of the cameras in the rig. std::vector GetCameraIds() const; // Get the snapshots of the camera rig. const std::vector>& Snapshots() const; // Add a new camera to the rig. The relative pose may contain dummy values and // can then be computed automatically from a given reconstruction using the // method `ComputeRelativePoses`. void AddCamera(const camera_t camera_id, const Eigen::Vector4d& rel_qvec, const Eigen::Vector3d& rel_tvec); // Add the images of a single snapshot to rig. A snapshot consists of the // captured images of all cameras of the rig. All images of a snapshot share // the same global camera rig pose, i.e. all images in the camera rig are // captured simultaneously. void AddSnapshot(const std::vector& image_ids); // Check whether the camera rig setup is valid. void Check(const Reconstruction& reconstruction) const; // Get the relative poses of the cameras in the rig. Eigen::Vector4d& RelativeQvec(const camera_t camera_id); const Eigen::Vector4d& RelativeQvec(const camera_t camera_id) const; Eigen::Vector3d& RelativeTvec(const camera_t camera_id); const Eigen::Vector3d& RelativeTvec(const camera_t camera_id) const; // Compute the scaling factor from the reconstruction to the camera rig // dimensions by averaging over the distances between the projection centers. // Note that this assumes that there is at least one camera pair in the rig // with non-zero baseline, otherwise the function returns NaN. double ComputeScale(const Reconstruction& reconstruction) const; // Compute the relative poses in the rig from the reconstruction by averaging // the relative poses over all snapshots. The pose of the reference camera // will be the identity transformation. This assumes that the camera rig has // snapshots that are registered in the reconstruction. void ComputeRelativePoses(const Reconstruction& reconstruction); // Compute the absolute camera pose of the rig. The absolute camera pose of // the rig is computed as the average of all relative camera poses in the rig // and their corresponding image poses in the reconstruction. void ComputeAbsolutePose(const size_t snapshot_idx, const Reconstruction& reconstruction, Eigen::Vector4d* abs_qvec, Eigen::Vector3d* abs_tvec) const; private: struct RigCamera { EIGEN_MAKE_ALIGNED_OPERATOR_NEW Eigen::Vector4d rel_qvec = ComposeIdentityQuaternion(); Eigen::Vector3d rel_tvec = Eigen::Vector3d(0, 0, 0); }; camera_t ref_camera_id_ = kInvalidCameraId; EIGEN_STL_UMAP(camera_t, RigCamera) rig_cameras_; std::vector> snapshots_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_CAMERA_RIG_H_ colmap-3.4/src/base/camera_rig_test.cc000066400000000000000000000260071323400541200177720ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/camera_rig" #include "util/testing.h" #include "base/camera_rig.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEmpty) { CameraRig camera_rig; BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 0); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 0); BOOST_CHECK_EQUAL(camera_rig.GetCameraIds().size(), 0); BOOST_CHECK_EQUAL(camera_rig.HasCamera(0), false); } BOOST_AUTO_TEST_CASE(TestAddCamera) { CameraRig camera_rig; BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 0); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 0); BOOST_CHECK_EQUAL(camera_rig.GetCameraIds().size(), 0); BOOST_CHECK_EQUAL(camera_rig.HasCamera(0), false); camera_rig.AddCamera(0, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2)); BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 1); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 0); BOOST_CHECK_EQUAL(camera_rig.GetCameraIds().size(), 1); BOOST_CHECK_EQUAL(camera_rig.GetCameraIds()[0], 0); BOOST_CHECK_EQUAL(camera_rig.HasCamera(0), true); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(0), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(0), Eigen::Vector3d(0, 1, 2)); camera_rig.AddCamera(1, ComposeIdentityQuaternion(), Eigen::Vector3d(3, 4, 5)); BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 2); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 0); BOOST_CHECK_EQUAL(camera_rig.GetCameraIds().size(), 2); BOOST_CHECK_EQUAL(camera_rig.HasCamera(0), true); BOOST_CHECK_EQUAL(camera_rig.HasCamera(1), true); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(1), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(1), Eigen::Vector3d(3, 4, 5)); } BOOST_AUTO_TEST_CASE(TestAddSnapshot) { CameraRig camera_rig; BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 0); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 0); BOOST_CHECK_EQUAL(camera_rig.GetCameraIds().size(), 0); BOOST_CHECK_EQUAL(camera_rig.Snapshots().size(), 0); camera_rig.AddCamera(0, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2)); camera_rig.AddCamera(1, ComposeIdentityQuaternion(), Eigen::Vector3d(3, 4, 5)); BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 2); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 0); BOOST_CHECK_EQUAL(camera_rig.Snapshots().size(), 0); const std::vector image_ids1 = {0, 1}; camera_rig.AddSnapshot(image_ids1); BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 2); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 1); BOOST_CHECK_EQUAL(camera_rig.Snapshots().size(), 1); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[0].size(), 2); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[0][0], 0); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[0][1], 1); const std::vector image_ids2 = {2, 3}; camera_rig.AddSnapshot(image_ids2); BOOST_CHECK_EQUAL(camera_rig.NumCameras(), 2); BOOST_CHECK_EQUAL(camera_rig.NumSnapshots(), 2); BOOST_CHECK_EQUAL(camera_rig.Snapshots().size(), 2); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[0].size(), 2); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[0][0], 0); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[0][1], 1); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[1].size(), 2); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[1][0], 2); BOOST_CHECK_EQUAL(camera_rig.Snapshots()[1][1], 3); } BOOST_AUTO_TEST_CASE(TestCheck) { CameraRig camera_rig; camera_rig.AddCamera(0, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2)); camera_rig.AddCamera(1, ComposeIdentityQuaternion(), Eigen::Vector3d(3, 4, 5)); const std::vector image_ids1 = {0, 1}; camera_rig.AddSnapshot(image_ids1); const std::vector image_ids2 = {2, 3}; camera_rig.AddSnapshot(image_ids2); Reconstruction reconstruction; Camera camera1; camera1.SetCameraId(0); camera1.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera1); Camera camera2; camera2.SetCameraId(1); camera2.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera2); Image image1; image1.SetImageId(0); image1.SetCameraId(camera1.CameraId()); reconstruction.AddImage(image1); Image image2; image2.SetImageId(1); image2.SetCameraId(camera2.CameraId()); reconstruction.AddImage(image2); Image image3; image3.SetImageId(2); image3.SetCameraId(camera1.CameraId()); reconstruction.AddImage(image3); Image image4; image4.SetImageId(3); image4.SetCameraId(camera2.CameraId()); reconstruction.AddImage(image4); camera_rig.SetRefCameraId(0); camera_rig.Check(reconstruction); } BOOST_AUTO_TEST_CASE(TestComputeScale) { CameraRig camera_rig; camera_rig.AddCamera(0, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0)); camera_rig.AddCamera(1, ComposeIdentityQuaternion(), Eigen::Vector3d(2, 4, 6)); const std::vector image_ids1 = {0, 1}; camera_rig.AddSnapshot(image_ids1); Reconstruction reconstruction; Camera camera1; camera1.SetCameraId(0); camera1.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera1); Camera camera2; camera2.SetCameraId(1); camera2.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera2); Image image1; image1.SetImageId(0); image1.SetCameraId(camera1.CameraId()); image1.SetQvec(ComposeIdentityQuaternion()); image1.SetTvec(Eigen::Vector3d(0, 0, 0)); reconstruction.AddImage(image1); Image image2; image2.SetImageId(1); image2.SetCameraId(camera2.CameraId()); image2.SetQvec(ComposeIdentityQuaternion()); image2.SetTvec(Eigen::Vector3d(1, 2, 3)); reconstruction.AddImage(image2); camera_rig.SetRefCameraId(0); camera_rig.Check(reconstruction); BOOST_CHECK_EQUAL(camera_rig.ComputeScale(reconstruction), 2.0); reconstruction.Image(1).SetTvec(Eigen::Vector3d(0, 0, 0)); BOOST_CHECK(IsNaN(camera_rig.ComputeScale(reconstruction))); } BOOST_AUTO_TEST_CASE(TestComputeRelativePoses) { CameraRig camera_rig; camera_rig.AddCamera(0, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0)); camera_rig.AddCamera(1, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0)); const std::vector image_ids1 = {0, 1}; camera_rig.AddSnapshot(image_ids1); Reconstruction reconstruction; Camera camera1; camera1.SetCameraId(0); camera1.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera1); Camera camera2; camera2.SetCameraId(1); camera2.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera2); Image image1; image1.SetImageId(0); image1.SetCameraId(camera1.CameraId()); image1.SetQvec(ComposeIdentityQuaternion()); image1.SetTvec(Eigen::Vector3d(0, 0, 0)); reconstruction.AddImage(image1); Image image2; image2.SetImageId(1); image2.SetCameraId(camera2.CameraId()); image2.SetQvec(ComposeIdentityQuaternion()); image2.SetTvec(Eigen::Vector3d(1, 2, 3)); reconstruction.AddImage(image2); camera_rig.SetRefCameraId(0); camera_rig.Check(reconstruction); camera_rig.ComputeRelativePoses(reconstruction); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(0), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(0), Eigen::Vector3d(0, 0, 0)); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(1), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(1), Eigen::Vector3d(1, 2, 3)); const std::vector image_ids2 = {2, 3}; camera_rig.AddSnapshot(image_ids2); Image image3; image3.SetImageId(2); image3.SetCameraId(camera1.CameraId()); image3.SetQvec(ComposeIdentityQuaternion()); image3.SetTvec(Eigen::Vector3d(0, 0, 0)); reconstruction.AddImage(image3); Image image4; image4.SetImageId(3); image4.SetCameraId(camera2.CameraId()); image4.SetQvec(ComposeIdentityQuaternion()); image4.SetTvec(Eigen::Vector3d(2, 4, 6)); reconstruction.AddImage(image4); camera_rig.Check(reconstruction); camera_rig.ComputeRelativePoses(reconstruction); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(0), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(0), Eigen::Vector3d(0, 0, 0)); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(1), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(1), Eigen::Vector3d(1.5, 3, 4.5)); const std::vector image_ids3 = {4}; camera_rig.AddSnapshot(image_ids3); Image image5; image5.SetImageId(4); image5.SetCameraId(camera1.CameraId()); image5.SetQvec(ComposeIdentityQuaternion()); image5.SetTvec(Eigen::Vector3d(0, 0, 0)); reconstruction.AddImage(image5); camera_rig.Check(reconstruction); camera_rig.ComputeRelativePoses(reconstruction); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(0), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(0), Eigen::Vector3d(0, 0, 0)); BOOST_CHECK_EQUAL(camera_rig.RelativeQvec(1), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(camera_rig.RelativeTvec(1), Eigen::Vector3d(1.5, 3, 4.5)); } BOOST_AUTO_TEST_CASE(TestComputeAbsolutePose) { CameraRig camera_rig; camera_rig.AddCamera(0, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2)); camera_rig.AddCamera(1, ComposeIdentityQuaternion(), Eigen::Vector3d(3, 4, 5)); const std::vector image_ids1 = {0, 1}; camera_rig.AddSnapshot(image_ids1); Reconstruction reconstruction; Camera camera1; camera1.SetCameraId(0); camera1.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera1); Camera camera2; camera2.SetCameraId(1); camera2.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction.AddCamera(camera2); Image image1; image1.SetImageId(0); image1.SetCameraId(camera1.CameraId()); image1.SetQvec(ComposeIdentityQuaternion()); image1.SetTvec(Eigen::Vector3d(0, 0, 0)); reconstruction.AddImage(image1); Image image2; image2.SetImageId(1); image2.SetCameraId(camera2.CameraId()); image2.SetQvec(ComposeIdentityQuaternion()); image2.SetTvec(Eigen::Vector3d(3, 3, 3)); reconstruction.AddImage(image2); camera_rig.SetRefCameraId(0); camera_rig.Check(reconstruction); Eigen::Vector4d abs_qvec; Eigen::Vector3d abs_tvec; camera_rig.ComputeAbsolutePose(0, reconstruction, &abs_qvec, &abs_tvec); BOOST_CHECK_EQUAL(abs_qvec, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(abs_tvec, Eigen::Vector3d(0, -1, -2)); } colmap-3.4/src/base/camera_test.cc000077500000000000000000000323021323400541200171270ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/camera" #include "util/testing.h" #include "base/camera.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEmpty) { Camera camera; BOOST_CHECK_EQUAL(camera.CameraId(), kInvalidCameraId); BOOST_CHECK_EQUAL(camera.ModelId(), kInvalidCameraModelId); BOOST_CHECK_EQUAL(camera.ModelName(), ""); BOOST_CHECK_EQUAL(camera.Width(), 0); BOOST_CHECK_EQUAL(camera.Height(), 0); BOOST_CHECK_EQUAL(camera.HasPriorFocalLength(), false); BOOST_CHECK_THROW(camera.FocalLengthIdxs(), std::domain_error); BOOST_CHECK_THROW(camera.ParamsInfo(), std::domain_error); BOOST_CHECK_EQUAL(camera.ParamsToString(), ""); BOOST_CHECK_EQUAL(camera.NumParams(), 0); BOOST_CHECK_EQUAL(camera.Params().size(), 0); BOOST_CHECK_EQUAL(camera.ParamsData(), camera.Params().data()); } BOOST_AUTO_TEST_CASE(TestCameraId) { Camera camera; BOOST_CHECK_EQUAL(camera.CameraId(), kInvalidCameraId); camera.SetCameraId(1); BOOST_CHECK_EQUAL(camera.CameraId(), 1); } BOOST_AUTO_TEST_CASE(TestModelId) { Camera camera; BOOST_CHECK_EQUAL(camera.ModelId(), kInvalidCameraModelId); BOOST_CHECK_EQUAL(camera.ModelName(), ""); camera.SetModelId(SimplePinholeCameraModel::model_id); BOOST_CHECK_EQUAL(camera.ModelId(), static_cast(SimplePinholeCameraModel::model_id)); BOOST_CHECK_EQUAL(camera.ModelName(), "SIMPLE_PINHOLE"); BOOST_CHECK_EQUAL(camera.NumParams(), SimplePinholeCameraModel::num_params); camera.SetModelIdFromName("SIMPLE_RADIAL"); BOOST_CHECK_EQUAL(camera.ModelId(), static_cast(SimpleRadialCameraModel::model_id)); BOOST_CHECK_EQUAL(camera.ModelName(), "SIMPLE_RADIAL"); BOOST_CHECK_EQUAL(camera.NumParams(), SimpleRadialCameraModel::num_params); } BOOST_AUTO_TEST_CASE(TestWidthHeight) { Camera camera; BOOST_CHECK_EQUAL(camera.Width(), 0); BOOST_CHECK_EQUAL(camera.Height(), 0); camera.SetWidth(1); BOOST_CHECK_EQUAL(camera.Width(), 1); BOOST_CHECK_EQUAL(camera.Height(), 0); camera.SetHeight(1); BOOST_CHECK_EQUAL(camera.Width(), 1); BOOST_CHECK_EQUAL(camera.Height(), 1); } BOOST_AUTO_TEST_CASE(TestFocalLength) { Camera camera; camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.FocalLength(), 1.0); camera.SetFocalLength(2.0); BOOST_CHECK_EQUAL(camera.FocalLength(), 2.0); camera.InitializeWithId(PinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.FocalLengthX(), 1.0); BOOST_CHECK_EQUAL(camera.FocalLengthY(), 1.0); camera.SetFocalLengthX(2.0); BOOST_CHECK_EQUAL(camera.FocalLengthX(), 2.0); BOOST_CHECK_EQUAL(camera.FocalLengthY(), 1.0); camera.SetFocalLengthY(2.0); BOOST_CHECK_EQUAL(camera.FocalLengthX(), 2.0); BOOST_CHECK_EQUAL(camera.FocalLengthY(), 2.0); } BOOST_AUTO_TEST_CASE(TestPriorFocalLength) { Camera camera; BOOST_CHECK_EQUAL(camera.HasPriorFocalLength(), false); camera.SetPriorFocalLength(true); BOOST_CHECK_EQUAL(camera.HasPriorFocalLength(), true); camera.SetPriorFocalLength(false); BOOST_CHECK_EQUAL(camera.HasPriorFocalLength(), false); } BOOST_AUTO_TEST_CASE(TestPrincipalPoint) { Camera camera; camera.InitializeWithId(PinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 0.5); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 0.5); camera.SetPrincipalPointX(2.0); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 2.0); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 0.5); camera.SetPrincipalPointY(2.0); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 2.0); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 2.0); } BOOST_AUTO_TEST_CASE(TestParamIdxs) { Camera camera; BOOST_CHECK_THROW(camera.FocalLengthIdxs(), std::domain_error); BOOST_CHECK_THROW(camera.PrincipalPointIdxs(), std::domain_error); BOOST_CHECK_THROW(camera.ExtraParamsIdxs(), std::domain_error); camera.SetModelId(FullOpenCVCameraModel::model_id); BOOST_CHECK_EQUAL(camera.FocalLengthIdxs().size(), 2); BOOST_CHECK_EQUAL(camera.PrincipalPointIdxs().size(), 2); BOOST_CHECK_EQUAL(camera.ExtraParamsIdxs().size(), 8); } BOOST_AUTO_TEST_CASE(TestCalibrationMatrix) { Camera camera; camera.InitializeWithId(PinholeCameraModel::model_id, 1.0, 1, 1); const Eigen::Matrix3d K = camera.CalibrationMatrix(); Eigen::Matrix3d K_ref; K_ref << 1, 0, 0.5, 0, 1, 0.5, 0, 0, 1; BOOST_CHECK_EQUAL(K, K_ref); } BOOST_AUTO_TEST_CASE(TestParamsInfo) { Camera camera; BOOST_CHECK_THROW(camera.ParamsInfo(), std::domain_error); camera.SetModelId(SimpleRadialCameraModel::model_id); BOOST_CHECK_EQUAL(camera.ParamsInfo(), "f, cx, cy, k"); } BOOST_AUTO_TEST_CASE(TestParams) { Camera camera; BOOST_CHECK_EQUAL(camera.NumParams(), 0); BOOST_CHECK_EQUAL(camera.Params().size(), camera.NumParams()); camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.NumParams(), 3); BOOST_CHECK_EQUAL(camera.Params().size(), camera.NumParams()); BOOST_CHECK_EQUAL(camera.ParamsData(), camera.Params().data()); BOOST_CHECK_EQUAL(camera.Params(0), 1.0); BOOST_CHECK_EQUAL(camera.Params(1), 0.5); BOOST_CHECK_EQUAL(camera.Params(2), 0.5); BOOST_CHECK_EQUAL(camera.Params()[0], 1.0); BOOST_CHECK_EQUAL(camera.Params()[1], 0.5); BOOST_CHECK_EQUAL(camera.Params()[2], 0.5); camera.SetParams({2.0, 1.0, 1.0}); BOOST_CHECK_EQUAL(camera.Params(0), 2.0); BOOST_CHECK_EQUAL(camera.Params(1), 1.0); BOOST_CHECK_EQUAL(camera.Params(2), 1.0); } BOOST_AUTO_TEST_CASE(TestParamsToString) { Camera camera; camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.ParamsToString(), "1.000000, 0.500000, 0.500000"); } BOOST_AUTO_TEST_CASE(TestParamsFromString) { Camera camera; camera.SetModelId(SimplePinholeCameraModel::model_id); camera.SetParamsFromString("1.000000, 0.500000, 0.500000"); const std::vector params{1.0, 0.5, 0.5}; BOOST_CHECK_EQUAL_COLLECTIONS(camera.Params().begin(), camera.Params().end(), params.begin(), params.end()); } BOOST_AUTO_TEST_CASE(TestVerifyParams) { Camera camera; BOOST_CHECK_THROW(camera.VerifyParams(), std::domain_error); camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.VerifyParams(), true); camera.Params().resize(2); BOOST_CHECK_EQUAL(camera.VerifyParams(), false); } BOOST_AUTO_TEST_CASE(TestHasBogusParams) { Camera camera; BOOST_CHECK_THROW(camera.HasBogusParams(0.0, 0.0, 0.0), std::domain_error); camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 1.1, 1.0), false); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 1.1, 0.0), false); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 0.99, 1.0), true); BOOST_CHECK_EQUAL(camera.HasBogusParams(1.01, 1.1, 1.0), true); camera.InitializeWithId(SimpleRadialCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 1.1, 1.0), false); camera.Params(3) = 1.01; BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 1.1, 1.0), true); camera.Params(3) = -0.5; BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 1.1, 1.0), false); camera.Params(3) = -1.01; BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 1.1, 1.0), true); } BOOST_AUTO_TEST_CASE(TestInitializeWithId) { Camera camera; camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.CameraId(), kInvalidCameraId); BOOST_CHECK_EQUAL(camera.ModelId(), static_cast(SimplePinholeCameraModel::model_id)); BOOST_CHECK_EQUAL(camera.ModelName(), "SIMPLE_PINHOLE"); BOOST_CHECK_EQUAL(camera.Width(), 1); BOOST_CHECK_EQUAL(camera.Height(), 1); BOOST_CHECK_EQUAL(camera.HasPriorFocalLength(), false); BOOST_CHECK_EQUAL(camera.FocalLengthIdxs().size(), 1); BOOST_CHECK_EQUAL(camera.PrincipalPointIdxs().size(), 2); BOOST_CHECK_EQUAL(camera.ExtraParamsIdxs().size(), 0); BOOST_CHECK_EQUAL(camera.ParamsInfo(), "f, cx, cy"); BOOST_CHECK_EQUAL(camera.ParamsToString(), "1.000000, 0.500000, 0.500000"); BOOST_CHECK_EQUAL(camera.FocalLength(), 1.0); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 0.5); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 0.5); BOOST_CHECK_EQUAL(camera.VerifyParams(), true); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 2.0, 1.0), false); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 0.5, 1.0), true); BOOST_CHECK_EQUAL(camera.NumParams(), static_cast(SimplePinholeCameraModel::num_params)); BOOST_CHECK_EQUAL(camera.Params().size(), static_cast(SimplePinholeCameraModel::num_params)); } BOOST_AUTO_TEST_CASE(TestInitializeWithName) { Camera camera; camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.CameraId(), kInvalidCameraId); BOOST_CHECK_EQUAL(camera.ModelId(), static_cast(SimplePinholeCameraModel::model_id)); BOOST_CHECK_EQUAL(camera.ModelName(), "SIMPLE_PINHOLE"); BOOST_CHECK_EQUAL(camera.Width(), 1); BOOST_CHECK_EQUAL(camera.Height(), 1); BOOST_CHECK_EQUAL(camera.HasPriorFocalLength(), false); BOOST_CHECK_EQUAL(camera.FocalLengthIdxs().size(), 1); BOOST_CHECK_EQUAL(camera.PrincipalPointIdxs().size(), 2); BOOST_CHECK_EQUAL(camera.ExtraParamsIdxs().size(), 0); BOOST_CHECK_EQUAL(camera.ParamsInfo(), "f, cx, cy"); BOOST_CHECK_EQUAL(camera.ParamsToString(), "1.000000, 0.500000, 0.500000"); BOOST_CHECK_EQUAL(camera.FocalLength(), 1.0); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 0.5); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 0.5); BOOST_CHECK_EQUAL(camera.VerifyParams(), true); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 2.0, 1.0), false); BOOST_CHECK_EQUAL(camera.HasBogusParams(0.1, 0.5, 1.0), true); BOOST_CHECK_EQUAL(camera.NumParams(), static_cast(SimplePinholeCameraModel::num_params)); BOOST_CHECK_EQUAL(camera.Params().size(), static_cast(SimplePinholeCameraModel::num_params)); } BOOST_AUTO_TEST_CASE(TestImageToWorld) { Camera camera; BOOST_CHECK_THROW(camera.ImageToWorld(Eigen::Vector2d::Zero()), std::domain_error); camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.ImageToWorld(Eigen::Vector2d(0.0, 0.0))(0), -0.5); BOOST_CHECK_EQUAL(camera.ImageToWorld(Eigen::Vector2d(0.0, 0.0))(1), -0.5); BOOST_CHECK_EQUAL(camera.ImageToWorld(Eigen::Vector2d(0.5, 0.5))(0), 0.0); BOOST_CHECK_EQUAL(camera.ImageToWorld(Eigen::Vector2d(0.5, 0.5))(1), 0.0); } BOOST_AUTO_TEST_CASE(TestImageToWorldThreshold) { Camera camera; BOOST_CHECK_THROW(camera.ImageToWorldThreshold(0), std::domain_error); camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.ImageToWorldThreshold(0), 0); BOOST_CHECK_EQUAL(camera.ImageToWorldThreshold(1), 1); camera.SetFocalLength(2.0); BOOST_CHECK_EQUAL(camera.ImageToWorldThreshold(1), 0.5); camera.InitializeWithName("PINHOLE", 1.0, 1, 1); camera.SetFocalLengthY(3.0); BOOST_CHECK_EQUAL(camera.ImageToWorldThreshold(1), 0.5); } BOOST_AUTO_TEST_CASE(TestWorldToImage) { Camera camera; BOOST_CHECK_THROW(camera.WorldToImage(Eigen::Vector2d::Zero()), std::domain_error); camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); BOOST_CHECK_EQUAL(camera.WorldToImage(Eigen::Vector2d(0.0, 0.0))(0), 0.5); BOOST_CHECK_EQUAL(camera.WorldToImage(Eigen::Vector2d(0.0, 0.0))(1), 0.5); BOOST_CHECK_EQUAL(camera.WorldToImage(Eigen::Vector2d(-0.5, -0.5))(0), 0.0); BOOST_CHECK_EQUAL(camera.WorldToImage(Eigen::Vector2d(-0.5, -0.5))(1), 0.0); } BOOST_AUTO_TEST_CASE(TestRescale) { Camera camera; camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); camera.Rescale(2.0); BOOST_CHECK_EQUAL(camera.Width(), 2); BOOST_CHECK_EQUAL(camera.Height(), 2); BOOST_CHECK_EQUAL(camera.FocalLength(), 2); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 1); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 1); camera.InitializeWithName("PINHOLE", 1.0, 1, 1); camera.Rescale(2.0); BOOST_CHECK_EQUAL(camera.Width(), 2); BOOST_CHECK_EQUAL(camera.Height(), 2); BOOST_CHECK_EQUAL(camera.FocalLengthX(), 2); BOOST_CHECK_EQUAL(camera.FocalLengthY(), 2); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 1); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 1); camera.InitializeWithName("PINHOLE", 1.0, 2, 2); camera.Rescale(0.5); BOOST_CHECK_EQUAL(camera.Width(), 1); BOOST_CHECK_EQUAL(camera.Height(), 1); BOOST_CHECK_EQUAL(camera.FocalLengthX(), 0.5); BOOST_CHECK_EQUAL(camera.FocalLengthY(), 0.5); BOOST_CHECK_EQUAL(camera.PrincipalPointX(), 0.5); BOOST_CHECK_EQUAL(camera.PrincipalPointY(), 0.5); } colmap-3.4/src/base/cost_functions.h000077500000000000000000000206011323400541200175410ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_COST_FUNCTIONS_H_ #define COLMAP_SRC_BASE_COST_FUNCTIONS_H_ #include #include #include namespace colmap { // Standard bundle adjustment cost function for variable // camera pose and calibration and point parameters. template class BundleAdjustmentCostFunction { public: explicit BundleAdjustmentCostFunction(const Eigen::Vector2d& point2D) : x_(point2D(0)), y_(point2D(1)) {} static ceres::CostFunction* Create(const Eigen::Vector2d& point2D) { return (new ceres::AutoDiffCostFunction< BundleAdjustmentCostFunction, 2, 4, 3, 3, CameraModel::kNumParams>( new BundleAdjustmentCostFunction(point2D))); } template bool operator()(const T* const qvec, const T* const tvec, const T* const point3D, const T* const camera_params, T* residuals) const { // Rotate and translate. T projection[3]; ceres::UnitQuaternionRotatePoint(qvec, point3D, projection); projection[0] += tvec[0]; projection[1] += tvec[1]; projection[2] += tvec[2]; // Project to image plane. projection[0] /= projection[2]; projection[1] /= projection[2]; // Distort and transform to pixel space. CameraModel::WorldToImage(camera_params, projection[0], projection[1], &residuals[0], &residuals[1]); // Re-projection error. residuals[0] -= T(x_); residuals[1] -= T(y_); return true; } private: const double x_; const double y_; }; // Bundle adjustment cost function for variable // camera calibration and point parameters, and fixed camera pose. template class BundleAdjustmentConstantPoseCostFunction { public: BundleAdjustmentConstantPoseCostFunction(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, const Eigen::Vector2d& point2D) : qw_(qvec(0)), qx_(qvec(1)), qy_(qvec(2)), qz_(qvec(3)), tx_(tvec(0)), ty_(tvec(1)), tz_(tvec(2)), x_(point2D(0)), y_(point2D(1)) {} static ceres::CostFunction* Create(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, const Eigen::Vector2d& point2D) { return (new ceres::AutoDiffCostFunction< BundleAdjustmentConstantPoseCostFunction, 2, 3, CameraModel::kNumParams>( new BundleAdjustmentConstantPoseCostFunction(qvec, tvec, point2D))); } template bool operator()(const T* const point3D, const T* const camera_params, T* residuals) const { const T qvec[4] = {T(qw_), T(qx_), T(qy_), T(qz_)}; // Rotate and translate. T projection[3]; ceres::UnitQuaternionRotatePoint(qvec, point3D, projection); projection[0] += T(tx_); projection[1] += T(ty_); projection[2] += T(tz_); // Project to image plane. projection[0] /= projection[2]; projection[1] /= projection[2]; // Distort and transform to pixel space. CameraModel::WorldToImage(camera_params, projection[0], projection[1], &residuals[0], &residuals[1]); // Re-projection error. residuals[0] -= T(x_); residuals[1] -= T(y_); return true; } private: double qw_; double qx_; double qy_; double qz_; double tx_; double ty_; double tz_; double x_; double y_; }; // Rig bundle adjustment cost function for variable camera pose and calibration // and point parameters. Different from the standard bundle adjustment function, // this cost function is suitable for camera rigs with consistent relative poses // of the cameras within the rig. The cost function first projects points into // the local system of the camera rig and then into the local system of the // camera within the rig. template class RigBundleAdjustmentCostFunction { public: explicit RigBundleAdjustmentCostFunction(const Eigen::Vector2d& point2D) : x_(point2D(0)), y_(point2D(1)) {} static ceres::CostFunction* Create(const Eigen::Vector2d& point2D) { return (new ceres::AutoDiffCostFunction< RigBundleAdjustmentCostFunction, 2, 4, 3, 4, 3, 3, CameraModel::kNumParams>( new RigBundleAdjustmentCostFunction(point2D))); } template bool operator()(const T* const rig_qvec, const T* const rig_tvec, const T* const rel_qvec, const T* const rel_tvec, const T* const point3D, const T* const camera_params, T* residuals) const { // Concatenate rotations. T qvec[4]; ceres::QuaternionProduct(rel_qvec, rig_qvec, qvec); // Concatenate translations. T tvec[3]; ceres::UnitQuaternionRotatePoint(rel_qvec, rig_tvec, tvec); tvec[0] += rel_tvec[0]; tvec[1] += rel_tvec[1]; tvec[2] += rel_tvec[2]; // Rotate and translate. T projection[3]; ceres::UnitQuaternionRotatePoint(qvec, point3D, projection); projection[0] += tvec[0]; projection[1] += tvec[1]; projection[2] += tvec[2]; // Project to image plane. projection[0] /= projection[2]; projection[1] /= projection[2]; // Distort and transform to pixel space. CameraModel::WorldToImage(camera_params, projection[0], projection[1], &residuals[0], &residuals[1]); // Re-projection error. residuals[0] -= T(x_); residuals[1] -= T(y_); return true; } private: const double x_; const double y_; }; // Cost function for refining two-view geometry based on the Sampson-Error. // // First pose is assumed to be located at the origin with 0 rotation. Second // pose is assumed to be on the unit sphere around the first pose, i.e. the // pose of the second camera is parameterized by a 3D rotation and a // 3D translation with unit norm. `tvec` is therefore over-parameterized as is // and should be down-projected using `HomogeneousVectorParameterization`. class RelativePoseCostFunction { public: RelativePoseCostFunction(const Eigen::Vector2d& x1, const Eigen::Vector2d& x2) : x1_(x1(0)), y1_(x1(1)), x2_(x2(0)), y2_(x2(1)) {} static ceres::CostFunction* Create(const Eigen::Vector2d& x1, const Eigen::Vector2d& x2) { return (new ceres::AutoDiffCostFunction( new RelativePoseCostFunction(x1, x2))); } template bool operator()(const T* const qvec, const T* const tvec, T* residuals) const { Eigen::Matrix R; ceres::QuaternionToRotation(qvec, R.data()); // Matrix representation of the cross product t x R. Eigen::Matrix t_x; t_x << T(0), -tvec[2], tvec[1], tvec[2], T(0), -tvec[0], -tvec[1], tvec[0], T(0); // Essential matrix. const Eigen::Matrix E = t_x * R; // Homogeneous image coordinates. const Eigen::Matrix x1_h(T(x1_), T(y1_), T(1)); const Eigen::Matrix x2_h(T(x2_), T(y2_), T(1)); // Squared sampson error. const Eigen::Matrix Ex1 = E * x1_h; const Eigen::Matrix Etx2 = E.transpose() * x2_h; const T x2tEx1 = x2_h.transpose() * Ex1; residuals[0] = x2tEx1 * x2tEx1 / (Ex1(0) * Ex1(0) + Ex1(1) * Ex1(1) + Etx2(0) * Etx2(0) + Etx2(1) * Etx2(1)); return true; } private: const double x1_; const double y1_; const double x2_; const double y2_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_COST_FUNCTIONS_H_ colmap-3.4/src/base/cost_functions_test.cc000077500000000000000000000124241323400541200207420ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/cost_functions" #include "util/testing.h" #include "base/camera_models.h" #include "base/cost_functions.h" #include "base/pose.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestBundleAdjustmentCostFunction) { ceres::CostFunction* cost_function = BundleAdjustmentCostFunction::Create( Eigen::Vector2d::Zero()); double qvec[4] = {1, 0, 0, 0}; double tvec[3] = {0, 0, 0}; double point3D[3] = {0, 0, 1}; double camera_params[3] = {1, 0, 0}; double residuals[2]; const double* parameters[4] = {qvec, tvec, point3D, camera_params}; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 0); point3D[1] = 1; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 1); camera_params[0] = 2; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 2); point3D[0] = -1; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], -2); BOOST_CHECK_EQUAL(residuals[1], 2); } BOOST_AUTO_TEST_CASE(TestBundleAdjustmentConstantPoseCostFunction) { ceres::CostFunction* cost_function = BundleAdjustmentConstantPoseCostFunction< SimplePinholeCameraModel>::Create(ComposeIdentityQuaternion(), Eigen::Vector3d::Zero(), Eigen::Vector2d::Zero()); double point3D[3] = {0, 0, 1}; double camera_params[3] = {1, 0, 0}; double residuals[2]; const double* parameters[2] = {point3D, camera_params}; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 0); point3D[1] = 1; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 1); camera_params[0] = 2; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 2); point3D[0] = -1; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], -2); BOOST_CHECK_EQUAL(residuals[1], 2); } BOOST_AUTO_TEST_CASE(TestRigBundleAdjustmentCostFunction) { ceres::CostFunction* cost_function = RigBundleAdjustmentCostFunction::Create( Eigen::Vector2d::Zero()); double rig_qvec[4] = {1, 0, 0, 0}; double rig_tvec[3] = {0, 0, -1}; double rel_qvec[4] = {1, 0, 0, 0}; double rel_tvec[3] = {0, 0, 1}; double point3D[3] = {0, 0, 1}; double camera_params[3] = {1, 0, 0}; double residuals[2]; const double* parameters[6] = {rig_qvec, rig_tvec, rel_qvec, rel_tvec, point3D, camera_params}; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 0); point3D[1] = 1; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 1); camera_params[0] = 2; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 2); point3D[0] = -1; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], -2); BOOST_CHECK_EQUAL(residuals[1], 2); } BOOST_AUTO_TEST_CASE(TestRelativePoseCostFunction) { ceres::CostFunction* cost_function = RelativePoseCostFunction::Create( Eigen::Vector2d(0, 0), Eigen::Vector2d(0, 0)); double qvec[4] = {1, 0, 0, 0}; double tvec[3] = {0, 1, 0}; double residuals[1]; const double* parameters[2] = {qvec, tvec}; BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0); cost_function = RelativePoseCostFunction::Create(Eigen::Vector2d(0, 0), Eigen::Vector2d(1, 0)); BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0.5); cost_function = RelativePoseCostFunction::Create(Eigen::Vector2d(0, 0), Eigen::Vector2d(1, 1)); BOOST_CHECK(cost_function->Evaluate(parameters, residuals, nullptr)); BOOST_CHECK_EQUAL(residuals[0], 0.5); } colmap-3.4/src/base/database.cc000077500000000000000000001321511323400541200164070ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/database.h" #include #include "util/sqlite3_utils.h" #include "util/string.h" #include "util/version.h" namespace colmap { namespace { typedef Eigen::Matrix FeatureKeypointsBlob; typedef Eigen::Matrix FeatureDescriptorsBlob; typedef Eigen::Matrix FeatureMatchesBlob; void SwapFeatureMatchesBlob(FeatureMatchesBlob* matches) { matches->col(0).swap(matches->col(1)); } FeatureKeypointsBlob FeatureKeypointsToBlob(const FeatureKeypoints& keypoints) { const FeatureKeypointsBlob::Index kNumCols = 6; FeatureKeypointsBlob blob(keypoints.size(), kNumCols); for (size_t i = 0; i < keypoints.size(); ++i) { blob(i, 0) = keypoints[i].x; blob(i, 1) = keypoints[i].y; blob(i, 2) = keypoints[i].a11; blob(i, 3) = keypoints[i].a12; blob(i, 4) = keypoints[i].a21; blob(i, 5) = keypoints[i].a22; } return blob; } FeatureKeypoints FeatureKeypointsFromBlob(const FeatureKeypointsBlob& blob) { FeatureKeypoints keypoints(static_cast(blob.rows())); if (blob.cols() == 2) { for (FeatureKeypointsBlob::Index i = 0; i < blob.rows(); ++i) { keypoints[i] = FeatureKeypoint(blob(i, 0), blob(i, 1)); } } else if (blob.cols() == 4) { for (FeatureKeypointsBlob::Index i = 0; i < blob.rows(); ++i) { keypoints[i] = FeatureKeypoint(blob(i, 0), blob(i, 1), blob(i, 2), blob(i, 3)); } } else if (blob.cols() == 6) { for (FeatureKeypointsBlob::Index i = 0; i < blob.rows(); ++i) { keypoints[i] = FeatureKeypoint(blob(i, 0), blob(i, 1), blob(i, 2), blob(i, 3), blob(i, 4), blob(i, 5)); } } else { LOG(FATAL) << "Keypoint format not supported"; } return keypoints; } FeatureMatchesBlob FeatureMatchesToBlob(const FeatureMatches& matches) { const FeatureMatchesBlob::Index kNumCols = 2; FeatureMatchesBlob blob(matches.size(), kNumCols); for (size_t i = 0; i < matches.size(); ++i) { blob(i, 0) = matches[i].point2D_idx1; blob(i, 1) = matches[i].point2D_idx2; } return blob; } FeatureMatches FeatureMatchesFromBlob(const FeatureMatchesBlob& blob) { CHECK_EQ(blob.cols(), 2); FeatureMatches matches(static_cast(blob.rows())); for (FeatureMatchesBlob::Index i = 0; i < blob.rows(); ++i) { matches[i].point2D_idx1 = blob(i, 0); matches[i].point2D_idx2 = blob(i, 1); } return matches; } template MatrixType ReadStaticMatrixBlob(sqlite3_stmt* sql_stmt, const int rc, const int col) { CHECK_GE(col, 0); MatrixType matrix; if (rc == SQLITE_ROW) { const size_t num_bytes = static_cast(sqlite3_column_bytes(sql_stmt, col)); if (num_bytes > 0) { CHECK_EQ(num_bytes, matrix.size() * sizeof(typename MatrixType::Scalar)); memcpy(reinterpret_cast(matrix.data()), sqlite3_column_blob(sql_stmt, col), num_bytes); } else { matrix = MatrixType::Zero(); } } else { matrix = MatrixType::Zero(); } return matrix; } template MatrixType ReadDynamicMatrixBlob(sqlite3_stmt* sql_stmt, const int rc, const int col) { CHECK_GE(col, 0); MatrixType matrix; if (rc == SQLITE_ROW) { const size_t rows = static_cast(sqlite3_column_int64(sql_stmt, col + 0)); const size_t cols = static_cast(sqlite3_column_int64(sql_stmt, col + 1)); CHECK_GE(rows, 0); CHECK_GE(cols, 0); matrix = MatrixType(rows, cols); const size_t num_bytes = static_cast(sqlite3_column_bytes(sql_stmt, col + 2)); CHECK_EQ(matrix.size() * sizeof(typename MatrixType::Scalar), num_bytes); memcpy(reinterpret_cast(matrix.data()), sqlite3_column_blob(sql_stmt, col + 2), num_bytes); } else { const typename MatrixType::Index rows = (MatrixType::RowsAtCompileTime == Eigen::Dynamic) ? 0 : MatrixType::RowsAtCompileTime; const typename MatrixType::Index cols = (MatrixType::ColsAtCompileTime == Eigen::Dynamic) ? 0 : MatrixType::ColsAtCompileTime; matrix = MatrixType(rows, cols); } return matrix; } template void WriteStaticMatrixBlob(sqlite3_stmt* sql_stmt, const MatrixType& matrix, const int col) { SQLITE3_CALL(sqlite3_bind_blob( sql_stmt, col, reinterpret_cast(matrix.data()), static_cast(matrix.size() * sizeof(typename MatrixType::Scalar)), SQLITE_STATIC)); } template void WriteDynamicMatrixBlob(sqlite3_stmt* sql_stmt, const MatrixType& matrix, const int col) { CHECK_GE(matrix.rows(), 0); CHECK_GE(matrix.cols(), 0); CHECK_GE(col, 0); const size_t num_bytes = matrix.size() * sizeof(typename MatrixType::Scalar); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt, col + 0, matrix.rows())); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt, col + 1, matrix.cols())); SQLITE3_CALL(sqlite3_bind_blob(sql_stmt, col + 2, reinterpret_cast(matrix.data()), static_cast(num_bytes), SQLITE_STATIC)); } Camera ReadCameraRow(sqlite3_stmt* sql_stmt) { Camera camera; camera.SetCameraId(static_cast(sqlite3_column_int64(sql_stmt, 0))); camera.SetModelId(sqlite3_column_int64(sql_stmt, 1)); camera.SetWidth(static_cast(sqlite3_column_int64(sql_stmt, 2))); camera.SetHeight(static_cast(sqlite3_column_int64(sql_stmt, 3))); const size_t num_params_bytes = static_cast(sqlite3_column_bytes(sql_stmt, 4)); const size_t num_params = num_params_bytes / sizeof(double); CHECK_EQ(num_params, camera.NumParams()); memcpy(camera.ParamsData(), sqlite3_column_blob(sql_stmt, 4), num_params_bytes); camera.SetPriorFocalLength(sqlite3_column_int64(sql_stmt, 5) != 0); return camera; } Image ReadImageRow(sqlite3_stmt* sql_stmt) { Image image; image.SetImageId(static_cast(sqlite3_column_int64(sql_stmt, 0))); image.SetName(std::string( reinterpret_cast(sqlite3_column_text(sql_stmt, 1)))); image.SetCameraId(static_cast(sqlite3_column_int64(sql_stmt, 2))); // NaNs are automatically converted to NULLs in SQLite. for (size_t i = 0; i < 4; ++i) { if (sqlite3_column_type(sql_stmt, i + 3) != SQLITE_NULL) { image.QvecPrior(i) = sqlite3_column_double(sql_stmt, i + 3); } } // NaNs are automatically converted to NULLs in SQLite. for (size_t i = 0; i < 3; ++i) { if (sqlite3_column_type(sql_stmt, i + 7) != SQLITE_NULL) { image.TvecPrior(i) = sqlite3_column_double(sql_stmt, i + 7); } } return image; } } // namespace const size_t Database::kMaxNumImages = static_cast(std::numeric_limits::max()); std::mutex Database::update_schema_mutex_; Database::Database() : database_(nullptr) {} Database::Database(const std::string& path) : Database() { Open(path); } Database::~Database() { Close(); } void Database::Open(const std::string& path) { Close(); // SQLITE_OPEN_NOMUTEX specifies that the connection should not have a // mutex (so that we don't serialize the connection's operations). // Modifications to the database will still be serialized, but multiple // connections can read concurrently. SQLITE3_CALL(sqlite3_open_v2( path.c_str(), &database_, SQLITE_OPEN_READWRITE | SQLITE_OPEN_CREATE | SQLITE_OPEN_NOMUTEX, nullptr)); // Don't wait for the operating system to write the changes to disk SQLITE3_EXEC(database_, "PRAGMA synchronous=OFF", nullptr); // Use faster journaling mode SQLITE3_EXEC(database_, "PRAGMA journal_mode=WAL", nullptr); // Store temporary tables and indices in memory SQLITE3_EXEC(database_, "PRAGMA temp_store=MEMORY", nullptr); // Disabled by default SQLITE3_EXEC(database_, "PRAGMA foreign_keys=ON", nullptr); CreateTables(); UpdateSchema(); PrepareSQLStatements(); } void Database::Close() { if (database_ != nullptr) { FinalizeSQLStatements(); sqlite3_close_v2(database_); database_ = nullptr; } } bool Database::ExistsCamera(const camera_t camera_id) const { return ExistsRowId(sql_stmt_exists_camera_, camera_id); } bool Database::ExistsImage(const image_t image_id) const { return ExistsRowId(sql_stmt_exists_image_id_, image_id); } bool Database::ExistsImageWithName(std::string name) const { return ExistsRowString(sql_stmt_exists_image_name_, name); } bool Database::ExistsKeypoints(const image_t image_id) const { return ExistsRowId(sql_stmt_exists_keypoints_, image_id); } bool Database::ExistsDescriptors(const image_t image_id) const { return ExistsRowId(sql_stmt_exists_descriptors_, image_id); } bool Database::ExistsMatches(const image_t image_id1, const image_t image_id2) const { return ExistsRowId(sql_stmt_exists_matches_, ImagePairToPairId(image_id1, image_id2)); } bool Database::ExistsInlierMatches(const image_t image_id1, const image_t image_id2) const { return ExistsRowId(sql_stmt_exists_inlier_matches_, ImagePairToPairId(image_id1, image_id2)); } size_t Database::NumCameras() const { return CountRows("cameras"); } size_t Database::NumImages() const { return CountRows("images"); } size_t Database::NumKeypoints() const { return SumColumn("rows", "keypoints"); } size_t Database::MaxNumKeypoints() const { return MaxColumn("rows", "keypoints"); } size_t Database::NumKeypointsForImage(const image_t image_id) const { return CountRowsForEntry(sql_stmt_num_keypoints_, image_id); } size_t Database::NumDescriptors() const { return SumColumn("rows", "descriptors"); } size_t Database::MaxNumDescriptors() const { return MaxColumn("rows", "descriptors"); } size_t Database::NumDescriptorsForImage(const image_t image_id) const { return CountRowsForEntry(sql_stmt_num_descriptors_, image_id); } size_t Database::NumMatches() const { return SumColumn("rows", "matches"); } size_t Database::NumInlierMatches() const { return SumColumn("rows", "inlier_matches"); } size_t Database::NumMatchedImagePairs() const { return CountRows("matches"); } size_t Database::NumVerifiedImagePairs() const { return CountRows("inlier_matches"); } Camera Database::ReadCamera(const camera_t camera_id) const { SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_read_camera_, 1, camera_id)); Camera camera; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_camera_)); if (rc == SQLITE_ROW) { camera = ReadCameraRow(sql_stmt_read_camera_); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_camera_)); return camera; } std::vector Database::ReadAllCameras() const { std::vector cameras; while (SQLITE3_CALL(sqlite3_step(sql_stmt_read_cameras_)) == SQLITE_ROW) { cameras.push_back(ReadCameraRow(sql_stmt_read_cameras_)); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_cameras_)); return cameras; } Image Database::ReadImage(const image_t image_id) const { SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_read_image_id_, 1, image_id)); Image image; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_image_id_)); if (rc == SQLITE_ROW) { image = ReadImageRow(sql_stmt_read_image_id_); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_image_id_)); return image; } Image Database::ReadImageWithName(const std::string& name) const { SQLITE3_CALL(sqlite3_bind_text(sql_stmt_read_image_name_, 1, name.c_str(), static_cast(name.size()), SQLITE_STATIC)); Image image; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_image_name_)); if (rc == SQLITE_ROW) { image = ReadImageRow(sql_stmt_read_image_name_); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_image_name_)); return image; } std::vector Database::ReadAllImages() const { std::vector images; images.reserve(NumImages()); while (SQLITE3_CALL(sqlite3_step(sql_stmt_read_images_)) == SQLITE_ROW) { images.push_back(ReadImageRow(sql_stmt_read_images_)); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_images_)); return images; } FeatureKeypoints Database::ReadKeypoints(const image_t image_id) const { SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_read_keypoints_, 1, image_id)); const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_keypoints_)); const FeatureKeypointsBlob blob = ReadDynamicMatrixBlob( sql_stmt_read_keypoints_, rc, 0); SQLITE3_CALL(sqlite3_reset(sql_stmt_read_keypoints_)); return FeatureKeypointsFromBlob(blob); } FeatureDescriptors Database::ReadDescriptors(const image_t image_id) const { SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_read_descriptors_, 1, image_id)); const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_descriptors_)); const FeatureDescriptors descriptors = ReadDynamicMatrixBlob(sql_stmt_read_descriptors_, rc, 0); SQLITE3_CALL(sqlite3_reset(sql_stmt_read_descriptors_)); return descriptors; } FeatureMatches Database::ReadMatches(image_t image_id1, image_t image_id2) const { const image_pair_t pair_id = ImagePairToPairId(image_id1, image_id2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_read_matches_, 1, pair_id)); const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_matches_)); FeatureMatchesBlob blob = ReadDynamicMatrixBlob(sql_stmt_read_matches_, rc, 0); SQLITE3_CALL(sqlite3_reset(sql_stmt_read_matches_)); if (SwapImagePair(image_id1, image_id2)) { SwapFeatureMatchesBlob(&blob); } return FeatureMatchesFromBlob(blob); } std::vector> Database::ReadAllMatches() const { std::vector> all_matches; int rc; while ((rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_matches_all_))) == SQLITE_ROW) { const image_pair_t pair_id = static_cast( sqlite3_column_int64(sql_stmt_read_matches_all_, 0)); const FeatureMatchesBlob blob = ReadDynamicMatrixBlob( sql_stmt_read_matches_all_, rc, 1); all_matches.emplace_back(pair_id, FeatureMatchesFromBlob(blob)); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_matches_all_)); return all_matches; } TwoViewGeometry Database::ReadInlierMatches(const image_t image_id1, const image_t image_id2) const { const image_pair_t pair_id = ImagePairToPairId(image_id1, image_id2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_read_inlier_matches_, 1, pair_id)); const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_inlier_matches_)); TwoViewGeometry two_view_geometry; FeatureMatchesBlob blob = ReadDynamicMatrixBlob( sql_stmt_read_inlier_matches_, rc, 0); two_view_geometry.config = static_cast(sqlite3_column_int64(sql_stmt_read_inlier_matches_, 3)); two_view_geometry.F = ReadStaticMatrixBlob( sql_stmt_read_inlier_matches_, rc, 4); two_view_geometry.E = ReadStaticMatrixBlob( sql_stmt_read_inlier_matches_, rc, 5); two_view_geometry.H = ReadStaticMatrixBlob( sql_stmt_read_inlier_matches_, rc, 6); SQLITE3_CALL(sqlite3_reset(sql_stmt_read_inlier_matches_)); if (SwapImagePair(image_id1, image_id2)) { SwapFeatureMatchesBlob(&blob); } two_view_geometry.inlier_matches = FeatureMatchesFromBlob(blob); two_view_geometry.F.transposeInPlace(); two_view_geometry.E.transposeInPlace(); two_view_geometry.H.transposeInPlace(); return two_view_geometry; } void Database::ReadAllInlierMatches( std::vector* image_pair_ids, std::vector* two_view_geometries) const { int rc; while ((rc = SQLITE3_CALL(sqlite3_step(sql_stmt_read_inlier_matches_all_))) == SQLITE_ROW) { const image_pair_t pair_id = static_cast( sqlite3_column_int64(sql_stmt_read_inlier_matches_all_, 0)); image_pair_ids->push_back(pair_id); TwoViewGeometry two_view_geometry; const FeatureMatchesBlob blob = ReadDynamicMatrixBlob( sql_stmt_read_inlier_matches_all_, rc, 1); two_view_geometry.config = static_cast( sqlite3_column_int64(sql_stmt_read_inlier_matches_all_, 4)); two_view_geometry.inlier_matches = FeatureMatchesFromBlob(blob); two_view_geometries->push_back(two_view_geometry); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_inlier_matches_all_)); } void Database::ReadInlierMatchesGraph( std::vector>* image_pairs, std::vector* num_inliers) const { const auto num_inlier_matches = NumInlierMatches(); image_pairs->reserve(num_inlier_matches); num_inliers->reserve(num_inlier_matches); while (SQLITE3_CALL(sqlite3_step(sql_stmt_read_inlier_matches_graph_)) == SQLITE_ROW) { image_t image_id1; image_t image_id2; const image_pair_t pair_id = static_cast( sqlite3_column_int64(sql_stmt_read_inlier_matches_graph_, 0)); PairIdToImagePair(pair_id, &image_id1, &image_id2); image_pairs->emplace_back(image_id1, image_id2); const int rows = static_cast( sqlite3_column_int64(sql_stmt_read_inlier_matches_graph_, 1)); num_inliers->push_back(rows); } SQLITE3_CALL(sqlite3_reset(sql_stmt_read_inlier_matches_graph_)); } camera_t Database::WriteCamera(const Camera& camera, const bool use_camera_id) const { if (use_camera_id) { CHECK(!ExistsCamera(camera.CameraId())) << "camera_id must be unique"; SQLITE3_CALL( sqlite3_bind_int64(sql_stmt_add_camera_, 1, camera.CameraId())); } else { SQLITE3_CALL(sqlite3_bind_null(sql_stmt_add_camera_, 1)); } SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_add_camera_, 2, camera.ModelId())); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_add_camera_, 3, static_cast(camera.Width()))); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_add_camera_, 4, static_cast(camera.Height()))); const size_t num_params_bytes = sizeof(double) * camera.NumParams(); SQLITE3_CALL(sqlite3_bind_blob(sql_stmt_add_camera_, 5, camera.ParamsData(), static_cast(num_params_bytes), SQLITE_STATIC)); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_add_camera_, 6, camera.HasPriorFocalLength())); SQLITE3_CALL(sqlite3_step(sql_stmt_add_camera_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_add_camera_)); return static_cast(sqlite3_last_insert_rowid(database_)); } image_t Database::WriteImage(const Image& image, const bool use_image_id) const { if (use_image_id) { CHECK(!ExistsImage(image.ImageId())) << "image_id must be unique"; SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_add_image_, 1, image.ImageId())); } else { SQLITE3_CALL(sqlite3_bind_null(sql_stmt_add_image_, 1)); } SQLITE3_CALL(sqlite3_bind_text(sql_stmt_add_image_, 2, image.Name().c_str(), static_cast(image.Name().size()), SQLITE_STATIC)); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_add_image_, 3, image.CameraId())); // NaNs are automatically converted to NULLs in SQLite. SQLITE3_CALL(sqlite3_bind_double(sql_stmt_add_image_, 4, image.QvecPrior(0))); SQLITE3_CALL(sqlite3_bind_double(sql_stmt_add_image_, 5, image.QvecPrior(1))); SQLITE3_CALL(sqlite3_bind_double(sql_stmt_add_image_, 6, image.QvecPrior(2))); SQLITE3_CALL(sqlite3_bind_double(sql_stmt_add_image_, 7, image.QvecPrior(3))); // NaNs are automatically converted to NULLs in SQLite. SQLITE3_CALL(sqlite3_bind_double(sql_stmt_add_image_, 8, image.TvecPrior(0))); SQLITE3_CALL(sqlite3_bind_double(sql_stmt_add_image_, 9, image.TvecPrior(1))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_add_image_, 10, image.TvecPrior(2))); SQLITE3_CALL(sqlite3_step(sql_stmt_add_image_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_add_image_)); return static_cast(sqlite3_last_insert_rowid(database_)); } void Database::WriteKeypoints(const image_t image_id, const FeatureKeypoints& keypoints) const { const FeatureKeypointsBlob blob = FeatureKeypointsToBlob(keypoints); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_write_keypoints_, 1, image_id)); WriteDynamicMatrixBlob(sql_stmt_write_keypoints_, blob, 2); SQLITE3_CALL(sqlite3_step(sql_stmt_write_keypoints_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_write_keypoints_)); } void Database::WriteDescriptors(const image_t image_id, const FeatureDescriptors& descriptors) const { SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_write_descriptors_, 1, image_id)); WriteDynamicMatrixBlob(sql_stmt_write_descriptors_, descriptors, 2); SQLITE3_CALL(sqlite3_step(sql_stmt_write_descriptors_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_write_descriptors_)); } void Database::WriteMatches(const image_t image_id1, const image_t image_id2, const FeatureMatches& matches) const { const image_pair_t pair_id = ImagePairToPairId(image_id1, image_id2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_write_matches_, 1, pair_id)); // Important: the swapped data must live until the query is executed. FeatureMatchesBlob blob = FeatureMatchesToBlob(matches); if (SwapImagePair(image_id1, image_id2)) { SwapFeatureMatchesBlob(&blob); WriteDynamicMatrixBlob(sql_stmt_write_matches_, blob, 2); } else { WriteDynamicMatrixBlob(sql_stmt_write_matches_, blob, 2); } SQLITE3_CALL(sqlite3_step(sql_stmt_write_matches_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_write_matches_)); } void Database::WriteInlierMatches( const image_t image_id1, const image_t image_id2, const TwoViewGeometry& two_view_geometry) const { const image_pair_t pair_id = ImagePairToPairId(image_id1, image_id2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_write_inlier_matches_, 1, pair_id)); // Important: the swapped data must live until the query is executed. FeatureMatchesBlob inlier_matches = FeatureMatchesToBlob(two_view_geometry.inlier_matches); if (SwapImagePair(image_id1, image_id2)) { SwapFeatureMatchesBlob(&inlier_matches); } WriteDynamicMatrixBlob(sql_stmt_write_inlier_matches_, inlier_matches, 2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_write_inlier_matches_, 5, two_view_geometry.config)); const Eigen::Matrix3d Ft = two_view_geometry.F.transpose(); const Eigen::Matrix3d Et = two_view_geometry.E.transpose(); const Eigen::Matrix3d Ht = two_view_geometry.H.transpose(); if (two_view_geometry.inlier_matches.size() > 0) { WriteStaticMatrixBlob(sql_stmt_write_inlier_matches_, Ft, 6); WriteStaticMatrixBlob(sql_stmt_write_inlier_matches_, Et, 7); WriteStaticMatrixBlob(sql_stmt_write_inlier_matches_, Ht, 8); } else { WriteStaticMatrixBlob(sql_stmt_write_inlier_matches_, Eigen::MatrixXd(0, 0), 6); WriteStaticMatrixBlob(sql_stmt_write_inlier_matches_, Eigen::MatrixXd(0, 0), 7); WriteStaticMatrixBlob(sql_stmt_write_inlier_matches_, Eigen::MatrixXd(0, 0), 8); } SQLITE3_CALL(sqlite3_step(sql_stmt_write_inlier_matches_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_write_inlier_matches_)); } void Database::UpdateCamera(const Camera& camera) const { SQLITE3_CALL( sqlite3_bind_int64(sql_stmt_update_camera_, 1, camera.ModelId())); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_update_camera_, 2, static_cast(camera.Width()))); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_update_camera_, 3, static_cast(camera.Height()))); const size_t num_params_bytes = sizeof(double) * camera.NumParams(); SQLITE3_CALL( sqlite3_bind_blob(sql_stmt_update_camera_, 4, camera.ParamsData(), static_cast(num_params_bytes), SQLITE_STATIC)); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_update_camera_, 5, camera.HasPriorFocalLength())); SQLITE3_CALL( sqlite3_bind_int64(sql_stmt_update_camera_, 6, camera.CameraId())); SQLITE3_CALL(sqlite3_step(sql_stmt_update_camera_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_update_camera_)); } void Database::UpdateImage(const Image& image) const { SQLITE3_CALL( sqlite3_bind_text(sql_stmt_update_image_, 1, image.Name().c_str(), static_cast(image.Name().size()), SQLITE_STATIC)); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_update_image_, 2, image.CameraId())); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 3, image.QvecPrior(0))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 4, image.QvecPrior(1))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 5, image.QvecPrior(2))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 6, image.QvecPrior(3))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 7, image.TvecPrior(0))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 8, image.TvecPrior(1))); SQLITE3_CALL( sqlite3_bind_double(sql_stmt_update_image_, 9, image.TvecPrior(2))); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_update_image_, 10, image.ImageId())); SQLITE3_CALL(sqlite3_step(sql_stmt_update_image_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_update_image_)); } void Database::DeleteMatches(const image_t image_id1, const image_t image_id2) const { const image_pair_t pair_id = ImagePairToPairId(image_id1, image_id2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_delete_matches_, 1, static_cast(pair_id))); SQLITE3_CALL(sqlite3_step(sql_stmt_delete_matches_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_delete_matches_)); } void Database::DeleteInlierMatches(const image_t image_id1, const image_t image_id2) const { const image_pair_t pair_id = ImagePairToPairId(image_id1, image_id2); SQLITE3_CALL(sqlite3_bind_int64(sql_stmt_delete_inlier_matches_, 1, static_cast(pair_id))); SQLITE3_CALL(sqlite3_step(sql_stmt_delete_inlier_matches_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_delete_inlier_matches_)); } void Database::ClearMatches() const { SQLITE3_CALL(sqlite3_step(sql_stmt_clear_matches_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_clear_matches_)); } void Database::ClearInlierMatches() const { SQLITE3_CALL(sqlite3_step(sql_stmt_clear_inlier_matches_)); SQLITE3_CALL(sqlite3_reset(sql_stmt_clear_inlier_matches_)); } void Database::BeginTransaction() const { SQLITE3_EXEC(database_, "BEGIN TRANSACTION", nullptr); } void Database::EndTransaction() const { SQLITE3_EXEC(database_, "END TRANSACTION", nullptr); } void Database::PrepareSQLStatements() { sql_stmts_.clear(); std::string sql; ////////////////////////////////////////////////////////////////////////////// // num_* ////////////////////////////////////////////////////////////////////////////// sql = "SELECT rows FROM keypoints WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_num_keypoints_, 0)); sql_stmts_.push_back(sql_stmt_num_keypoints_); sql = "SELECT rows FROM descriptors WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_num_descriptors_, 0)); sql_stmts_.push_back(sql_stmt_num_descriptors_); ////////////////////////////////////////////////////////////////////////////// // exists_* ////////////////////////////////////////////////////////////////////////////// sql = "SELECT 1 FROM cameras WHERE camera_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_camera_, 0)); sql_stmts_.push_back(sql_stmt_exists_camera_); sql = "SELECT 1 FROM images WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_image_id_, 0)); sql_stmts_.push_back(sql_stmt_exists_image_id_); sql = "SELECT 1 FROM images WHERE name = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_image_name_, 0)); sql_stmts_.push_back(sql_stmt_exists_image_name_); sql = "SELECT 1 FROM keypoints WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_keypoints_, 0)); sql_stmts_.push_back(sql_stmt_exists_keypoints_); sql = "SELECT 1 FROM descriptors WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_descriptors_, 0)); sql_stmts_.push_back(sql_stmt_exists_descriptors_); sql = "SELECT 1 FROM matches WHERE pair_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_matches_, 0)); sql_stmts_.push_back(sql_stmt_exists_matches_); sql = "SELECT 1 FROM inlier_matches WHERE pair_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_exists_inlier_matches_, 0)); sql_stmts_.push_back(sql_stmt_exists_inlier_matches_); ////////////////////////////////////////////////////////////////////////////// // add_* ////////////////////////////////////////////////////////////////////////////// sql = "INSERT INTO cameras(camera_id, model, width, height, params, " "prior_focal_length) VALUES(?, ?, ?, ?, ?, ?);"; SQLITE3_CALL( sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_add_camera_, 0)); sql_stmts_.push_back(sql_stmt_add_camera_); sql = "INSERT INTO images(image_id, name, camera_id, prior_qw, prior_qx, " "prior_qy, prior_qz, prior_tx, prior_ty, prior_tz) VALUES(?, ?, ?, ?, ?, " "?, ?, ?, ?, ?);"; SQLITE3_CALL( sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_add_image_, 0)); sql_stmts_.push_back(sql_stmt_add_image_); ////////////////////////////////////////////////////////////////////////////// // update_* ////////////////////////////////////////////////////////////////////////////// sql = "UPDATE cameras SET model=?, width=?, height=?, params=?, " "prior_focal_length=? WHERE camera_id=?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_update_camera_, 0)); sql_stmts_.push_back(sql_stmt_update_camera_); sql = "UPDATE images SET name=?, camera_id=?, prior_qw=?, prior_qx=?, " "prior_qy=?, prior_qz=?, prior_tx=?, prior_ty=?, prior_tz=? WHERE " "image_id=?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_update_image_, 0)); sql_stmts_.push_back(sql_stmt_update_image_); ////////////////////////////////////////////////////////////////////////////// // read_* ////////////////////////////////////////////////////////////////////////////// sql = "SELECT * FROM cameras WHERE camera_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_camera_, 0)); sql_stmts_.push_back(sql_stmt_read_camera_); sql = "SELECT * FROM cameras;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_cameras_, 0)); sql_stmts_.push_back(sql_stmt_read_cameras_); sql = "SELECT * FROM images WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_image_id_, 0)); sql_stmts_.push_back(sql_stmt_read_image_id_); sql = "SELECT * FROM images WHERE name = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_image_name_, 0)); sql_stmts_.push_back(sql_stmt_read_image_name_); sql = "SELECT * FROM images;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_images_, 0)); sql_stmts_.push_back(sql_stmt_read_images_); sql = "SELECT rows, cols, data FROM keypoints WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_keypoints_, 0)); sql_stmts_.push_back(sql_stmt_read_keypoints_); sql = "SELECT rows, cols, data FROM descriptors WHERE image_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_descriptors_, 0)); sql_stmts_.push_back(sql_stmt_read_descriptors_); sql = "SELECT rows, cols, data FROM matches WHERE pair_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_matches_, 0)); sql_stmts_.push_back(sql_stmt_read_matches_); sql = "SELECT * FROM matches WHERE rows > 0;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_matches_all_, 0)); sql_stmts_.push_back(sql_stmt_read_matches_all_); sql = "SELECT rows, cols, data, config, F, E, H FROM inlier_matches " "WHERE pair_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_inlier_matches_, 0)); sql_stmts_.push_back(sql_stmt_read_inlier_matches_); sql = "SELECT * FROM inlier_matches WHERE rows > 0;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_inlier_matches_all_, 0)); sql_stmts_.push_back(sql_stmt_read_inlier_matches_all_); sql = "SELECT pair_id, rows FROM inlier_matches WHERE rows > 0;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_read_inlier_matches_graph_, 0)); sql_stmts_.push_back(sql_stmt_read_inlier_matches_graph_); ////////////////////////////////////////////////////////////////////////////// // write_* ////////////////////////////////////////////////////////////////////////////// sql = "INSERT INTO keypoints(image_id, rows, cols, data) VALUES(?, ?, ?, ?);"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_write_keypoints_, 0)); sql_stmts_.push_back(sql_stmt_write_keypoints_); sql = "INSERT INTO descriptors(image_id, rows, cols, data) VALUES(?, ?, ?, ?);"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_write_descriptors_, 0)); sql_stmts_.push_back(sql_stmt_write_descriptors_); sql = "INSERT INTO matches(pair_id, rows, cols, data) VALUES(?, ?, ?, ?);"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_write_matches_, 0)); sql_stmts_.push_back(sql_stmt_write_matches_); sql = "INSERT INTO inlier_matches(pair_id, rows, cols, data, config, F, E, H) " "VALUES(?, ?, ?, ?, ?, ?, ?, ?);"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_write_inlier_matches_, 0)); sql_stmts_.push_back(sql_stmt_write_inlier_matches_); ////////////////////////////////////////////////////////////////////////////// // delete_* ////////////////////////////////////////////////////////////////////////////// sql = "DELETE FROM matches WHERE pair_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_delete_matches_, 0)); sql_stmts_.push_back(sql_stmt_delete_matches_); sql = "DELETE FROM inlier_matches WHERE pair_id = ?;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_delete_inlier_matches_, 0)); sql_stmts_.push_back(sql_stmt_delete_inlier_matches_); ////////////////////////////////////////////////////////////////////////////// // clear_* ////////////////////////////////////////////////////////////////////////////// sql = "DELETE FROM matches;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_clear_matches_, 0)); sql_stmts_.push_back(sql_stmt_clear_matches_); sql = "DELETE FROM inlier_matches;"; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt_clear_inlier_matches_, 0)); sql_stmts_.push_back(sql_stmt_clear_inlier_matches_); } void Database::FinalizeSQLStatements() { for (const auto& sql_stmt : sql_stmts_) { SQLITE3_CALL(sqlite3_finalize(sql_stmt)); } } void Database::CreateTables() const { CreateCameraTable(); CreateImageTable(); CreateKeypointsTable(); CreateDescriptorsTable(); CreateMatchesTable(); CreateInlierMatchesTable(); } void Database::CreateCameraTable() const { const std::string sql = "CREATE TABLE IF NOT EXISTS cameras" " (camera_id INTEGER PRIMARY KEY AUTOINCREMENT NOT NULL," " model INTEGER NOT NULL," " width INTEGER NOT NULL," " height INTEGER NOT NULL," " params BLOB," " prior_focal_length INTEGER NOT NULL);"; SQLITE3_EXEC(database_, sql.c_str(), nullptr); } void Database::CreateImageTable() const { const std::string sql = StringPrintf( "CREATE TABLE IF NOT EXISTS images" " (image_id INTEGER PRIMARY KEY AUTOINCREMENT NOT NULL," " name TEXT NOT NULL UNIQUE," " camera_id INTEGER NOT NULL," " prior_qw REAL," " prior_qx REAL," " prior_qy REAL," " prior_qz REAL," " prior_tx REAL," " prior_ty REAL," " prior_tz REAL," "CONSTRAINT image_id_check CHECK(image_id >= 0 and image_id < %d)," "FOREIGN KEY(camera_id) REFERENCES cameras(camera_id));" "CREATE UNIQUE INDEX IF NOT EXISTS index_name ON images(name);", kMaxNumImages); SQLITE3_EXEC(database_, sql.c_str(), nullptr); } void Database::CreateKeypointsTable() const { const std::string sql = "CREATE TABLE IF NOT EXISTS keypoints" " (image_id INTEGER PRIMARY KEY NOT NULL," " rows INTEGER NOT NULL," " cols INTEGER NOT NULL," " data BLOB," "FOREIGN KEY(image_id) REFERENCES images(image_id) ON DELETE CASCADE);"; SQLITE3_EXEC(database_, sql.c_str(), nullptr); } void Database::CreateDescriptorsTable() const { const std::string sql = "CREATE TABLE IF NOT EXISTS descriptors" " (image_id INTEGER PRIMARY KEY NOT NULL," " rows INTEGER NOT NULL," " cols INTEGER NOT NULL," " data BLOB," "FOREIGN KEY(image_id) REFERENCES images(image_id) ON DELETE CASCADE);"; SQLITE3_EXEC(database_, sql.c_str(), nullptr); } void Database::CreateMatchesTable() const { const std::string sql = "CREATE TABLE IF NOT EXISTS matches" " (pair_id INTEGER PRIMARY KEY NOT NULL," " rows INTEGER NOT NULL," " cols INTEGER NOT NULL," " data BLOB);"; SQLITE3_EXEC(database_, sql.c_str(), nullptr); } void Database::CreateInlierMatchesTable() const { const std::string sql = "CREATE TABLE IF NOT EXISTS inlier_matches" " (pair_id INTEGER PRIMARY KEY NOT NULL," " rows INTEGER NOT NULL," " cols INTEGER NOT NULL," " data BLOB," " config INTEGER NOT NULL," " F BLOB," " E BLOB," " H BLOB);"; SQLITE3_EXEC(database_, sql.c_str(), nullptr); } void Database::UpdateSchema() const { if (!ExistsColumn("inlier_matches", "F")) { SQLITE3_EXEC(database_, "ALTER TABLE inlier_matches ADD COLUMN F BLOB;", nullptr); } if (!ExistsColumn("inlier_matches", "E")) { SQLITE3_EXEC(database_, "ALTER TABLE inlier_matches ADD COLUMN E BLOB;", nullptr); } if (!ExistsColumn("inlier_matches", "H")) { SQLITE3_EXEC(database_, "ALTER TABLE inlier_matches ADD COLUMN H BLOB;", nullptr); } // Update user version number. std::unique_lock lock(update_schema_mutex_); const std::string update_user_version_sql = "PRAGMA user_version = " + std::to_string(COLMAP_VERSION_NUMBER) + ";"; SQLITE3_EXEC(database_, update_user_version_sql.c_str(), nullptr); } bool Database::ExistsColumn(const std::string& table_name, const std::string& column_name) const { const std::string sql = StringPrintf("PRAGMA table_info(%s);", table_name.c_str()); sqlite3_stmt* sql_stmt; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt, 0)); bool exists_column = false; while (SQLITE3_CALL(sqlite3_step(sql_stmt)) == SQLITE_ROW) { const std::string result = reinterpret_cast(sqlite3_column_text(sql_stmt, 1)); if (column_name == result) { exists_column = true; break; } } SQLITE3_CALL(sqlite3_finalize(sql_stmt)); return exists_column; } bool Database::ExistsRowId(sqlite3_stmt* sql_stmt, const sqlite3_int64 row_id) const { SQLITE3_CALL( sqlite3_bind_int64(sql_stmt, 1, static_cast(row_id))); const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt)); const bool exists = rc == SQLITE_ROW; SQLITE3_CALL(sqlite3_reset(sql_stmt)); return exists; } bool Database::ExistsRowString(sqlite3_stmt* sql_stmt, const std::string& row_entry) const { SQLITE3_CALL(sqlite3_bind_text(sql_stmt, 1, row_entry.c_str(), static_cast(row_entry.size()), SQLITE_STATIC)); const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt)); const bool exists = rc == SQLITE_ROW; SQLITE3_CALL(sqlite3_reset(sql_stmt)); return exists; } size_t Database::CountRows(const std::string& table) const { const std::string sql = "SELECT COUNT(*) FROM " + table + ";"; sqlite3_stmt* sql_stmt; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt, 0)); size_t count = 0; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt)); if (rc == SQLITE_ROW) { count = static_cast(sqlite3_column_int64(sql_stmt, 0)); } SQLITE3_CALL(sqlite3_finalize(sql_stmt)); return count; } size_t Database::CountRowsForEntry(sqlite3_stmt* sql_stmt, const sqlite3_int64 row_id) const { SQLITE3_CALL(sqlite3_bind_int64(sql_stmt, 1, row_id)); size_t count = 0; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt)); if (rc == SQLITE_ROW) { count = static_cast(sqlite3_column_int64(sql_stmt, 0)); } SQLITE3_CALL(sqlite3_reset(sql_stmt)); return count; } size_t Database::SumColumn(const std::string& column, const std::string& table) const { const std::string sql = "SELECT SUM(" + column + ") FROM " + table + ";"; sqlite3_stmt* sql_stmt; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt, 0)); size_t sum = 0; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt)); if (rc == SQLITE_ROW) { sum = static_cast(sqlite3_column_int64(sql_stmt, 0)); } SQLITE3_CALL(sqlite3_finalize(sql_stmt)); return sum; } size_t Database::MaxColumn(const std::string& column, const std::string& table) const { const std::string sql = "SELECT MAX(" + column + ") FROM " + table + ";"; sqlite3_stmt* sql_stmt; SQLITE3_CALL(sqlite3_prepare_v2(database_, sql.c_str(), -1, &sql_stmt, 0)); size_t max = 0; const int rc = SQLITE3_CALL(sqlite3_step(sql_stmt)); if (rc == SQLITE_ROW) { max = static_cast(sqlite3_column_int64(sql_stmt, 0)); } SQLITE3_CALL(sqlite3_finalize(sql_stmt)); return max; } DatabaseTransaction::DatabaseTransaction(Database* database) : database_(database), database_lock_(database->transaction_mutex_) { CHECK_NOTNULL(database_); database_->BeginTransaction(); } DatabaseTransaction::~DatabaseTransaction() { database_->EndTransaction(); } } // namespace colmap colmap-3.4/src/base/database.h000077500000000000000000000333441323400541200162550ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_DATABASE_H_ #define COLMAP_SRC_BASE_DATABASE_H_ #include #include #include #include #include "base/camera.h" #include "base/image.h" #include "estimators/two_view_geometry.h" #include "ext/SQLite/sqlite3.h" #include "feature/types.h" #include "util/types.h" namespace colmap { // Database class to read and write images, features, cameras, matches, etc. // from a SQLite database. The class is not thread-safe and must not be accessed // concurrently. The class is optimized for single-thread speed and for optimal // performance, wrap multiple method calls inside a leading `BeginTransaction` // and trailing `EndTransaction`. class Database { public: const static int kSchemaVersion = 1; // The maximum number of images, that can be stored in the database. // This limitation arises due to the fact, that we generate unique IDs for // image pairs manually. Note: do not change this to // another type than `size_t`. const static size_t kMaxNumImages; Database(); explicit Database(const std::string& path); ~Database(); // Open and close database. The same database should not be opened // concurrently in multiple threads or processes. void Open(const std::string& path); void Close(); // Check if entry already exists in database. For image pairs, the order of // `image_id1` and `image_id2` does not matter. bool ExistsCamera(const camera_t camera_id) const; bool ExistsImage(const image_t image_id) const; bool ExistsImageWithName(std::string name) const; bool ExistsKeypoints(const image_t image_id) const; bool ExistsDescriptors(const image_t image_id) const; bool ExistsMatches(const image_t image_id1, const image_t image_id2) const; bool ExistsInlierMatches(const image_t image_id1, const image_t image_id2) const; // Number of rows in `cameras` table. size_t NumCameras() const; // Number of rows in `images` table. size_t NumImages() const; // Sum of `rows` column in `keypoints` table, i.e. number of total keypoints. size_t NumKeypoints() const; // The number of keypoints for the image with most features. size_t MaxNumKeypoints() const; // Number of descriptors for specific image. size_t NumKeypointsForImage(const image_t image_id) const; // Sum of `rows` column in `descriptors` table, // i.e. number of total descriptors. size_t NumDescriptors() const; // The number of descriptors for the image with most features. size_t MaxNumDescriptors() const; // Number of descriptors for specific image. size_t NumDescriptorsForImage(const image_t image_id) const; // Sum of `rows` column in `matches` table, i.e. number of total matches. size_t NumMatches() const; // Sum of `rows` column in `inlier_matches` table, // i.e. number of total inlier matches. size_t NumInlierMatches() const; // Number of rows in `matches` table. size_t NumMatchedImagePairs() const; // Number of rows in `inlier_matches` table. size_t NumVerifiedImagePairs() const; // Each image pair is assigned an unique ID in the `matches` and // `inlier_matches` table. We intentionally avoid to store the pairs in a // separate table by using e.g. AUTOINCREMENT, since the overhead of querying // the unique pair ID is significant. inline static image_pair_t ImagePairToPairId(const image_t image_id1, const image_t image_id2); inline static void PairIdToImagePair(const image_pair_t pair_id, image_t* image_id1, image_t* image_id2); // Return true if image pairs should be swapped. Used to enforce a specific // image order to generate unique image pair identifiers independent of the // order in which the image identifiers are used. inline static bool SwapImagePair(const image_t image_id1, const image_t image_id2); // Read an existing entry in the database. The user is responsible for making // sure that the entry actually exists. For image pairs, the order of // `image_id1` and `image_id2` does not matter. Camera ReadCamera(const camera_t camera_id) const; std::vector ReadAllCameras() const; Image ReadImage(const image_t image_id) const; Image ReadImageWithName(const std::string& name) const; std::vector ReadAllImages() const; FeatureKeypoints ReadKeypoints(const image_t image_id) const; FeatureDescriptors ReadDescriptors(const image_t image_id) const; FeatureMatches ReadMatches(const image_t image_id1, const image_t image_id2) const; std::vector> ReadAllMatches() const; TwoViewGeometry ReadInlierMatches(const image_t image_id1, const image_t image_id2) const; void ReadAllInlierMatches( std::vector* image_pair_ids, std::vector* two_view_geometries) const; // Read all image pairs that have an entry in the `inlier_matches` table with // at least one inlier match and their corresponding number of inlier matches. void ReadInlierMatchesGraph( std::vector>* image_pairs, std::vector* num_inliers) const; // Add new camera and return its database identifier. If `use_camera_id` // is false a new identifier is automatically generated. camera_t WriteCamera(const Camera& camera, const bool use_camera_id = false) const; // Add new image and return its database identifier. If `use_image_id` // is false a new identifier is automatically generated. image_t WriteImage(const Image& image, const bool use_image_id = false) const; // Write a new entry in the database. The user is responsible for making sure // that the entry does not yet exist. For image pairs, the order of // `image_id1` and `image_id2` does not matter. void WriteKeypoints(const image_t image_id, const FeatureKeypoints& keypoints) const; void WriteDescriptors(const image_t image_id, const FeatureDescriptors& descriptors) const; void WriteMatches(const image_t image_id1, const image_t image_id2, const FeatureMatches& matches) const; void WriteInlierMatches(const image_t image_id1, const image_t image_id2, const TwoViewGeometry& two_view_geometry) const; // Update an existing camera in the database. The user is responsible for // making sure that the entry already exists. void UpdateCamera(const Camera& camera) const; // Update an existing image in the database. The user is responsible for // making sure that the entry already exists. void UpdateImage(const Image& image) const; // Delete matches of an image pair. void DeleteMatches(const image_t image_id1, const image_t image_id2) const; // Delete inlier matches of an image pair. void DeleteInlierMatches(const image_t image_id1, const image_t image_id2) const; // Clear the entire matches table. void ClearMatches() const; // Clear the entire inlier matches table. void ClearInlierMatches() const; private: friend class DatabaseTransaction; // Combine multiple queries into one transaction by wrapping a code section // into a `BeginTransaction` and `EndTransaction`. You can create a scoped // transaction with `DatabaseTransaction` that ends when the transaction // object is destructed. Combining queries results in faster transaction time // due to reduced locking of the database etc. void BeginTransaction() const; void EndTransaction() const; // Prepare SQL statements once at construction of the database, and reuse // the statements for multiple queries by resetting their states. void PrepareSQLStatements(); void FinalizeSQLStatements(); // Create database tables, if not existing, called when opening a database. void CreateTables() const; void CreateCameraTable() const; void CreateImageTable() const; void CreateKeypointsTable() const; void CreateDescriptorsTable() const; void CreateMatchesTable() const; void CreateInlierMatchesTable() const; void UpdateSchema() const; bool ExistsColumn(const std::string& table_name, const std::string& column_name) const; bool ExistsRowId(sqlite3_stmt* sql_stmt, const sqlite3_int64 row_id) const; bool ExistsRowString(sqlite3_stmt* sql_stmt, const std::string& row_entry) const; size_t CountRows(const std::string& table) const; size_t CountRowsForEntry(sqlite3_stmt* sql_stmt, const sqlite3_int64 row_id) const; size_t SumColumn(const std::string& column, const std::string& table) const; size_t MaxColumn(const std::string& column, const std::string& table) const; sqlite3* database_ = nullptr; // Ensure that only one database object at a time updates the schema of a // database. Since the schema is updated every time a database is opened, this // is to ensure that there are no race conditions ("database locked" error // messages) when the user actually only intends to read from the database, // which requires to open it. static std::mutex update_schema_mutex_; // Used to ensure that only one transaction is active at the same time. std::mutex transaction_mutex_; // A collection of all `sqlite3_stmt` objects for deletion in the destructor. std::vector sql_stmts_; // num_* sqlite3_stmt* sql_stmt_num_keypoints_ = nullptr; sqlite3_stmt* sql_stmt_num_descriptors_ = nullptr; // exists_* sqlite3_stmt* sql_stmt_exists_camera_ = nullptr; sqlite3_stmt* sql_stmt_exists_image_id_ = nullptr; sqlite3_stmt* sql_stmt_exists_image_name_ = nullptr; sqlite3_stmt* sql_stmt_exists_keypoints_ = nullptr; sqlite3_stmt* sql_stmt_exists_descriptors_ = nullptr; sqlite3_stmt* sql_stmt_exists_matches_ = nullptr; sqlite3_stmt* sql_stmt_exists_inlier_matches_ = nullptr; // add_* sqlite3_stmt* sql_stmt_add_camera_ = nullptr; sqlite3_stmt* sql_stmt_add_image_ = nullptr; // update_* sqlite3_stmt* sql_stmt_update_camera_ = nullptr; sqlite3_stmt* sql_stmt_update_image_ = nullptr; // read_* sqlite3_stmt* sql_stmt_read_camera_ = nullptr; sqlite3_stmt* sql_stmt_read_cameras_ = nullptr; sqlite3_stmt* sql_stmt_read_image_id_ = nullptr; sqlite3_stmt* sql_stmt_read_image_name_ = nullptr; sqlite3_stmt* sql_stmt_read_images_ = nullptr; sqlite3_stmt* sql_stmt_read_keypoints_ = nullptr; sqlite3_stmt* sql_stmt_read_descriptors_ = nullptr; sqlite3_stmt* sql_stmt_read_matches_ = nullptr; sqlite3_stmt* sql_stmt_read_matches_all_ = nullptr; sqlite3_stmt* sql_stmt_read_inlier_matches_ = nullptr; sqlite3_stmt* sql_stmt_read_inlier_matches_all_ = nullptr; sqlite3_stmt* sql_stmt_read_inlier_matches_graph_ = nullptr; // write_* sqlite3_stmt* sql_stmt_write_keypoints_ = nullptr; sqlite3_stmt* sql_stmt_write_descriptors_ = nullptr; sqlite3_stmt* sql_stmt_write_matches_ = nullptr; sqlite3_stmt* sql_stmt_write_inlier_matches_ = nullptr; // delete_* sqlite3_stmt* sql_stmt_delete_matches_ = nullptr; sqlite3_stmt* sql_stmt_delete_inlier_matches_ = nullptr; // clear_* sqlite3_stmt* sql_stmt_clear_matches_ = nullptr; sqlite3_stmt* sql_stmt_clear_inlier_matches_ = nullptr; }; // This class automatically manages the scope of a database transaction by // calling `BeginTransaction` and `EndTransaction` during construction and // destruction, respectively. class DatabaseTransaction { public: explicit DatabaseTransaction(Database* database); ~DatabaseTransaction(); private: NON_COPYABLE(DatabaseTransaction) NON_MOVABLE(DatabaseTransaction) Database* database_; std::unique_lock database_lock_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// image_pair_t Database::ImagePairToPairId(const image_t image_id1, const image_t image_id2) { CHECK_GE(image_id1, 0); CHECK_GE(image_id2, 0); CHECK_LT(image_id1, kMaxNumImages); CHECK_LT(image_id2, kMaxNumImages); if (SwapImagePair(image_id1, image_id2)) { return kMaxNumImages * image_id2 + image_id1; } else { return kMaxNumImages * image_id1 + image_id2; } } void Database::PairIdToImagePair(const image_pair_t pair_id, image_t* image_id1, image_t* image_id2) { *image_id2 = static_cast(pair_id % kMaxNumImages); *image_id1 = static_cast((pair_id - *image_id2) / kMaxNumImages); CHECK_GE(*image_id1, 0); CHECK_GE(*image_id2, 0); CHECK_LT(*image_id1, kMaxNumImages); CHECK_LT(*image_id2, kMaxNumImages); } // Return true if image pairs should be swapped. Used to enforce a specific // image order to generate unique image pair identifiers independent of the // order in which the image identifiers are used. bool Database::SwapImagePair(const image_t image_id1, const image_t image_id2) { return image_id1 > image_id2; } } // namespace colmap #endif // COLMAP_SRC_BASE_DATABASE_H_ colmap-3.4/src/base/database_cache.cc000077500000000000000000000152261323400541200175350ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/database_cache.h" #include #include "feature/utils.h" #include "util/string.h" #include "util/timer.h" namespace colmap { DatabaseCache::DatabaseCache() {} void DatabaseCache::AddCamera(const class Camera& camera) { CHECK(!ExistsCamera(camera.CameraId())); cameras_.emplace(camera.CameraId(), camera); } void DatabaseCache::AddImage(const class Image& image) { CHECK(!ExistsImage(image.ImageId())); images_.emplace(image.ImageId(), image); scene_graph_.AddImage(image.ImageId(), image.NumPoints2D()); } void DatabaseCache::Load(const Database& database, const size_t min_num_matches, const bool ignore_watermarks, const std::set& image_names) { ////////////////////////////////////////////////////////////////////////////// // Load cameras ////////////////////////////////////////////////////////////////////////////// Timer timer; timer.Start(); std::cout << "Loading cameras..." << std::flush; { const std::vector cameras = database.ReadAllCameras(); cameras_.reserve(cameras.size()); for (const auto& camera : cameras) { cameras_.emplace(camera.CameraId(), camera); } } std::cout << StringPrintf(" %d in %.3fs", cameras_.size(), timer.ElapsedSeconds()) << std::endl; ////////////////////////////////////////////////////////////////////////////// // Load matches ////////////////////////////////////////////////////////////////////////////// timer.Restart(); std::cout << "Loading matches..." << std::flush; std::vector image_pair_ids; std::vector two_view_geometries; database.ReadAllInlierMatches(&image_pair_ids, &two_view_geometries); std::cout << StringPrintf(" %d in %.3fs", image_pair_ids.size(), timer.ElapsedSeconds()) << std::endl; auto UseInlierMatchesCheck = [min_num_matches, ignore_watermarks]( const TwoViewGeometry& two_view_geometry) { return static_cast(two_view_geometry.inlier_matches.size()) >= min_num_matches && (!ignore_watermarks || two_view_geometry.config != TwoViewGeometry::WATERMARK); }; ////////////////////////////////////////////////////////////////////////////// // Load images ////////////////////////////////////////////////////////////////////////////// timer.Restart(); std::cout << "Loading images..." << std::flush; std::unordered_set image_ids; { const std::vector images = database.ReadAllImages(); // Determines for which images data should be loaded. if (image_names.empty()) { for (const auto& image : images) { image_ids.insert(image.ImageId()); } } else { for (const auto& image : images) { if (image_names.count(image.Name()) > 0) { image_ids.insert(image.ImageId()); } } } // Collect all images that are connected in the scene graph. std::unordered_set connected_image_ids; connected_image_ids.reserve(image_ids.size()); for (size_t i = 0; i < image_pair_ids.size(); ++i) { if (UseInlierMatchesCheck(two_view_geometries[i])) { image_t image_id1; image_t image_id2; Database::PairIdToImagePair(image_pair_ids[i], &image_id1, &image_id2); if (image_ids.count(image_id1) > 0 && image_ids.count(image_id2) > 0) { connected_image_ids.insert(image_id1); connected_image_ids.insert(image_id2); } } } // Load images with correspondences and discard images without // correspondences, as those images are useless for SfM. images_.reserve(connected_image_ids.size()); for (const auto& image : images) { if (image_ids.count(image.ImageId()) > 0 && connected_image_ids.count(image.ImageId()) > 0) { images_.emplace(image.ImageId(), image); const FeatureKeypoints keypoints = database.ReadKeypoints(image.ImageId()); const std::vector points = FeatureKeypointsToPointsVector(keypoints); images_[image.ImageId()].SetPoints2D(points); } } std::cout << StringPrintf(" %d in %.3fs (connected %d)", images.size(), timer.ElapsedSeconds(), connected_image_ids.size()) << std::endl; } ////////////////////////////////////////////////////////////////////////////// // Build scene graph ////////////////////////////////////////////////////////////////////////////// timer.Restart(); std::cout << "Building scene graph..." << std::flush; for (const auto& image : images_) { scene_graph_.AddImage(image.first, image.second.NumPoints2D()); } size_t num_ignored_image_pairs = 0; for (size_t i = 0; i < image_pair_ids.size(); ++i) { if (UseInlierMatchesCheck(two_view_geometries[i])) { image_t image_id1; image_t image_id2; Database::PairIdToImagePair(image_pair_ids[i], &image_id1, &image_id2); if (image_ids.count(image_id1) > 0 && image_ids.count(image_id2) > 0) { scene_graph_.AddCorrespondences(image_id1, image_id2, two_view_geometries[i].inlier_matches); } else { num_ignored_image_pairs += 1; } } else { num_ignored_image_pairs += 1; } } scene_graph_.Finalize(); // Set number of observations and correspondences per image. for (auto& image : images_) { image.second.SetNumObservations( scene_graph_.NumObservationsForImage(image.first)); image.second.SetNumCorrespondences( scene_graph_.NumCorrespondencesForImage(image.first)); } std::cout << StringPrintf(" in %.3fs (ignored %d)", timer.ElapsedSeconds(), num_ignored_image_pairs) << std::endl; } } // namespace colmap colmap-3.4/src/base/database_cache.h000077500000000000000000000105311323400541200173710ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_DATABASE_CACHE_H_ #define COLMAP_SRC_BASE_DATABASE_CACHE_H_ #include #include #include #include #include #include "base/camera.h" #include "base/camera_models.h" #include "base/database.h" #include "base/image.h" #include "base/scene_graph.h" #include "util/alignment.h" #include "util/types.h" namespace colmap { // A class that caches the contents of the database in memory, used to quickly // create new reconstruction instances when multiple models are reconstructed. class DatabaseCache { public: DatabaseCache(); // Get number of objects. inline size_t NumCameras() const; inline size_t NumImages() const; // Get specific objects. inline class Camera& Camera(const camera_t camera_id); inline const class Camera& Camera(const camera_t camera_id) const; inline class Image& Image(const image_t image_id); inline const class Image& Image(const image_t image_id) const; // Get all objects. inline const EIGEN_STL_UMAP(camera_t, class Camera) & Cameras() const; inline const EIGEN_STL_UMAP(image_t, class Image) & Images() const; // Check whether specific object exists. inline bool ExistsCamera(const camera_t camera_id) const; inline bool ExistsImage(const image_t image_id) const; // Get reference to scene graph. inline const class SceneGraph& SceneGraph() const; // Manually add data to cache. void AddCamera(const class Camera& camera); void AddImage(const class Image& image); // Load cameras, images, features, and matches from database. // // @param database Source database from which to load data. // @param min_num_matches Only load image pairs with a minimum number // of matches. // @param ignore_watermarks Whether to ignore watermark image pairs. // @param image_names Whether to use only load the data for a subset // of the images. All images are used if empty. void Load(const Database& database, const size_t min_num_matches, const bool ignore_watermarks, const std::set& image_names); private: class SceneGraph scene_graph_; EIGEN_STL_UMAP(camera_t, class Camera) cameras_; EIGEN_STL_UMAP(image_t, class Image) images_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// size_t DatabaseCache::NumCameras() const { return cameras_.size(); } size_t DatabaseCache::NumImages() const { return images_.size(); } class Camera& DatabaseCache::Camera(const camera_t camera_id) { return cameras_.at(camera_id); } const class Camera& DatabaseCache::Camera(const camera_t camera_id) const { return cameras_.at(camera_id); } class Image& DatabaseCache::Image(const image_t image_id) { return images_.at(image_id); } const class Image& DatabaseCache::Image(const image_t image_id) const { return images_.at(image_id); } const EIGEN_STL_UMAP(camera_t, class Camera) & DatabaseCache::Cameras() const { return cameras_; } const EIGEN_STL_UMAP(image_t, class Image) & DatabaseCache::Images() const { return images_; } bool DatabaseCache::ExistsCamera(const camera_t camera_id) const { return cameras_.find(camera_id) != cameras_.end(); } bool DatabaseCache::ExistsImage(const image_t image_id) const { return images_.find(image_id) != images_.end(); } inline const class SceneGraph& DatabaseCache::SceneGraph() const { return scene_graph_; } } // namespace colmap #endif // COLMAP_SRC_BASE_DATABASE_CACHE_H_ colmap-3.4/src/base/database_cache_test.cc000077500000000000000000000050351323400541200205710ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/database_cache" #include "util/testing.h" #include "base/database_cache.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEmpty) { DatabaseCache cache; BOOST_CHECK_EQUAL(cache.NumCameras(), 0); BOOST_CHECK_EQUAL(cache.NumImages(), 0); } BOOST_AUTO_TEST_CASE(TestAddCamera) { DatabaseCache cache; Camera camera; camera.SetCameraId(1); camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1, 1, 1); cache.AddCamera(camera); BOOST_CHECK_EQUAL(cache.NumCameras(), 1); BOOST_CHECK_EQUAL(cache.NumImages(), 0); BOOST_CHECK(cache.ExistsCamera(camera.CameraId())); BOOST_CHECK_EQUAL(cache.Camera(camera.CameraId()).ModelId(), camera.ModelId()); } BOOST_AUTO_TEST_CASE(TestDegenerateCamera) { DatabaseCache cache; Camera camera; camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1, 1, 1); cache.AddCamera(camera); BOOST_CHECK_EQUAL(cache.NumCameras(), 1); BOOST_CHECK_EQUAL(cache.NumImages(), 0); BOOST_CHECK(cache.ExistsCamera(camera.CameraId())); BOOST_CHECK_EQUAL(cache.Camera(camera.CameraId()).MeanFocalLength(), 1); } BOOST_AUTO_TEST_CASE(TestAddImage) { DatabaseCache cache; Image image; image.SetImageId(1); image.SetPoints2D(std::vector(10)); cache.AddImage(image); BOOST_CHECK_EQUAL(cache.NumCameras(), 0); BOOST_CHECK_EQUAL(cache.NumImages(), 1); BOOST_CHECK(cache.ExistsImage(image.ImageId())); BOOST_CHECK_EQUAL(cache.Image(image.ImageId()).NumPoints2D(), image.NumPoints2D()); BOOST_CHECK(cache.SceneGraph().ExistsImage(image.ImageId())); BOOST_CHECK_EQUAL( cache.SceneGraph().NumCorrespondencesForImage(image.ImageId()), 0); BOOST_CHECK_EQUAL(cache.SceneGraph().NumObservationsForImage(image.ImageId()), 0); } colmap-3.4/src/base/database_test.cc000077500000000000000000000353351323400541200174540ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/database" #include "util/testing.h" #include #include "base/database.h" using namespace colmap; const static std::string kMemoryDatabasePath = ":memory:"; BOOST_AUTO_TEST_CASE(TestOpenCloseConstructorDestructor) { Database database(kMemoryDatabasePath); } BOOST_AUTO_TEST_CASE(TestOpenClose) { Database database(kMemoryDatabasePath); database.Close(); } BOOST_AUTO_TEST_CASE(TestTransaction) { Database database(kMemoryDatabasePath); DatabaseTransaction database_transaction(&database); } BOOST_AUTO_TEST_CASE(TestTransactionMultiThreaded) { Database database(kMemoryDatabasePath); std::thread thread1([&database]() { DatabaseTransaction database_transaction(&database); std::this_thread::sleep_for(std::chrono::milliseconds(100)); }); std::thread thread2([&database]() { DatabaseTransaction database_transaction(&database); std::this_thread::sleep_for(std::chrono::milliseconds(100)); }); thread1.join(); thread2.join(); } BOOST_AUTO_TEST_CASE(TestEmpty) { Database database(kMemoryDatabasePath); BOOST_CHECK_EQUAL(database.NumCameras(), 0); BOOST_CHECK_EQUAL(database.NumImages(), 0); BOOST_CHECK_EQUAL(database.NumKeypoints(), 0); BOOST_CHECK_EQUAL(database.MaxNumKeypoints(), 0); BOOST_CHECK_EQUAL(database.NumDescriptors(), 0); BOOST_CHECK_EQUAL(database.MaxNumDescriptors(), 0); BOOST_CHECK_EQUAL(database.NumMatches(), 0); BOOST_CHECK_EQUAL(database.NumMatchedImagePairs(), 0); BOOST_CHECK_EQUAL(database.NumVerifiedImagePairs(), 0); } BOOST_AUTO_TEST_CASE(TestImagePairToPairId) { BOOST_CHECK_EQUAL(Database::ImagePairToPairId(0, 0), 0); BOOST_CHECK_EQUAL(Database::ImagePairToPairId(0, 1), 1); BOOST_CHECK_EQUAL(Database::ImagePairToPairId(0, 2), 2); BOOST_CHECK_EQUAL(Database::ImagePairToPairId(0, 3), 3); BOOST_CHECK_EQUAL(Database::ImagePairToPairId(1, 2), Database::kMaxNumImages + 2); for (image_t i = 0; i < 20; ++i) { for (image_t j = 0; j < 20; ++j) { const image_pair_t pair_id = Database::ImagePairToPairId(i, j); image_t image_id1; image_t image_id2; Database::PairIdToImagePair(pair_id, &image_id1, &image_id2); if (i < j) { BOOST_CHECK_EQUAL(i, image_id1); BOOST_CHECK_EQUAL(j, image_id2); } else { BOOST_CHECK_EQUAL(i, image_id2); BOOST_CHECK_EQUAL(j, image_id1); } } } } BOOST_AUTO_TEST_CASE(TestSwapImagePair) { BOOST_CHECK(!Database::SwapImagePair(0, 0)); BOOST_CHECK(!Database::SwapImagePair(0, 1)); BOOST_CHECK(Database::SwapImagePair(1, 0)); BOOST_CHECK(!Database::SwapImagePair(1, 1)); } BOOST_AUTO_TEST_CASE(TestCamera) { Database database(kMemoryDatabasePath); BOOST_CHECK_EQUAL(database.NumCameras(), 0); Camera camera; camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); camera.SetCameraId(database.WriteCamera(camera)); BOOST_CHECK_EQUAL(database.NumCameras(), 1); BOOST_CHECK_EQUAL(database.ExistsCamera(camera.CameraId()), true); BOOST_CHECK_EQUAL(database.ReadCamera(camera.CameraId()).CameraId(), camera.CameraId()); BOOST_CHECK_EQUAL(database.ReadCamera(camera.CameraId()).ModelId(), camera.ModelId()); BOOST_CHECK_EQUAL(database.ReadCamera(camera.CameraId()).FocalLength(), camera.FocalLength()); BOOST_CHECK_EQUAL(database.ReadCamera(camera.CameraId()).PrincipalPointX(), camera.PrincipalPointX()); BOOST_CHECK_EQUAL(database.ReadCamera(camera.CameraId()).PrincipalPointY(), camera.PrincipalPointY()); camera.SetFocalLength(2.0); database.UpdateCamera(camera); BOOST_CHECK_EQUAL(database.ReadCamera(camera.CameraId()).FocalLength(), camera.FocalLength()); Camera camera2 = camera; camera2.SetCameraId(camera.CameraId() + 1); database.WriteCamera(camera2, true); BOOST_CHECK_EQUAL(database.NumCameras(), 2); BOOST_CHECK_EQUAL(database.ExistsCamera(camera.CameraId()), true); BOOST_CHECK_EQUAL(database.ExistsCamera(camera2.CameraId()), true); BOOST_CHECK_EQUAL(database.ReadAllCameras().size(), 2); BOOST_CHECK_EQUAL(database.ReadAllCameras()[0].CameraId(), camera.CameraId()); BOOST_CHECK_EQUAL(database.ReadAllCameras()[1].CameraId(), camera2.CameraId()); } BOOST_AUTO_TEST_CASE(TestImage) { Database database(kMemoryDatabasePath); Camera camera; camera.InitializeWithName("SIMPLE_PINHOLE", 1.0, 1, 1); camera.SetCameraId(database.WriteCamera(camera)); BOOST_CHECK_EQUAL(database.NumImages(), 0); Image image; image.SetName("test"); image.SetCameraId(camera.CameraId()); image.SetQvecPrior(Eigen::Vector4d(0.1, 0.2, 0.3, 0.4)); image.SetTvecPrior(Eigen::Vector3d(0.1, 0.2, 0.3)); image.SetImageId(database.WriteImage(image)); BOOST_CHECK_EQUAL(database.NumImages(), 1); BOOST_CHECK_EQUAL(database.ExistsImage(image.ImageId()), true); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).ImageId(), image.ImageId()); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).CameraId(), image.CameraId()); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(0), image.QvecPrior(0)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(1), image.QvecPrior(1)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(2), image.QvecPrior(2)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(3), image.QvecPrior(3)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).TvecPrior(0), image.TvecPrior(0)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).TvecPrior(1), image.TvecPrior(1)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).TvecPrior(2), image.TvecPrior(2)); image.TvecPrior(0) += 2; database.UpdateImage(image); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).ImageId(), image.ImageId()); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).CameraId(), image.CameraId()); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(0), image.QvecPrior(0)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(1), image.QvecPrior(1)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(2), image.QvecPrior(2)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).QvecPrior(3), image.QvecPrior(3)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).TvecPrior(0), image.TvecPrior(0)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).TvecPrior(1), image.TvecPrior(1)); BOOST_CHECK_EQUAL(database.ReadImage(image.ImageId()).TvecPrior(2), image.TvecPrior(2)); Image image2 = image; image2.SetName("test2"); image2.SetImageId(image.ImageId() + 1); database.WriteImage(image2, true); BOOST_CHECK_EQUAL(database.NumImages(), 2); BOOST_CHECK_EQUAL(database.ExistsImage(image.ImageId()), true); BOOST_CHECK_EQUAL(database.ExistsImage(image2.ImageId()), true); BOOST_CHECK_EQUAL(database.ReadAllImages().size(), 2); } BOOST_AUTO_TEST_CASE(TestKeypoints) { Database database(kMemoryDatabasePath); Camera camera; camera.SetCameraId(database.WriteCamera(camera)); Image image; image.SetName("test"); image.SetCameraId(camera.CameraId()); image.SetImageId(database.WriteImage(image)); BOOST_CHECK_EQUAL(database.NumKeypoints(), 0); BOOST_CHECK_EQUAL(database.NumKeypointsForImage(image.ImageId()), 0); const FeatureKeypoints keypoints = FeatureKeypoints(10); database.WriteKeypoints(image.ImageId(), keypoints); const FeatureKeypoints keypoints_read = database.ReadKeypoints(image.ImageId()); BOOST_CHECK_EQUAL(keypoints.size(), keypoints_read.size()); for (size_t i = 0; i < keypoints.size(); ++i) { BOOST_CHECK_EQUAL(keypoints[i].x, keypoints_read[i].x); BOOST_CHECK_EQUAL(keypoints[i].y, keypoints_read[i].y); BOOST_CHECK_EQUAL(keypoints[i].a11, keypoints_read[i].a11); BOOST_CHECK_EQUAL(keypoints[i].a12, keypoints_read[i].a12); BOOST_CHECK_EQUAL(keypoints[i].a21, keypoints_read[i].a21); BOOST_CHECK_EQUAL(keypoints[i].a22, keypoints_read[i].a22); } BOOST_CHECK_EQUAL(database.NumKeypoints(), 10); BOOST_CHECK_EQUAL(database.MaxNumKeypoints(), 10); BOOST_CHECK_EQUAL(database.NumKeypointsForImage(image.ImageId()), 10); const FeatureKeypoints keypoints2 = FeatureKeypoints(20); image.SetName("test2"); image.SetImageId(database.WriteImage(image)); database.WriteKeypoints(image.ImageId(), keypoints2); BOOST_CHECK_EQUAL(database.NumKeypoints(), 30); BOOST_CHECK_EQUAL(database.MaxNumKeypoints(), 20); BOOST_CHECK_EQUAL(database.NumKeypointsForImage(image.ImageId()), 20); } BOOST_AUTO_TEST_CASE(TestDescriptors) { Database database(kMemoryDatabasePath); Camera camera; camera.SetCameraId(database.WriteCamera(camera)); Image image; image.SetName("test"); image.SetCameraId(camera.CameraId()); image.SetImageId(database.WriteImage(image)); BOOST_CHECK_EQUAL(database.NumDescriptors(), 0); BOOST_CHECK_EQUAL(database.NumDescriptorsForImage(image.ImageId()), 0); const FeatureDescriptors descriptors = FeatureDescriptors::Random(10, 128); database.WriteDescriptors(image.ImageId(), descriptors); const FeatureDescriptors descriptors_read = database.ReadDescriptors(image.ImageId()); BOOST_CHECK_EQUAL(descriptors.rows(), descriptors_read.rows()); BOOST_CHECK_EQUAL(descriptors.cols(), descriptors_read.cols()); for (FeatureDescriptors::Index r = 0; r < descriptors.rows(); ++r) { for (FeatureDescriptors::Index c = 0; c < descriptors.cols(); ++c) { BOOST_CHECK_EQUAL(descriptors(r, c), descriptors_read(r, c)); } } BOOST_CHECK_EQUAL(database.NumDescriptors(), 10); BOOST_CHECK_EQUAL(database.MaxNumDescriptors(), 10); BOOST_CHECK_EQUAL(database.NumDescriptorsForImage(image.ImageId()), 10); const FeatureDescriptors descriptors2 = FeatureDescriptors(20, 128); image.SetName("test2"); image.SetImageId(database.WriteImage(image)); database.WriteDescriptors(image.ImageId(), descriptors2); BOOST_CHECK_EQUAL(database.NumDescriptors(), 30); BOOST_CHECK_EQUAL(database.MaxNumDescriptors(), 20); BOOST_CHECK_EQUAL(database.NumDescriptorsForImage(image.ImageId()), 20); } BOOST_AUTO_TEST_CASE(TestMatches) { Database database(kMemoryDatabasePath); const image_t image_id1 = 1; const image_t image_id2 = 2; const FeatureMatches matches = FeatureMatches(1000); database.WriteMatches(image_id1, image_id2, matches); const FeatureMatches matches_read = database.ReadMatches(image_id1, image_id2); BOOST_CHECK_EQUAL(matches.size(), matches_read.size()); for (size_t i = 0; i < matches.size(); ++i) { BOOST_CHECK_EQUAL(matches[i].point2D_idx1, matches_read[i].point2D_idx1); BOOST_CHECK_EQUAL(matches[i].point2D_idx2, matches_read[i].point2D_idx2); } BOOST_CHECK_EQUAL(database.ReadAllMatches().size(), 1); BOOST_CHECK_EQUAL(database.ReadAllMatches()[0].first, Database::ImagePairToPairId(image_id1, image_id2)); BOOST_CHECK_EQUAL(database.NumMatches(), 1000); database.DeleteMatches(image_id1, image_id2); BOOST_CHECK_EQUAL(database.NumMatches(), 0); database.WriteMatches(image_id1, image_id2, matches); BOOST_CHECK_EQUAL(database.NumMatches(), 1000); database.ClearMatches(); BOOST_CHECK_EQUAL(database.NumMatches(), 0); } BOOST_AUTO_TEST_CASE(TestInlierMatches) { Database database(kMemoryDatabasePath); const image_t image_id1 = 1; const image_t image_id2 = 2; TwoViewGeometry two_view_geometry; two_view_geometry.inlier_matches = FeatureMatches(1000); two_view_geometry.config = TwoViewGeometry::ConfigurationType::PLANAR_OR_PANORAMIC; two_view_geometry.F = Eigen::Matrix3d::Random(); two_view_geometry.E = Eigen::Matrix3d::Random(); two_view_geometry.H = Eigen::Matrix3d::Random(); database.WriteInlierMatches(image_id1, image_id2, two_view_geometry); const TwoViewGeometry two_view_geometry_read = database.ReadInlierMatches(image_id1, image_id2); BOOST_CHECK_EQUAL(two_view_geometry.inlier_matches.size(), two_view_geometry_read.inlier_matches.size()); for (size_t i = 0; i < two_view_geometry_read.inlier_matches.size(); ++i) { BOOST_CHECK_EQUAL(two_view_geometry.inlier_matches[i].point2D_idx1, two_view_geometry_read.inlier_matches[i].point2D_idx1); BOOST_CHECK_EQUAL(two_view_geometry.inlier_matches[i].point2D_idx2, two_view_geometry_read.inlier_matches[i].point2D_idx2); } BOOST_CHECK_EQUAL(two_view_geometry.config, two_view_geometry_read.config); BOOST_CHECK_EQUAL(two_view_geometry.F, two_view_geometry_read.F); BOOST_CHECK_EQUAL(two_view_geometry.E, two_view_geometry_read.E); BOOST_CHECK_EQUAL(two_view_geometry.H, two_view_geometry_read.H); std::vector image_pair_ids; std::vector two_view_geometries; database.ReadAllInlierMatches(&image_pair_ids, &two_view_geometries); BOOST_CHECK_EQUAL(image_pair_ids.size(), 1); BOOST_CHECK_EQUAL(two_view_geometries.size(), 1); BOOST_CHECK_EQUAL(image_pair_ids[0], Database::ImagePairToPairId(image_id1, image_id2)); std::vector> image_pairs; std::vector num_inliers; database.ReadInlierMatchesGraph(&image_pairs, &num_inliers); BOOST_CHECK_EQUAL(image_pairs.size(), 1); BOOST_CHECK_EQUAL(num_inliers.size(), 1); BOOST_CHECK_EQUAL(image_pairs[0].first, image_id1); BOOST_CHECK_EQUAL(image_pairs[0].second, image_id2); BOOST_CHECK_EQUAL(num_inliers[0], two_view_geometry.inlier_matches.size()); BOOST_CHECK_EQUAL(database.NumInlierMatches(), 1000); database.DeleteInlierMatches(image_id1, image_id2); BOOST_CHECK_EQUAL(database.NumInlierMatches(), 0); database.WriteInlierMatches(image_id1, image_id2, two_view_geometry); BOOST_CHECK_EQUAL(database.NumInlierMatches(), 1000); database.ClearInlierMatches(); BOOST_CHECK_EQUAL(database.NumInlierMatches(), 0); } colmap-3.4/src/base/essential_matrix.cc000077500000000000000000000152121323400541200202140ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/essential_matrix.h" #include #include "base/pose.h" #include "estimators/pose.h" namespace colmap { void DecomposeEssentialMatrix(const Eigen::Matrix3d& E, Eigen::Matrix3d* R1, Eigen::Matrix3d* R2, Eigen::Vector3d* t) { Eigen::JacobiSVD svd( E, Eigen::ComputeFullU | Eigen::ComputeFullV); Eigen::Matrix3d U = svd.matrixU(); Eigen::Matrix3d V = svd.matrixV().transpose(); if (U.determinant() < 0) { U *= -1; } if (V.determinant() < 0) { V *= -1; } Eigen::Matrix3d W; W << 0, 1, 0, -1, 0, 0, 0, 0, 1; *R1 = U * W * V; *R2 = U * W.transpose() * V; *t = U.col(2).normalized(); } void PoseFromEssentialMatrix(const Eigen::Matrix3d& E, const std::vector& points1, const std::vector& points2, Eigen::Matrix3d* R, Eigen::Vector3d* t, std::vector* points3D) { CHECK_EQ(points1.size(), points2.size()); Eigen::Matrix3d R1; Eigen::Matrix3d R2; DecomposeEssentialMatrix(E, &R1, &R2, t); // Generate all possible projection matrix combinations. const std::array R_cmbs{{R1, R2, R1, R2}}; const std::array t_cmbs{{*t, *t, -*t, -*t}}; points3D->clear(); for (size_t i = 0; i < R_cmbs.size(); ++i) { std::vector points3D_cmb; CheckCheirality(R_cmbs[i], t_cmbs[i], points1, points2, &points3D_cmb); if (points3D_cmb.size() >= points3D->size()) { *R = R_cmbs[i]; *t = t_cmbs[i]; *points3D = points3D_cmb; } } } Eigen::Matrix3d EssentialMatrixFromPose(const Eigen::Matrix3d& R, const Eigen::Vector3d& t) { return CrossProductMatrix(t.normalized()) * R; } Eigen::Matrix3d EssentialMatrixFromAbsolutePoses( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2) { const Eigen::Matrix3d R1 = proj_matrix1.leftCols<3>(); const Eigen::Matrix3d R2 = proj_matrix2.leftCols<3>(); const Eigen::Vector3d t1 = proj_matrix1.rightCols<1>(); const Eigen::Vector3d t2 = proj_matrix2.rightCols<1>(); // Relative transformation between to cameras. const Eigen::Matrix3d R = R1.transpose() * R2; const Eigen::Vector3d t = (R1.transpose() * (t2 - t1)).normalized(); return EssentialMatrixFromPose(R, t); } void FindOptimalImageObservations(const Eigen::Matrix3d& E, const Eigen::Vector2d& point1, const Eigen::Vector2d& point2, Eigen::Vector2d* optimal_point1, Eigen::Vector2d* optimal_point2) { const Eigen::Vector3d& point1h = point1.homogeneous(); const Eigen::Vector3d& point2h = point2.homogeneous(); Eigen::Matrix S; S << 1, 0, 0, 0, 1, 0; // Epipolar lines. Eigen::Vector2d n1 = S * E * point2h; Eigen::Vector2d n2 = S * E.transpose() * point1h; const Eigen::Matrix2d E_tilde = E.block<2, 2>(0, 0); const double a = n1.transpose() * E_tilde * n2; const double b = (n1.squaredNorm() + n2.squaredNorm()) / 2.0; const double c = point1h.transpose() * E * point2h; const double d = sqrt(b * b - a * c); double lambda = c / (b + d); n1 -= E_tilde * lambda * n1; n2 -= E_tilde.transpose() * lambda * n2; lambda *= (2.0 * d) / (n1.squaredNorm() + n2.squaredNorm()); *optimal_point1 = (point1h - S.transpose() * lambda * n1).hnormalized(); *optimal_point2 = (point2h - S.transpose() * lambda * n2).hnormalized(); } Eigen::Vector3d EpipoleFromEssentialMatrix(const Eigen::Matrix3d& E, const bool left_image) { Eigen::Vector3d e; if (left_image) { Eigen::JacobiSVD svd(E, Eigen::ComputeFullV); e = svd.matrixV().block<3, 1>(0, 2); } else { Eigen::JacobiSVD svd(E.transpose(), Eigen::ComputeFullV); e = svd.matrixV().block<3, 1>(0, 2); } return e; } Eigen::Matrix3d InvertEssentialMatrix(const Eigen::Matrix3d& E) { return E.transpose(); } bool RefineEssentialMatrix(const ceres::Solver::Options& options, const std::vector& points1, const std::vector& points2, const std::vector& inlier_mask, Eigen::Matrix3d* E) { CHECK_EQ(points1.size(), points2.size()); CHECK_EQ(points1.size(), inlier_mask.size()); // Extract inlier points for decomposing the essential matrix into // rotation and translation components. size_t num_inliers = 0; for (const auto inlier : inlier_mask) { if (inlier) { num_inliers += 1; } } std::vector inlier_points1(num_inliers); std::vector inlier_points2(num_inliers); size_t j = 0; for (size_t i = 0; i < inlier_mask.size(); ++i) { if (inlier_mask[i]) { inlier_points1[j] = points1[i]; inlier_points2[j] = points2[i]; j += 1; } } // Extract relative pose from essential matrix. Eigen::Matrix3d R; Eigen::Vector3d tvec; std::vector points3D; PoseFromEssentialMatrix(*E, inlier_points1, inlier_points2, &R, &tvec, &points3D); Eigen::Vector4d qvec = RotationMatrixToQuaternion(R); if (points3D.size() == 0) { return false; } // Refine essential matrix, use all points so that refinement is able to // consider points as inliers that were originally outliers. const bool refinement_success = RefineRelativePose(options, inlier_points1, inlier_points2, &qvec, &tvec); if (!refinement_success) { return false; } // Compose refined essential matrix. const Eigen::Matrix3d rot_mat = QuaternionToRotationMatrix(qvec); *E = EssentialMatrixFromPose(rot_mat, tvec); return true; } } // namespace colmap colmap-3.4/src/base/essential_matrix.h000077500000000000000000000141251323400541200200600ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_ESSENTIAL_MATRIX_H_ #define COLMAP_SRC_BASE_ESSENTIAL_MATRIX_H_ #include #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Decompose an essential matrix into the possible rotations and translations. // // The first pose is assumed to be P = [I | 0] and the set of four other // possible second poses are defined as: {[R1 | t], [R2 | t], // [R1 | -t], [R2 | -t]} // // @param E 3x3 essential matrix. // @param R1 First possible 3x3 rotation matrix. // @param R2 Second possible 3x3 rotation matrix. // @param t 3x1 possible translation vector (also -t possible). void DecomposeEssentialMatrix(const Eigen::Matrix3d& E, Eigen::Matrix3d* R1, Eigen::Matrix3d* R2, Eigen::Vector3d* t); // Recover the most probable pose from the given essential matrix. // // The pose of the first image is assumed to be P = [I | 0]. // // @param E 3x3 essential matrix. // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param inlier_mask Only points with `true` in the inlier mask are // considered in the cheirality test. Size of the // inlier mask must match the number of points N. // @param R Most probable 3x3 rotation matrix. // @param t Most probable 3x1 translation vector. // @param points3D Triangulated 3D points infront of camera. void PoseFromEssentialMatrix(const Eigen::Matrix3d& E, const std::vector& points1, const std::vector& points2, Eigen::Matrix3d* R, Eigen::Vector3d* t, std::vector* points3D); // Compose essential matrix from relative camera poses. // // Assumes that first camera pose has projection matrix P = [I | 0], and // pose of second camera is given as transformation from world to camera system. // // @param R 3x3 rotation matrix. // @param t 3x1 translation vector. // // @return 3x3 essential matrix. Eigen::Matrix3d EssentialMatrixFromPose(const Eigen::Matrix3d& R, const Eigen::Vector3d& t); // Compose essential matrix from two absolute camera poses. // // @param proj_matrix1 3x4 projection matrix. // @param proj_matrix2 3x4 projection matrix. // // @return 3x3 essential matrix. Eigen::Matrix3d EssentialMatrixFromAbsolutePoses( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2); // Find optimal image points, such that: // // optimal_point1^t * E * optimal_point2 = 0 // // as described in: // // Lindstrom, P., "Triangulation made easy", // Computer Vision and Pattern Recognition (CVPR), // 2010 IEEE Conference on , vol., no., pp.1554,1561, 13-18 June 2010 // // @param E Essential or fundamental matrix. // @param point1 Corresponding 2D point in first image. // @param point2 Corresponding 2D point in second image. // @param optimal_point1 Estimated optimal image point in the first image. // @param optimal_point2 Estimated optimal image point in the second image. void FindOptimalImageObservations(const Eigen::Matrix3d& E, const Eigen::Vector2d& point1, const Eigen::Vector2d& point2, Eigen::Vector2d* optimal_point1, Eigen::Vector2d* optimal_point2); // Compute the location of the epipole in homogeneous coordinates. // // @param E 3x3 essential matrix. // @param left_image If true, epipole in left image is computed, // else in right image. // // @return Epipole in homogeneous coordinates. Eigen::Vector3d EpipoleFromEssentialMatrix(const Eigen::Matrix3d& E, const bool left_image); // Invert the essential matrix, i.e. if the essential matrix E describes the // transformation from camera A to B, the inverted essential matrix E' describes // the transformation from camera B to A. // // @param E 3x3 essential matrix. // // @return Inverted essential matrix. Eigen::Matrix3d InvertEssentialMatrix(const Eigen::Matrix3d& matrix); // Refine essential matrix. // // Decomposes the essential matrix into rotation and translation components // and refines the relative pose using the function `RefineRelativePose`. // // @param E 3x3 essential matrix. // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param inlier_mask Inlier mask for corresponding points. // @param options Solver options. // // @return Flag indicating if solution is usable. bool RefineEssentialMatrix(const ceres::Solver::Options& options, const std::vector& points1, const std::vector& points2, const std::vector& inlier_mask, Eigen::Matrix3d* E); } // namespace colmap #endif // COLMAP_SRC_BASE_ESSENTIAL_MATRIX_H_ colmap-3.4/src/base/essential_matrix_test.cc000077500000000000000000000170331323400541200212560ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/essential_matrix" #include "util/testing.h" #include #include "base/essential_matrix.h" #include "base/pose.h" #include "base/projection.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDecomposeEssentialMatrix) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 1, 1); const Eigen::Vector3d t = Eigen::Vector3d(0.5, 1, 1).normalized(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R, t); Eigen::Matrix3d R1; Eigen::Matrix3d R2; Eigen::Vector3d tt; DecomposeEssentialMatrix(E, &R1, &R2, &tt); BOOST_CHECK((R1 - R).norm() < 1e-10 || (R2 - R).norm() < 1e-10); BOOST_CHECK((tt - t).norm() < 1e-10 || (tt + t).norm() < 1e-10); } BOOST_AUTO_TEST_CASE(TestEssentialMatrixFromPose) { BOOST_CHECK_EQUAL( EssentialMatrixFromPose(EulerAnglesToRotationMatrix(0, 0, 0), Eigen::Vector3d(0, 0, 1)), (Eigen::MatrixXd(3, 3) << 0, -1, 0, 1, 0, 0, 0, 0, 0).finished()); BOOST_CHECK_EQUAL( EssentialMatrixFromPose(EulerAnglesToRotationMatrix(0, 0, 0), Eigen::Vector3d(0, 0, 2)), (Eigen::MatrixXd(3, 3) << 0, -1, 0, 1, 0, 0, 0, 0, 0).finished()); } BOOST_AUTO_TEST_CASE(TestEssentialMatrixFromPoses) { const Eigen::Matrix3d R1 = EulerAnglesToRotationMatrix(0, 0, 0); const Eigen::Matrix3d R2 = EulerAnglesToRotationMatrix(0, 1, 2); const Eigen::Vector3d t1(0, 0, 0); const Eigen::Vector3d t2 = Eigen::Vector3d(0.5, 1, 1).normalized(); const Eigen::Matrix3d E1 = EssentialMatrixFromPose(R2, t2); const Eigen::Matrix3d E2 = EssentialMatrixFromAbsolutePoses( ComposeProjectionMatrix(R1, t1), ComposeProjectionMatrix(R2, t2)); BOOST_CHECK_CLOSE((E1 - E2).norm(), 0, 1e-6); } BOOST_AUTO_TEST_CASE(TestPoseFromEssentialMatrix) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 0, 0); const Eigen::Vector3d t = Eigen::Vector3d(1, 0, 0).normalized(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R, t); const Eigen::Matrix3x4d proj_matrix1 = Eigen::Matrix3x4d::Identity(); const Eigen::Matrix3x4d proj_matrix2 = ComposeProjectionMatrix(R, t); std::vector points3D(4); points3D[0] = Eigen::Vector3d(0, 0, 1); points3D[1] = Eigen::Vector3d(0, 0.1, 1); points3D[2] = Eigen::Vector3d(0.1, 0, 1); points3D[3] = Eigen::Vector3d(0.1, 0.1, 1); std::vector points1(4); std::vector points2(4); for (size_t i = 0; i < points3D.size(); ++i) { const Eigen::Vector3d point1 = proj_matrix1 * points3D[i].homogeneous(); points1[i] = point1.hnormalized(); const Eigen::Vector3d point2 = proj_matrix2 * points3D[i].homogeneous(); points2[i] = point2.hnormalized(); } points3D.clear(); Eigen::Matrix3d RR; Eigen::Vector3d tt; PoseFromEssentialMatrix(E, points1, points2, &RR, &tt, &points3D); BOOST_CHECK_EQUAL(points3D.size(), 4); BOOST_CHECK(RR.isApprox(R)); BOOST_CHECK(tt.isApprox(t)); } BOOST_AUTO_TEST_CASE(TestFindOptimalImageObservations) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 0, 0); const Eigen::Vector3d t = Eigen::Vector3d(1, 0, 0).normalized(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R, t); const Eigen::Matrix3x4d proj_matrix1 = Eigen::Matrix3x4d::Identity(); const Eigen::Matrix3x4d proj_matrix2 = ComposeProjectionMatrix(R, t); std::vector points3D(4); points3D[0] = Eigen::Vector3d(0, 0, 1); points3D[1] = Eigen::Vector3d(0, 0.1, 1); points3D[2] = Eigen::Vector3d(0.1, 0, 1); points3D[3] = Eigen::Vector3d(0.1, 0.1, 1); // Test if perfect projection is equivalent to optimal image observations. for (size_t i = 0; i < points3D.size(); ++i) { const Eigen::Vector3d point1_homogeneous = proj_matrix1 * points3D[i].homogeneous(); const Eigen::Vector2d point1 = point1_homogeneous.hnormalized(); const Eigen::Vector3d point2_homogeneous = proj_matrix2 * points3D[i].homogeneous(); const Eigen::Vector2d point2 = point2_homogeneous.hnormalized(); Eigen::Vector2d optimal_point1; Eigen::Vector2d optimal_point2; FindOptimalImageObservations(E, point1, point2, &optimal_point1, &optimal_point2); BOOST_CHECK(point1.isApprox(optimal_point1)); BOOST_CHECK(point2.isApprox(optimal_point2)); } } BOOST_AUTO_TEST_CASE(TestEpipoleFromEssentialMatrix) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 0, 0); const Eigen::Vector3d t = Eigen::Vector3d(0, 0, -1).normalized(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R, t); const Eigen::Vector3d left_epipole = EpipoleFromEssentialMatrix(E, true); const Eigen::Vector3d right_epipole = EpipoleFromEssentialMatrix(E, false); BOOST_CHECK(left_epipole.isApprox(Eigen::Vector3d(0, 0, 1))); BOOST_CHECK(right_epipole.isApprox(Eigen::Vector3d(0, 0, 1))); } BOOST_AUTO_TEST_CASE(TestInvertEssentialMatrix) { for (size_t i = 1; i < 10; ++i) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 0.1, 0); const Eigen::Vector3d t = Eigen::Vector3d(0, 0, i).normalized(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R, t); const Eigen::Matrix3d inv_inv_E = InvertEssentialMatrix(InvertEssentialMatrix(E)); BOOST_CHECK(E.isApprox(inv_inv_E)); } } BOOST_AUTO_TEST_CASE(TestRefineEssentialMatrix) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 0, 0); const Eigen::Vector3d t = Eigen::Vector3d(1, 0, 0).normalized(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R, t); const Eigen::Matrix3x4d proj_matrix1 = Eigen::Matrix3x4d::Identity(); const Eigen::Matrix3x4d proj_matrix2 = ComposeProjectionMatrix(R, t); std::vector points3D(150); for (size_t i = 0; i < points3D.size() / 3; ++i) { points3D[3 * i + 0] = Eigen::Vector3d(i * 0.01, 0, 1); points3D[3 * i + 1] = Eigen::Vector3d(0, i * 0.01, 1); points3D[3 * i + 2] = Eigen::Vector3d(i * 0.01, i * 0.01, 1); } std::vector points1(points3D.size()); std::vector points2(points3D.size()); for (size_t i = 0; i < points3D.size(); ++i) { const Eigen::Vector3d point1 = proj_matrix1 * points3D[i].homogeneous(); points1[i] = point1.hnormalized(); const Eigen::Vector3d point2 = proj_matrix2 * points3D[i].homogeneous(); points2[i] = point2.hnormalized(); } const Eigen::Matrix3d R_pertubated = EulerAnglesToRotationMatrix(0, 0, 0); const Eigen::Vector3d t_pertubated = Eigen::Vector3d(1.02, 0.02, 0.02).normalized(); const Eigen::Matrix3d E_pertubated = EssentialMatrixFromPose(R_pertubated, t_pertubated); Eigen::Matrix3d E_refined = E_pertubated; ceres::Solver::Options options; RefineEssentialMatrix(options, points1, points2, std::vector(points1.size(), true), &E_refined); BOOST_CHECK_LE((E - E_refined).norm(), (E - E_pertubated).norm()); } colmap-3.4/src/base/gps.cc000077500000000000000000000061061323400541200154340ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/gps.h" #include "util/math.h" namespace colmap { GPSTransform::GPSTransform(const int ellipsoid) { switch (ellipsoid) { case GRS80: a_ = 6378137; b_ = 6.356752314140356e+06; f_ = 0.003352810681182; break; case WGS84: a_ = 6378137; b_ = 6.356752314245179e+06; f_ = 0.003352810664747; break; default: a_ = std::numeric_limits::quiet_NaN(); b_ = std::numeric_limits::quiet_NaN(); f_ = std::numeric_limits::quiet_NaN(); throw std::invalid_argument("Ellipsoid not defined"); } e2_ = (a_ * a_ - b_ * b_) / (a_ * a_); } std::vector GPSTransform::EllToXYZ( const std::vector& ell) const { std::vector xyz(ell.size()); for (size_t i = 0; i < ell.size(); ++i) { const double lat = DegToRad(ell[i](0)); const double lon = DegToRad(ell[i](1)); const double alt = ell[i](2); const double sin_lat = sin(lat); const double sin_lon = sin(lon); const double cos_lat = cos(lat); const double cos_lon = cos(lon); // Normalized radius const double N = a_ / sqrt(1 - e2_ * sin_lat * sin_lat); xyz[i](0) = (N + alt) * cos_lat * cos_lon; xyz[i](1) = (N + alt) * cos_lat * sin_lon; xyz[i](2) = (N * (1 - e2_) + alt) * sin_lat; } return xyz; } std::vector GPSTransform::XYZToEll( const std::vector& xyz) const { std::vector ell(xyz.size()); for (size_t i = 0; i < ell.size(); ++i) { const double x = xyz[i](0); const double y = xyz[i](1); const double z = xyz[i](2); const double xx = x * x; const double yy = y * y; const double kEps = 1e-12; // Latitude double lat = atan2(z, sqrt(xx + yy)); double alt; for (size_t j = 0; j < 100; ++j) { const double sin_lat0 = sin(lat); const double N = a_ / sqrt(1 - e2_ * sin_lat0 * sin_lat0); alt = sqrt(xx + yy) / cos(lat) - N; const double prev_lat = lat; lat = atan((z / sqrt(xx + yy)) * 1 / (1 - e2_ * N / (N + alt))); if (std::abs(prev_lat - lat) < kEps) { break; } } ell[i](0) = RadToDeg(lat); // Longitude ell[i](1) = RadToDeg(atan2(y, x)); // Alt ell[i](2) = alt; } return ell; } } // namespace colmap colmap-3.4/src/base/gps.h000077500000000000000000000030601323400541200152720ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_GPS_H_ #define COLMAP_SRC_BASE_GPS_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Transform ellipsoidal GPS coordinates to Cartesian GPS coordinate // representation and vice versa. class GPSTransform { public: enum ELLIPSOID { GRS80, WGS84 }; explicit GPSTransform(const int ellipsoid = GRS80); std::vector EllToXYZ( const std::vector& ell) const; std::vector XYZToEll( const std::vector& xyz) const; private: // Semimajor axis. double a_; // Semiminor axis. double b_; // Flattening. double f_; // Numerical eccentricity. double e2_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_GPS_H_ colmap-3.4/src/base/gps_test.cc000077500000000000000000000132021323400541200164660ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/gps" #include "util/testing.h" #include "base/gps.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEllToXYZGRS80) { std::vector ell; ell.emplace_back(48 + 8. / 60 + 51.70361 / 3600, 11 + 34. / 60 + 10.51777 / 3600, 561.1851); ell.emplace_back(48 + 8. / 60 + 52.40575 / 3600, 11 + 34. / 60 + 11.77179 / 3600, 561.1509); std::vector ref_xyz; ref_xyz.emplace_back(4.177239709080851e6, 0.855153779931214e6, 4.728267404656370e6); ref_xyz.emplace_back(4.177218660490202e6, 0.855175931351848e6, 4.728281850269709e6); GPSTransform gps_tform(GPSTransform::GRS80); const auto xyz = gps_tform.EllToXYZ(ell); for (size_t i = 0; i < ell.size(); ++i) { BOOST_CHECK(std::abs(xyz[i](0) - ref_xyz[i](0)) < 1e-8); BOOST_CHECK(std::abs(xyz[i](1) - ref_xyz[i](1)) < 1e-8); BOOST_CHECK(std::abs(xyz[i](2) - ref_xyz[i](2)) < 1e-8); } } BOOST_AUTO_TEST_CASE(TestEllToXYZWGS84) { std::vector ell; ell.emplace_back(48 + 8. / 60 + 51.70361 / 3600, 11 + 34. / 60 + 10.51777 / 3600, 561.1851); ell.emplace_back(48 + 8. / 60 + 52.40575 / 3600, 11 + 34. / 60 + 11.77179 / 3600, 561.1509); std::vector ref_xyz; ref_xyz.emplace_back(4.177239709042750e6, 0.855153779923415e6, 4.728267404769168e6); ref_xyz.emplace_back(4.177218660452103e6, 0.855175931344048e6, 4.728281850382507e6); GPSTransform gps_tform(GPSTransform::WGS84); const auto xyz = gps_tform.EllToXYZ(ell); for (size_t i = 0; i < ell.size(); ++i) { BOOST_CHECK(std::abs(xyz[i](0) - ref_xyz[i](0)) < 1e-8); BOOST_CHECK(std::abs(xyz[i](1) - ref_xyz[i](1)) < 1e-8); BOOST_CHECK(std::abs(xyz[i](2) - ref_xyz[i](2)) < 1e-8); } } BOOST_AUTO_TEST_CASE(TestXYZToEll_GRS80) { std::vector xyz; xyz.emplace_back(4.177239709080851e6, 0.855153779931214e6, 4.728267404656370e6); xyz.emplace_back(4.177218660490202e6, 0.855175931351848e6, 4.728281850269709e6); std::vector ref_ell; ref_ell.emplace_back(48 + 8. / 60 + 51.70361 / 3600, 11 + 34. / 60 + 10.51777 / 3600, 561.1851); ref_ell.emplace_back(48 + 8. / 60 + 52.40575 / 3600, 11 + 34. / 60 + 11.77179 / 3600, 561.1509); GPSTransform gps_tform(GPSTransform::GRS80); const auto ell = gps_tform.XYZToEll(xyz); for (size_t i = 0; i < xyz.size(); ++i) { BOOST_CHECK(std::abs(ell[i](0) - ref_ell[i](0)) < 1e-5); BOOST_CHECK(std::abs(ell[i](1) - ref_ell[i](1)) < 1e-5); BOOST_CHECK(std::abs(ell[i](2) - ref_ell[i](2)) < 1e-5); } } BOOST_AUTO_TEST_CASE(TestXYZToEll_WGS84) { std::vector xyz; xyz.emplace_back(4.177239709042750e6, 0.855153779923415e6, 4.728267404769168e6); xyz.emplace_back(4.177218660452103e6, 0.855175931344048e6, 4.728281850382507e6); std::vector ref_ell; ref_ell.emplace_back(48 + 8. / 60 + 51.70361 / 3600, 11 + 34. / 60 + 10.51777 / 3600, 561.1851); ref_ell.emplace_back(48 + 8. / 60 + 52.40575 / 3600, 11 + 34. / 60 + 11.77179 / 3600, 561.1509); GPSTransform gps_tform(GPSTransform::WGS84); const auto ell = gps_tform.XYZToEll(xyz); for (size_t i = 0; i < xyz.size(); ++i) { BOOST_CHECK(std::abs(ell[i](0) - ref_ell[i](0)) < 1e-5); BOOST_CHECK(std::abs(ell[i](1) - ref_ell[i](1)) < 1e-5); BOOST_CHECK(std::abs(ell[i](2) - ref_ell[i](2)) < 1e-5); } } BOOST_AUTO_TEST_CASE(TestXYZToEllToXYZ_GRS80) { std::vector xyz; xyz.emplace_back(4.177239709080851e6, 0.855153779931214e6, 4.728267404656370e6); xyz.emplace_back(4.177218660490202e6, 0.855175931351848e6, 4.728281850269709e6); GPSTransform gps_tform(GPSTransform::GRS80); const auto ell = gps_tform.XYZToEll(xyz); const auto xyz2 = gps_tform.EllToXYZ(ell); for (size_t i = 0; i < xyz.size(); ++i) { BOOST_CHECK(std::abs(xyz[i](0) - xyz2[i](0)) < 1e-5); BOOST_CHECK(std::abs(xyz[i](1) - xyz2[i](1)) < 1e-5); BOOST_CHECK(std::abs(xyz[i](2) - xyz2[i](2)) < 1e-5); } } BOOST_AUTO_TEST_CASE(TestXYZToEllToXYZ_WGS84) { std::vector xyz; xyz.emplace_back(4.177239709080851e6, 0.855153779931214e6, 4.728267404656370e6); xyz.emplace_back(4.177218660490202e6, 0.855175931351848e6, 4.728281850269709e6); GPSTransform gps_tform(GPSTransform::WGS84); const auto ell = gps_tform.XYZToEll(xyz); const auto xyz2 = gps_tform.EllToXYZ(ell); for (size_t i = 0; i < xyz.size(); ++i) { BOOST_CHECK(std::abs(xyz[i](0) - xyz2[i](0)) < 1e-5); BOOST_CHECK(std::abs(xyz[i](1) - xyz2[i](1)) < 1e-5); BOOST_CHECK(std::abs(xyz[i](2) - xyz2[i](2)) < 1e-5); } } colmap-3.4/src/base/graph_cut.cc000066400000000000000000000145411323400541200166160ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/graph_cut.h" #include #include #include #include #include #include #include extern "C" { #include "ext/Graclus/metisLib/metis.h" } #include "util/logging.h" namespace colmap { namespace { // Wrapper class for weighted, undirected Graclus graph. class GraclusGraph { public: GraclusGraph(const std::vector>& edges, const std::vector& weights) { CHECK_EQ(edges.size(), weights.size()); std::unordered_map>> adjacency_list; for (size_t i = 0; i < edges.size(); ++i) { const auto& edge = edges[i]; const auto weight = weights[i]; const int vertex_idx1 = GetVertexIdx(edge.first); const int vertex_idx2 = GetVertexIdx(edge.second); adjacency_list[vertex_idx1].emplace_back(vertex_idx2, weight); adjacency_list[vertex_idx2].emplace_back(vertex_idx1, weight); } xadj_.reserve(vertex_id_to_idx_.size() + 1); adjncy_.reserve(2 * edges.size()); adjwgt_.reserve(2 * edges.size()); idxtype edge_idx = 0; for (size_t i = 0; i < vertex_id_to_idx_.size(); ++i) { xadj_.push_back(edge_idx); if (adjacency_list.count(i) == 0) { continue; } for (const auto& edge : adjacency_list[i]) { edge_idx += 1; adjncy_.push_back(edge.first); adjwgt_.push_back(edge.second); } } xadj_.push_back(edge_idx); CHECK_EQ(edge_idx, 2 * edges.size()); CHECK_EQ(xadj_.size(), vertex_id_to_idx_.size() + 1); CHECK_EQ(adjncy_.size(), 2 * edges.size()); CHECK_EQ(adjwgt_.size(), 2 * edges.size()); data.gdata = data.rdata = nullptr; data.nvtxs = vertex_id_to_idx_.size(); data.nedges = 2 * edges.size(); data.mincut = data.minvol = -1; data.xadj = xadj_.data(); data.adjncy = adjncy_.data(); data.vwgt = nullptr; data.adjwgt = adjwgt_.data(); data.adjwgtsum = nullptr; data.label = nullptr; data.cmap = nullptr; data.where = data.pwgts = nullptr; data.id = data.ed = nullptr; data.bndptr = data.bndind = nullptr; data.rinfo = nullptr; data.vrinfo = nullptr; data.nrinfo = nullptr; data.ncon = 1; data.nvwgt = nullptr; data.npwgts = nullptr; data.vsize = nullptr; data.coarser = data.finer = nullptr; } int GetVertexIdx(const int id) { const auto it = vertex_id_to_idx_.find(id); if (it == vertex_id_to_idx_.end()) { const int idx = vertex_id_to_idx_.size(); vertex_id_to_idx_.emplace(id, idx); vertex_idx_to_id_.emplace(idx, id); return idx; } else { return it->second; } } int GetVertexId(const int idx) { return vertex_idx_to_id_.at(idx); } GraphType data; private: std::unordered_map vertex_id_to_idx_; std::unordered_map vertex_idx_to_id_; std::vector xadj_; std::vector adjncy_; std::vector adjwgt_; }; } // namespace void ComputeMinGraphCut(const std::vector>& edges, const std::vector& weights, int* cut_weight, std::vector* cut_labels) { CHECK_EQ(edges.size(), weights.size()); CHECK_GE(edges.size(), 2); typedef boost::property edge_weight_t; typedef boost::adjacency_list undirected_graph_t; int max_vertex_index = 0; for (const auto& edge : edges) { CHECK_GE(edge.first, 0); CHECK_GE(edge.second, 0); max_vertex_index = std::max(max_vertex_index, edge.first); max_vertex_index = std::max(max_vertex_index, edge.second); } const undirected_graph_t graph(edges.begin(), edges.end(), weights.begin(), max_vertex_index + 1, edges.size()); const auto parities = boost::make_one_bit_color_map( boost::num_vertices(graph), boost::get(boost::vertex_index, graph)); *cut_weight = boost::stoer_wagner_min_cut(graph, boost::get(boost::edge_weight, graph), boost::parity_map(parities)); cut_labels->resize(boost::num_vertices(graph)); for (size_t i = 0; i < boost::num_vertices(graph); ++i) { (*cut_labels)[i] = boost::get(parities, i); } } std::unordered_map ComputeNormalizedMinGraphCut( const std::vector>& edges, const std::vector& weights, const int num_parts) { GraclusGraph graph(edges, weights); const int levels = amax((graph.data.nvtxs) / (40 * log2_metis(num_parts)), 20 * (num_parts)); std::vector cut_labels(graph.data.nvtxs); int options[11]; options[0] = 0; int wgtflag = 1; int numflag = 0; int chain_length = 0; int edgecut; int var_num_parts = num_parts; MLKKM_PartGraphKway(&graph.data.nvtxs, graph.data.xadj, graph.data.adjncy, graph.data.vwgt, graph.data.adjwgt, &wgtflag, &numflag, &var_num_parts, &chain_length, options, &edgecut, cut_labels.data(), levels); float lbvec[MAXNCON]; ComputePartitionBalance(&graph.data, num_parts, cut_labels.data(), lbvec); ComputeNCut(&graph.data, &cut_labels[0], num_parts); std::unordered_map labels; for (size_t idx = 0; idx < cut_labels.size(); ++idx) { labels.emplace(graph.GetVertexId(idx), cut_labels[idx]); } return labels; } } // namespace colmap colmap-3.4/src/base/graph_cut.h000066400000000000000000000030601323400541200164520ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_GRAPH_CUT_H_ #define COLMAP_SRC_BASE_GRAPH_CUT_H_ #include #include namespace colmap { // Compute the min-cut of a undirected graph using the Stoer Wagner algorithm. void ComputeMinGraphCut(const std::vector>& edges, const std::vector& weights, int* cut_weight, std::vector* cut_labels); // Compute the normalized min-cut of an undirected graph using Graclus. // Partitions the graph into clusters and returns the cluster labels per vertex. std::unordered_map ComputeNormalizedMinGraphCut( const std::vector>& edges, const std::vector& weights, const int num_parts); } // namespace colmap #endif // COLMAP_SRC_BASE_GRAPH_CUT_H_ colmap-3.4/src/base/graph_cut_test.cc000066400000000000000000000127501323400541200176550ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/graph_cut" #include "util/testing.h" #include "base/graph_cut.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestComputeMinGraphCut) { const std::vector> edges = { {3, 4}, {3, 6}, {3, 5}, {0, 4}, {0, 1}, {0, 6}, {0, 7}, {0, 5}, {0, 2}, {4, 1}, {1, 6}, {1, 5}, {6, 7}, {7, 5}, {5, 2}, {3, 4}}; const std::vector weights = {0, 3, 1, 3, 1, 2, 6, 1, 8, 1, 1, 80, 2, 1, 1, 4}; int cut_weight; std::vector cut_labels; ComputeMinGraphCut(edges, weights, &cut_weight, &cut_labels); BOOST_CHECK_EQUAL(cut_weight, 7); BOOST_CHECK_EQUAL(cut_labels.size(), 8); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label, 0); BOOST_CHECK_LT(label, 2); } } BOOST_AUTO_TEST_CASE(TestComputeMinGraphCutDuplicateEdge) { const std::vector> edges = { {3, 4}, {3, 6}, {3, 5}, {0, 4}, {0, 1}, {0, 6}, {0, 7}, {0, 5}, {0, 2}, {4, 1}, {1, 6}, {1, 5}, {6, 7}, {7, 5}, {5, 2}, {3, 4}, {3, 4}}; const std::vector weights = {0, 3, 1, 3, 1, 2, 6, 1, 8, 1, 1, 80, 2, 1, 1, 4, 4}; int cut_weight; std::vector cut_labels; ComputeMinGraphCut(edges, weights, &cut_weight, &cut_labels); BOOST_CHECK_EQUAL(cut_weight, 7); BOOST_CHECK_EQUAL(cut_labels.size(), 8); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label, 0); BOOST_CHECK_LT(label, 2); } } BOOST_AUTO_TEST_CASE(TestComputeMinGraphCutMissingVertex) { const std::vector> edges = { {3, 4}, {3, 6}, {3, 5}, {0, 1}, {0, 6}, {0, 7}, {0, 5}, {0, 2}, {4, 1}, {1, 6}, {1, 5}, {6, 7}, {7, 5}, {5, 2}}; const std::vector weights = {0, 3, 1, 3, 1, 2, 6, 1, 8, 1, 1, 80, 2, 1}; int cut_weight; std::vector cut_labels; ComputeMinGraphCut(edges, weights, &cut_weight, &cut_labels); BOOST_CHECK_EQUAL(cut_weight, 2); BOOST_CHECK_EQUAL(cut_labels.size(), 8); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label, 0); BOOST_CHECK_LT(label, 2); } } BOOST_AUTO_TEST_CASE(TestComputeMinGraphCutDisconnected) { const std::vector> edges = {{0, 1}, {1, 2}, {3, 4}}; const std::vector weights = {1, 3, 1}; int cut_weight; std::vector cut_labels; ComputeMinGraphCut(edges, weights, &cut_weight, &cut_labels); BOOST_CHECK_EQUAL(cut_weight, 0); BOOST_CHECK_EQUAL(cut_labels.size(), 5); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label, 0); BOOST_CHECK_LT(label, 2); } } BOOST_AUTO_TEST_CASE(TestComputeNormalizedMinGraphCut) { const std::vector> edges = { {3, 4}, {3, 6}, {3, 5}, {0, 4}, {0, 1}, {0, 6}, {0, 7}, {0, 5}, {0, 2}, {4, 1}, {1, 6}, {1, 5}, {6, 7}, {7, 5}, {5, 2}, {3, 4}}; const std::vector weights = {0, 3, 1, 3, 1, 2, 6, 1, 8, 1, 1, 80, 2, 1, 1, 4}; const auto cut_labels = ComputeNormalizedMinGraphCut(edges, weights, 2); BOOST_CHECK_EQUAL(cut_labels.size(), 8); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label.second, 0); BOOST_CHECK_LT(label.second, 2); } } BOOST_AUTO_TEST_CASE(TestComputeNormalizedMinGraphCutDuplicateEdge) { const std::vector> edges = { {3, 4}, {3, 6}, {3, 5}, {0, 4}, {0, 1}, {0, 6}, {0, 7}, {0, 5}, {0, 2}, {4, 1}, {1, 6}, {1, 5}, {6, 7}, {7, 5}, {5, 2}, {3, 4}, {3, 4}}; const std::vector weights = {0, 3, 1, 3, 1, 2, 6, 1, 8, 1, 1, 80, 2, 1, 1, 4, 4}; const auto cut_labels = ComputeNormalizedMinGraphCut(edges, weights, 2); BOOST_CHECK_EQUAL(cut_labels.size(), 8); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label.second, 0); BOOST_CHECK_LT(label.second, 2); } } BOOST_AUTO_TEST_CASE(TestComputeNormalizedMinGraphCutMissingVertex) { const std::vector> edges = { {3, 4}, {3, 6}, {3, 5}, {0, 1}, {0, 6}, {0, 7}, {0, 5}, {0, 2}, {4, 1}, {1, 6}, {1, 5}, {6, 7}, {7, 5}, {5, 2}}; const std::vector weights = {0, 3, 1, 3, 1, 2, 6, 1, 8, 1, 1, 80, 2, 1}; const auto cut_labels = ComputeNormalizedMinGraphCut(edges, weights, 2); BOOST_CHECK_EQUAL(cut_labels.size(), 8); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label.second, 0); BOOST_CHECK_LT(label.second, 2); } } BOOST_AUTO_TEST_CASE(TestComputeNormalizedMinGraphCutDisconnected) { const std::vector> edges = {{0, 1}, {1, 2}, {3, 4}}; const std::vector weights = {1, 3, 1}; const auto cut_labels = ComputeNormalizedMinGraphCut(edges, weights, 2); BOOST_CHECK_EQUAL(cut_labels.size(), 5); for (const auto& label : cut_labels) { BOOST_CHECK_GE(label.second, 0); BOOST_CHECK_LT(label.second, 2); } } colmap-3.4/src/base/homography_matrix.cc000077500000000000000000000152241323400541200204050ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/homography_matrix.h" #include #include #include "base/pose.h" #include "util/logging.h" #include "util/math.h" namespace colmap { namespace { double ComputeOppositeOfMinor(const Eigen::Matrix3d& matrix, const size_t row, const size_t col) { const size_t col1 = col == 0 ? 1 : 0; const size_t col2 = col == 2 ? 1 : 2; const size_t row1 = row == 0 ? 1 : 0; const size_t row2 = row == 2 ? 1 : 2; return (matrix(row1, col2) * matrix(row2, col1) - matrix(row1, col1) * matrix(row2, col2)); } Eigen::Matrix3d ComputeHomographyRotation(const Eigen::Matrix3d& hmatrix_norm, const Eigen::Vector3d& tstar, const Eigen::Vector3d& n, const double v) { return hmatrix_norm * (Eigen::Matrix3d::Identity() - (2.0 / v) * tstar * n.transpose()); } } // namespace void DecomposeHomographyMatrix(const Eigen::Matrix3d& H, const Eigen::Matrix3d& K1, const Eigen::Matrix3d& K2, std::vector* R, std::vector* t, std::vector* n) { // Remove calibration from homography. Eigen::Matrix3d hmatrix_norm = K2.inverse() * H * K1; // Remove scale from normalized homography. Eigen::JacobiSVD hmatrix_norm_svd(hmatrix_norm); hmatrix_norm.array() /= hmatrix_norm_svd.singularValues()[1]; const Eigen::Matrix3d S = hmatrix_norm.transpose() * hmatrix_norm - Eigen::Matrix3d::Identity(); // Check if H is rotation matrix. const double kMinInfinityNorm = 1e-3; if (S.lpNorm() < kMinInfinityNorm) { *R = {hmatrix_norm}; *t = {Eigen::Vector3d::Zero()}; *n = {Eigen::Vector3d::Zero()}; return; } const double M00 = ComputeOppositeOfMinor(S, 0, 0); const double M11 = ComputeOppositeOfMinor(S, 1, 1); const double M22 = ComputeOppositeOfMinor(S, 2, 2); const double rtM00 = std::sqrt(M00); const double rtM11 = std::sqrt(M11); const double rtM22 = std::sqrt(M22); const double M01 = ComputeOppositeOfMinor(S, 0, 1); const double M12 = ComputeOppositeOfMinor(S, 1, 2); const double M02 = ComputeOppositeOfMinor(S, 0, 2); const int e12 = SignOfNumber(M12); const int e02 = SignOfNumber(M02); const int e01 = SignOfNumber(M01); const double nS00 = std::abs(S(0, 0)); const double nS11 = std::abs(S(1, 1)); const double nS22 = std::abs(S(2, 2)); const std::array nS{{nS00, nS11, nS22}}; const size_t idx = std::distance(nS.begin(), std::max_element(nS.begin(), nS.end())); Eigen::Vector3d np1; Eigen::Vector3d np2; if (idx == 0) { np1[0] = S(0, 0); np2[0] = S(0, 0); np1[1] = S(0, 1) + rtM22; np2[1] = S(0, 1) - rtM22; np1[2] = S(0, 2) + e12 * rtM11; np2[2] = S(0, 2) - e12 * rtM11; } else if (idx == 1) { np1[0] = S(0, 1) + rtM22; np2[0] = S(0, 1) - rtM22; np1[1] = S(1, 1); np2[1] = S(1, 1); np1[2] = S(1, 2) - e02 * rtM00; np2[2] = S(1, 2) + e02 * rtM00; } else if (idx == 2) { np1[0] = S(0, 2) + e01 * rtM11; np2[0] = S(0, 2) - e01 * rtM11; np1[1] = S(1, 2) + rtM00; np2[1] = S(1, 2) - rtM00; np1[2] = S(2, 2); np2[2] = S(2, 2); } const double traceS = S.trace(); const double v = 2.0 * std::sqrt(1.0 + traceS - M00 - M11 - M22); const double ESii = SignOfNumber(S(idx, idx)); const double r_2 = 2 + traceS + v; const double nt_2 = 2 + traceS - v; const double r = std::sqrt(r_2); const double n_t = std::sqrt(nt_2); const Eigen::Vector3d n1 = np1.normalized(); const Eigen::Vector3d n2 = np2.normalized(); const double half_nt = 0.5 * n_t; const double esii_t_r = ESii * r; const Eigen::Vector3d t1_star = half_nt * (esii_t_r * n2 - n_t * n1); const Eigen::Vector3d t2_star = half_nt * (esii_t_r * n1 - n_t * n2); const Eigen::Matrix3d R1 = ComputeHomographyRotation(hmatrix_norm, t1_star, n1, v); const Eigen::Vector3d t1 = R1 * t1_star; const Eigen::Matrix3d R2 = ComputeHomographyRotation(hmatrix_norm, t2_star, n2, v); const Eigen::Vector3d t2 = R2 * t2_star; *R = {R1, R1, R2, R2}; *t = {t1, -t1, t2, -t2}; *n = {-n1, n1, -n2, n2}; } void PoseFromHomographyMatrix(const Eigen::Matrix3d& H, const Eigen::Matrix3d& K1, const Eigen::Matrix3d& K2, const std::vector& points1, const std::vector& points2, Eigen::Matrix3d* R, Eigen::Vector3d* t, Eigen::Vector3d* n, std::vector* points3D) { CHECK_EQ(points1.size(), points2.size()); std::vector R_cmbs; std::vector t_cmbs; std::vector n_cmbs; DecomposeHomographyMatrix(H, K1, K2, &R_cmbs, &t_cmbs, &n_cmbs); points3D->clear(); for (size_t i = 0; i < R_cmbs.size(); ++i) { std::vector points3D_cmb; CheckCheirality(R_cmbs[i], t_cmbs[i], points1, points2, &points3D_cmb); if (points3D_cmb.size() >= points3D->size()) { *R = R_cmbs[i]; *t = t_cmbs[i]; *n = n_cmbs[i]; *points3D = points3D_cmb; } } } Eigen::Matrix3d HomographyMatrixFromPose(const Eigen::Matrix3d& K1, const Eigen::Matrix3d& K2, const Eigen::Matrix3d& R, const Eigen::Vector3d& t, const Eigen::Vector3d& n, const double d) { CHECK_GT(d, 0); return K2 * (R - t * n.normalized().transpose() / d) * K1.inverse(); } } // namespace colmap colmap-3.4/src/base/homography_matrix.h000077500000000000000000000105241323400541200202450ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_HOMOGRAPHY_MATRIX_UTILS_H_ #define COLMAP_SRC_BASE_HOMOGRAPHY_MATRIX_UTILS_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Decompose an homography matrix into the possible rotations, translations, // and plane normal vectors, according to: // // Malis, Ezio, and Manuel Vargas. "Deeper understanding of the homography // decomposition for vision-based control." (2007): 90. // // The first pose is assumed to be P = [I | 0]. Note that the homography is // plane-induced if `R.size() == t.size() == n.size() == 4`. If `R.size() == // t.size() == n.size() == 1` the homography is pure-rotational. // // @param H 3x3 homography matrix. // @param K 3x3 calibration matrix. // @param R Possible 3x3 rotation matrices. // @param t Possible translation vectors. // @param n Possible normal vectors. void DecomposeHomographyMatrix(const Eigen::Matrix3d& H, const Eigen::Matrix3d& K1, const Eigen::Matrix3d& K2, std::vector* R, std::vector* t, std::vector* n); // Recover the most probable pose from the given homography matrix. // // The pose of the first image is assumed to be P = [I | 0]. // // @param H 3x3 homography matrix. // @param K1 3x3 calibration matrix of first camera. // @param K2 3x3 calibration matrix of second camera. // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param inlier_mask Only points with `true` in the inlier mask are // considered in the cheirality test. Size of the // inlier mask must match the number of points N. // @param R Most probable 3x3 rotation matrix. // @param t Most probable 3x1 translation vector. // @param n Most probable 3x1 normal vector. // @param points3D Triangulated 3D points infront of camera // (only if homography is not pure-rotational). void PoseFromHomographyMatrix(const Eigen::Matrix3d& H, const Eigen::Matrix3d& K1, const Eigen::Matrix3d& K2, const std::vector& points1, const std::vector& points2, Eigen::Matrix3d* R, Eigen::Vector3d* t, Eigen::Vector3d* n, std::vector* points3D); // Compose homography matrix from relative pose. // // @param K1 3x3 calibration matrix of first camera. // @param K2 3x3 calibration matrix of second camera. // @param R Most probable 3x3 rotation matrix. // @param t Most probable 3x1 translation vector. // @param n Most probable 3x1 normal vector. // @param d Orthogonal distance from plane. // // @return 3x3 homography matrix. Eigen::Matrix3d HomographyMatrixFromPose(const Eigen::Matrix3d& K1, const Eigen::Matrix3d& K2, const Eigen::Matrix3d& R, const Eigen::Vector3d& t, const Eigen::Vector3d& n, const double d); } // namespace colmap #endif // COLMAP_SRC_BASE_HOMOGRAPHY_MATRIX_UTILS_H_ colmap-3.4/src/base/homography_matrix_test.cc000077500000000000000000000105251323400541200214430ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/homography_matrix" #include "util/testing.h" #include #include "base/homography_matrix.h" using namespace colmap; // Note that the test case values are obtained from OpenCV. BOOST_AUTO_TEST_CASE(TestDecomposeHomographyMatrix) { Eigen::Matrix3d H; H << 2.649157564634028, 4.583875997496426, 70.694447785121326, -1.072756858861583, 3.533262150437228, 1513.656999614321649, 0.001303887589576, 0.003042206876298, 1; H *= 3; Eigen::Matrix3d K; K << 640, 0, 320, 0, 640, 240, 0, 0, 1; std::vector R; std::vector t; std::vector n; DecomposeHomographyMatrix(H, K, K, &R, &t, &n); BOOST_CHECK_EQUAL(R.size(), 4); BOOST_CHECK_EQUAL(t.size(), 4); BOOST_CHECK_EQUAL(n.size(), 4); Eigen::Matrix3d R_ref; R_ref << 0.43307983549125, 0.545749113549648, -0.717356090899523, -0.85630229674426, 0.497582023798831, -0.138414255706431, 0.281404038139784, 0.67421809131173, 0.682818960388909; const Eigen::Vector3d t_ref(1.826751712278038, 1.264718492450820, 0.195080809998819); const Eigen::Vector3d n_ref(-0.244875830334816, -0.480857890778889, -0.841909446789566); bool ref_solution_exists = false; for (size_t i = 0; i < 4; ++i) { const double kEps = 1e-6; if ((R[i] - R_ref).norm() < kEps && (t[i] - t_ref).norm() < kEps && (n[i] - n_ref).norm() < kEps) { ref_solution_exists = true; } } BOOST_CHECK(ref_solution_exists); } BOOST_AUTO_TEST_CASE(TestPoseFromHomographyMatrix) { const Eigen::Matrix3d K1 = Eigen::Matrix3d::Identity(); const Eigen::Matrix3d K2 = Eigen::Matrix3d::Identity(); const Eigen::Matrix3d R_ref = Eigen::Matrix3d::Identity(); const Eigen::Vector3d t_ref(1, 0, 0); const Eigen::Vector3d n_ref(-1, 0, 0); const double d_ref = 1; const Eigen::Matrix3d H = HomographyMatrixFromPose(K1, K2, R_ref, t_ref, n_ref, d_ref); std::vector points1; points1.emplace_back(0.1, 0.4); points1.emplace_back(0.2, 0.3); points1.emplace_back(0.3, 0.2); points1.emplace_back(0.4, 0.1); std::vector points2; for (const auto& point1 : points1) { const Eigen::Vector3d point2 = H * point1.homogeneous(); points2.push_back(point2.hnormalized()); } Eigen::Matrix3d R; Eigen::Vector3d t; Eigen::Vector3d n; std::vector points3D; PoseFromHomographyMatrix(H, K1, K2, points1, points2, &R, &t, &n, &points3D); BOOST_CHECK_EQUAL(R, R_ref); BOOST_CHECK_EQUAL(t, t_ref); BOOST_CHECK_EQUAL(n, n_ref); BOOST_CHECK_EQUAL(points3D.size(), points1.size()); } BOOST_AUTO_TEST_CASE(TestHomographyMatrixFromPosePureRotation) { const Eigen::Matrix3d K1 = Eigen::Matrix3d::Identity(); const Eigen::Matrix3d K2 = Eigen::Matrix3d::Identity(); const Eigen::Matrix3d R = Eigen::Matrix3d::Identity(); const Eigen::Vector3d t(0, 0, 0); const Eigen::Vector3d n(-1, 0, 0); const double d = 1; const Eigen::Matrix3d H = HomographyMatrixFromPose(K1, K2, R, t, n, d); BOOST_CHECK_EQUAL(H, Eigen::Matrix3d::Identity()); } BOOST_AUTO_TEST_CASE(TestHomographyMatrixFromPosePlanarScene) { const Eigen::Matrix3d K1 = Eigen::Matrix3d::Identity(); const Eigen::Matrix3d K2 = Eigen::Matrix3d::Identity(); const Eigen::Matrix3d R = Eigen::Matrix3d::Identity(); const Eigen::Vector3d t(1, 0, 0); const Eigen::Vector3d n(-1, 0, 0); const double d = 1; const Eigen::Matrix3d H = HomographyMatrixFromPose(K1, K2, R, t, n, d); Eigen::Matrix3d H_ref; H_ref << 2, 0, 0, 0, 1, 0, 0, 0, 1; BOOST_CHECK_EQUAL(H, H_ref); } colmap-3.4/src/base/image.cc000077500000000000000000000106771323400541200157350ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/image.h" #include "base/pose.h" #include "base/projection.h" namespace colmap { namespace { static const double kNaN = std::numeric_limits::quiet_NaN(); } // namespace const int Image::kNumPoint3DVisibilityPyramidLevels = 6; Image::Image() : image_id_(kInvalidImageId), name_(""), camera_id_(kInvalidCameraId), registered_(false), num_points3D_(0), num_observations_(0), num_correspondences_(0), num_visible_points3D_(0), qvec_(1.0, 0.0, 0.0, 0.0), tvec_(0.0, 0.0, 0.0), qvec_prior_(kNaN, kNaN, kNaN, kNaN), tvec_prior_(kNaN, kNaN, kNaN) {} void Image::SetUp(const class Camera& camera) { CHECK_EQ(camera_id_, camera.CameraId()); point3D_visibility_pyramid_ = VisibilityPyramid( kNumPoint3DVisibilityPyramidLevels, camera.Width(), camera.Height()); } void Image::TearDown() { point3D_visibility_pyramid_ = VisibilityPyramid(0, 0, 0); } void Image::SetPoints2D(const std::vector& points) { CHECK(points2D_.empty()); points2D_.resize(points.size()); num_correspondences_have_point3D_.resize(points.size(), 0); for (point2D_t point2D_idx = 0; point2D_idx < points.size(); ++point2D_idx) { points2D_[point2D_idx].SetXY(points[point2D_idx]); } } void Image::SetPoints2D(const std::vector& points) { CHECK(points2D_.empty()); points2D_ = points; num_correspondences_have_point3D_.resize(points.size(), 0); } void Image::SetPoint3DForPoint2D(const point2D_t point2D_idx, const point3D_t point3D_id) { CHECK_NE(point3D_id, kInvalidPoint3DId); class Point2D& point2D = points2D_.at(point2D_idx); if (!point2D.HasPoint3D()) { num_points3D_ += 1; } point2D.SetPoint3DId(point3D_id); } void Image::ResetPoint3DForPoint2D(const point2D_t point2D_idx) { class Point2D& point2D = points2D_.at(point2D_idx); if (point2D.HasPoint3D()) { point2D.SetPoint3DId(kInvalidPoint3DId); num_points3D_ -= 1; } } bool Image::HasPoint3D(const point3D_t point3D_id) const { return std::find_if(points2D_.begin(), points2D_.end(), [point3D_id](const class Point2D& point2D) { return point2D.Point3DId() == point3D_id; }) != points2D_.end(); } void Image::IncrementCorrespondenceHasPoint3D(const point2D_t point2D_idx) { const class Point2D& point2D = points2D_.at(point2D_idx); num_correspondences_have_point3D_[point2D_idx] += 1; if (num_correspondences_have_point3D_[point2D_idx] == 1) { num_visible_points3D_ += 1; } point3D_visibility_pyramid_.SetPoint(point2D.X(), point2D.Y()); assert(num_visible_points3D_ <= num_observations_); } void Image::DecrementCorrespondenceHasPoint3D(const point2D_t point2D_idx) { const class Point2D& point2D = points2D_.at(point2D_idx); num_correspondences_have_point3D_[point2D_idx] -= 1; if (num_correspondences_have_point3D_[point2D_idx] == 0) { num_visible_points3D_ -= 1; } point3D_visibility_pyramid_.ResetPoint(point2D.X(), point2D.Y()); assert(num_visible_points3D_ <= num_observations_); } void Image::NormalizeQvec() { qvec_ = NormalizeQuaternion(qvec_); } Eigen::Matrix3x4d Image::ProjectionMatrix() const { return ComposeProjectionMatrix(qvec_, tvec_); } Eigen::Matrix3x4d Image::InverseProjectionMatrix() const { return InvertProjectionMatrix(ComposeProjectionMatrix(qvec_, tvec_)); } Eigen::Matrix3d Image::RotationMatrix() const { return QuaternionToRotationMatrix(qvec_); } Eigen::Vector3d Image::ProjectionCenter() const { return ProjectionCenterFromParameters(qvec_, tvec_); } Eigen::Vector3d Image::ViewingDirection() const { return RotationMatrix().row(2); } } // namespace colmap colmap-3.4/src/base/image.h000077500000000000000000000310421323400541200155640ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_IMAGE_H_ #define COLMAP_SRC_BASE_IMAGE_H_ #include #include #include #include "base/camera.h" #include "base/point2d.h" #include "base/visibility_pyramid.h" #include "util/alignment.h" #include "util/logging.h" #include "util/math.h" #include "util/types.h" namespace colmap { // Class that holds information about an image. An image is the product of one // camera shot at a certain location (parameterized as the pose). An image may // share a camera with multiple other images, if its intrinsics are the same. class Image { public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW Image(); // Setup / tear down the image and necessary internal data structures before // and after being used in reconstruction. void SetUp(const Camera& camera); void TearDown(); // Access the unique identifier of the image. inline image_t ImageId() const; inline void SetImageId(const image_t image_id); // Access the name of the image. inline const std::string& Name() const; inline std::string& Name(); inline void SetName(const std::string& name); // Access the unique identifier of the camera. Note that multiple images // might share the same camera. inline camera_t CameraId() const; inline void SetCameraId(const camera_t camera_id); // Check whether identifier of camera has been set. inline bool HasCamera() const; // Check if image is registered. inline bool IsRegistered() const; inline void SetRegistered(const bool registered); // Get the number of image points. inline point2D_t NumPoints2D() const; // Get the number of triangulations, i.e. the number of points that // are part of a 3D point track. inline point2D_t NumPoints3D() const; // Get the number of observations, i.e. the number of image points that // have at least one correspondence to another image. inline point2D_t NumObservations() const; inline void SetNumObservations(const point2D_t num_observations); // Get the number of correspondences for all image points. inline point2D_t NumCorrespondences() const; inline void SetNumCorrespondences(const point2D_t num_observations); // Get the number of observations that see a triangulated point, i.e. the // number of image points that have at least one correspondence to a // triangulated point in another image. inline point2D_t NumVisiblePoints3D() const; // Get the score of triangulated observations. In contrast to // `NumVisiblePoints3D`, this score also captures the distribution // of triangulated observations in the image. This is useful to select // the next best image in incremental reconstruction, because a more // uniform distribution of observations results in more robust registration. inline size_t Point3DVisibilityScore() const; // Access quaternion vector as (qw, qx, qy, qz) specifying the rotation of the // pose which is defined as the transformation from world to image space. inline const Eigen::Vector4d& Qvec() const; inline Eigen::Vector4d& Qvec(); inline double Qvec(const size_t idx) const; inline double& Qvec(const size_t idx); inline void SetQvec(const Eigen::Vector4d& qvec); // Quaternion prior, e.g. given by EXIF gyroscope tag. inline const Eigen::Vector4d& QvecPrior() const; inline Eigen::Vector4d& QvecPrior(); inline double QvecPrior(const size_t idx) const; inline double& QvecPrior(const size_t idx); inline bool HasQvecPrior() const; inline void SetQvecPrior(const Eigen::Vector4d& qvec); // Access quaternion vector as (tx, ty, tz) specifying the translation of the // pose which is defined as the transformation from world to image space. inline const Eigen::Vector3d& Tvec() const; inline Eigen::Vector3d& Tvec(); inline double Tvec(const size_t idx) const; inline double& Tvec(const size_t idx); inline void SetTvec(const Eigen::Vector3d& tvec); // Quaternion prior, e.g. given by EXIF GPS tag. inline const Eigen::Vector3d& TvecPrior() const; inline Eigen::Vector3d& TvecPrior(); inline double TvecPrior(const size_t idx) const; inline double& TvecPrior(const size_t idx); inline bool HasTvecPrior() const; inline void SetTvecPrior(const Eigen::Vector3d& tvec); // Access the coordinates of image points. inline const class Point2D& Point2D(const point2D_t point2D_idx) const; inline class Point2D& Point2D(const point2D_t point2D_idx); inline const std::vector& Points2D() const; void SetPoints2D(const std::vector& points); void SetPoints2D(const std::vector& points); // Set the point as triangulated, i.e. it is part of a 3D point track. void SetPoint3DForPoint2D(const point2D_t point2D_idx, const point3D_t point3D_id); // Set the point as not triangulated, i.e. it is not part of a 3D point track. void ResetPoint3DForPoint2D(const point2D_t point2D_idx); // Check whether an image point has a correspondence to an image point in // another image that has a 3D point. inline bool IsPoint3DVisible(const point2D_t point2D_idx) const; // Check whether one of the image points is part of the 3D point track. bool HasPoint3D(const point3D_t point3D_id) const; // Indicate that another image has a point that is triangulated and has // a correspondence to this image point. Note that this must only be called // after calling `SetUp`. void IncrementCorrespondenceHasPoint3D(const point2D_t point2D_idx); // Indicate that another image has a point that is not triangulated any more // and has a correspondence to this image point. This assumes that // `IncrementCorrespondenceHasPoint3D` was called for the same image point // and correspondence before. Note that this must only be called // after calling `SetUp`. void DecrementCorrespondenceHasPoint3D(const point2D_t point2D_idx); // Normalize the quaternion vector. void NormalizeQvec(); // Compose the projection matrix from world to image space. Eigen::Matrix3x4d ProjectionMatrix() const; // Compose the inverse projection matrix from image to world space Eigen::Matrix3x4d InverseProjectionMatrix() const; // Compose rotation matrix from quaternion vector. Eigen::Matrix3d RotationMatrix() const; // Extract the projection center in world space. Eigen::Vector3d ProjectionCenter() const; // Extract the viewing direction of the image. Eigen::Vector3d ViewingDirection() const; // The number of levels in the 3D point multi-resolution visibility pyramid. static const int kNumPoint3DVisibilityPyramidLevels; private: // Identifier of the image, if not specified `kInvalidImageId`. image_t image_id_; // The name of the image, i.e. the relative path. std::string name_; // The identifier of the associated camera. Note that multiple images might // share the same camera. If not specified `kInvalidCameraId`. camera_t camera_id_; // Whether the image is successfully registered in the reconstruction. bool registered_; // The number of 3D points the image observes, i.e. the sum of its `points2D` // where `point3D_id != kInvalidPoint3DId`. point2D_t num_points3D_; // The number of image points that have at least one correspondence to // another image. point2D_t num_observations_; // The sum of correspondences per image point. point2D_t num_correspondences_; // The number of 2D points, which have at least one corresponding 2D point in // another image that is part of a 3D point track, i.e. the sum of `points2D` // where `num_tris > 0`. point2D_t num_visible_points3D_; // The pose of the image, defined as the transformation from world to image. Eigen::Vector4d qvec_; Eigen::Vector3d tvec_; // The pose prior of the image, e.g. extracted from EXIF tags. Eigen::Vector4d qvec_prior_; Eigen::Vector3d tvec_prior_; // All image points, including points that are not part of a 3D point track. std::vector points2D_; // Per image point, the number of correspondences that have a 3D point. std::vector num_correspondences_have_point3D_; // Data structure to compute the distribution of triangulated correspondences // in the image. Note that this structure is only usable after `SetUp`. VisibilityPyramid point3D_visibility_pyramid_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// image_t Image::ImageId() const { return image_id_; } void Image::SetImageId(const image_t image_id) { image_id_ = image_id; } const std::string& Image::Name() const { return name_; } std::string& Image::Name() { return name_; } void Image::SetName(const std::string& name) { name_ = name; } inline camera_t Image::CameraId() const { return camera_id_; } inline void Image::SetCameraId(const camera_t camera_id) { CHECK_NE(camera_id, kInvalidCameraId); camera_id_ = camera_id; } inline bool Image::HasCamera() const { return camera_id_ != kInvalidCameraId; } bool Image::IsRegistered() const { return registered_; } void Image::SetRegistered(const bool registered) { registered_ = registered; } point2D_t Image::NumPoints2D() const { return static_cast(points2D_.size()); } point2D_t Image::NumPoints3D() const { return num_points3D_; } point2D_t Image::NumObservations() const { return num_observations_; } void Image::SetNumObservations(const point2D_t num_observations) { num_observations_ = num_observations; } point2D_t Image::NumCorrespondences() const { return num_correspondences_; } void Image::SetNumCorrespondences(const point2D_t num_correspondences) { num_correspondences_ = num_correspondences; } point2D_t Image::NumVisiblePoints3D() const { return num_visible_points3D_; } size_t Image::Point3DVisibilityScore() const { return point3D_visibility_pyramid_.Score(); } const Eigen::Vector4d& Image::Qvec() const { return qvec_; } Eigen::Vector4d& Image::Qvec() { return qvec_; } inline double Image::Qvec(const size_t idx) const { return qvec_(idx); } inline double& Image::Qvec(const size_t idx) { return qvec_(idx); } void Image::SetQvec(const Eigen::Vector4d& qvec) { qvec_ = qvec; } const Eigen::Vector4d& Image::QvecPrior() const { return qvec_prior_; } Eigen::Vector4d& Image::QvecPrior() { return qvec_prior_; } inline double Image::QvecPrior(const size_t idx) const { return qvec_prior_(idx); } inline double& Image::QvecPrior(const size_t idx) { return qvec_prior_(idx); } inline bool Image::HasQvecPrior() const { return !IsNaN(qvec_prior_.sum()); } void Image::SetQvecPrior(const Eigen::Vector4d& qvec) { qvec_prior_ = qvec; } const Eigen::Vector3d& Image::Tvec() const { return tvec_; } Eigen::Vector3d& Image::Tvec() { return tvec_; } inline double Image::Tvec(const size_t idx) const { return tvec_(idx); } inline double& Image::Tvec(const size_t idx) { return tvec_(idx); } void Image::SetTvec(const Eigen::Vector3d& tvec) { tvec_ = tvec; } const Eigen::Vector3d& Image::TvecPrior() const { return tvec_prior_; } Eigen::Vector3d& Image::TvecPrior() { return tvec_prior_; } inline double Image::TvecPrior(const size_t idx) const { return tvec_prior_(idx); } inline double& Image::TvecPrior(const size_t idx) { return tvec_prior_(idx); } inline bool Image::HasTvecPrior() const { return !IsNaN(tvec_prior_.sum()); } void Image::SetTvecPrior(const Eigen::Vector3d& tvec) { tvec_prior_ = tvec; } const class Point2D& Image::Point2D(const point2D_t point2D_idx) const { return points2D_.at(point2D_idx); } class Point2D& Image::Point2D(const point2D_t point2D_idx) { return points2D_.at(point2D_idx); } const std::vector& Image::Points2D() const { return points2D_; } bool Image::IsPoint3DVisible(const point2D_t point2D_idx) const { return num_correspondences_have_point3D_.at(point2D_idx) > 0; } } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::Image) #endif // COLMAP_SRC_BASE_IMAGE_H_ colmap-3.4/src/base/image_reader.cc000066400000000000000000000156771323400541200172610ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/image_reader.h" #include "util/misc.h" namespace colmap { bool ImageReaderOptions::Check() const { CHECK_OPTION_GT(default_focal_length_factor, 0.0); CHECK_OPTION(ExistsCameraModelWithName(camera_model)); const int model_id = CameraModelNameToId(camera_model); if (!camera_params.empty()) { CHECK_OPTION( CameraModelVerifyParams(model_id, CSVToVector(camera_params))); } return true; } ImageReader::ImageReader(const ImageReaderOptions& options, Database* database) : options_(options), database_(database), image_index_(0) { CHECK(options_.Check()); // Ensure trailing slash, so that we can build the correct image name. options_.image_path = EnsureTrailingSlash(StringReplace(options_.image_path, "\\", "/")); // Get a list of all files in the image path, sorted by image name. if (options_.image_list.empty()) { options_.image_list = GetRecursiveFileList(options_.image_path); std::sort(options_.image_list.begin(), options_.image_list.end()); } else { for (auto& image_name : options_.image_list) { image_name = JoinPaths(options_.image_path, image_name); } } // Set the manually specified camera parameters. prev_camera_.SetCameraId(kInvalidCameraId); prev_camera_.SetModelIdFromName(options_.camera_model); if (!options_.camera_params.empty()) { prev_camera_.SetParamsFromString(options_.camera_params); } } ImageReader::Status ImageReader::Next(Camera* camera, Image* image, Bitmap* bitmap) { CHECK_NOTNULL(camera); CHECK_NOTNULL(image); CHECK_NOTNULL(bitmap); image_index_ += 1; CHECK_LE(image_index_, options_.image_list.size()); const std::string image_path = options_.image_list.at(image_index_ - 1); DatabaseTransaction database_transaction(database_); ////////////////////////////////////////////////////////////////////////////// // Set the image name. ////////////////////////////////////////////////////////////////////////////// image->SetName(image_path); image->SetName(StringReplace(image->Name(), "\\", "/")); image->SetName( image->Name().substr(options_.image_path.size(), image->Name().size() - options_.image_path.size())); ////////////////////////////////////////////////////////////////////////////// // Check if image already read. ////////////////////////////////////////////////////////////////////////////// const bool exists_image = database_->ExistsImageWithName(image->Name()); if (exists_image) { *image = database_->ReadImageWithName(image->Name()); const bool exists_keypoints = database_->ExistsKeypoints(image->ImageId()); const bool exists_descriptors = database_->ExistsDescriptors(image->ImageId()); if (exists_keypoints && exists_descriptors) { return Status::IMAGE_EXISTS; } } ////////////////////////////////////////////////////////////////////////////// // Read image. ////////////////////////////////////////////////////////////////////////////// if (!bitmap->Read(image_path, false)) { return Status::BITMAP_ERROR; } ////////////////////////////////////////////////////////////////////////////// // Check for well-formed data. ////////////////////////////////////////////////////////////////////////////// if (exists_image) { const Camera camera = database_->ReadCamera(image->CameraId()); if (options_.single_camera && prev_camera_.CameraId() != kInvalidCameraId && (camera.Width() != prev_camera_.Width() || camera.Height() != prev_camera_.Height())) { return Status::CAMERA_SINGLE_ERROR; } if (static_cast(bitmap->Width()) != camera.Width() || static_cast(bitmap->Height()) != camera.Height()) { return Status::CAMERA_DIM_ERROR; } } ////////////////////////////////////////////////////////////////////////////// // Extract image dimensions. ////////////////////////////////////////////////////////////////////////////// if (options_.single_camera && prev_camera_.CameraId() != kInvalidCameraId && (prev_camera_.Width() != static_cast(bitmap->Width()) || prev_camera_.Height() != static_cast(bitmap->Height()))) { return Status::CAMERA_SINGLE_ERROR; } prev_camera_.SetWidth(static_cast(bitmap->Width())); prev_camera_.SetHeight(static_cast(bitmap->Height())); ////////////////////////////////////////////////////////////////////////////// // Extract camera model and focal length ////////////////////////////////////////////////////////////////////////////// if (!options_.single_camera || prev_camera_.CameraId() == kInvalidCameraId) { if (options_.camera_params.empty()) { // Extract focal length. double focal_length = 0.0; if (bitmap->ExifFocalLength(&focal_length)) { prev_camera_.SetPriorFocalLength(true); } else { focal_length = options_.default_focal_length_factor * std::max(bitmap->Width(), bitmap->Height()); prev_camera_.SetPriorFocalLength(false); } prev_camera_.InitializeWithId(prev_camera_.ModelId(), focal_length, prev_camera_.Width(), prev_camera_.Height()); } if (!prev_camera_.VerifyParams()) { return Status::CAMERA_PARAM_ERROR; } prev_camera_.SetCameraId(database_->WriteCamera(prev_camera_)); } image->SetCameraId(prev_camera_.CameraId()); ////////////////////////////////////////////////////////////////////////////// // Extract GPS data. ////////////////////////////////////////////////////////////////////////////// if (!bitmap->ExifLatitude(&image->TvecPrior(0)) || !bitmap->ExifLongitude(&image->TvecPrior(1)) || !bitmap->ExifAltitude(&image->TvecPrior(2))) { image->TvecPrior(0) = std::numeric_limits::quiet_NaN(); image->TvecPrior(1) = std::numeric_limits::quiet_NaN(); image->TvecPrior(2) = std::numeric_limits::quiet_NaN(); } *camera = prev_camera_; return Status::SUCCESS; } size_t ImageReader::NextIndex() const { return image_index_; } size_t ImageReader::NumImages() const { return options_.image_list.size(); } } // namespace colmap colmap-3.4/src/base/image_reader.h000066400000000000000000000054261323400541200171120ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_IMAGE_READER_H_ #define COLMAP_SRC_BASE_IMAGE_READER_H_ #include "base/database.h" #include "util/bitmap.h" #include "util/threading.h" namespace colmap { struct ImageReaderOptions { // Path to database in which to store the extracted data. std::string database_path = ""; // Root path to folder which contains the image. std::string image_path = ""; // Optional list of images to read. The list must contain the relative path // of the images with respect to the image_path. std::vector image_list; // Name of the camera model. std::string camera_model = "SIMPLE_RADIAL"; // Whether to use the same camera for all images. bool single_camera = false; // Specification of manual camera parameters. If empty, camera parameters // will be extracted from EXIF, i.e. principal point and focal length. std::string camera_params = ""; // If camera parameters are not specified manually and the image does not // have focal length EXIF information, the focal length is set to the // value `default_focal_length_factor * max(width, height)`. double default_focal_length_factor = 1.2; bool Check() const; }; // Recursively iterate over the images in a directory. Skips an image if it // already exists in the database. Extracts the camera intrinsics from EXIF and // writes the camera information to the database. class ImageReader { public: enum class Status { FAILURE, SUCCESS, IMAGE_EXISTS, BITMAP_ERROR, CAMERA_SINGLE_ERROR, CAMERA_DIM_ERROR, CAMERA_PARAM_ERROR }; explicit ImageReader(const ImageReaderOptions& options, Database* database); Status Next(Camera* camera, Image* image, Bitmap* bitmap); size_t NextIndex() const; size_t NumImages() const; private: // Image reader options. ImageReaderOptions options_; Database* database_; // Index of previously processed image. size_t image_index_; // Previously processed camera. Camera prev_camera_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_IMAGE_READER_H_ colmap-3.4/src/base/image_test.cc000077500000000000000000000305711323400541200167670ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/image" #include "util/testing.h" #include "base/image.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDefault) { Image image; BOOST_CHECK_EQUAL(image.ImageId(), kInvalidImageId); BOOST_CHECK_EQUAL(image.Name(), ""); BOOST_CHECK_EQUAL(image.CameraId(), kInvalidCameraId); BOOST_CHECK_EQUAL(image.HasCamera(), false); BOOST_CHECK_EQUAL(image.IsRegistered(), false); BOOST_CHECK_EQUAL(image.NumPoints2D(), 0); BOOST_CHECK_EQUAL(image.NumPoints3D(), 0); BOOST_CHECK_EQUAL(image.NumObservations(), 0); BOOST_CHECK_EQUAL(image.NumCorrespondences(), 0); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 0); BOOST_CHECK_EQUAL(image.Point3DVisibilityScore(), 0); BOOST_CHECK_EQUAL(image.Qvec(0), 1.0); BOOST_CHECK_EQUAL(image.Qvec(1), 0.0); BOOST_CHECK_EQUAL(image.Qvec(2), 0.0); BOOST_CHECK_EQUAL(image.Qvec(3), 0.0); BOOST_CHECK(IsNaN(image.QvecPrior(0))); BOOST_CHECK(IsNaN(image.QvecPrior(1))); BOOST_CHECK(IsNaN(image.QvecPrior(2))); BOOST_CHECK(IsNaN(image.QvecPrior(3))); BOOST_CHECK_EQUAL(image.Tvec(0), 0.0); BOOST_CHECK_EQUAL(image.Tvec(1), 0.0); BOOST_CHECK_EQUAL(image.Tvec(2), 0.0); BOOST_CHECK(IsNaN(image.TvecPrior(0))); BOOST_CHECK(IsNaN(image.TvecPrior(1))); BOOST_CHECK(IsNaN(image.TvecPrior(2))); BOOST_CHECK_EQUAL(image.HasQvecPrior(), false); BOOST_CHECK_EQUAL(image.HasTvecPrior(), false); BOOST_CHECK_EQUAL(image.Points2D().size(), 0); } BOOST_AUTO_TEST_CASE(TestImageId) { Image image; BOOST_CHECK_EQUAL(image.ImageId(), kInvalidImageId); image.SetImageId(1); BOOST_CHECK_EQUAL(image.ImageId(), 1); } BOOST_AUTO_TEST_CASE(TestName) { Image image; BOOST_CHECK_EQUAL(image.Name(), ""); image.SetName("test1"); BOOST_CHECK_EQUAL(image.Name(), "test1"); image.Name() = "test2"; BOOST_CHECK_EQUAL(image.Name(), "test2"); } BOOST_AUTO_TEST_CASE(TestCameraId) { Image image; BOOST_CHECK_EQUAL(image.CameraId(), kInvalidCameraId); image.SetCameraId(1); BOOST_CHECK_EQUAL(image.CameraId(), 1); } BOOST_AUTO_TEST_CASE(TestRegistered) { Image image; BOOST_CHECK_EQUAL(image.IsRegistered(), false); image.SetRegistered(true); BOOST_CHECK_EQUAL(image.IsRegistered(), true); image.SetRegistered(false); BOOST_CHECK_EQUAL(image.IsRegistered(), false); } BOOST_AUTO_TEST_CASE(TestNumPoints2D) { Image image; BOOST_CHECK_EQUAL(image.NumPoints2D(), 0); image.SetPoints2D(std::vector(10)); BOOST_CHECK_EQUAL(image.NumPoints2D(), 10); } BOOST_AUTO_TEST_CASE(TestNumPoints3D) { Image image; image.SetPoints2D(std::vector(10)); BOOST_CHECK_EQUAL(image.NumPoints3D(), 0); image.SetPoint3DForPoint2D(0, 0); BOOST_CHECK_EQUAL(image.NumPoints3D(), 1); image.SetPoint3DForPoint2D(0, 1); image.SetPoint3DForPoint2D(1, 2); BOOST_CHECK_EQUAL(image.NumPoints3D(), 2); } BOOST_AUTO_TEST_CASE(TestNumObservations) { Image image; BOOST_CHECK_EQUAL(image.NumObservations(), 0); image.SetNumObservations(10); BOOST_CHECK_EQUAL(image.NumObservations(), 10); } BOOST_AUTO_TEST_CASE(TestNumCorrespondences) { Image image; BOOST_CHECK_EQUAL(image.NumCorrespondences(), 0); image.SetNumCorrespondences(10); BOOST_CHECK_EQUAL(image.NumCorrespondences(), 10); } BOOST_AUTO_TEST_CASE(TestNumVisiblePoints3D) { Image image; image.SetPoints2D(std::vector(10)); image.SetNumObservations(10); Camera camera; camera.SetWidth(10); camera.SetHeight(10); image.SetUp(camera); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 0); image.IncrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 1); image.IncrementCorrespondenceHasPoint3D(0); image.IncrementCorrespondenceHasPoint3D(1); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 2); image.DecrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 2); image.DecrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 1); image.DecrementCorrespondenceHasPoint3D(1); BOOST_CHECK_EQUAL(image.NumVisiblePoints3D(), 0); } BOOST_AUTO_TEST_CASE(TestPoint3DVisibilityScore) { Image image; std::vector points2D; for (size_t i = 0; i < 4; ++i) { for (size_t j = 0; j < 4; ++j) { points2D.emplace_back(i, j); } } image.SetPoints2D(points2D); image.SetNumObservations(16); Camera camera; camera.SetWidth(4); camera.SetHeight(4); image.SetUp(camera); Eigen::Matrix scores( image.kNumPoint3DVisibilityPyramidLevels, 1); for (int i = 1; i <= image.kNumPoint3DVisibilityPyramidLevels; ++i) { scores(i - 1) = (1 << i) * (1 << i); } BOOST_CHECK_EQUAL(image.Point3DVisibilityScore(), 0); image.IncrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL(image.Point3DVisibilityScore(), scores.sum()); image.IncrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL(image.Point3DVisibilityScore(), scores.sum()); image.IncrementCorrespondenceHasPoint3D(1); BOOST_CHECK_EQUAL(image.Point3DVisibilityScore(), scores.sum() + scores.bottomRows(scores.size() - 1).sum()); image.IncrementCorrespondenceHasPoint3D(1); image.IncrementCorrespondenceHasPoint3D(1); image.IncrementCorrespondenceHasPoint3D(4); BOOST_CHECK_EQUAL( image.Point3DVisibilityScore(), scores.sum() + 2 * scores.bottomRows(scores.size() - 1).sum()); image.IncrementCorrespondenceHasPoint3D(4); image.IncrementCorrespondenceHasPoint3D(5); BOOST_CHECK_EQUAL( image.Point3DVisibilityScore(), scores.sum() + 3 * scores.bottomRows(scores.size() - 1).sum()); image.DecrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL( image.Point3DVisibilityScore(), scores.sum() + 3 * scores.bottomRows(scores.size() - 1).sum()); image.DecrementCorrespondenceHasPoint3D(0); BOOST_CHECK_EQUAL( image.Point3DVisibilityScore(), scores.sum() + 2 * scores.bottomRows(scores.size() - 1).sum()); image.IncrementCorrespondenceHasPoint3D(2); BOOST_CHECK_EQUAL( image.Point3DVisibilityScore(), 2 * scores.sum() + 2 * scores.bottomRows(scores.size() - 1).sum()); } BOOST_AUTO_TEST_CASE(TestQvec) { Image image; BOOST_CHECK_EQUAL(image.Qvec(0), 1.0); BOOST_CHECK_EQUAL(image.Qvec(1), 0.0); BOOST_CHECK_EQUAL(image.Qvec(2), 0.0); BOOST_CHECK_EQUAL(image.Qvec(3), 0.0); image.Qvec(0) = 2.0; BOOST_CHECK_EQUAL(image.Qvec(0), 2.0); image.SetQvec(Eigen::Vector4d(3.0, 0.0, 0.0, 0.0)); BOOST_CHECK_EQUAL(image.Qvec(0), 3.0); image.Qvec() = Eigen::Vector4d(4.0, 0.0, 0.0, 0.0); BOOST_CHECK_EQUAL(image.Qvec(0), 4.0); } BOOST_AUTO_TEST_CASE(TestQvecPrior) { Image image; BOOST_CHECK(IsNaN(image.QvecPrior(0))); BOOST_CHECK(IsNaN(image.QvecPrior(1))); BOOST_CHECK(IsNaN(image.QvecPrior(2))); BOOST_CHECK(IsNaN(image.QvecPrior(3))); BOOST_CHECK_EQUAL(image.HasQvecPrior(), false); image.QvecPrior(0) = 2.0; BOOST_CHECK_EQUAL(image.HasQvecPrior(), false); image.QvecPrior(1) = 2.0; BOOST_CHECK_EQUAL(image.HasQvecPrior(), false); image.QvecPrior(2) = 2.0; BOOST_CHECK_EQUAL(image.HasQvecPrior(), false); image.QvecPrior(3) = 2.0; BOOST_CHECK_EQUAL(image.HasQvecPrior(), true); BOOST_CHECK_EQUAL(image.QvecPrior(0), 2.0); BOOST_CHECK_EQUAL(image.QvecPrior(1), 2.0); BOOST_CHECK_EQUAL(image.QvecPrior(2), 2.0); BOOST_CHECK_EQUAL(image.QvecPrior(3), 2.0); image.SetQvecPrior(Eigen::Vector4d(3.0, 0.0, 0.0, 0.0)); BOOST_CHECK_EQUAL(image.QvecPrior(0), 3.0); image.QvecPrior() = Eigen::Vector4d(4.0, 0.0, 0.0, 0.0); BOOST_CHECK_EQUAL(image.QvecPrior(0), 4.0); } BOOST_AUTO_TEST_CASE(TestTvec) { Image image; BOOST_CHECK_EQUAL(image.Tvec(0), 0.0); BOOST_CHECK_EQUAL(image.Tvec(1), 0.0); BOOST_CHECK_EQUAL(image.Tvec(2), 0.0); image.Tvec(0) = 2.0; BOOST_CHECK_EQUAL(image.Tvec(0), 2.0); image.SetTvec(Eigen::Vector3d(3.0, 0.0, 0.0)); BOOST_CHECK_EQUAL(image.Tvec(0), 3.0); image.Tvec() = Eigen::Vector3d(4.0, 0.0, 0.0); BOOST_CHECK_EQUAL(image.Tvec(0), 4.0); } BOOST_AUTO_TEST_CASE(TestTvecPrior) { Image image; BOOST_CHECK(IsNaN(image.TvecPrior(0))); BOOST_CHECK(IsNaN(image.TvecPrior(1))); BOOST_CHECK(IsNaN(image.TvecPrior(2))); BOOST_CHECK_EQUAL(image.HasTvecPrior(), false); image.TvecPrior(0) = 2.0; BOOST_CHECK_EQUAL(image.HasTvecPrior(), false); image.TvecPrior(1) = 2.0; BOOST_CHECK_EQUAL(image.HasTvecPrior(), false); image.TvecPrior(2) = 2.0; BOOST_CHECK_EQUAL(image.HasTvecPrior(), true); BOOST_CHECK_EQUAL(image.TvecPrior(0), 2.0); BOOST_CHECK_EQUAL(image.TvecPrior(1), 2.0); BOOST_CHECK_EQUAL(image.TvecPrior(2), 2.0); image.SetTvecPrior(Eigen::Vector3d(3.0, 0.0, 0.0)); BOOST_CHECK_EQUAL(image.TvecPrior(0), 3.0); image.TvecPrior() = Eigen::Vector3d(4.0, 0.0, 0.0); BOOST_CHECK_EQUAL(image.TvecPrior(0), 4.0); } BOOST_AUTO_TEST_CASE(TestPoints2D) { Image image; BOOST_CHECK_EQUAL(image.Points2D().size(), 0); std::vector points2D(10); points2D[0] = Eigen::Vector2d(1.0, 2.0); image.SetPoints2D(points2D); BOOST_CHECK_EQUAL(image.Points2D().size(), 10); BOOST_CHECK_EQUAL(image.Point2D(0).X(), 1.0); BOOST_CHECK_EQUAL(image.Point2D(0).Y(), 2.0); } BOOST_AUTO_TEST_CASE(TestPoint3D) { Image image; image.SetPoints2D(std::vector(2)); BOOST_CHECK(!image.Point2D(0).HasPoint3D()); BOOST_CHECK(!image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 0); image.SetPoint3DForPoint2D(0, 0); BOOST_CHECK(image.Point2D(0).HasPoint3D()); BOOST_CHECK(!image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 1); BOOST_CHECK(image.HasPoint3D(0)); image.SetPoint3DForPoint2D(0, 1); BOOST_CHECK(image.Point2D(0).HasPoint3D()); BOOST_CHECK(!image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 1); BOOST_CHECK(!image.HasPoint3D(0)); BOOST_CHECK(image.HasPoint3D(1)); image.SetPoint3DForPoint2D(1, 0); BOOST_CHECK(image.Point2D(0).HasPoint3D()); BOOST_CHECK(image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 2); BOOST_CHECK(image.HasPoint3D(0)); BOOST_CHECK(image.HasPoint3D(1)); image.ResetPoint3DForPoint2D(0); BOOST_CHECK(!image.Point2D(0).HasPoint3D()); BOOST_CHECK(image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 1); BOOST_CHECK(image.HasPoint3D(0)); BOOST_CHECK(!image.HasPoint3D(1)); image.ResetPoint3DForPoint2D(1); BOOST_CHECK(!image.Point2D(0).HasPoint3D()); BOOST_CHECK(!image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 0); BOOST_CHECK(!image.HasPoint3D(0)); BOOST_CHECK(!image.HasPoint3D(1)); image.ResetPoint3DForPoint2D(0); BOOST_CHECK(!image.Point2D(0).HasPoint3D()); BOOST_CHECK(!image.Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(image.NumPoints3D(), 0); BOOST_CHECK(!image.HasPoint3D(0)); BOOST_CHECK(!image.HasPoint3D(1)); } BOOST_AUTO_TEST_CASE(TestNormalizeQvec) { Image image; BOOST_CHECK_LT(std::abs(image.Qvec().norm() - 1.0), 1e-10); image.Qvec(0) = 2.0; BOOST_CHECK_LT(std::abs(image.Qvec().norm() - 2.0), 1e-10); image.NormalizeQvec(); BOOST_CHECK_LT(std::abs(image.Qvec().norm() - 1.0), 1e-10); } BOOST_AUTO_TEST_CASE(TestProjectionMatrix) { Image image; BOOST_CHECK(image.ProjectionMatrix().isApprox(Eigen::Matrix3x4d::Identity())); } BOOST_AUTO_TEST_CASE(TestInverseProjectionMatrix) { Image image; BOOST_CHECK( image.InverseProjectionMatrix().isApprox(Eigen::Matrix3x4d::Identity())); } BOOST_AUTO_TEST_CASE(TestRotationMatrix) { Image image; BOOST_CHECK(image.RotationMatrix().isApprox(Eigen::Matrix3d::Identity())); } BOOST_AUTO_TEST_CASE(TestProjectionCenter) { Image image; BOOST_CHECK(image.ProjectionCenter().isApprox(Eigen::Vector3d::Zero())); } BOOST_AUTO_TEST_CASE(TestViewingDirection) { Image image; BOOST_CHECK(image.ViewingDirection().isApprox(Eigen::Vector3d(0, 0, 1))); } colmap-3.4/src/base/line.cc000066400000000000000000000057021323400541200155700ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/line.h" #include "util/logging.h" extern "C" { #include "ext/LSD/lsd.h" } namespace colmap { std::vector DetectLineSegments(const Bitmap& bitmap, const double min_length) { const double min_length_squared = min_length * min_length; std::vector bitmap_data; if (bitmap.IsGrey()) { bitmap_data = bitmap.ConvertToRowMajorArray(); } else { const Bitmap bitmap_gray = bitmap.CloneAsGrey(); bitmap_data = bitmap_gray.ConvertToRowMajorArray(); } std::vector bitmap_data_double(bitmap_data.begin(), bitmap_data.end()); int num_segments; std::unique_ptr segments_data(lsd(&num_segments, bitmap_data_double.data(), bitmap.Width(), bitmap.Height())); std::vector segments; segments.reserve(num_segments); for (int i = 0; i < num_segments; ++i) { const Eigen::Vector2d start(segments_data.get()[i * 7], segments_data.get()[i * 7 + 1]); const Eigen::Vector2d end(segments_data.get()[i * 7 + 2], segments_data.get()[i * 7 + 3]); if ((start - end).squaredNorm() >= min_length_squared) { segments.emplace_back(); segments.back().start = start; segments.back().end = end; } } return segments; } std::vector ClassifyLineSegmentOrientations( const std::vector& segments, const double tolerance) { CHECK_LE(tolerance, 0.5); std::vector orientations; orientations.reserve(segments.size()); for (const auto& segment : segments) { const Eigen::Vector2d direction = (segment.end - segment.start).normalized(); if (std::abs(direction.x()) + tolerance > 1) { orientations.push_back(LineSegmentOrientation::HORIZONTAL); } else if (std::abs(direction.y()) + tolerance > 1) { orientations.push_back(LineSegmentOrientation::VERTICAL); } else { orientations.push_back(LineSegmentOrientation::UNDEFINED); } } return orientations; } } // namespace colmap colmap-3.4/src/base/line.h000066400000000000000000000031711323400541200154300ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_LINE_H_ #define COLMAP_SRC_BASE_LINE_H_ #include #include "util/alignment.h" #include "util/bitmap.h" namespace colmap { struct LineSegment { EIGEN_MAKE_ALIGNED_OPERATOR_NEW Eigen::Vector2d start; Eigen::Vector2d end; }; enum class LineSegmentOrientation { HORIZONTAL = 1, VERTICAL = -1, UNDEFINED = 0, }; // Detect line segments in the given bitmap image. std::vector DetectLineSegments(const Bitmap& bitmap, const double min_length = 3); // Classify line segments into horizontal/vertical. std::vector ClassifyLineSegmentOrientations( const std::vector& segments, const double tolerance = 0.25); } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::LineSegment) #endif // COLMAP_SRC_BASE_LINE_H_ colmap-3.4/src/base/line_test.cc000066400000000000000000000050001323400541200166160ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/line" #include "util/testing.h" #include "base/line.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDetectLineSegments) { Bitmap bitmap; bitmap.Allocate(100, 100, false); for (size_t i = 0; i < 100; ++i) { bitmap.SetPixel(i, i, BitmapColor(255)); } const auto line_segments = DetectLineSegments(bitmap, 0); BOOST_CHECK_EQUAL(line_segments.size(), 2); const Eigen::Vector2d ref_start(0, 0); const Eigen::Vector2d ref_end(100, 100); BOOST_CHECK_LT((line_segments[0].start - ref_start).norm(), 5); BOOST_CHECK_LT((line_segments[0].end - ref_end).norm(), 5); BOOST_CHECK_LT((line_segments[1].start - ref_end).norm(), 5); BOOST_CHECK_LT((line_segments[1].end - ref_start).norm(), 5); BOOST_CHECK_EQUAL(DetectLineSegments(bitmap, 150).size(), 0); } BOOST_AUTO_TEST_CASE(TestClassifyLineSegmentOrientations) { Bitmap bitmap; bitmap.Allocate(100, 100, false); for (size_t i = 60; i < 100; ++i) { bitmap.SetPixel(i, 50, BitmapColor(255)); bitmap.SetPixel(50, i, BitmapColor(255)); bitmap.SetPixel(i, i, BitmapColor(255)); } const auto line_segments = DetectLineSegments(bitmap, 0); BOOST_CHECK_EQUAL(line_segments.size(), 6); const auto orientations = ClassifyLineSegmentOrientations(line_segments); BOOST_CHECK_EQUAL(orientations.size(), 6); BOOST_CHECK(orientations[0] == LineSegmentOrientation::VERTICAL); BOOST_CHECK(orientations[1] == LineSegmentOrientation::VERTICAL); BOOST_CHECK(orientations[2] == LineSegmentOrientation::HORIZONTAL); BOOST_CHECK(orientations[3] == LineSegmentOrientation::HORIZONTAL); BOOST_CHECK(orientations[4] == LineSegmentOrientation::UNDEFINED); BOOST_CHECK(orientations[5] == LineSegmentOrientation::UNDEFINED); } colmap-3.4/src/base/point2d.cc000077500000000000000000000016511323400541200162220ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/point2d.h" namespace colmap { Point2D::Point2D() : xy_(Eigen::Vector2d::Zero()), point3D_id_(kInvalidPoint3DId) {} } // namespace colmap colmap-3.4/src/base/point2d.h000077500000000000000000000052771323400541200160740ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_POINT2D_H_ #define COLMAP_SRC_BASE_POINT2D_H_ #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // 2D point class corresponds to a feature in an image. It may or may not have a // corresponding 3D point if it is part of a triangulated track. class Point2D { public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW Point2D(); // The coordinate in image space in pixels. inline const Eigen::Vector2d& XY() const; inline Eigen::Vector2d& XY(); inline double X() const; inline double Y() const; inline void SetXY(const Eigen::Vector2d& xy); // The identifier of the observed 3D point. If the image point does not // observe a 3D point, the identifier is `kInvalidPoint3Did`. inline point3D_t Point3DId() const; inline bool HasPoint3D() const; inline void SetPoint3DId(const point3D_t point3D_id); private: // The image coordinates in pixels, starting at upper left corner with 0. Eigen::Vector2d xy_; // The identifier of the 3D point. If the 2D point is not part of a 3D point // track the identifier is `kInvalidPoint3DId` and `HasPoint3D() = false`. point3D_t point3D_id_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// const Eigen::Vector2d& Point2D::XY() const { return xy_; } Eigen::Vector2d& Point2D::XY() { return xy_; } double Point2D::X() const { return xy_.x(); } double Point2D::Y() const { return xy_.y(); } void Point2D::SetXY(const Eigen::Vector2d& xy) { xy_ = xy; } point3D_t Point2D::Point3DId() const { return point3D_id_; } bool Point2D::HasPoint3D() const { return point3D_id_ != kInvalidPoint3DId; } void Point2D::SetPoint3DId(const point3D_t point3D_id) { point3D_id_ = point3D_id; } } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::Point2D) #endif // COLMAP_SRC_BASE_POINT2D_H_ colmap-3.4/src/base/point2d_test.cc000077500000000000000000000041241323400541200172570ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/point2d" #include "util/testing.h" #include "base/point2d.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDefault) { Point2D point2D; BOOST_CHECK_EQUAL(point2D.X(), 0); BOOST_CHECK_EQUAL(point2D.Y(), 0); BOOST_CHECK_EQUAL(point2D.XY()[0], point2D.X()); BOOST_CHECK_EQUAL(point2D.XY()[1], point2D.Y()); BOOST_CHECK_EQUAL(point2D.Point3DId(), kInvalidPoint3DId); BOOST_CHECK_EQUAL(point2D.HasPoint3D(), false); } BOOST_AUTO_TEST_CASE(TestXY) { Point2D point2D; BOOST_CHECK_EQUAL(point2D.X(), 0); BOOST_CHECK_EQUAL(point2D.Y(), 0); BOOST_CHECK_EQUAL(point2D.XY()[0], point2D.X()); BOOST_CHECK_EQUAL(point2D.XY()[1], point2D.Y()); point2D.SetXY(Eigen::Vector2d(0.1, 0.2)); BOOST_CHECK_EQUAL(point2D.X(), 0.1); BOOST_CHECK_EQUAL(point2D.Y(), 0.2); BOOST_CHECK_EQUAL(point2D.XY()[0], point2D.X()); BOOST_CHECK_EQUAL(point2D.XY()[1], point2D.Y()); } BOOST_AUTO_TEST_CASE(TestPoint3DId) { Point2D point2D; BOOST_CHECK_EQUAL(point2D.Point3DId(), kInvalidPoint3DId); BOOST_CHECK_EQUAL(point2D.HasPoint3D(), false); point2D.SetPoint3DId(1); BOOST_CHECK_EQUAL(point2D.Point3DId(), 1); BOOST_CHECK_EQUAL(point2D.HasPoint3D(), true); point2D.SetPoint3DId(kInvalidPoint3DId); BOOST_CHECK_EQUAL(point2D.Point3DId(), kInvalidPoint3DId); BOOST_CHECK_EQUAL(point2D.HasPoint3D(), false); } colmap-3.4/src/base/point3d.cc000077500000000000000000000016331323400541200162230ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/point3d.h" namespace colmap { Point3D::Point3D() : xyz_(0.0, 0.0, 0.0), color_(0, 0, 0), error_(-1.0) {} } // namespace colmap colmap-3.4/src/base/point3d.h000077500000000000000000000072621323400541200160710ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_POINT3D_H_ #define COLMAP_SRC_BASE_POINT3D_H_ #include #include #include "base/track.h" #include "util/logging.h" #include "util/types.h" namespace colmap { // 3D point class that holds information about triangulated 2D points. class Point3D { public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW Point3D(); // The point coordinate in world space. inline const Eigen::Vector3d& XYZ() const; inline Eigen::Vector3d& XYZ(); inline double XYZ(const size_t idx) const; inline double& XYZ(const size_t idx); inline double X() const; inline double Y() const; inline double Z() const; inline void SetXYZ(const Eigen::Vector3d& xyz); // The RGB color of the point. inline const Eigen::Vector3ub& Color() const; inline Eigen::Vector3ub& Color(); inline uint8_t Color(const size_t idx) const; inline uint8_t& Color(const size_t idx); inline void SetColor(const Eigen::Vector3ub& color); // The mean reprojection error in image space. inline double Error() const; inline bool HasError() const; inline void SetError(const double error); inline const class Track& Track() const; inline class Track& Track(); inline void SetTrack(const class Track& track); private: // The 3D position of the point. Eigen::Vector3d xyz_; // The color of the point in the range [0, 255]. Eigen::Vector3ub color_; // The mean reprojection error in pixels. double error_; // The track of the point as a list of image observations. class Track track_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// const Eigen::Vector3d& Point3D::XYZ() const { return xyz_; } Eigen::Vector3d& Point3D::XYZ() { return xyz_; } double Point3D::XYZ(const size_t idx) const { return xyz_(idx); } double& Point3D::XYZ(const size_t idx) { return xyz_(idx); } double Point3D::X() const { return xyz_.x(); } double Point3D::Y() const { return xyz_.y(); } double Point3D::Z() const { return xyz_.z(); } void Point3D::SetXYZ(const Eigen::Vector3d& xyz) { xyz_ = xyz; } const Eigen::Vector3ub& Point3D::Color() const { return color_; } Eigen::Vector3ub& Point3D::Color() { return color_; } uint8_t Point3D::Color(const size_t idx) const { return color_(idx); } uint8_t& Point3D::Color(const size_t idx) { return color_(idx); } void Point3D::SetColor(const Eigen::Vector3ub& color) { color_ = color; } double Point3D::Error() const { return error_; } bool Point3D::HasError() const { return error_ != -1.0; } void Point3D::SetError(const double error) { error_ = error; } const class Track& Point3D::Track() const { return track_; } class Track& Point3D::Track() { return track_; } void Point3D::SetTrack(const class Track& track) { track_ = track; } } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::Point3D) #endif // COLMAP_SRC_BASE_POINT3D_H_ colmap-3.4/src/base/point3d_test.cc000077500000000000000000000070251323400541200172630ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/point3d" #include "util/testing.h" #include "base/point3d.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDefault) { Point3D point3D; BOOST_CHECK_EQUAL(point3D.X(), 0); BOOST_CHECK_EQUAL(point3D.Y(), 0); BOOST_CHECK_EQUAL(point3D.Z(), 0); BOOST_CHECK_EQUAL(point3D.XYZ()[0], point3D.X()); BOOST_CHECK_EQUAL(point3D.XYZ()[1], point3D.Y()); BOOST_CHECK_EQUAL(point3D.XYZ()[2], point3D.Z()); BOOST_CHECK_EQUAL(point3D.Color()[0], 0); BOOST_CHECK_EQUAL(point3D.Color()[1], 0); BOOST_CHECK_EQUAL(point3D.Color()[2], 0); BOOST_CHECK_EQUAL(point3D.Error(), -1.0); BOOST_CHECK_EQUAL(point3D.HasError(), false); BOOST_CHECK_EQUAL(point3D.Track().Length(), 0); } BOOST_AUTO_TEST_CASE(TestXYZ) { Point3D point3D; BOOST_CHECK_EQUAL(point3D.X(), 0); BOOST_CHECK_EQUAL(point3D.Y(), 0); BOOST_CHECK_EQUAL(point3D.Z(), 0); BOOST_CHECK_EQUAL(point3D.XYZ()[0], point3D.X()); BOOST_CHECK_EQUAL(point3D.XYZ()[1], point3D.Y()); BOOST_CHECK_EQUAL(point3D.XYZ()[2], point3D.Z()); point3D.SetXYZ(Eigen::Vector3d(0.1, 0.2, 0.3)); BOOST_CHECK_EQUAL(point3D.X(), 0.1); BOOST_CHECK_EQUAL(point3D.Y(), 0.2); BOOST_CHECK_EQUAL(point3D.Z(), 0.3); BOOST_CHECK_EQUAL(point3D.XYZ()[0], point3D.X()); BOOST_CHECK_EQUAL(point3D.XYZ()[1], point3D.Y()); BOOST_CHECK_EQUAL(point3D.XYZ()[2], point3D.Z()); point3D.XYZ() = Eigen::Vector3d(0.2, 0.3, 0.4); BOOST_CHECK_EQUAL(point3D.X(), 0.2); BOOST_CHECK_EQUAL(point3D.Y(), 0.3); BOOST_CHECK_EQUAL(point3D.Z(), 0.4); BOOST_CHECK_EQUAL(point3D.XYZ()[0], point3D.X()); BOOST_CHECK_EQUAL(point3D.XYZ()[1], point3D.Y()); BOOST_CHECK_EQUAL(point3D.XYZ()[2], point3D.Z()); } BOOST_AUTO_TEST_CASE(TestRGB) { Point3D point3D; BOOST_CHECK_EQUAL(point3D.Color()[0], 0); BOOST_CHECK_EQUAL(point3D.Color()[1], 0); BOOST_CHECK_EQUAL(point3D.Color()[2], 0); point3D.SetColor(Eigen::Vector3ub(1, 2, 3)); BOOST_CHECK_EQUAL(point3D.Color()[0], 1); BOOST_CHECK_EQUAL(point3D.Color()[1], 2); BOOST_CHECK_EQUAL(point3D.Color()[2], 3); } BOOST_AUTO_TEST_CASE(TestError) { Point3D point3D; BOOST_CHECK_EQUAL(point3D.Error(), -1.0); BOOST_CHECK_EQUAL(point3D.HasError(), false); point3D.SetError(1.0); BOOST_CHECK_EQUAL(point3D.Error(), 1.0); BOOST_CHECK_EQUAL(point3D.HasError(), true); point3D.SetError(-1.0); BOOST_CHECK_EQUAL(point3D.Error(), -1.0); BOOST_CHECK_EQUAL(point3D.HasError(), false); } BOOST_AUTO_TEST_CASE(TestTrack) { Point3D point3D; BOOST_CHECK_EQUAL(point3D.Track().Length(), 0); point3D.SetTrack(Track()); BOOST_CHECK_EQUAL(point3D.Track().Length(), 0); Track track; track.AddElement(0, 1); track.AddElement(0, 2); point3D.SetTrack(track); BOOST_CHECK_EQUAL(point3D.Track().Length(), 2); track.AddElement(0, 3); BOOST_CHECK_EQUAL(point3D.Track().Length(), 2); } colmap-3.4/src/base/polynomial.cc000066400000000000000000000160001323400541200170150ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/polynomial.h" #include #include "util/logging.h" namespace colmap { namespace { // Remove leading zero coefficients. Eigen::VectorXd RemoveLeadingZeros(const Eigen::VectorXd& coeffs) { Eigen::VectorXd::Index num_zeros = 0; for (; num_zeros < coeffs.size(); ++num_zeros) { if (coeffs(num_zeros) != 0) { break; } } return coeffs.tail(coeffs.size() - num_zeros); } // Remove trailing zero coefficients. Eigen::VectorXd RemoveTrailingZeros(const Eigen::VectorXd& coeffs) { Eigen::VectorXd::Index num_zeros = 0; for (; num_zeros < coeffs.size(); ++num_zeros) { if (coeffs(coeffs.size() - 1 - num_zeros) != 0) { break; } } return coeffs.head(coeffs.size() - num_zeros); } } // namespace bool FindLinearPolynomialRoots(const Eigen::VectorXd& coeffs, Eigen::VectorXd* real, Eigen::VectorXd* imag) { CHECK_EQ(coeffs.size(), 2); if (coeffs(0) == 0) { return false; } if (real != nullptr) { real->resize(1); (*real)(0) = -coeffs(1) / coeffs(0); } if (imag != nullptr) { imag->resize(1); (*imag)(0) = 0; } return true; } bool FindQuadraticPolynomialRoots(const Eigen::VectorXd& coeffs, Eigen::VectorXd* real, Eigen::VectorXd* imag) { CHECK_EQ(coeffs.size(), 3); const double a = coeffs(0); if (a == 0) { return FindLinearPolynomialRoots(coeffs.tail(2), real, imag); } const double b = coeffs(1); const double c = coeffs(2); if (b == 0 && c == 0) { if (real != nullptr) { real->resize(1); (*real)(0) = 0; } if (imag != nullptr) { imag->resize(1); (*imag)(0) = 0; } return true; } const double d = b * b - 4 * a * c; if (d >= 0) { const double sqrt_d = std::sqrt(d); if (real != nullptr) { real->resize(2); if (b >= 0) { (*real)(0) = (-b - sqrt_d) / (2 * a); (*real)(1) = (2 * c) / (-b - sqrt_d); } else { (*real)(0) = (2 * c) / (-b + sqrt_d); (*real)(1) = (-b + sqrt_d) / (2 * a); } } if (imag != nullptr) { imag->resize(2); imag->setZero(); } } else { if (real != nullptr) { real->resize(2); real->setConstant(-b / (2 * a)); } if (imag != nullptr) { imag->resize(2); (*imag)(0) = std::sqrt(-d) / (2 * a); (*imag)(1) = -(*imag)(0); } } return true; } bool FindPolynomialRootsDurandKerner(const Eigen::VectorXd& coeffs_all, Eigen::VectorXd* real, Eigen::VectorXd* imag) { CHECK_GE(coeffs_all.size(), 2); const Eigen::VectorXd coeffs = RemoveLeadingZeros(coeffs_all); const int degree = coeffs.size() - 1; if (degree <= 0) { return false; } else if (degree == 1) { return FindLinearPolynomialRoots(coeffs, real, imag); } else if (degree == 2) { return FindQuadraticPolynomialRoots(coeffs, real, imag); } // Initialize roots. Eigen::VectorXcd roots(degree); roots(degree - 1) = std::complex(1, 0); for (int i = degree - 2; i >= 0; --i) { roots(i) = roots(i + 1) * std::complex(1, 1); } // Iterative solver. const int kMaxNumIterations = 100; const double kMaxRootChange = 1e-10; for (int iter = 0; iter < kMaxNumIterations; ++iter) { double max_root_change = 0.0; for (int i = 0; i < degree; ++i) { const std::complex root_i = roots(i); std::complex numerator = coeffs[0]; std::complex denominator = coeffs[0]; for (int j = 0; j < degree; ++j) { numerator = numerator * root_i + coeffs[j + 1]; if (i != j) { denominator = denominator * (root_i - roots(j)); } } const std::complex root_i_change = numerator / denominator; roots(i) = root_i - root_i_change; max_root_change = std::max(max_root_change, std::abs(root_i_change.real())); max_root_change = std::max(max_root_change, std::abs(root_i_change.imag())); } // Break, if roots do not change anymore. if (max_root_change < kMaxRootChange) { break; } } if (real != nullptr) { real->resize(degree); *real = roots.real(); } if (imag != nullptr) { imag->resize(degree); *imag = roots.imag(); } return true; } bool FindPolynomialRootsCompanionMatrix(const Eigen::VectorXd& coeffs_all, Eigen::VectorXd* real, Eigen::VectorXd* imag) { CHECK_GE(coeffs_all.size(), 2); Eigen::VectorXd coeffs = RemoveLeadingZeros(coeffs_all); const int degree = coeffs.size() - 1; if (degree <= 0) { return false; } else if (degree == 1) { return FindLinearPolynomialRoots(coeffs, real, imag); } else if (degree == 2) { return FindQuadraticPolynomialRoots(coeffs, real, imag); } // Remove the coefficients where zero is a solution. coeffs = RemoveTrailingZeros(coeffs); // Check if only zero is a solution. if (coeffs.size() == 1) { if (real != nullptr) { real->resize(1); (*real)(0) = 0; } if (imag != nullptr) { imag->resize(1); (*imag)(0) = 0; } return true; } // Fill the companion matrix. Eigen::MatrixXd C(coeffs.size() - 1, coeffs.size() - 1); C.setZero(); for (Eigen::MatrixXd::Index i = 1; i < C.rows(); ++i) { C(i, i - 1) = 1; } C.row(0) = -coeffs.tail(coeffs.size() - 1) / coeffs(0); // Solve for the roots of the polynomial. Eigen::EigenSolver solver(C, false); if (solver.info() != Eigen::Success) { return false; } // If there are trailing zeros, we must add zero as a solution. const int effective_degree = coeffs.size() - 1 < degree ? coeffs.size() : coeffs.size() - 1; if (real != nullptr) { real->resize(effective_degree); real->head(coeffs.size() - 1) = solver.eigenvalues().real(); if (effective_degree > coeffs.size() - 1) { (*real)(real->size() - 1) = 0; } } if (imag != nullptr) { imag->resize(effective_degree); imag->head(coeffs.size() - 1) = solver.eigenvalues().imag(); if (effective_degree > coeffs.size() - 1) { (*imag)(imag->size() - 1) = 0; } } return true; } } // namespace colmap colmap-3.4/src/base/polynomial.h000066400000000000000000000071051323400541200166650ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_POLYNOMIAL_H_ #define COLMAP_SRC_BASE_POLYNOMIAL_H_ #include namespace colmap { // All polynomials are assumed to be the form: // // sum_{i=0}^N polynomial(i) x^{N-i}. // // and are given by a vector of coefficients of size N + 1. // // The implementation is based on COLMAP's old polynomial functionality and is // inspired by Ceres-Solver's/Theia's implementation to support complex // polynomials. The companion matrix implementation is based on NumPy. // Evaluate the polynomial for the given coefficients at x using the Horner // scheme. This function is templated such that the polynomial may be evaluated // at real and/or imaginary points. template T EvaluatePolynomial(const Eigen::VectorXd& coeffs, const T& x); // Find the root of polynomials of the form: a * x + b = 0. // The real and/or imaginary variable may be NULL if the output is not needed. bool FindLinearPolynomialRoots(const Eigen::VectorXd& coeffs, Eigen::VectorXd* real, Eigen::VectorXd* imag); // Find the roots of polynomials of the form: a * x^2 + b * x + c = 0. // The real and/or imaginary variable may be NULL if the output is not needed. bool FindQuadraticPolynomialRoots(const Eigen::VectorXd& coeffs, Eigen::VectorXd* real, Eigen::VectorXd* imag); // Find the roots of a polynomial using the Durand-Kerner method, based on: // // https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method // // The Durand-Kerner is comparatively fast but often unstable/inaccurate. // The real and/or imaginary variable may be NULL if the output is not needed. bool FindPolynomialRootsDurandKerner(const Eigen::VectorXd& coeffs, Eigen::VectorXd* real, Eigen::VectorXd* imag); // Find the roots of a polynomial using the companion matrix method, based on: // // R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, // UK: Cambridge University Press, 1999, pp. 146-7. // // Compared to Durand-Kerner, this method is slower but more stable/accurate. // The real and/or imaginary variable may be NULL if the output is not needed. bool FindPolynomialRootsCompanionMatrix(const Eigen::VectorXd& coeffs, Eigen::VectorXd* real, Eigen::VectorXd* imag); //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// template T EvaluatePolynomial(const Eigen::VectorXd& coeffs, const T& x) { T value = 0.0; for (Eigen::VectorXd::Index i = 0; i < coeffs.size(); ++i) { value = value * x + coeffs(i); } return value; } } // namespace colmap #endif // COLMAP_SRC_BASE_POLYNOMIAL_H_ colmap-3.4/src/base/polynomial_test.cc000066400000000000000000000165631323400541200200720ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/polynomial" #include "util/testing.h" #include "base/polynomial.h" using namespace colmap; #define CHECK_EQUAL_RESULT(find_func1, coeffs1, find_func2, coeffs2) \ { \ Eigen::VectorXd real1; \ Eigen::VectorXd imag1; \ const bool success1 = find_func1(coeffs1, &real1, &imag1); \ Eigen::VectorXd real2; \ Eigen::VectorXd imag2; \ const bool success2 = find_func2(coeffs2, &real2, &imag2); \ BOOST_CHECK_EQUAL(success1, success2); \ if (success1) { \ BOOST_CHECK_EQUAL(real1, real2); \ BOOST_CHECK_EQUAL(imag1, imag2); \ } \ } BOOST_AUTO_TEST_CASE(TestEvaluatePolynomial) { BOOST_CHECK_EQUAL(EvaluatePolynomial( (Eigen::VectorXd(5) << 1, -3, 3, -5, 10).finished(), 1), 1 - 3 + 3 - 5 + 10); BOOST_CHECK_CLOSE( EvaluatePolynomial((Eigen::VectorXd(4) << 1, -3, 3, -5).finished(), 2.0), 1 * 2 * 2 * 2 - 3 * 2 * 2 + 3 * 2 - 5, 1e-6); } BOOST_AUTO_TEST_CASE(TestFindLinearPolynomialRoots) { Eigen::VectorXd real; Eigen::VectorXd imag; BOOST_CHECK(FindLinearPolynomialRoots(Eigen::Vector2d(3, -2), &real, &imag)); BOOST_CHECK_EQUAL(real(0), 2.0 / 3.0); BOOST_CHECK_EQUAL(imag(0), 0); BOOST_CHECK_CLOSE(EvaluatePolynomial(Eigen::Vector2d(3, -2), std::complex(real(0), imag(0))) .real(), 0.0, 1e-6); BOOST_CHECK_CLOSE(EvaluatePolynomial(Eigen::Vector2d(3, -2), std::complex(real(0), imag(0))) .imag(), 0.0, 1e-6); BOOST_CHECK(!FindLinearPolynomialRoots(Eigen::Vector2d(0, 1), &real, &imag)); } BOOST_AUTO_TEST_CASE(TestFindQuadraticPolynomialRootsReal) { Eigen::VectorXd real; Eigen::VectorXd imag; Eigen::Vector3d coeffs(3, -2, -4); BOOST_CHECK(FindQuadraticPolynomialRoots(coeffs, &real, &imag)); BOOST_CHECK(real.isApprox(Eigen::Vector2d(-0.868517092, 1.535183758), 1e-6)); BOOST_CHECK_EQUAL(imag, Eigen::Vector2d(0, 0)); BOOST_CHECK_CLOSE( EvaluatePolynomial(coeffs, std::complex(real(0), imag(0))).real(), 0.0, 1e-6); BOOST_CHECK_CLOSE( EvaluatePolynomial(coeffs, std::complex(real(1), imag(1))).imag(), 0.0, 1e-6); } BOOST_AUTO_TEST_CASE(TestFindQuadraticPolynomialRootsComplex) { Eigen::VectorXd real; Eigen::VectorXd imag; const Eigen::Vector3d coeffs(0.276025076998578, 0.679702676853675, 0.655098003973841); BOOST_CHECK(FindQuadraticPolynomialRoots(coeffs, &real, &imag)); BOOST_CHECK(real.isApprox( Eigen::Vector2d(-1.231233560813707, -1.231233560813707), 1e-6)); BOOST_CHECK(imag.isApprox( Eigen::Vector2d(0.925954520440279, -0.925954520440279), 1e-6)); BOOST_CHECK_CLOSE( EvaluatePolynomial(coeffs, std::complex(real(0), imag(0))).real(), 0.0, 1e-6); BOOST_CHECK_CLOSE( EvaluatePolynomial(coeffs, std::complex(real(1), imag(1))).imag(), 0.0, 1e-6); } BOOST_AUTO_TEST_CASE(TestFindPolynomialRootsDurandKerner) { Eigen::VectorXd real; Eigen::VectorXd imag; Eigen::VectorXd coeffs(5); coeffs << 10, -5, 3, -3, 1; BOOST_CHECK(FindPolynomialRootsDurandKerner(coeffs, &real, &imag)); // Reference values generated with OpenCV/Matlab. Eigen::VectorXd ref_real(4); ref_real << -0.201826, -0.201826, 0.451826, 0.451826; BOOST_CHECK(real.isApprox(ref_real, 1e-6)); Eigen::VectorXd ref_imag(4); ref_imag << -0.627696, 0.627696, 0.160867, -0.160867; BOOST_CHECK(imag.isApprox(ref_imag, 1e-6)); } BOOST_AUTO_TEST_CASE(TestFindPolynomialRootsDurandKernerLinearQuadratic) { CHECK_EQUAL_RESULT(FindPolynomialRootsDurandKerner, Eigen::Vector2d(1, 2), FindLinearPolynomialRoots, Eigen::Vector2d(1, 2)); CHECK_EQUAL_RESULT(FindPolynomialRootsDurandKerner, (Eigen::VectorXd(4) << 0, 0, 1, 2).finished(), FindLinearPolynomialRoots, Eigen::Vector2d(1, 2)); CHECK_EQUAL_RESULT(FindPolynomialRootsDurandKerner, Eigen::Vector3d(1, 2, 3), FindQuadraticPolynomialRoots, Eigen::Vector3d(1, 2, 3)); CHECK_EQUAL_RESULT(FindPolynomialRootsDurandKerner, (Eigen::VectorXd(5) << 0, 0, 1, 2, 3).finished(), FindQuadraticPolynomialRoots, Eigen::Vector3d(1, 2, 3)); } BOOST_AUTO_TEST_CASE(TestFindPolynomialRootsCompanionMatrix) { Eigen::VectorXd real; Eigen::VectorXd imag; Eigen::VectorXd coeffs(5); coeffs << 10, -5, 3, -3, 1; BOOST_CHECK(FindPolynomialRootsCompanionMatrix(coeffs, &real, &imag)); // Reference values generated with OpenCV/Matlab. Eigen::VectorXd ref_real(4); ref_real << -0.201826, -0.201826, 0.451826, 0.451826; BOOST_CHECK(real.isApprox(ref_real, 1e-6)); Eigen::VectorXd ref_imag(4); ref_imag << 0.627696, -0.627696, 0.160867, -0.160867; BOOST_CHECK(imag.isApprox(ref_imag, 1e-6)); } BOOST_AUTO_TEST_CASE(TestFindPolynomialRootsCompanionMatrixLinearQuadratic) { CHECK_EQUAL_RESULT(FindPolynomialRootsCompanionMatrix, Eigen::Vector2d(1, 2), FindLinearPolynomialRoots, Eigen::Vector2d(1, 2)); CHECK_EQUAL_RESULT(FindPolynomialRootsCompanionMatrix, (Eigen::VectorXd(4) << 0, 0, 1, 2).finished(), FindLinearPolynomialRoots, Eigen::Vector2d(1, 2)); CHECK_EQUAL_RESULT(FindPolynomialRootsCompanionMatrix, Eigen::Vector3d(1, 2, 3), FindQuadraticPolynomialRoots, Eigen::Vector3d(1, 2, 3)); CHECK_EQUAL_RESULT(FindPolynomialRootsCompanionMatrix, (Eigen::VectorXd(5) << 0, 0, 1, 2, 3).finished(), FindQuadraticPolynomialRoots, Eigen::Vector3d(1, 2, 3)); } BOOST_AUTO_TEST_CASE(TestFindPolynomialRootsCompanionMatrixZeroSolution) { Eigen::VectorXd real; Eigen::VectorXd imag; Eigen::VectorXd coeffs(5); coeffs << 10, -5, 3, -3, 0; BOOST_CHECK(FindPolynomialRootsCompanionMatrix(coeffs, &real, &imag)); // Reference values generated with Matlab. Eigen::VectorXd ref_real(4); ref_real << 0.692438, -0.0962191, -0.0962191, 0; BOOST_CHECK(real.isApprox(ref_real, 1e-6)); Eigen::VectorXd ref_imag(4); ref_imag << 0, 0.651148, -0.651148, 0; BOOST_CHECK(imag.isApprox(ref_imag, 1e-6)); } colmap-3.4/src/base/pose.cc000077500000000000000000000230211323400541200156040ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/pose.h" #include #include "base/projection.h" #include "base/triangulation.h" namespace colmap { Eigen::Matrix3d CrossProductMatrix(const Eigen::Vector3d& vector) { Eigen::Matrix3d matrix; matrix << 0, -vector(2), vector(1), vector(2), 0, -vector(0), -vector(1), vector(0), 0; return matrix; } void RotationMatrixToEulerAngles(const Eigen::Matrix3d& R, double* rx, double* ry, double* rz) { *rx = std::atan2(-R(1, 2), R(2, 2)); *ry = std::asin(R(0, 2)); *rz = std::atan2(-R(0, 1), R(0, 0)); *rx = IsNaN(*rx) ? 0 : *rx; *ry = IsNaN(*ry) ? 0 : *ry; *rz = IsNaN(*rz) ? 0 : *rz; } Eigen::Matrix3d EulerAnglesToRotationMatrix(const double rx, const double ry, const double rz) { const Eigen::Matrix3d Rx = Eigen::AngleAxisd(rx, Eigen::Vector3d::UnitX()).toRotationMatrix(); const Eigen::Matrix3d Ry = Eigen::AngleAxisd(ry, Eigen::Vector3d::UnitY()).toRotationMatrix(); const Eigen::Matrix3d Rz = Eigen::AngleAxisd(rz, Eigen::Vector3d::UnitZ()).toRotationMatrix(); return Rz * Ry * Rx; } Eigen::Vector4d RotationMatrixToQuaternion(const Eigen::Matrix3d& rot_mat) { const Eigen::Quaterniond quat(rot_mat); return Eigen::Vector4d(quat.w(), quat.x(), quat.y(), quat.z()); } Eigen::Matrix3d QuaternionToRotationMatrix(const Eigen::Vector4d& qvec) { const Eigen::Vector4d normalized_qvec = NormalizeQuaternion(qvec); const Eigen::Quaterniond quat(normalized_qvec(0), normalized_qvec(1), normalized_qvec(2), normalized_qvec(3)); return quat.toRotationMatrix(); } Eigen::Vector4d NormalizeQuaternion(const Eigen::Vector4d& qvec) { const double norm = qvec.norm(); if (norm == 0) { // We do not just use (1, 0, 0, 0) because that is a constant and when used // for automatic differentiation that would lead to a zero derivative. return Eigen::Vector4d(1.0, qvec(1), qvec(2), qvec(3)); } else { const double inv_norm = 1.0 / norm; return inv_norm * qvec; } } Eigen::Vector4d InvertQuaternion(const Eigen::Vector4d& qvec) { const Eigen::Vector4d normalized_qvec = NormalizeQuaternion(qvec); return Eigen::Vector4d(normalized_qvec(0), -normalized_qvec(1), -normalized_qvec(2), -normalized_qvec(3)); } Eigen::Vector4d ConcatenateQuaternions(const Eigen::Vector4d& qvec1, const Eigen::Vector4d& qvec2) { const Eigen::Vector4d normalized_qvec1 = NormalizeQuaternion(qvec1); const Eigen::Vector4d normalized_qvec2 = NormalizeQuaternion(qvec2); const Eigen::Quaterniond quat1(normalized_qvec1(0), normalized_qvec1(1), normalized_qvec1(2), normalized_qvec1(3)); const Eigen::Quaterniond quat2(normalized_qvec2(0), normalized_qvec2(1), normalized_qvec2(2), normalized_qvec2(3)); const Eigen::Quaterniond cat_quat = quat2 * quat1; return NormalizeQuaternion( Eigen::Vector4d(cat_quat.w(), cat_quat.x(), cat_quat.y(), cat_quat.z())); } Eigen::Vector3d QuaternionRotatePoint(const Eigen::Vector4d& qvec, const Eigen::Vector3d& point) { const Eigen::Vector4d normalized_qvec = NormalizeQuaternion(qvec); const Eigen::Quaterniond quat(normalized_qvec(0), normalized_qvec(1), normalized_qvec(2), normalized_qvec(3)); return quat * point; } Eigen::Vector4d AverageQuaternions(const std::vector& qvecs, const std::vector& weights) { CHECK_EQ(qvecs.size(), weights.size()); CHECK_GT(qvecs.size(), 0); if (qvecs.size() == 1) { return qvecs[0]; } Eigen::Matrix4d A = Eigen::Matrix4d::Zero(); double weight_sum = 0; for (size_t i = 0; i < qvecs.size(); ++i) { CHECK_GT(weights[i], 0); const Eigen::Vector4d qvec = NormalizeQuaternion(qvecs[i]); A += weights[i] * qvec * qvec.transpose(); weight_sum += weights[i]; } A.array() /= weight_sum; const Eigen::Matrix4d eigenvectors = Eigen::SelfAdjointEigenSolver(A).eigenvectors(); return eigenvectors.col(3); } Eigen::Matrix3d RotationFromUnitVectors(const Eigen::Vector3d& vector1, const Eigen::Vector3d& vector2) { const Eigen::Vector3d v1 = vector1.normalized(); const Eigen::Vector3d v2 = vector2.normalized(); const Eigen::Vector3d v = v1.cross(v2); const Eigen::Matrix3d v_x = CrossProductMatrix(v); const double c = v1.dot(v2); if (c == -1) { return Eigen::Matrix3d::Identity(); } else { return Eigen::Matrix3d::Identity() + v_x + 1 / (1 + c) * (v_x * v_x); } } Eigen::Vector3d ProjectionCenterFromMatrix( const Eigen::Matrix3x4d& proj_matrix) { return -proj_matrix.leftCols<3>().transpose() * proj_matrix.rightCols<1>(); } Eigen::Vector3d ProjectionCenterFromParameters(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec) { // Inverse rotation as conjugate quaternion. const Eigen::Vector4d normalized_qvec = NormalizeQuaternion(qvec); const Eigen::Quaterniond quat(normalized_qvec(0), -normalized_qvec(1), -normalized_qvec(2), -normalized_qvec(3)); return quat * -tvec; } void ComputeRelativePose(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2, Eigen::Vector4d* qvec12, Eigen::Vector3d* tvec12) { const Eigen::Vector4d inv_qvec1 = InvertQuaternion(qvec1); *qvec12 = ConcatenateQuaternions(inv_qvec1, qvec2); *tvec12 = tvec2 - QuaternionRotatePoint(*qvec12, tvec1); } void ConcatenatePoses(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2, Eigen::Vector4d* qvec12, Eigen::Vector3d* tvec12) { *qvec12 = ConcatenateQuaternions(qvec1, qvec2); *tvec12 = tvec2 + QuaternionRotatePoint(qvec2, tvec1); } void InvertPose(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, Eigen::Vector4d* inv_qvec, Eigen::Vector3d* inv_tvec) { *inv_qvec = InvertQuaternion(qvec); *inv_tvec = -QuaternionRotatePoint(*inv_qvec, tvec); } void InterpolatePose(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2, const double t, Eigen::Vector4d* qveci, Eigen::Vector3d* tveci) { const Eigen::Vector4d normalized_qvec1 = NormalizeQuaternion(qvec1); const Eigen::Vector4d normalized_qvec2 = NormalizeQuaternion(qvec2); const Eigen::Quaterniond quat1(normalized_qvec1(0), normalized_qvec1(1), normalized_qvec1(2), normalized_qvec1(3)); const Eigen::Quaterniond quat2(normalized_qvec2(0), normalized_qvec2(1), normalized_qvec2(2), normalized_qvec2(3)); const Eigen::Vector3d tvec12 = tvec2 - tvec1; const Eigen::Quaterniond quati = quat1.slerp(t, quat2); *qveci = Eigen::Vector4d(quati.w(), quati.x(), quati.y(), quati.z()); *tveci = tvec1 + tvec12 * t; } Eigen::Vector3d CalculateBaseline(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2) { const Eigen::Vector3d center1 = ProjectionCenterFromParameters(qvec1, tvec1); const Eigen::Vector3d center2 = ProjectionCenterFromParameters(qvec2, tvec2); return center2 - center1; } bool CheckCheirality(const Eigen::Matrix3d& R, const Eigen::Vector3d& t, const std::vector& points1, const std::vector& points2, std::vector* points3D) { CHECK_EQ(points1.size(), points2.size()); const Eigen::Matrix3x4d proj_matrix1 = Eigen::Matrix3x4d::Identity(); const Eigen::Matrix3x4d proj_matrix2 = ComposeProjectionMatrix(R, t); const double kMinDepth = std::numeric_limits::epsilon(); const double max_depth = 1000.0f * (R.transpose() * t).norm(); points3D->clear(); for (size_t i = 0; i < points1.size(); ++i) { const Eigen::Vector3d point3D = TriangulatePoint(proj_matrix1, proj_matrix2, points1[i], points2[i]); const double depth1 = CalculateDepth(proj_matrix1, point3D); if (depth1 > kMinDepth && depth1 < max_depth) { const double depth2 = CalculateDepth(proj_matrix2, point3D); if (depth2 > kMinDepth && depth2 < max_depth) { points3D->push_back(point3D); } } } return !points3D->empty(); } } // namespace colmap colmap-3.4/src/base/pose.h000077500000000000000000000216221323400541200154530ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_POSE_H_ #define COLMAP_SRC_BASE_POSE_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Compose the skew symmetric cross product matrix from a vector. Eigen::Matrix3d CrossProductMatrix(const Eigen::Vector3d& vector); // Convert 3D rotation matrix to Euler angles. // // The convention `R = Rx * Ry * Rz` is used, // using a right-handed coordinate system. // // @param R 3x3 rotation matrix. // @param rx, ry, rz Euler angles in radians. void RotationMatrixToEulerAngles(const Eigen::Matrix3d& R, double* rx, double* ry, double* rz); // Convert Euler angles to 3D rotation matrix. // // The convention `R = Rz * Ry * Rx` is used, // using a right-handed coordinate system. // // @param rx, ry, rz Euler angles in radians. // // @return 3x3 rotation matrix. Eigen::Matrix3d EulerAnglesToRotationMatrix(const double rx, const double ry, const double rz); // Convert 3D rotation matrix to Quaternion representation. // // @param rot_mat 3x3 rotation matrix. // // @return Unit Quaternion rotation coefficients (w, x, y, z). Eigen::Vector4d RotationMatrixToQuaternion(const Eigen::Matrix3d& rot_mat); // Convert Quaternion representation to 3D rotation matrix. // // @param qvec Unit Quaternion rotation coefficients (w, x, y, z). // // @return 3x3 rotation matrix. Eigen::Matrix3d QuaternionToRotationMatrix(const Eigen::Vector4d& qvec); // Compose the Quaternion vector corresponding to a identity transformation. inline Eigen::Vector4d ComposeIdentityQuaternion(); // Normalize Quaternion vector. // // @param qvec Quaternion rotation coefficients (w, x, y, z). // // @return Unit Quaternion rotation coefficients (w, x, y, z). Eigen::Vector4d NormalizeQuaternion(const Eigen::Vector4d& qvec); // Invert Quaternion vector to return Quaternion of inverse rotation. // // @param qvec Quaternion rotation coefficients (w, x, y, z). // // @return Inverse Quaternion rotation coefficients (w, x, y, z). Eigen::Vector4d InvertQuaternion(const Eigen::Vector4d& qvec); // Concatenate Quaternion rotations such that the rotation of `qvec1` is applied // before the rotation of `qvec2`. // // @param qvec1 Quaternion rotation coefficients (w, x, y, z). // @param qvec2 Quaternion rotation coefficients (w, x, y, z). // // @return Concatenated Quaternion coefficients (w, x, y, z). Eigen::Vector4d ConcatenateQuaternions(const Eigen::Vector4d& qvec1, const Eigen::Vector4d& qvec2); // Transform point by quaternion rotation. // // @param qvec Quaternion rotation coefficients (w, x, y, z). // @param point Point to rotate. // // @return Rotated point. Eigen::Vector3d QuaternionRotatePoint(const Eigen::Vector4d& qvec, const Eigen::Vector3d& point); // Compute the weighted average of multiple Quaternions according to: // // Markley, F. Landis, et al. "Averaging quaternions." // Journal of Guidance, Control, and Dynamics 30.4 (2007): 1193-1197. // // @param qvecs The Quaternions to be averaged. // @param weights Non-negative weights. // // @return The average Quaternion. Eigen::Vector4d AverageQuaternions(const std::vector& qvecs, const std::vector& weights); // Compose rotation matrix that rotates unit vector 1 to unit vector 2. // Note that when vector 1 points into the opposite direction of vector 2, // the function returns an identity rotation. Eigen::Matrix3d RotationFromUnitVectors(const Eigen::Vector3d& vec1, const Eigen::Vector3d& vec2); // Extract camera projection center from projection matrix, i.e. the projection // center in world coordinates `-R^T t`. // // @param 3x4 projection matrix. // // @return 3x1 camera projection center. Eigen::Vector3d ProjectionCenterFromMatrix( const Eigen::Matrix3x4d& proj_matrix); // Extract camera projection center from projection parameters. // // @param qvec Unit Quaternion rotation coefficients (w, x, y, z). // @param tvec 3x1 translation vector. // // @return 3x1 camera projection center. Eigen::Vector3d ProjectionCenterFromParameters(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec); // Compute the relative transformation from pose 1 to 2. // // @param qvec1, tvec1 First camera pose. // @param qvec2, tvec2 Second camera pose. // @param qvec12, tvec12 Relative pose. void ComputeRelativePose(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2, Eigen::Vector4d* qvec12, Eigen::Vector3d* tvec12); // Concatenate the transformations of the two poses. // // @param qvec1, tvec1 First camera pose. // @param qvec2, tvec2 Second camera pose. // @param qvec12, tvec12 Concatenated pose. void ConcatenatePoses(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2, Eigen::Vector4d* qvec12, Eigen::Vector3d* tvec12); // Invert transformation of the pose. // @param qvec, tvec Input camera pose. // @param inv_qvec, inv_tvec Inverse camera pose. void InvertPose(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, Eigen::Vector4d* inv_qvec, Eigen::Vector3d* inv_tvec); // Linearly interpolate camera pose. // // @param qvec1, tvec1 Camera pose at t0 = 0. // @param qvec2, tvec2 Camera pose at t1 = 1. // @param t Interpolation time. // @param qveci, tveci Camera pose at time t. void InterpolatePose(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2, const double t, Eigen::Vector4d* qveci, Eigen::Vector3d* tveci); // Calculate baseline vector from first to second pose. // // The given rotation and orientation is expected as the // world to camera transformation. // // @param qvec1 Unit Quaternion rotation coefficients (w, x, y, z). // @param tvec1 3x1 translation vector. // @param qvec2 Unit Quaternion rotation coefficients (w, x, y, z). // @param tvec2 3x1 translation vector. // // @return Baseline vector from 1 to 2. Eigen::Vector3d CalculateBaseline(const Eigen::Vector4d& qvec1, const Eigen::Vector3d& tvec1, const Eigen::Vector4d& qvec2, const Eigen::Vector3d& tvec2); // Perform cheirality constraint test, i.e., determine which of the triangulated // correspondences lie in front of of both cameras. The first camera has the // projection matrix P1 = [I | 0] and the second camera has the projection // matrix P2 = [R | t]. // // @param R 3x3 rotation matrix of second projection matrix. // @param t 3x1 translation vector of second projection matrix. // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param points3D Points that lie in front of both cameras. bool CheckCheirality(const Eigen::Matrix3d& R, const Eigen::Vector3d& t, const std::vector& points1, const std::vector& points2, std::vector* points3D); //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// Eigen::Vector4d ComposeIdentityQuaternion() { return Eigen::Vector4d(1, 0, 0, 0); } } // namespace colmap #endif // COLMAP_SRC_BASE_POSE_H_ colmap-3.4/src/base/pose_test.cc000077500000000000000000000377141323400541200166610ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/pose" #include "util/testing.h" #include #include "base/pose.h" #include "base/projection.h" #include "util/math.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestCrossProductMatrix) { BOOST_CHECK_EQUAL(CrossProductMatrix(Eigen::Vector3d(0, 0, 0)), Eigen::Matrix3d::Zero()); Eigen::Matrix3d ref_matrix; ref_matrix << 0, -3, 2, 3, 0, -1, -2, 1, 0; BOOST_CHECK_EQUAL(CrossProductMatrix(Eigen::Vector3d(1, 2, 3)), ref_matrix); } BOOST_AUTO_TEST_CASE(TestEulerAnglesX) { const double rx = 0.3; const double ry = 0; const double rz = 0; double rxx, ryy, rzz; RotationMatrixToEulerAngles(EulerAnglesToRotationMatrix(rx, ry, rz), &rxx, &ryy, &rzz); BOOST_CHECK_CLOSE(rx, rxx, 1e-6); BOOST_CHECK_CLOSE(ry, ryy, 1e-6); BOOST_CHECK_CLOSE(rz, rzz, 1e-6); } BOOST_AUTO_TEST_CASE(TestEulerAnglesY) { const double rx = 0; const double ry = 0.3; const double rz = 0; double rxx, ryy, rzz; RotationMatrixToEulerAngles(EulerAnglesToRotationMatrix(rx, ry, rz), &rxx, &ryy, &rzz); BOOST_CHECK_CLOSE(rx, rxx, 1e-6); BOOST_CHECK_CLOSE(ry, ryy, 1e-6); BOOST_CHECK_CLOSE(rz, rzz, 1e-6); } BOOST_AUTO_TEST_CASE(TestEulerAnglesZ) { const double rx = 0; const double ry = 0; const double rz = 0.3; double rxx, ryy, rzz; RotationMatrixToEulerAngles(EulerAnglesToRotationMatrix(rx, ry, rz), &rxx, &ryy, &rzz); BOOST_CHECK_CLOSE(rx, rxx, 1e-6); BOOST_CHECK_CLOSE(ry, ryy, 1e-6); BOOST_CHECK_CLOSE(rz, rzz, 1e-6); } BOOST_AUTO_TEST_CASE(TestQuaternionToRotationMatrix) { const double rx = 0; const double ry = 0; const double rz = 0.3; const Eigen::Matrix3d rot_mat0 = EulerAnglesToRotationMatrix(rx, ry, rz); const Eigen::Matrix3d rot_mat1 = QuaternionToRotationMatrix(RotationMatrixToQuaternion(rot_mat0)); BOOST_CHECK(rot_mat0.isApprox(rot_mat1)); } BOOST_AUTO_TEST_CASE(TestComposeIdentityQuaternion) { BOOST_CHECK_EQUAL(ComposeIdentityQuaternion(), Eigen::Vector4d(1, 0, 0, 0)); } BOOST_AUTO_TEST_CASE(TestNormalizeQuaternion) { BOOST_CHECK_EQUAL(NormalizeQuaternion(ComposeIdentityQuaternion()), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(NormalizeQuaternion(Eigen::Vector4d(2, 0, 0, 0)), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(NormalizeQuaternion(Eigen::Vector4d(0.5, 0, 0, 0)), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(NormalizeQuaternion(Eigen::Vector4d(0, 0, 0, 0)), ComposeIdentityQuaternion()); BOOST_CHECK( NormalizeQuaternion(Eigen::Vector4d(1, 1, 0, 0)) .isApprox(Eigen::Vector4d(std::sqrt(2) / 2, std::sqrt(2) / 2, 0, 0))); BOOST_CHECK( NormalizeQuaternion(Eigen::Vector4d(0.5, 0.5, 0, 0)) .isApprox(Eigen::Vector4d(std::sqrt(2) / 2, std::sqrt(2) / 2, 0, 0))); } BOOST_AUTO_TEST_CASE(TestInvertQuaternion) { BOOST_CHECK_EQUAL(InvertQuaternion(ComposeIdentityQuaternion()), Eigen::Vector4d(1, -0, -0, -0)); BOOST_CHECK_EQUAL(InvertQuaternion(Eigen::Vector4d(2, 0, 0, 0)), Eigen::Vector4d(1, -0, -0, -0)); BOOST_CHECK( InvertQuaternion(InvertQuaternion(Eigen::Vector4d(0.1, 0.2, 0.3, 0.4))) .isApprox(NormalizeQuaternion(Eigen::Vector4d(0.1, 0.2, 0.3, 0.4)))); } BOOST_AUTO_TEST_CASE(TestConcatenateQuaternions) { BOOST_CHECK_EQUAL(ConcatenateQuaternions(ComposeIdentityQuaternion(), ComposeIdentityQuaternion()), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(ConcatenateQuaternions(Eigen::Vector4d(2, 0, 0, 0), ComposeIdentityQuaternion()), ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(ConcatenateQuaternions(ComposeIdentityQuaternion(), Eigen::Vector4d(2, 0, 0, 0)), ComposeIdentityQuaternion()); BOOST_CHECK(ConcatenateQuaternions( Eigen::Vector4d(0.1, 0.2, 0.3, 0.4), InvertQuaternion(Eigen::Vector4d(0.1, 0.2, 0.3, 0.4))) .isApprox(ComposeIdentityQuaternion())); BOOST_CHECK(ConcatenateQuaternions( InvertQuaternion(Eigen::Vector4d(0.1, 0.2, 0.3, 0.4)), Eigen::Vector4d(0.1, 0.2, 0.3, 0.4)) .isApprox(ComposeIdentityQuaternion())); } BOOST_AUTO_TEST_CASE(TestQuaternionRotatePoint) { BOOST_CHECK_EQUAL(QuaternionRotatePoint(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0)), Eigen::Vector3d(0, 0, 0)); BOOST_CHECK_EQUAL(QuaternionRotatePoint(Eigen::Vector4d(0.1, 0, 0, 0), Eigen::Vector3d(0, 0, 0)), Eigen::Vector3d(0, 0, 0)); BOOST_CHECK_EQUAL(QuaternionRotatePoint(ComposeIdentityQuaternion(), Eigen::Vector3d(1, 1, 0)), Eigen::Vector3d(1, 1, 0)); BOOST_CHECK_EQUAL(QuaternionRotatePoint(Eigen::Vector4d(0.1, 0, 0, 0), Eigen::Vector3d(1, 1, 0)), Eigen::Vector3d(1, 1, 0)); BOOST_CHECK( QuaternionRotatePoint( RotationMatrixToQuaternion(EulerAnglesToRotationMatrix(M_PI, 0, 0)), Eigen::Vector3d(1, 1, 0)) .isApprox(Eigen::Vector3d(1, -1, 0))); } BOOST_AUTO_TEST_CASE(TestAverageQuaternions) { std::vector qvecs; std::vector weights; qvecs = {{ComposeIdentityQuaternion()}}; weights = {1.0}; BOOST_CHECK_EQUAL(AverageQuaternions(qvecs, weights), ComposeIdentityQuaternion()); qvecs = {ComposeIdentityQuaternion()}; weights = {2.0}; BOOST_CHECK_EQUAL(AverageQuaternions(qvecs, weights), ComposeIdentityQuaternion()); qvecs = {ComposeIdentityQuaternion(), ComposeIdentityQuaternion()}; weights = {1.0, 1.0}; BOOST_CHECK_EQUAL(AverageQuaternions(qvecs, weights), ComposeIdentityQuaternion()); qvecs = {ComposeIdentityQuaternion(), ComposeIdentityQuaternion()}; weights = {1.0, 2.0}; BOOST_CHECK_EQUAL(AverageQuaternions(qvecs, weights), ComposeIdentityQuaternion()); qvecs = {ComposeIdentityQuaternion(), Eigen::Vector4d(2, 0, 0, 0)}; weights = {1.0, 2.0}; BOOST_CHECK_EQUAL(AverageQuaternions(qvecs, weights), ComposeIdentityQuaternion()); qvecs = {ComposeIdentityQuaternion(), Eigen::Vector4d(1, 1, 0, 0)}; weights = {1.0, 1.0}; BOOST_CHECK(AverageQuaternions(qvecs, weights) .isApprox(Eigen::Vector4d(0.92388, 0.382683, 0, 0), 1e-6)); qvecs = {ComposeIdentityQuaternion(), Eigen::Vector4d(1, 1, 0, 0)}; weights = {1.0, 2.0}; BOOST_CHECK(AverageQuaternions(qvecs, weights) .isApprox(Eigen::Vector4d(0.850651, 0.525731, 0, 0), 1e-6)); } BOOST_AUTO_TEST_CASE(TestRotationFromUnitVectors) { BOOST_CHECK_EQUAL(RotationFromUnitVectors(Eigen::Vector3d(0, 0, 1), Eigen::Vector3d(0, 0, 1)), Eigen::Matrix3d::Identity()); BOOST_CHECK_EQUAL(RotationFromUnitVectors(Eigen::Vector3d(0, 0, 2), Eigen::Vector3d(0, 0, 2)), Eigen::Matrix3d::Identity()); Eigen::Matrix3d ref_matrix1; ref_matrix1 << 1, 0, 0, 0, 0, 1, 0, -1, 0; BOOST_CHECK_EQUAL(RotationFromUnitVectors(Eigen::Vector3d(0, 0, 1), Eigen::Vector3d(0, 1, 0)), ref_matrix1); BOOST_CHECK_EQUAL(ref_matrix1 * Eigen::Vector3d(0, 0, 1), Eigen::Vector3d(0, 1, 0)); BOOST_CHECK_EQUAL(RotationFromUnitVectors(Eigen::Vector3d(0, 0, 2), Eigen::Vector3d(0, 2, 0)), ref_matrix1); BOOST_CHECK_EQUAL(ref_matrix1 * Eigen::Vector3d(0, 0, 2), Eigen::Vector3d(0, 2, 0)); BOOST_CHECK_EQUAL(RotationFromUnitVectors(Eigen::Vector3d(0, 0, 1), Eigen::Vector3d(0, 0, -1)), Eigen::Matrix3d::Identity()); } BOOST_AUTO_TEST_CASE(TestPoseFromProjectionMatrix) { const Eigen::Vector4d qvec = Eigen::Vector4d::Random().normalized(); const Eigen::Vector3d tvec(3, 4, 5); const Eigen::Matrix3x4d proj_matrix = ComposeProjectionMatrix(qvec, tvec); const Eigen::Matrix3x4d inv_proj_matrix = InvertProjectionMatrix(proj_matrix); const Eigen::Vector3d pose = ProjectionCenterFromMatrix(proj_matrix); BOOST_CHECK_CLOSE((inv_proj_matrix.rightCols<1>() - pose).norm(), 0, 1e-6); } BOOST_AUTO_TEST_CASE(TestPoseFromProjectionParameters) { const Eigen::Vector4d qvec = Eigen::Vector4d::Random().normalized(); const Eigen::Vector3d tvec(3, 4, 5); const Eigen::Matrix3x4d proj_matrix = ComposeProjectionMatrix(qvec, tvec); const Eigen::Matrix3x4d inv_proj_matrix = InvertProjectionMatrix(proj_matrix); const Eigen::Vector3d pose = ProjectionCenterFromParameters(qvec, tvec); BOOST_CHECK((inv_proj_matrix.rightCols<1>() - pose).norm() < 1e-6); } BOOST_AUTO_TEST_CASE(TestComputeRelativePose) { Eigen::Vector4d qvec12; Eigen::Vector3d tvec12; ComputeRelativePose(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), &qvec12, &tvec12); BOOST_CHECK_EQUAL(qvec12, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(0, 0, 0)); ComputeRelativePose(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), ComposeIdentityQuaternion(), Eigen::Vector3d(1, 0, 0), &qvec12, &tvec12); BOOST_CHECK_EQUAL(qvec12, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(1, 0, 0)); ComputeRelativePose(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(0, 0, 0), &qvec12, &tvec12); BOOST_CHECK(qvec12.isApprox(Eigen::Vector4d(0.707107, 0.707107, 0, 0), 1e-6)); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(0, 0, 0)); ComputeRelativePose(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(1, 0, 0), &qvec12, &tvec12); BOOST_CHECK(qvec12.isApprox(Eigen::Vector4d(0.707107, 0.707107, 0, 0), 1e-6)); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(1, 0, 0)); ComputeRelativePose(Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(0, 0, 0), Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(1, 0, 0), &qvec12, &tvec12); BOOST_CHECK(qvec12.isApprox(ComposeIdentityQuaternion())); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(1, 0, 0)); ComputeRelativePose(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 1), Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(0, 0, 0), &qvec12, &tvec12); BOOST_CHECK(qvec12.isApprox(Eigen::Vector4d(0.707107, 0.707107, 0, 0), 1e-6)); BOOST_CHECK(tvec12.isApprox(Eigen::Vector3d(0, 1, 0))); } BOOST_AUTO_TEST_CASE(TestConcatenatePoses) { Eigen::Vector4d qvec12; Eigen::Vector3d tvec12; ConcatenatePoses(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), &qvec12, &tvec12); BOOST_CHECK_EQUAL(qvec12, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(0, 0, 0)); ConcatenatePoses(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2), &qvec12, &tvec12); BOOST_CHECK_EQUAL(qvec12, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(0, 1, 2)); ConcatenatePoses(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2), ComposeIdentityQuaternion(), Eigen::Vector3d(3, 4, 5), &qvec12, &tvec12); BOOST_CHECK_EQUAL(qvec12, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(tvec12, Eigen::Vector3d(3, 5, 7)); Eigen::Vector4d rel_qvec12; Eigen::Vector3d rel_tvec12; ComputeRelativePose(Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(0, 1, 2), Eigen::Vector4d(1, 3, 0, 0), Eigen::Vector3d(3, 4, 5), &rel_qvec12, &rel_tvec12); ConcatenatePoses(Eigen::Vector4d(1, 1, 0, 0), Eigen::Vector3d(0, 1, 2), rel_qvec12, rel_tvec12, &qvec12, &tvec12); BOOST_CHECK( qvec12.isApprox(NormalizeQuaternion(Eigen::Vector4d(1, 3, 0, 0)))); BOOST_CHECK(tvec12.isApprox(Eigen::Vector3d(3, 4, 5))); } BOOST_AUTO_TEST_CASE(TestInvertPose) { Eigen::Vector4d inv_qvec; Eigen::Vector3d inv_tvec; InvertPose(ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0), &inv_qvec, &inv_tvec); BOOST_CHECK_EQUAL(inv_qvec, ComposeIdentityQuaternion()); BOOST_CHECK_EQUAL(inv_tvec, Eigen::Vector3d(0, 0, 0)); InvertPose(Eigen::Vector4d(0, 1, 2, 3), Eigen::Vector3d(0, 1, 2), &inv_qvec, &inv_tvec); Eigen::Vector4d inv_inv_qvec; Eigen::Vector3d inv_inv_tvec; InvertPose(inv_qvec, inv_tvec, &inv_inv_qvec, &inv_inv_tvec); BOOST_CHECK( inv_inv_qvec.isApprox(NormalizeQuaternion(Eigen::Vector4d(0, 1, 2, 3)))); BOOST_CHECK(inv_inv_tvec.isApprox(Eigen::Vector3d(0, 1, 2))); } BOOST_AUTO_TEST_CASE(TestInterpolatePose) { const Eigen::Vector4d qvec1 = Eigen::Vector4d::Random().normalized(); const Eigen::Vector3d tvec1 = Eigen::Vector3d::Random(); const Eigen::Vector4d qvec2 = Eigen::Vector4d::Random().normalized(); const Eigen::Vector3d tvec2 = Eigen::Vector3d::Random(); Eigen::Vector4d qveci; Eigen::Vector3d tveci; InterpolatePose(qvec1, tvec1, qvec2, tvec2, 0, &qveci, &tveci); BOOST_CHECK(tvec1.isApprox(tveci)); InterpolatePose(qvec1, tvec1, qvec2, tvec2, 1, &qveci, &tveci); BOOST_CHECK(tvec2.isApprox(tveci)); InterpolatePose(qvec1, tvec1, qvec2, tvec2, 0.5, &qveci, &tveci); BOOST_CHECK(((tvec1 + tvec2) / 2).isApprox(tveci)); } BOOST_AUTO_TEST_CASE(TestCalculateBaseline) { Eigen::Vector4d qvec1(1, 0, 0, 0); Eigen::Vector4d qvec2(1, 0, 0, 0); Eigen::Vector3d tvec1(0, 0, 0); Eigen::Vector3d tvec2(0, 0, 1); const double baseline1 = CalculateBaseline(qvec1, tvec1, qvec2, tvec2).norm(); BOOST_CHECK_CLOSE(baseline1, 1, 1e-10); tvec2(2) = 2; const double baseline2 = CalculateBaseline(qvec1, tvec1, qvec2, tvec2).norm(); BOOST_CHECK_CLOSE(baseline2, 2, 1e-10); } BOOST_AUTO_TEST_CASE(TestCheckCheirality) { const Eigen::Matrix3d R = Eigen::Matrix3d::Identity(); const Eigen::Vector3d t(1, 0, 0); std::vector points1; std::vector points2; std::vector points3D; points1.emplace_back(0, 0); points2.emplace_back(0.1, 0); BOOST_CHECK(CheckCheirality(R, t, points1, points2, &points3D)); BOOST_CHECK_EQUAL(points3D.size(), 1); points1.emplace_back(0, 0); points2.emplace_back(-0.1, 0); BOOST_CHECK(CheckCheirality(R, t, points1, points2, &points3D)); BOOST_CHECK_EQUAL(points3D.size(), 1); points2[1][0] = 0.2; BOOST_CHECK(CheckCheirality(R, t, points1, points2, &points3D)); BOOST_CHECK_EQUAL(points3D.size(), 2); points2[0][0] = -0.2; points2[1][0] = -0.2; BOOST_CHECK(!CheckCheirality(R, t, points1, points2, &points3D)); BOOST_CHECK_EQUAL(points3D.size(), 0); } colmap-3.4/src/base/projection.cc000077500000000000000000000112551323400541200170200ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/projection.h" #include "base/pose.h" #include "util/matrix.h" namespace colmap { Eigen::Matrix3x4d ComposeProjectionMatrix(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec) { Eigen::Matrix3x4d proj_matrix; proj_matrix.leftCols<3>() = QuaternionToRotationMatrix(qvec); proj_matrix.rightCols<1>() = tvec; return proj_matrix; } Eigen::Matrix3x4d ComposeProjectionMatrix(const Eigen::Matrix3d& R, const Eigen::Vector3d& T) { Eigen::Matrix3x4d proj_matrix; proj_matrix.leftCols<3>() = R; proj_matrix.rightCols<1>() = T; return proj_matrix; } Eigen::Matrix3x4d InvertProjectionMatrix(const Eigen::Matrix3x4d& proj_matrix) { Eigen::Matrix3x4d inv_proj_matrix; inv_proj_matrix.leftCols<3>() = proj_matrix.leftCols<3>().transpose(); inv_proj_matrix.rightCols<1>() = ProjectionCenterFromMatrix(proj_matrix); return inv_proj_matrix; } Eigen::Matrix3d ComputeClosestRotationMatrix(const Eigen::Matrix3d& matrix) { const Eigen::JacobiSVD svd( matrix, Eigen::ComputeFullU | Eigen::ComputeFullV); Eigen::Matrix3d R = svd.matrixU() * (svd.matrixV().transpose()); if (R.determinant() < 0.0) { R *= -1.0; } return R; } bool DecomposeProjectionMatrix(const Eigen::Matrix3x4d& P, Eigen::Matrix3d* K, Eigen::Matrix3d* R, Eigen::Vector3d* T) { Eigen::Matrix3d RR; Eigen::Matrix3d QQ; DecomposeMatrixRQ(P.leftCols<3>().eval(), &RR, &QQ); *R = ComputeClosestRotationMatrix(QQ); const double det_K = RR.determinant(); if (det_K == 0) { return false; } else if (det_K > 0) { *K = RR; } else { *K = -RR; } for (int i = 0; i < 3; ++i) { if ((*K)(i, i) < 0.0) { K->col(i) = -K->col(i); R->row(i) = -R->row(i); } } *T = K->triangularView().solve(P.col(3)); if (det_K < 0) { *T = -(*T); } return true; } Eigen::Vector2d ProjectPointToImage(const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix, const Camera& camera) { const Eigen::Vector3d world_point = proj_matrix * point3D.homogeneous(); return camera.WorldToImage(world_point.hnormalized()); } double CalculateReprojectionError(const Eigen::Vector2d& point2D, const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix, const Camera& camera) { const auto image_point = ProjectPointToImage(point3D, proj_matrix, camera); return (image_point - point2D).norm(); } double CalculateAngularError(const Eigen::Vector2d& point2D, const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix, const Camera& camera) { return CalculateAngularError(camera.ImageToWorld(point2D), point3D, proj_matrix); } double CalculateAngularError(const Eigen::Vector2d& point2D, const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix) { const Eigen::Vector3d ray1 = point2D.homogeneous(); const Eigen::Vector3d ray2 = proj_matrix * point3D.homogeneous(); return std::acos(ray1.normalized().transpose() * ray2.normalized()); } double CalculateDepth(const Eigen::Matrix3x4d& proj_matrix, const Eigen::Vector3d& point3D) { const double d = (proj_matrix.row(2) * point3D.homogeneous()).sum(); return d * proj_matrix.col(2).norm(); } bool HasPointPositiveDepth(const Eigen::Matrix3x4d& proj_matrix, const Eigen::Vector3d& point3D) { return (proj_matrix(2, 0) * point3D(0) + proj_matrix(2, 1) * point3D(1) + proj_matrix(2, 2) * point3D(2) + proj_matrix(2, 3)) > std::numeric_limits::epsilon(); } } // namespace colmap colmap-3.4/src/base/projection.h000077500000000000000000000142771323400541200166710ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_PROJECTION_H_ #define COLMAP_SRC_BASE_PROJECTION_H_ #include #include #include #include #include "base/camera.h" namespace colmap { // Compose projection matrix from rotation and translation components. // // The projection matrix transforms 3D world to image points. // // @param qvec Unit Quaternion rotation coefficients (w, x, y, z). // @param tvec 3x1 translation vector. // // @return 3x4 projection matrix. Eigen::Matrix3x4d ComposeProjectionMatrix(const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec); // Compose projection matrix from rotation matrix and translation components). // // The projection matrix transforms 3D world to image points. // // @param R 3x3 rotation matrix. // @param t 3x1 translation vector. // // @return 3x4 projection matrix. Eigen::Matrix3x4d ComposeProjectionMatrix(const Eigen::Matrix3d& R, const Eigen::Vector3d& T); // Invert projection matrix, defined as: // // P = [R | t] with R \in SO(3) and t \in R^3 // // and the inverse projection matrix as: // // P' = [R^T | -R^T t] // // @param proj_matrix 3x4 projection matrix. // // @return 3x4 inverse projection matrix. Eigen::Matrix3x4d InvertProjectionMatrix(const Eigen::Matrix3x4d& proj_matrix); // Compute the closes rotation matrix with the closest Frobenius norm by setting // the singular values of the given matrix to 1. Eigen::Matrix3d ComputeClosestRotationMatrix(const Eigen::Matrix3d& matrix); // Decompose projection matrix into intrinsic camera matrix, rotation matrix and // translation vector. Returns false if decomposition fails. This implementation // is inspired by the OpenCV implementation with some additional checks. bool DecomposeProjectionMatrix(const Eigen::Matrix3x4d& proj_matrix, Eigen::Matrix3d* K, Eigen::Matrix3d* R, Eigen::Vector3d* T); // Project 3D point to image. // // @param points3D 3D world point as 3x1 vector. // @param proj_matrix 3x4 projection matrix. // @param camera Camera used to project to image plane. // // @return Projected image point. Eigen::Vector2d ProjectPointToImage(const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix, const Camera& camera); // Calculate the reprojection error. // // The reprojection error is the Euclidean distance between the observation // in the image and the projection of the 3D point into the image. // // @param points2D 2D image point as 2x1 vector. // @param points3D 3D world point as 3x1 vector. // @param proj_matrix 3x4 projection matrix. // @param camera Camera used to project to image plane. // // @return Reprojection error. double CalculateReprojectionError(const Eigen::Vector2d& point2D, const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix, const Camera& camera); // Calculate the angular error. // // The angular error is the angle between the observed viewing ray and the // actual viewing ray from the camera center to the 3D point. // // @param points2D 2D image point as 2x1 vector. // @param points3D 3D world point as 3x1 vector. // @param proj_matrix 3x4 projection matrix. // @param camera Camera used to project to image plane. // // @return Angular error. double CalculateAngularError(const Eigen::Vector2d& point2D, const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix, const Camera& camera); // Calculate angulate error using normalized image points. // // The angular error is the angle between the observed viewing ray and the // actual viewing ray from the camera center to the 3D point. // // @param points2D Normalized 2D image point as 2x1 vector. // @param points3D 3D world point as 3x1 vector. // @param proj_matrix 3x4 projection matrix. // // @return Angular error. double CalculateAngularError(const Eigen::Vector2d& point2D, const Eigen::Vector3d& point3D, const Eigen::Matrix3x4d& proj_matrix); // Calculate depth of 3D point with respect to camera. // // The depth is defined as the Euclidean distance of a 3D point from the // camera and is positive if the 3D point is in front and negative if // behind of the camera. // // @param proj_matrix 3x4 projection matrix. // @param point3D 3D point as 3x1 vector. // // @return Depth of 3D point. double CalculateDepth(const Eigen::Matrix3x4d& proj_matrix, const Eigen::Vector3d& point3D); // Check if 3D point passes cheirality constraint, // i.e. it lies in front of the camera and not in the image plane. // // @param proj_matrix 3x4 projection matrix. // @param point3D 3D point as 3x1 vector. // // @return True if point lies in front of camera. bool HasPointPositiveDepth(const Eigen::Matrix3x4d& proj_matrix, const Eigen::Vector3d& point3D); } // namespace colmap #endif // COLMAP_SRC_BASE_PROJECTION_H_ colmap-3.4/src/base/projection_test.cc000077500000000000000000000167751323400541200200730ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/projection" #include "util/testing.h" #include #include "base/camera_models.h" #include "base/pose.h" #include "base/projection.h" #include "util/math.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestComposeProjectionMatrix) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 1, 2); const Eigen::Vector4d qvec = RotationMatrixToQuaternion(R); const Eigen::Vector3d tvec = Eigen::Vector3d::Random(); const auto proj_matrix1 = ComposeProjectionMatrix(qvec, tvec); const auto proj_matrix2 = ComposeProjectionMatrix(R, tvec); BOOST_CHECK((proj_matrix1 - proj_matrix2).norm() < 1e-6); BOOST_CHECK((proj_matrix1.leftCols<3>() - R).norm() < 1e-6); BOOST_CHECK_CLOSE((proj_matrix1.rightCols<1>() - tvec).norm(), 0, 1e-6); BOOST_CHECK_CLOSE((proj_matrix2.leftCols<3>() - R).norm(), 0, 1e-6); BOOST_CHECK_CLOSE((proj_matrix2.rightCols<1>() - tvec).norm(), 0, 1e-6); } BOOST_AUTO_TEST_CASE(TestInvertProjectionMatrix) { const Eigen::Matrix3d R = EulerAnglesToRotationMatrix(0, 1, 2); const Eigen::Vector3d tvec = Eigen::Vector3d::Random(); const auto proj_matrix = ComposeProjectionMatrix(R, tvec); const auto inv_proj_matrix = InvertProjectionMatrix(proj_matrix); const auto inv_inv_proj_matrix = InvertProjectionMatrix(inv_proj_matrix); BOOST_CHECK((proj_matrix - inv_inv_proj_matrix).norm() < 1e-6); } BOOST_AUTO_TEST_CASE(TestComputeClosestRotationMatrix) { const Eigen::Matrix3d A = Eigen::Matrix3d::Identity(); BOOST_CHECK_LT((ComputeClosestRotationMatrix(A) - A).norm(), 1e-6); BOOST_CHECK_LT((ComputeClosestRotationMatrix(2 * A) - A).norm(), 1e-6); } BOOST_AUTO_TEST_CASE(TestDecomposeProjectionMatrix) { for (int i = 1; i < 100; ++i) { Eigen::Matrix3d ref_K = i * Eigen::Matrix3d::Identity(); ref_K(0, 2) = i; ref_K(1, 2) = 2 * i; const Eigen::Matrix3d ref_R = EulerAnglesToRotationMatrix(i, 2 * i, 3 * i); const Eigen::Vector3d ref_T = Eigen::Vector3d::Random(); const Eigen::Matrix3x4d ref_P = ref_K * ComposeProjectionMatrix(ref_R, ref_T); Eigen::Matrix3d K; Eigen::Matrix3d R; Eigen::Vector3d T; DecomposeProjectionMatrix(ref_P, &K, &R, &T); BOOST_CHECK(ref_K.isApprox(K, 1e-6)); BOOST_CHECK(ref_R.isApprox(R, 1e-6)); BOOST_CHECK(ref_T.isApprox(T, 1e-6)); } } BOOST_AUTO_TEST_CASE(TestCalculateReprojectionError) { const Eigen::Vector4d qvec = Eigen::Vector4d::Random().normalized(); const Eigen::Vector3d tvec = Eigen::Vector3d::Random(); const auto proj_matrix = ComposeProjectionMatrix(qvec, tvec); const Eigen::Vector3d point3D = Eigen::Vector3d::Random(); const Eigen::Vector3d point2D_h = proj_matrix * point3D.homogeneous(); const Eigen::Vector2d point2D = point2D_h.hnormalized(); Camera camera; camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1, 0, 0); const double error1 = CalculateReprojectionError(point2D, point3D, proj_matrix, camera); BOOST_CHECK_CLOSE(error1, 0, 1e-6); const double error2 = CalculateReprojectionError(point2D.array() + 1, point3D, proj_matrix, camera); BOOST_CHECK_CLOSE(error2, std::sqrt(2), 1e-6); } BOOST_AUTO_TEST_CASE(TestCalculateAngularError) { const Eigen::Vector4d qvec = ComposeIdentityQuaternion(); const Eigen::Vector3d tvec = Eigen::Vector3d(0, 0, 0); const auto proj_matrix = ComposeProjectionMatrix(qvec, tvec); Camera camera; camera.SetModelId(SimplePinholeCameraModel::model_id); camera.Params() = {1, 0, 0}; const double error1 = CalculateAngularError( Eigen::Vector2d(0, 0), Eigen::Vector3d(0, 0, 1), proj_matrix, camera); BOOST_CHECK_CLOSE(error1, 0, 1e-6); const double error2 = CalculateAngularError( Eigen::Vector2d(0, 0), Eigen::Vector3d(0, 1, 1), proj_matrix, camera); BOOST_CHECK_CLOSE(error2, M_PI / 4, 1e-6); const double error3 = CalculateAngularError( Eigen::Vector2d(0, 0), Eigen::Vector3d(0, 5, 5), proj_matrix, camera); BOOST_CHECK_CLOSE(error3, M_PI / 4, 1e-6); const double error4 = CalculateAngularError( Eigen::Vector2d(1, 0), Eigen::Vector3d(0, 0, 1), proj_matrix, camera); BOOST_CHECK_CLOSE(error4, M_PI / 4, 1e-6); const double error5 = CalculateAngularError( Eigen::Vector2d(2, 0), Eigen::Vector3d(0, 0, 1), proj_matrix, camera); BOOST_CHECK_CLOSE(error5, 1.10714872, 1e-6); const double error6 = CalculateAngularError( Eigen::Vector2d(2, 0), Eigen::Vector3d(1, 0, 1), proj_matrix, camera); BOOST_CHECK_CLOSE(error6, 1.10714872 - M_PI / 4, 1e-6); const double error7 = CalculateAngularError( Eigen::Vector2d(2, 0), Eigen::Vector3d(5, 0, 5), proj_matrix, camera); BOOST_CHECK_CLOSE(error7, 1.10714872 - M_PI / 4, 1e-6); const double error8 = CalculateAngularError( Eigen::Vector2d(1, 0), Eigen::Vector3d(-1, 0, 1), proj_matrix, camera); BOOST_CHECK_CLOSE(error8, M_PI / 2, 1e-6); const double error9 = CalculateAngularError( Eigen::Vector2d(1, 0), Eigen::Vector3d(-1, 0, 0), proj_matrix, camera); BOOST_CHECK_CLOSE(error9, M_PI * 3 / 4, 1e-6); const double error10 = CalculateAngularError( Eigen::Vector2d(1, 0), Eigen::Vector3d(-1, 0, -1), proj_matrix, camera); BOOST_CHECK_CLOSE(error10, M_PI, 1e-6); const double error11 = CalculateAngularError( Eigen::Vector2d(1, 0), Eigen::Vector3d(0, 0, -1), proj_matrix, camera); BOOST_CHECK_CLOSE(error11, M_PI * 3 / 4, 1e-6); } BOOST_AUTO_TEST_CASE(TestCalculateDepth) { const Eigen::Vector4d qvec(1, 0, 0, 0); const Eigen::Vector3d tvec(0, 0, 0); const auto proj_matrix = ComposeProjectionMatrix(qvec, tvec); // In the image plane const double depth1 = CalculateDepth(proj_matrix, Eigen::Vector3d(0, 0, 0)); BOOST_CHECK_CLOSE(depth1, 0, 1e-10); const double depth2 = CalculateDepth(proj_matrix, Eigen::Vector3d(0, 2, 0)); BOOST_CHECK_CLOSE(depth2, 0, 1e-10); // Infront of camera const double depth3 = CalculateDepth(proj_matrix, Eigen::Vector3d(0, 0, 1)); BOOST_CHECK_CLOSE(depth3, 1, 1e-10); // Behind camera const double depth4 = CalculateDepth(proj_matrix, Eigen::Vector3d(0, 0, -1)); BOOST_CHECK_CLOSE(depth4, -1, 1e-10); } BOOST_AUTO_TEST_CASE(TestHasPointPositiveDepth) { const Eigen::Vector4d qvec(1, 0, 0, 0); const Eigen::Vector3d tvec(0, 0, 0); const auto proj_matrix = ComposeProjectionMatrix(qvec, tvec); // In the image plane const bool check1 = HasPointPositiveDepth(proj_matrix, Eigen::Vector3d(0, 0, 0)); BOOST_CHECK(!check1); const bool check2 = HasPointPositiveDepth(proj_matrix, Eigen::Vector3d(0, 2, 0)); BOOST_CHECK(!check2); // Infront of camera const bool check3 = HasPointPositiveDepth(proj_matrix, Eigen::Vector3d(0, 0, 1)); BOOST_CHECK(check3); // Behind camera const bool check4 = HasPointPositiveDepth(proj_matrix, Eigen::Vector3d(0, 0, -1)); BOOST_CHECK(!check4); } colmap-3.4/src/base/reconstruction.cc000077500000000000000000002107601323400541200177270ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/reconstruction.h" #include #include "base/pose.h" #include "base/projection.h" #include "base/similarity_transform.h" #include "base/triangulation.h" #include "estimators/similarity_transform.h" #include "optim/loransac.h" #include "util/bitmap.h" #include "util/misc.h" namespace colmap { Reconstruction::Reconstruction() : scene_graph_(nullptr), num_added_points3D_(0) {} std::unordered_set Reconstruction::Point3DIds() const { std::unordered_set point3D_ids; point3D_ids.reserve(points3D_.size()); for (const auto& point3D : points3D_) { point3D_ids.insert(point3D.first); } return point3D_ids; } void Reconstruction::Load(const DatabaseCache& database_cache) { scene_graph_ = nullptr; // Add cameras. cameras_.reserve(database_cache.NumCameras()); for (const auto& camera : database_cache.Cameras()) { if (!ExistsCamera(camera.first)) { AddCamera(camera.second); } // Else: camera was added before, e.g. with `ReadAllCameras`. } // Add images. images_.reserve(database_cache.NumImages()); for (const auto& image : database_cache.Images()) { if (ExistsImage(image.second.ImageId())) { class Image& existing_image = Image(image.second.ImageId()); CHECK_EQ(existing_image.Name(), image.second.Name()); if (existing_image.NumPoints2D() == 0) { existing_image.SetPoints2D(image.second.Points2D()); } else { CHECK_EQ(image.second.NumPoints2D(), existing_image.NumPoints2D()); } existing_image.SetNumObservations(image.second.NumObservations()); existing_image.SetNumCorrespondences(image.second.NumCorrespondences()); } else { AddImage(image.second); } } // Add image pairs. for (const auto& image_pair : database_cache.SceneGraph().NumCorrespondencesBetweenImages()) { image_pairs_[image_pair.first] = std::make_pair(0, image_pair.second); } } void Reconstruction::SetUp(const SceneGraph* scene_graph) { CHECK_NOTNULL(scene_graph); for (auto& image : images_) { image.second.SetUp(Camera(image.second.CameraId())); } scene_graph_ = scene_graph; // If an existing model was loaded from disk and there were already images // registered previously, we need to set observations as triangulated. for (const auto image_id : reg_image_ids_) { const class Image& image = Image(image_id); for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { if (image.Point2D(point2D_idx).HasPoint3D()) { const bool kIsContinuedPoint3D = false; SetObservationAsTriangulated(image_id, point2D_idx, kIsContinuedPoint3D); } } } } void Reconstruction::TearDown() { scene_graph_ = nullptr; // Remove all not yet registered images. std::unordered_set keep_camera_ids; for (auto it = images_.begin(); it != images_.end();) { if (it->second.IsRegistered()) { keep_camera_ids.insert(it->second.CameraId()); it->second.TearDown(); ++it; } else { it = images_.erase(it); } } // Remove all unused cameras. for (auto it = cameras_.begin(); it != cameras_.end();) { if (keep_camera_ids.count(it->first) == 0) { it = cameras_.erase(it); } else { ++it; } } // Compress tracks. for (auto& point3D : points3D_) { point3D.second.Track().Compress(); } } void Reconstruction::AddCamera(const class Camera& camera) { CHECK(!ExistsCamera(camera.CameraId())); CHECK(camera.VerifyParams()); cameras_.emplace(camera.CameraId(), camera); } void Reconstruction::AddImage(const class Image& image) { CHECK(!ExistsImage(image.ImageId())); images_[image.ImageId()] = image; } point3D_t Reconstruction::AddPoint3D(const Eigen::Vector3d& xyz, const Track& track) { const point3D_t point3D_id = ++num_added_points3D_; CHECK(!ExistsPoint3D(point3D_id)); class Point3D& point3D = points3D_[point3D_id]; point3D.SetXYZ(xyz); point3D.SetTrack(track); for (const auto& track_el : track.Elements()) { class Image& image = Image(track_el.image_id); CHECK(!image.Point2D(track_el.point2D_idx).HasPoint3D()); image.SetPoint3DForPoint2D(track_el.point2D_idx, point3D_id); CHECK_LE(image.NumPoints3D(), image.NumPoints2D()); } const bool kIsContinuedPoint3D = false; for (const auto& track_el : track.Elements()) { SetObservationAsTriangulated(track_el.image_id, track_el.point2D_idx, kIsContinuedPoint3D); } return point3D_id; } void Reconstruction::AddObservation(const point3D_t point3D_id, const TrackElement& track_el) { class Image& image = Image(track_el.image_id); CHECK(!image.Point2D(track_el.point2D_idx).HasPoint3D()); image.SetPoint3DForPoint2D(track_el.point2D_idx, point3D_id); CHECK_LE(image.NumPoints3D(), image.NumPoints2D()); class Point3D& point3D = Point3D(point3D_id); point3D.Track().AddElement(track_el); const bool kIsContinuedPoint3D = true; SetObservationAsTriangulated(track_el.image_id, track_el.point2D_idx, kIsContinuedPoint3D); } point3D_t Reconstruction::MergePoints3D(const point3D_t point3D_id1, const point3D_t point3D_id2) { const class Point3D& point3D1 = Point3D(point3D_id1); const class Point3D& point3D2 = Point3D(point3D_id2); const Eigen::Vector3d merged_xyz = (point3D1.Track().Length() * point3D1.XYZ() + point3D2.Track().Length() * point3D2.XYZ()) / (point3D1.Track().Length() + point3D2.Track().Length()); const Eigen::Vector3d merged_rgb = (point3D1.Track().Length() * point3D1.Color().cast() + point3D2.Track().Length() * point3D2.Color().cast()) / (point3D1.Track().Length() + point3D2.Track().Length()); Track merged_track; merged_track.Reserve(point3D1.Track().Length() + point3D2.Track().Length()); merged_track.AddElements(point3D1.Track().Elements()); merged_track.AddElements(point3D2.Track().Elements()); DeletePoint3D(point3D_id1); DeletePoint3D(point3D_id2); const point3D_t merged_point3D_id = AddPoint3D(merged_xyz, merged_track); class Point3D& merged_point3D = Point3D(merged_point3D_id); merged_point3D.SetColor(merged_rgb.cast()); return merged_point3D_id; } void Reconstruction::DeletePoint3D(const point3D_t point3D_id) { // Note: Do not change order of these instructions, especially with respect to // `Reconstruction::ResetTriObservations` const class Track& track = Point3D(point3D_id).Track(); const bool kIsDeletedPoint3D = true; for (const auto& track_el : track.Elements()) { ResetTriObservations(track_el.image_id, track_el.point2D_idx, kIsDeletedPoint3D); } for (const auto& track_el : track.Elements()) { class Image& image = Image(track_el.image_id); image.ResetPoint3DForPoint2D(track_el.point2D_idx); } points3D_.erase(point3D_id); } void Reconstruction::DeleteObservation(const image_t image_id, const point2D_t point2D_idx) { // Note: Do not change order of these instructions, especially with respect to // `Reconstruction::ResetTriObservations` class Image& image = Image(image_id); const point3D_t point3D_id = image.Point2D(point2D_idx).Point3DId(); class Point3D& point3D = Point3D(point3D_id); if (point3D.Track().Length() <= 2) { DeletePoint3D(point3D_id); return; } point3D.Track().DeleteElement(image_id, point2D_idx); const bool kIsDeletedPoint3D = false; ResetTriObservations(image_id, point2D_idx, kIsDeletedPoint3D); image.ResetPoint3DForPoint2D(point2D_idx); } void Reconstruction::RegisterImage(const image_t image_id) { class Image& image = Image(image_id); if (!image.IsRegistered()) { image.SetRegistered(true); reg_image_ids_.push_back(image_id); } } void Reconstruction::DeRegisterImage(const image_t image_id) { class Image& image = Image(image_id); for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { if (image.Point2D(point2D_idx).HasPoint3D()) { DeleteObservation(image_id, point2D_idx); } } image.SetRegistered(false); reg_image_ids_.erase( std::remove(reg_image_ids_.begin(), reg_image_ids_.end(), image_id), reg_image_ids_.end()); } void Reconstruction::Normalize(const double extent, const double p0, const double p1, const bool use_images) { CHECK_GT(extent, 0); CHECK_GE(p0, 0); CHECK_LE(p0, 1); CHECK_GE(p1, 0); CHECK_LE(p1, 1); CHECK_LE(p0, p1); if ((use_images && reg_image_ids_.size() < 2) || (!use_images && points3D_.size() < 2)) { return; } EIGEN_STL_UMAP(class Image*, Eigen::Vector3d) proj_centers; for (size_t i = 0; i < reg_image_ids_.size(); ++i) { class Image& image = Image(reg_image_ids_[i]); const Eigen::Vector3d proj_center = image.ProjectionCenter(); proj_centers[&image] = proj_center; } // Coordinates of image centers or point locations. std::vector coords_x; std::vector coords_y; std::vector coords_z; if (use_images) { coords_x.reserve(proj_centers.size()); coords_y.reserve(proj_centers.size()); coords_z.reserve(proj_centers.size()); for (const auto& proj_center : proj_centers) { coords_x.push_back(static_cast(proj_center.second(0))); coords_y.push_back(static_cast(proj_center.second(1))); coords_z.push_back(static_cast(proj_center.second(2))); } } else { coords_x.reserve(points3D_.size()); coords_y.reserve(points3D_.size()); coords_z.reserve(points3D_.size()); for (const auto& point3D : points3D_) { coords_x.push_back(static_cast(point3D.second.X())); coords_y.push_back(static_cast(point3D.second.Y())); coords_z.push_back(static_cast(point3D.second.Z())); } } // Determine robust bounding box and mean. std::sort(coords_x.begin(), coords_x.end()); std::sort(coords_y.begin(), coords_y.end()); std::sort(coords_z.begin(), coords_z.end()); const size_t P0 = static_cast( (coords_x.size() > 3) ? p0 * (coords_x.size() - 1) : 0); const size_t P1 = static_cast( (coords_x.size() > 3) ? p1 * (coords_x.size() - 1) : coords_x.size() - 1); const Eigen::Vector3d bbox_min(coords_x[P0], coords_y[P0], coords_z[P0]); const Eigen::Vector3d bbox_max(coords_x[P1], coords_y[P1], coords_z[P1]); Eigen::Vector3d mean_coord(0, 0, 0); for (size_t i = P0; i <= P1; ++i) { mean_coord(0) += coords_x[i]; mean_coord(1) += coords_y[i]; mean_coord(2) += coords_z[i]; } mean_coord /= P1 - P0 + 1; // Calculate scale and translation, such that // translation is applied before scaling. const double old_extent = (bbox_max - bbox_min).norm(); double scale; if (old_extent < std::numeric_limits::epsilon()) { scale = 1; } else { scale = extent / old_extent; } const Eigen::Vector3d translation = mean_coord; // Transform images. for (auto& elem : proj_centers) { elem.second -= translation; elem.second *= scale; const Eigen::Quaterniond quat(elem.first->Qvec(0), elem.first->Qvec(1), elem.first->Qvec(2), elem.first->Qvec(3)); elem.first->SetTvec(quat * -elem.second); } // Transform points. for (auto& point3D : points3D_) { point3D.second.XYZ() -= translation; point3D.second.XYZ() *= scale; } } void Reconstruction::Transform(const double scale, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec) { CHECK_GT(scale, 0); const SimilarityTransform3 tform(scale, qvec, tvec); for (auto& image : images_) { tform.TransformPose(&image.second.Qvec(), &image.second.Tvec()); } for (auto& point3D : points3D_) { tform.TransformPoint(&point3D.second.XYZ()); } } bool Reconstruction::Merge(const Reconstruction& reconstruction, const int min_common_images) { CHECK_GE(min_common_images, 3); // Find common and missing images in the two reconstructions. std::set common_image_ids; std::set missing_image_ids; for (const auto& image_id : reconstruction.RegImageIds()) { if (ExistsImage(image_id)) { CHECK(IsImageRegistered(image_id)) << "Make sure to tear down the reconstructions before merging"; common_image_ids.insert(image_id); } else { missing_image_ids.insert(image_id); } } if (common_image_ids.size() < static_cast(min_common_images)) { return false; } // Estimate the similarity transformation between the two reconstructions. std::vector src; src.reserve(common_image_ids.size()); std::vector dst; dst.reserve(common_image_ids.size()); for (const auto image_id : common_image_ids) { src.push_back(reconstruction.Image(image_id).ProjectionCenter()); dst.push_back(Image(image_id).ProjectionCenter()); } SimilarityTransform3 tform; tform.Estimate(src, dst); // Register the missing images in this reconstruction. for (const auto image_id : missing_image_ids) { auto reg_image = reconstruction.Image(image_id); reg_image.SetRegistered(false); AddImage(reg_image); RegisterImage(image_id); if (!ExistsCamera(reg_image.CameraId())) { AddCamera(reconstruction.Camera(reg_image.CameraId())); } auto& image = Image(image_id); tform.TransformPose(&image.Qvec(), &image.Tvec()); } // Merge the two point clouds using the following two rules: // - copy points to this reconstruction with non-conflicting tracks, // i.e. points that do not have an already triangulated observation // in this reconstruction. // - merge tracks that are unambiguous, i.e. only merge points in the two // reconstructions if they have a one-to-one mapping. // Note that in both cases no cheirality or reprojection test is performed. for (const auto& point3D : reconstruction.Points3D()) { Track new_track; Track old_track; std::set old_point3D_ids; for (const auto& track_el : point3D.second.Track().Elements()) { if (common_image_ids.count(track_el.image_id) > 0) { const auto& point2D = Image(track_el.image_id).Point2D(track_el.point2D_idx); if (point2D.HasPoint3D()) { old_track.AddElement(track_el); old_point3D_ids.insert(point2D.Point3DId()); } else { new_track.AddElement(track_el); } } else if (missing_image_ids.count(track_el.image_id) > 0) { Image(track_el.image_id).ResetPoint3DForPoint2D(track_el.point2D_idx); new_track.AddElement(track_el); } } const bool create_new_point = new_track.Length() >= 2; const bool merge_new_and_old_point = (new_track.Length() + old_track.Length()) >= 2 && old_point3D_ids.size() == 1; if (create_new_point || merge_new_and_old_point) { Eigen::Vector3d xyz = point3D.second.XYZ(); tform.TransformPoint(&xyz); const auto point3D_id = AddPoint3D(xyz, new_track); Point3D(point3D_id).SetColor(point3D.second.Color()); if (old_point3D_ids.size() == 1) { MergePoints3D(point3D_id, *old_point3D_ids.begin()); } } } return true; } bool Reconstruction::Align(const std::vector& image_names, const std::vector& locations, const int min_common_images) { CHECK_GE(min_common_images, 3); CHECK_EQ(image_names.size(), locations.size()); // Find out which images are contained in the reconstruction and get the // positions of their camera centers. std::set common_image_ids; std::vector src; std::vector dst; for (size_t i = 0; i < image_names.size(); ++i) { const class Image* image = FindImageWithName(image_names[i]); if (image == nullptr) { continue; } if (!IsImageRegistered(image->ImageId())) { continue; } // Ignore duplicate images. if (common_image_ids.count(image->ImageId()) > 0) { continue; } common_image_ids.insert(image->ImageId()); src.push_back(image->ProjectionCenter()); dst.push_back(locations[i]); } // Only compute the alignment if there are enough correspondences. if (common_image_ids.size() < static_cast(min_common_images)) { return false; } // Estimate the similarity transformation between the two reconstructions. SimilarityTransform3 tform; tform.Estimate(src, dst); // Update the cameras and points using the estimated transform. for (auto& image : images_) { tform.TransformPose(&image.second.Qvec(), &image.second.Tvec()); } for (auto& point3D : points3D_) { tform.TransformPoint(&point3D.second.XYZ()); } return true; } bool Reconstruction::AlignRobust(const std::vector& image_names, const std::vector& locations, const int min_common_images, const RANSACOptions& ransac_options) { CHECK_GE(min_common_images, 3); CHECK_EQ(image_names.size(), locations.size()); // Find out which images are contained in the reconstruction and get the // positions of their camera centers. std::set common_image_ids; std::vector src; std::vector dst; for (size_t i = 0; i < image_names.size(); ++i) { const class Image* image = FindImageWithName(image_names[i]); if (image == nullptr) { continue; } if (!IsImageRegistered(image->ImageId())) { continue; } // Ignore duplicate images. if (common_image_ids.count(image->ImageId()) > 0) { continue; } common_image_ids.insert(image->ImageId()); src.push_back(image->ProjectionCenter()); dst.push_back(locations[i]); } // Only compute the alignment if there are enough correspondences. if (common_image_ids.size() < static_cast(min_common_images)) { return false; } LORANSAC, SimilarityTransformEstimator<3>> ransac(ransac_options); const auto report = ransac.Estimate(src, dst); if (report.support.num_inliers < static_cast(min_common_images)) { return false; } SimilarityTransform3 tform(report.model); // Update the cameras and points using the estimated transform. for (auto& image : images_) { tform.TransformPose(&image.second.Qvec(), &image.second.Tvec()); } for (auto& point3D : points3D_) { tform.TransformPoint(&point3D.second.XYZ()); } return true; } const class Image* Reconstruction::FindImageWithName( const std::string& name) const { for (const auto& elem : images_) { if (elem.second.Name() == name) { return &elem.second; } } return nullptr; } size_t Reconstruction::FilterPoints3D( const double max_reproj_error, const double min_tri_angle, const std::unordered_set& point3D_ids) { size_t num_filtered = 0; num_filtered += FilterPoints3DWithLargeReprojectionError(max_reproj_error, point3D_ids); num_filtered += FilterPoints3DWithSmallTriangulationAngle(min_tri_angle, point3D_ids); return num_filtered; } size_t Reconstruction::FilterPoints3DInImages( const double max_reproj_error, const double min_tri_angle, const std::unordered_set& image_ids) { std::unordered_set point3D_ids; for (const image_t image_id : image_ids) { const class Image& image = Image(image_id); for (const Point2D& point2D : image.Points2D()) { if (point2D.HasPoint3D()) { point3D_ids.insert(point2D.Point3DId()); } } } return FilterPoints3D(max_reproj_error, min_tri_angle, point3D_ids); } size_t Reconstruction::FilterAllPoints3D(const double max_reproj_error, const double min_tri_angle) { // Important: First filter observations and points with large reprojection // error, so that observations with large reprojection error do not make // a point stable through a large triangulation angle. const std::unordered_set& point3D_ids = Point3DIds(); size_t num_filtered = 0; num_filtered += FilterPoints3DWithLargeReprojectionError(max_reproj_error, point3D_ids); num_filtered += FilterPoints3DWithSmallTriangulationAngle(min_tri_angle, point3D_ids); return num_filtered; } size_t Reconstruction::FilterObservationsWithNegativeDepth() { size_t num_filtered = 0; for (const auto image_id : reg_image_ids_) { const class Image& image = Image(image_id); const Eigen::Matrix3x4d proj_matrix = image.ProjectionMatrix(); for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { const Point2D& point2D = image.Point2D(point2D_idx); if (point2D.HasPoint3D()) { const class Point3D& point3D = Point3D(point2D.Point3DId()); if (!HasPointPositiveDepth(proj_matrix, point3D.XYZ())) { DeleteObservation(image_id, point2D_idx); num_filtered += 1; } } } } return num_filtered; } std::vector Reconstruction::FilterImages( const double min_focal_length_ratio, const double max_focal_length_ratio, const double max_extra_param) { std::vector filtered_image_ids; for (const image_t image_id : RegImageIds()) { const class Image& image = Image(image_id); const class Camera& camera = Camera(image.CameraId()); if (image.NumPoints3D() == 0) { filtered_image_ids.push_back(image_id); } else if (camera.HasBogusParams(min_focal_length_ratio, max_focal_length_ratio, max_extra_param)) { filtered_image_ids.push_back(image_id); } } // Only de-register after iterating over reg_image_ids_ to avoid // simultaneous iteration and modification of the vector. for (const image_t image_id : filtered_image_ids) { DeRegisterImage(image_id); } return filtered_image_ids; } size_t Reconstruction::ComputeNumObservations() const { size_t num_obs = 0; for (const image_t image_id : reg_image_ids_) { num_obs += Image(image_id).NumPoints3D(); } return num_obs; } double Reconstruction::ComputeMeanTrackLength() const { if (points3D_.empty()) { return 0.0; } else { return ComputeNumObservations() / static_cast(points3D_.size()); } } double Reconstruction::ComputeMeanObservationsPerRegImage() const { if (reg_image_ids_.empty()) { return 0.0; } else { return ComputeNumObservations() / static_cast(reg_image_ids_.size()); } } double Reconstruction::ComputeMeanReprojectionError() const { double error_sum = 0.0; size_t num_valid_errors = 0; for (const auto& point3D : points3D_) { if (point3D.second.HasError()) { error_sum += point3D.second.Error(); num_valid_errors += 1; } } if (num_valid_errors == 0) { return 0.0; } else { return error_sum / num_valid_errors; } } void Reconstruction::Read(const std::string& path) { if (ExistsFile(JoinPaths(path, "cameras.bin")) && ExistsFile(JoinPaths(path, "images.bin")) && ExistsFile(JoinPaths(path, "points3D.bin"))) { ReadBinary(path); } else if (ExistsFile(JoinPaths(path, "cameras.txt")) && ExistsFile(JoinPaths(path, "images.txt")) && ExistsFile(JoinPaths(path, "points3D.txt"))) { ReadText(path); } else { LOG(FATAL) << "cameras, images, points3D files do not exist at " << path; } } void Reconstruction::Write(const std::string& path) const { WriteBinary(path); } void Reconstruction::ReadText(const std::string& path) { ReadCamerasText(JoinPaths(path, "cameras.txt")); ReadImagesText(JoinPaths(path, "images.txt")); ReadPoints3DText(JoinPaths(path, "points3D.txt")); } void Reconstruction::ReadBinary(const std::string& path) { ReadCamerasBinary(JoinPaths(path, "cameras.bin")); ReadImagesBinary(JoinPaths(path, "images.bin")); ReadPoints3DBinary(JoinPaths(path, "points3D.bin")); } void Reconstruction::WriteText(const std::string& path) const { WriteCamerasText(JoinPaths(path, "cameras.txt")); WriteImagesText(JoinPaths(path, "images.txt")); WritePoints3DText(JoinPaths(path, "points3D.txt")); } void Reconstruction::WriteBinary(const std::string& path) const { WriteCamerasBinary(JoinPaths(path, "cameras.bin")); WriteImagesBinary(JoinPaths(path, "images.bin")); WritePoints3DBinary(JoinPaths(path, "points3D.bin")); } void Reconstruction::ImportPLY(const std::string& path) { points3D_.clear(); std::ifstream file(path, std::ios::binary); CHECK(file.is_open()) << path; std::string line; int X_index = -1; int Y_index = -1; int Z_index = -1; int R_index = -1; int G_index = -1; int B_index = -1; int X_byte_pos = -1; int Y_byte_pos = -1; int Z_byte_pos = -1; int R_byte_pos = -1; int G_byte_pos = -1; int B_byte_pos = -1; bool in_vertex_section = false; bool is_binary = false; bool is_little_endian = false; size_t num_bytes_per_line = 0; size_t num_vertices = 0; int index = 0; while (std::getline(file, line)) { StringTrim(&line); if (line.empty()) { continue; } if (line == "end_header") { break; } if (line.size() >= 6 && line.substr(0, 6) == "format") { if (line == "format ascii 1.0") { is_binary = false; } else if (line == "format binary_little_endian 1.0") { is_binary = true; is_little_endian = true; } else if (line == "format binary_big_endian 1.0") { is_binary = true; is_little_endian = false; } } const std::vector line_elems = StringSplit(line, " "); if (line_elems.size() >= 3 && line_elems[0] == "element") { in_vertex_section = false; if (line_elems[1] == "vertex") { num_vertices = std::stoll(line_elems[2]); in_vertex_section = true; } else if (std::stoll(line_elems[2]) > 0) { LOG(FATAL) << "Only vertex elements supported"; } } if (!in_vertex_section) { continue; } // Just render diffuse, ambient, specular colors as normal colors. if (line_elems.size() >= 3 && line_elems[0] == "property") { CHECK(line_elems[1] == "float" || line_elems[1] == "uchar") << "PLY import only supports the float and uchar data types"; if (line == "property float x") { X_index = index; X_byte_pos = num_bytes_per_line; } else if (line == "property float y") { Y_index = index; Y_byte_pos = num_bytes_per_line; } else if (line == "property float z") { Z_index = index; Z_byte_pos = num_bytes_per_line; } else if (line == "property uchar r" || line == "property uchar red" || line == "property uchar diffuse_red" || line == "property uchar ambient_red" || line == "property uchar specular_red") { R_index = index; R_byte_pos = num_bytes_per_line; } else if (line == "property uchar g" || line == "property uchar green" || line == "property uchar diffuse_green" || line == "property uchar ambient_green" || line == "property uchar specular_green") { G_index = index; G_byte_pos = num_bytes_per_line; } else if (line == "property uchar b" || line == "property uchar blue" || line == "property uchar diffuse_blue" || line == "property uchar ambient_blue" || line == "property uchar specular_blue") { B_index = index; B_byte_pos = num_bytes_per_line; } index += 1; if (line_elems[1] == "float") { num_bytes_per_line += 4; } else if (line_elems[1] == "uchar") { num_bytes_per_line += 1; } else { LOG(FATAL) << "Invalid data type: " << line_elems[1]; } } } const bool is_rgb_missing = R_index == -1 || G_index == -1 || B_index == -1; CHECK(X_index != -1 && Y_index != -1 && Z_index) << "Invalid PLY file format: x, y, z properties missing"; if (is_binary) { std::vector buffer(num_bytes_per_line); for (size_t i = 0; i < num_vertices; ++i) { file.read(buffer.data(), num_bytes_per_line); Eigen::Vector3d xyz; Eigen::Vector3i rgb; if (is_little_endian) { xyz(0) = LittleEndianToNative( *reinterpret_cast(&buffer[X_byte_pos])); xyz(1) = LittleEndianToNative( *reinterpret_cast(&buffer[Y_byte_pos])); xyz(2) = LittleEndianToNative( *reinterpret_cast(&buffer[Z_byte_pos])); if (is_rgb_missing) { rgb.setZero(); } else { rgb(0) = LittleEndianToNative( *reinterpret_cast(&buffer[R_byte_pos])); rgb(1) = LittleEndianToNative( *reinterpret_cast(&buffer[G_byte_pos])); rgb(2) = LittleEndianToNative( *reinterpret_cast(&buffer[B_byte_pos])); } } else { xyz(0) = BigEndianToNative(*reinterpret_cast(&buffer[X_byte_pos])); xyz(1) = BigEndianToNative(*reinterpret_cast(&buffer[Y_byte_pos])); xyz(2) = BigEndianToNative(*reinterpret_cast(&buffer[Z_byte_pos])); if (is_rgb_missing) { rgb.setZero(); } else { rgb(0) = BigEndianToNative( *reinterpret_cast(&buffer[R_byte_pos])); rgb(1) = BigEndianToNative( *reinterpret_cast(&buffer[G_byte_pos])); rgb(2) = BigEndianToNative( *reinterpret_cast(&buffer[B_byte_pos])); } } const point3D_t point3D_id = AddPoint3D(xyz, Track()); Point3D(point3D_id).SetColor(rgb.cast()); } } else { while (std::getline(file, line)) { StringTrim(&line); std::stringstream line_stream(line); std::string item; std::vector items; while (!line_stream.eof()) { std::getline(line_stream, item, ' '); StringTrim(&item); items.push_back(item); } Eigen::Vector3d xyz; xyz(0) = std::stold(items.at(X_index)); xyz(1) = std::stold(items.at(Y_index)); xyz(2) = std::stold(items.at(Z_index)); Eigen::Vector3i rgb; if (is_rgb_missing) { rgb.setZero(); } else { rgb(0) = std::stoi(items.at(R_index)); rgb(1) = std::stoi(items.at(G_index)); rgb(2) = std::stoi(items.at(B_index)); } const point3D_t point3D_id = AddPoint3D(xyz, Track()); Point3D(point3D_id).SetColor(rgb.cast()); } } } bool Reconstruction::ExportNVM(const std::string& path) const { std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "NVM_V3" << std::endl << std::endl; file << reg_image_ids_.size() << std::endl; std::unordered_map image_id_to_idx_; size_t image_idx = 0; for (const auto image_id : reg_image_ids_) { const class Image& image = Image(image_id); const class Camera& camera = Camera(image.CameraId()); if (camera.ModelId() != SimpleRadialCameraModel::model_id) { std::cout << "WARNING: NVM only supports `SIMPLE_RADIAL` camera model." << std::endl; return false; } const double f = camera.Params(SimpleRadialCameraModel::focal_length_idxs[0]); const double k = -1 * camera.Params(SimpleRadialCameraModel::extra_params_idxs[0]); const Eigen::Vector3d proj_center = image.ProjectionCenter(); file << image.Name() << " "; file << f << " "; file << image.Qvec(0) << " "; file << image.Qvec(1) << " "; file << image.Qvec(2) << " "; file << image.Qvec(3) << " "; file << proj_center(0) << " "; file << proj_center(1) << " "; file << proj_center(2) << " "; file << k << " "; file << 0 << std::endl; image_id_to_idx_[image_id] = image_idx; image_idx += 1; } file << std::endl << points3D_.size() << std::endl; for (const auto& point3D : points3D_) { file << point3D.second.XYZ()(0) << " "; file << point3D.second.XYZ()(1) << " "; file << point3D.second.XYZ()(2) << " "; file << static_cast(point3D.second.Color(0)) << " "; file << static_cast(point3D.second.Color(1)) << " "; file << static_cast(point3D.second.Color(2)) << " "; std::ostringstream line; std::unordered_set image_ids; for (const auto& track_el : point3D.second.Track().Elements()) { // Make sure that each point only has a single observation per image, // since VisualSfM does not support with multiple observations. if (image_ids.count(track_el.image_id) == 0) { const class Image& image = Image(track_el.image_id); const Point2D& point2D = image.Point2D(track_el.point2D_idx); line << image_id_to_idx_[track_el.image_id] << " "; line << track_el.point2D_idx << " "; line << point2D.X() << " "; line << point2D.Y() << " "; image_ids.insert(track_el.image_id); } } std::string line_string = line.str(); line_string = line_string.substr(0, line_string.size() - 1); file << image_ids.size() << " "; file << line_string << std::endl; } return true; } bool Reconstruction::ExportBundler(const std::string& path, const std::string& list_path) const { std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; std::ofstream list_file(list_path, std::ios::trunc); CHECK(list_file.is_open()) << list_path; file << "# Bundle file v0.3" << std::endl; file << reg_image_ids_.size() << " " << points3D_.size() << std::endl; std::unordered_map image_id_to_idx_; size_t image_idx = 0; for (const image_t image_id : reg_image_ids_) { const class Image& image = Image(image_id); const class Camera& camera = Camera(image.CameraId()); double f; double k1; double k2; if (camera.ModelId() == SimplePinholeCameraModel::model_id || camera.ModelId() == PinholeCameraModel::model_id) { f = camera.MeanFocalLength(); k1 = 0.0; k2 = 0.0; } else if (camera.ModelId() == SimpleRadialCameraModel::model_id) { f = camera.Params(SimpleRadialCameraModel::focal_length_idxs[0]); k1 = camera.Params(SimpleRadialCameraModel::extra_params_idxs[0]); k2 = 0.0; } else if (camera.ModelId() == RadialCameraModel::model_id) { f = camera.Params(RadialCameraModel::focal_length_idxs[0]); k1 = camera.Params(RadialCameraModel::extra_params_idxs[0]); k2 = camera.Params(RadialCameraModel::extra_params_idxs[1]); } else { std::cout << "WARNING: Bundler only supports `SIMPLE_RADIAL` and " "`RADIAL` camera models." << std::endl; return false; } file << f << " " << k1 << " " << k2 << std::endl; const Eigen::Matrix3d R = image.RotationMatrix(); file << R(0, 0) << " " << R(0, 1) << " " << R(0, 2) << std::endl; file << -R(1, 0) << " " << -R(1, 1) << " " << -R(1, 2) << std::endl; file << -R(2, 0) << " " << -R(2, 1) << " " << -R(2, 2) << std::endl; file << image.Tvec(0) << " "; file << -image.Tvec(1) << " "; file << -image.Tvec(2) << std::endl; list_file << image.Name() << std::endl; image_id_to_idx_[image_id] = image_idx; image_idx += 1; } for (const auto& point3D : points3D_) { file << point3D.second.XYZ()(0) << " "; file << point3D.second.XYZ()(1) << " "; file << point3D.second.XYZ()(2) << std::endl; file << static_cast(point3D.second.Color(0)) << " "; file << static_cast(point3D.second.Color(1)) << " "; file << static_cast(point3D.second.Color(2)) << std::endl; std::ostringstream line; line << point3D.second.Track().Length() << " "; for (const auto& track_el : point3D.second.Track().Elements()) { const class Image& image = Image(track_el.image_id); const class Camera& camera = Camera(image.CameraId()); // Bundler output assumes image coordinate system origin // in the lower left corner of the image with the center of // the lower left pixel being (0, 0). Our coordinate system // starts in the upper left corner with the center of the // upper left pixel being (0.5, 0.5). const Point2D& point2D = image.Point2D(track_el.point2D_idx); line << image_id_to_idx_.at(track_el.image_id) << " "; line << track_el.point2D_idx << " "; line << point2D.X() - camera.PrincipalPointX() << " "; line << camera.PrincipalPointY() - point2D.Y() << " "; } std::string line_string = line.str(); line_string = line_string.substr(0, line_string.size() - 1); file << line_string << std::endl; } return true; } void Reconstruction::ExportPLY(const std::string& path) const { std::fstream text_file(path, std::ios::out); CHECK(text_file.is_open()) << path; text_file << "ply" << std::endl; text_file << "format binary_little_endian 1.0" << std::endl; text_file << "element vertex " << points3D_.size() << std::endl; text_file << "property float x" << std::endl; text_file << "property float y" << std::endl; text_file << "property float z" << std::endl; text_file << "property uchar red" << std::endl; text_file << "property uchar green" << std::endl; text_file << "property uchar blue" << std::endl; text_file << "end_header" << std::endl; text_file.close(); std::fstream binary_file(path, std::ios::out | std::ios::binary | std::ios::app); CHECK(binary_file.is_open()) << path; for (const auto& point3D : points3D_) { WriteBinaryLittleEndian(&binary_file, point3D.second.X()); WriteBinaryLittleEndian(&binary_file, point3D.second.Y()); WriteBinaryLittleEndian(&binary_file, point3D.second.Z()); WriteBinaryLittleEndian(&binary_file, point3D.second.Color(0)); WriteBinaryLittleEndian(&binary_file, point3D.second.Color(1)); WriteBinaryLittleEndian(&binary_file, point3D.second.Color(2)); } binary_file.close(); } void Reconstruction::ExportVRML(const std::string& images_path, const std::string& points3D_path, const double image_scale, const Eigen::Vector3d& image_rgb) const { std::ofstream images_file(images_path, std::ios::trunc); CHECK(images_file.is_open()) << images_path; const double six = image_scale * 0.15; const double siy = image_scale * 0.1; std::vector points; points.emplace_back(-six, -siy, six * 1.0 * 2.0); points.emplace_back(+six, -siy, six * 1.0 * 2.0); points.emplace_back(+six, +siy, six * 1.0 * 2.0); points.emplace_back(-six, +siy, six * 1.0 * 2.0); points.emplace_back(0, 0, 0); points.emplace_back(-six / 3.0, -siy / 3.0, six * 1.0 * 2.0); points.emplace_back(+six / 3.0, -siy / 3.0, six * 1.0 * 2.0); points.emplace_back(+six / 3.0, +siy / 3.0, six * 1.0 * 2.0); points.emplace_back(-six / 3.0, +siy / 3.0, six * 1.0 * 2.0); for (const auto& image : images_) { if (!image.second.IsRegistered()) { continue; } images_file << "Shape{\n"; images_file << " appearance Appearance {\n"; images_file << " material DEF Default-ffRffGffB Material {\n"; images_file << " ambientIntensity 0\n"; images_file << " diffuseColor " << " " << image_rgb(0) << " " << image_rgb(1) << " " << image_rgb(2) << "\n"; images_file << " emissiveColor 0.1 0.1 0.1 } }\n"; images_file << " geometry IndexedFaceSet {\n"; images_file << " solid FALSE \n"; images_file << " colorPerVertex TRUE \n"; images_file << " ccw TRUE \n"; images_file << " coord Coordinate {\n"; images_file << " point [\n"; Eigen::Transform transform; transform.matrix().topLeftCorner<3, 4>() = image.second.InverseProjectionMatrix(); // Move camera base model to camera pose. for (size_t i = 0; i < points.size(); i++) { const Eigen::Vector3d point = transform * points[i]; images_file << point(0) << " " << point(1) << " " << point(2) << "\n"; } images_file << " ] }\n"; images_file << "color Color {color [\n"; for (size_t p = 0; p < points.size(); p++) { images_file << " " << image_rgb(0) << " " << image_rgb(1) << " " << image_rgb(2) << "\n"; } images_file << "\n] }\n"; images_file << "coordIndex [\n"; images_file << " 0, 1, 2, 3, -1\n"; images_file << " 5, 6, 4, -1\n"; images_file << " 6, 7, 4, -1\n"; images_file << " 7, 8, 4, -1\n"; images_file << " 8, 5, 4, -1\n"; images_file << " \n] \n"; images_file << " texCoord TextureCoordinate { point [\n"; images_file << " 1 1,\n"; images_file << " 0 1,\n"; images_file << " 0 0,\n"; images_file << " 1 0,\n"; images_file << " 0 0,\n"; images_file << " 0 0,\n"; images_file << " 0 0,\n"; images_file << " 0 0,\n"; images_file << " 0 0,\n"; images_file << " ] }\n"; images_file << "} }\n"; } // Write 3D points std::ofstream points3D_file(points3D_path, std::ios::trunc); CHECK(points3D_file.is_open()) << points3D_path; points3D_file << "#VRML V2.0 utf8\n"; points3D_file << "Background { skyColor [1.0 1.0 1.0] } \n"; points3D_file << "Shape{ appearance Appearance {\n"; points3D_file << " material Material {emissiveColor 1 1 1} }\n"; points3D_file << " geometry PointSet {\n"; points3D_file << " coord Coordinate {\n"; points3D_file << " point [\n"; for (const auto& point3D : points3D_) { points3D_file << point3D.second.XYZ()(0) << ", "; points3D_file << point3D.second.XYZ()(1) << ", "; points3D_file << point3D.second.XYZ()(2) << std::endl; } points3D_file << " ] }\n"; points3D_file << " color Color { color [\n"; for (const auto& point3D : points3D_) { points3D_file << point3D.second.Color(0) / 255.0 << ", "; points3D_file << point3D.second.Color(1) / 255.0 << ", "; points3D_file << point3D.second.Color(2) / 255.0 << std::endl; } points3D_file << " ] } } }\n"; } bool Reconstruction::ExtractColorsForImage(const image_t image_id, const std::string& path) { const class Image& image = Image(image_id); Bitmap bitmap; if (!bitmap.Read(JoinPaths(path, image.Name()))) { return false; } const Eigen::Vector3ub kBlackColor(0, 0, 0); for (const Point2D point2D : image.Points2D()) { if (point2D.HasPoint3D()) { class Point3D& point3D = Point3D(point2D.Point3DId()); if (point3D.Color() == kBlackColor) { BitmapColor color; // COLMAP assumes that the upper left pixel center is (0.5, 0.5). if (bitmap.InterpolateBilinear(point2D.X() - 0.5, point2D.Y() - 0.5, &color)) { const BitmapColor color_ub = color.Cast(); point3D.SetColor( Eigen::Vector3ub(color_ub.r, color_ub.g, color_ub.b)); } } } } return true; } void Reconstruction::ExtractColorsForAllImages(const std::string& path) { EIGEN_STL_UMAP(point3D_t, Eigen::Vector3d) color_sums; std::unordered_map color_counts; for (size_t i = 0; i < reg_image_ids_.size(); ++i) { const class Image& image = Image(reg_image_ids_[i]); const std::string image_path = JoinPaths(path, image.Name()); Bitmap bitmap; if (!bitmap.Read(image_path)) { std::cout << StringPrintf("Could not read image %s at path %s.", image.Name().c_str(), image_path.c_str()) << std::endl; continue; } for (const Point2D point2D : image.Points2D()) { if (point2D.HasPoint3D()) { BitmapColor color; // COLMAP assumes that the upper left pixel center is (0.5, 0.5). if (bitmap.InterpolateBilinear(point2D.X() - 0.5, point2D.Y() - 0.5, &color)) { if (color_sums.count(point2D.Point3DId())) { Eigen::Vector3d& color_sum = color_sums[point2D.Point3DId()]; color_sum(0) += color.r; color_sum(1) += color.g; color_sum(2) += color.b; color_counts[point2D.Point3DId()] += 1; } else { color_sums.emplace(point2D.Point3DId(), Eigen::Vector3d(color.r, color.g, color.b)); color_counts.emplace(point2D.Point3DId(), 1); } } } } } const Eigen::Vector3ub kBlackColor(0, 0, 0); for (auto& point3D : points3D_) { if (color_sums.count(point3D.first)) { Eigen::Vector3d color = color_sums[point3D.first] / color_counts[point3D.first]; color.unaryExpr(std::ptr_fun(std::round)); point3D.second.SetColor(color.cast()); } else { point3D.second.SetColor(kBlackColor); } } } void Reconstruction::CreateImageDirs(const std::string& path) const { std::set image_dirs; for (const auto& image : images_) { const std::vector name_split = StringSplit(image.second.Name(), "/"); if (name_split.size() > 1) { std::string dir = path; for (size_t i = 0; i < name_split.size() - 1; ++i) { dir = JoinPaths(dir, name_split[i]); image_dirs.insert(dir); } } } for (const auto& dir : image_dirs) { CreateDirIfNotExists(dir); } } size_t Reconstruction::FilterPoints3DWithSmallTriangulationAngle( const double min_tri_angle, const std::unordered_set& point3D_ids) { // Number of filtered points. size_t num_filtered = 0; // Minimum triangulation angle in radians. const double min_tri_angle_rad = DegToRad(min_tri_angle); // Cache for image projection centers. EIGEN_STL_UMAP(image_t, Eigen::Vector3d) proj_centers; for (const auto point3D_id : point3D_ids) { if (!ExistsPoint3D(point3D_id)) { continue; } const class Point3D& point3D = Point3D(point3D_id); // Calculate triangulation angle for all pairwise combinations of image // poses in the track. Only delete point if none of the combinations // has a sufficient triangulation angle. bool keep_point = false; for (size_t i1 = 0; i1 < point3D.Track().Length(); ++i1) { const image_t image_id1 = point3D.Track().Element(i1).image_id; Eigen::Vector3d proj_center1; if (proj_centers.count(image_id1) == 0) { const class Image& image1 = Image(image_id1); proj_center1 = image1.ProjectionCenter(); proj_centers.emplace(image_id1, proj_center1); } else { proj_center1 = proj_centers.at(image_id1); } for (size_t i2 = 0; i2 < i1; ++i2) { const image_t image_id2 = point3D.Track().Element(i2).image_id; const Eigen::Vector3d proj_center2 = proj_centers.at(image_id2); const double tri_angle = CalculateTriangulationAngle( proj_center1, proj_center2, point3D.XYZ()); if (tri_angle >= min_tri_angle_rad) { keep_point = true; break; } } if (keep_point) { break; } } if (!keep_point) { num_filtered += 1; DeletePoint3D(point3D_id); } } return num_filtered; } size_t Reconstruction::FilterPoints3DWithLargeReprojectionError( const double max_reproj_error, const std::unordered_set& point3D_ids) { // Number of filtered points. size_t num_filtered = 0; // Cache for projection matrices. EIGEN_STL_UMAP(image_t, Eigen::Matrix3x4d) proj_matrices; for (const auto point3D_id : point3D_ids) { if (!ExistsPoint3D(point3D_id)) { continue; } class Point3D& point3D = Point3D(point3D_id); if (point3D.Track().Length() < 2) { DeletePoint3D(point3D_id); continue; } double reproj_error_sum = 0.0; std::vector track_els_to_delete; for (const auto& track_el : point3D.Track().Elements()) { const class Image& image = Image(track_el.image_id); Eigen::Matrix3x4d proj_matrix; if (proj_matrices.count(track_el.image_id) == 0) { proj_matrix = image.ProjectionMatrix(); proj_matrices[track_el.image_id] = proj_matrix; } else { proj_matrix = proj_matrices[track_el.image_id]; } if (HasPointPositiveDepth(proj_matrix, point3D.XYZ())) { const class Camera& camera = Camera(image.CameraId()); const Point2D& point2D = image.Point2D(track_el.point2D_idx); const double reproj_error = CalculateReprojectionError( point2D.XY(), point3D.XYZ(), proj_matrix, camera); if (reproj_error > max_reproj_error) { track_els_to_delete.push_back(track_el); } else { reproj_error_sum += reproj_error; } } else { track_els_to_delete.push_back(track_el); } } if (track_els_to_delete.size() == point3D.Track().Length() || track_els_to_delete.size() == point3D.Track().Length() - 1) { num_filtered += point3D.Track().Length(); DeletePoint3D(point3D_id); } else { num_filtered += track_els_to_delete.size(); for (const auto& track_el : track_els_to_delete) { DeleteObservation(track_el.image_id, track_el.point2D_idx); } point3D.SetError(reproj_error_sum / point3D.Track().Length()); } } return num_filtered; } void Reconstruction::ReadCamerasText(const std::string& path) { cameras_.clear(); std::ifstream file(path); CHECK(file.is_open()) << path; std::string line; std::string item; while (std::getline(file, line)) { StringTrim(&line); if (line.empty() || line[0] == '#') { continue; } std::stringstream line_stream(line); class Camera camera; // ID std::getline(line_stream, item, ' '); camera.SetCameraId(std::stoul(item)); // MODEL std::getline(line_stream, item, ' '); camera.SetModelIdFromName(item); // WIDTH std::getline(line_stream, item, ' '); camera.SetWidth(std::stoll(item)); // HEIGHT std::getline(line_stream, item, ' '); camera.SetHeight(std::stoll(item)); // PARAMS camera.Params().clear(); while (!line_stream.eof()) { std::getline(line_stream, item, ' '); camera.Params().push_back(std::stold(item)); } CHECK(camera.VerifyParams()); cameras_.emplace(camera.CameraId(), camera); } } void Reconstruction::ReadImagesText(const std::string& path) { images_.clear(); std::ifstream file(path); CHECK(file.is_open()) << path; std::string line; std::string item; while (std::getline(file, line)) { StringTrim(&line); if (line.empty() || line[0] == '#') { continue; } std::stringstream line_stream1(line); // ID std::getline(line_stream1, item, ' '); const image_t image_id = std::stoul(item); class Image image; image.SetImageId(image_id); image.SetRegistered(true); reg_image_ids_.push_back(image_id); // QVEC (qw, qx, qy, qz) std::getline(line_stream1, item, ' '); image.Qvec(0) = std::stold(item); std::getline(line_stream1, item, ' '); image.Qvec(1) = std::stold(item); std::getline(line_stream1, item, ' '); image.Qvec(2) = std::stold(item); std::getline(line_stream1, item, ' '); image.Qvec(3) = std::stold(item); image.NormalizeQvec(); // TVEC std::getline(line_stream1, item, ' '); image.Tvec(0) = std::stold(item); std::getline(line_stream1, item, ' '); image.Tvec(1) = std::stold(item); std::getline(line_stream1, item, ' '); image.Tvec(2) = std::stold(item); // CAMERA_ID std::getline(line_stream1, item, ' '); image.SetCameraId(std::stoul(item)); // NAME std::getline(line_stream1, item, ' '); image.SetName(item); // POINTS2D if (!std::getline(file, line)) { break; } StringTrim(&line); std::stringstream line_stream2(line); std::vector points2D; std::vector point3D_ids; if (!line.empty()) { while (!line_stream2.eof()) { Eigen::Vector2d point; std::getline(line_stream2, item, ' '); point.x() = std::stold(item); std::getline(line_stream2, item, ' '); point.y() = std::stold(item); points2D.push_back(point); std::getline(line_stream2, item, ' '); if (item == "-1") { point3D_ids.push_back(kInvalidPoint3DId); } else { point3D_ids.push_back(std::stoll(item)); } } } image.SetUp(Camera(image.CameraId())); image.SetPoints2D(points2D); for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { if (point3D_ids[point2D_idx] != kInvalidPoint3DId) { image.SetPoint3DForPoint2D(point2D_idx, point3D_ids[point2D_idx]); } } images_.emplace(image.ImageId(), image); } } void Reconstruction::ReadPoints3DText(const std::string& path) { points3D_.clear(); std::ifstream file(path); CHECK(file.is_open()) << path; std::string line; std::string item; while (std::getline(file, line)) { StringTrim(&line); if (line.empty() || line[0] == '#') { continue; } std::stringstream line_stream(line); // ID std::getline(line_stream, item, ' '); const point3D_t point3D_id = std::stoll(item); // Make sure, that we can add new 3D points after reading 3D points // without overwriting existing 3D points. num_added_points3D_ = std::max(num_added_points3D_, point3D_id); class Point3D point3D; // XYZ std::getline(line_stream, item, ' '); point3D.XYZ(0) = std::stold(item); std::getline(line_stream, item, ' '); point3D.XYZ(1) = std::stold(item); std::getline(line_stream, item, ' '); point3D.XYZ(2) = std::stold(item); // Color std::getline(line_stream, item, ' '); point3D.Color(0) = static_cast(std::stoi(item)); std::getline(line_stream, item, ' '); point3D.Color(1) = static_cast(std::stoi(item)); std::getline(line_stream, item, ' '); point3D.Color(2) = static_cast(std::stoi(item)); // ERROR std::getline(line_stream, item, ' '); point3D.SetError(std::stold(item)); // TRACK while (!line_stream.eof()) { TrackElement track_el; std::getline(line_stream, item, ' '); StringTrim(&item); if (item.empty()) { break; } track_el.image_id = std::stoul(item); std::getline(line_stream, item, ' '); track_el.point2D_idx = std::stoul(item); point3D.Track().AddElement(track_el); } point3D.Track().Compress(); points3D_.emplace(point3D_id, point3D); } } void Reconstruction::ReadCamerasBinary(const std::string& path) { std::ifstream file(path, std::ios::binary); CHECK(file.is_open()) << path; const size_t num_cameras = ReadBinaryLittleEndian(&file); for (size_t i = 0; i < num_cameras; ++i) { class Camera camera; camera.SetCameraId(ReadBinaryLittleEndian(&file)); camera.SetModelId(ReadBinaryLittleEndian(&file)); camera.SetWidth(ReadBinaryLittleEndian(&file)); camera.SetHeight(ReadBinaryLittleEndian(&file)); ReadBinaryLittleEndian(&file, &camera.Params()); CHECK(camera.VerifyParams()); cameras_.emplace(camera.CameraId(), camera); } } void Reconstruction::ReadImagesBinary(const std::string& path) { std::ifstream file(path, std::ios::binary); CHECK(file.is_open()) << path; const size_t num_reg_images = ReadBinaryLittleEndian(&file); for (size_t i = 0; i < num_reg_images; ++i) { class Image image; image.SetImageId(ReadBinaryLittleEndian(&file)); image.Qvec(0) = ReadBinaryLittleEndian(&file); image.Qvec(1) = ReadBinaryLittleEndian(&file); image.Qvec(2) = ReadBinaryLittleEndian(&file); image.Qvec(3) = ReadBinaryLittleEndian(&file); image.NormalizeQvec(); image.Tvec(0) = ReadBinaryLittleEndian(&file); image.Tvec(1) = ReadBinaryLittleEndian(&file); image.Tvec(2) = ReadBinaryLittleEndian(&file); image.SetCameraId(ReadBinaryLittleEndian(&file)); char name_char; do { file.read(&name_char, 1); if (name_char != '\0') { image.Name() += name_char; } } while (name_char != '\0'); const size_t num_points2D = ReadBinaryLittleEndian(&file); std::vector points2D; points2D.reserve(num_points2D); std::vector point3D_ids; point3D_ids.reserve(num_points2D); for (size_t j = 0; j < num_points2D; ++j) { const double x = ReadBinaryLittleEndian(&file); const double y = ReadBinaryLittleEndian(&file); points2D.emplace_back(x, y); point3D_ids.push_back(ReadBinaryLittleEndian(&file)); } image.SetUp(Camera(image.CameraId())); image.SetPoints2D(points2D); for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { if (point3D_ids[point2D_idx] != kInvalidPoint3DId) { image.SetPoint3DForPoint2D(point2D_idx, point3D_ids[point2D_idx]); } } image.SetRegistered(true); reg_image_ids_.push_back(image.ImageId()); images_.emplace(image.ImageId(), image); } } void Reconstruction::ReadPoints3DBinary(const std::string& path) { std::ifstream file(path, std::ios::binary); CHECK(file.is_open()) << path; const size_t num_points3D = ReadBinaryLittleEndian(&file); for (size_t i = 0; i < num_points3D; ++i) { class Point3D point3D; const point3D_t point3D_id = ReadBinaryLittleEndian(&file); num_added_points3D_ = std::max(num_added_points3D_, point3D_id); point3D.XYZ()(0) = ReadBinaryLittleEndian(&file); point3D.XYZ()(1) = ReadBinaryLittleEndian(&file); point3D.XYZ()(2) = ReadBinaryLittleEndian(&file); point3D.Color(0) = ReadBinaryLittleEndian(&file); point3D.Color(1) = ReadBinaryLittleEndian(&file); point3D.Color(2) = ReadBinaryLittleEndian(&file); point3D.SetError(ReadBinaryLittleEndian(&file)); const size_t track_length = ReadBinaryLittleEndian(&file); for (size_t j = 0; j < track_length; ++j) { const image_t image_id = ReadBinaryLittleEndian(&file); const point2D_t point2D_idx = ReadBinaryLittleEndian(&file); point3D.Track().AddElement(image_id, point2D_idx); } point3D.Track().Compress(); points3D_.emplace(point3D_id, point3D); } } void Reconstruction::WriteCamerasText(const std::string& path) const { std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# Camera list with one line of data per camera:" << std::endl; file << "# CAMERA_ID, MODEL, WIDTH, HEIGHT, PARAMS[]" << std::endl; file << "# Number of cameras: " << cameras_.size() << std::endl; for (const auto& camera : cameras_) { std::ostringstream line; line << camera.first << " "; line << camera.second.ModelName() << " "; line << camera.second.Width() << " "; line << camera.second.Height() << " "; for (const double param : camera.second.Params()) { line << param << " "; } std::string line_string = line.str(); line_string = line_string.substr(0, line_string.size() - 1); file << line_string << std::endl; } } void Reconstruction::WriteImagesText(const std::string& path) const { std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# Image list with two lines of data per image:" << std::endl; file << "# IMAGE_ID, QW, QX, QY, QZ, TX, TY, TZ, CAMERA_ID, " "NAME" << std::endl; file << "# POINTS2D[] as (X, Y, POINT3D_ID)" << std::endl; file << "# Number of images: " << reg_image_ids_.size() << ", mean observations per image: " << ComputeMeanObservationsPerRegImage() << std::endl; for (const auto& image : images_) { if (!image.second.IsRegistered()) { continue; } std::ostringstream line; std::string line_string; line << image.first << " "; // QVEC (qw, qx, qy, qz) const Eigen::Vector4d normalized_qvec = NormalizeQuaternion(image.second.Qvec()); line << normalized_qvec(0) << " "; line << normalized_qvec(1) << " "; line << normalized_qvec(2) << " "; line << normalized_qvec(3) << " "; // TVEC line << image.second.Tvec(0) << " "; line << image.second.Tvec(1) << " "; line << image.second.Tvec(2) << " "; line << image.second.CameraId() << " "; line << image.second.Name(); file << line.str() << std::endl; line.str(""); line.clear(); for (const Point2D& point2D : image.second.Points2D()) { line << point2D.X() << " "; line << point2D.Y() << " "; if (point2D.HasPoint3D()) { line << point2D.Point3DId() << " "; } else { line << -1 << " "; } } line_string = line.str(); line_string = line_string.substr(0, line_string.size() - 1); file << line_string << std::endl; } } void Reconstruction::WritePoints3DText(const std::string& path) const { std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# 3D point list with one line of data per point:" << std::endl; file << "# POINT3D_ID, X, Y, Z, R, G, B, ERROR, " "TRACK[] as (IMAGE_ID, POINT2D_IDX)" << std::endl; file << "# Number of points: " << points3D_.size() << ", mean track length: " << ComputeMeanTrackLength() << std::endl; for (const auto& point3D : points3D_) { file << point3D.first << " "; file << point3D.second.XYZ()(0) << " "; file << point3D.second.XYZ()(1) << " "; file << point3D.second.XYZ()(2) << " "; file << static_cast(point3D.second.Color(0)) << " "; file << static_cast(point3D.second.Color(1)) << " "; file << static_cast(point3D.second.Color(2)) << " "; file << point3D.second.Error() << " "; std::ostringstream line; for (const auto& track_el : point3D.second.Track().Elements()) { line << track_el.image_id << " "; line << track_el.point2D_idx << " "; } std::string line_string = line.str(); line_string = line_string.substr(0, line_string.size() - 1); file << line_string << std::endl; } } void Reconstruction::WriteCamerasBinary(const std::string& path) const { std::ofstream file(path, std::ios::trunc | std::ios::binary); CHECK(file.is_open()) << path; WriteBinaryLittleEndian(&file, cameras_.size()); for (const auto& camera : cameras_) { WriteBinaryLittleEndian(&file, camera.first); WriteBinaryLittleEndian(&file, camera.second.ModelId()); WriteBinaryLittleEndian(&file, camera.second.Width()); WriteBinaryLittleEndian(&file, camera.second.Height()); for (const double param : camera.second.Params()) { WriteBinaryLittleEndian(&file, param); } } } void Reconstruction::WriteImagesBinary(const std::string& path) const { std::ofstream file(path, std::ios::trunc | std::ios::binary); CHECK(file.is_open()) << path; WriteBinaryLittleEndian(&file, reg_image_ids_.size()); for (const auto& image : images_) { if (!image.second.IsRegistered()) { continue; } WriteBinaryLittleEndian(&file, image.first); const Eigen::Vector4d normalized_qvec = NormalizeQuaternion(image.second.Qvec()); WriteBinaryLittleEndian(&file, normalized_qvec(0)); WriteBinaryLittleEndian(&file, normalized_qvec(1)); WriteBinaryLittleEndian(&file, normalized_qvec(2)); WriteBinaryLittleEndian(&file, normalized_qvec(3)); WriteBinaryLittleEndian(&file, image.second.Tvec(0)); WriteBinaryLittleEndian(&file, image.second.Tvec(1)); WriteBinaryLittleEndian(&file, image.second.Tvec(2)); WriteBinaryLittleEndian(&file, image.second.CameraId()); const std::string name = image.second.Name() + '\0'; file.write(name.c_str(), name.size()); WriteBinaryLittleEndian(&file, image.second.NumPoints2D()); for (const Point2D& point2D : image.second.Points2D()) { WriteBinaryLittleEndian(&file, point2D.X()); WriteBinaryLittleEndian(&file, point2D.Y()); WriteBinaryLittleEndian(&file, point2D.Point3DId()); } } } void Reconstruction::WritePoints3DBinary(const std::string& path) const { std::ofstream file(path, std::ios::trunc | std::ios::binary); CHECK(file.is_open()) << path; WriteBinaryLittleEndian(&file, points3D_.size()); for (const auto& point3D : points3D_) { WriteBinaryLittleEndian(&file, point3D.first); WriteBinaryLittleEndian(&file, point3D.second.XYZ()(0)); WriteBinaryLittleEndian(&file, point3D.second.XYZ()(1)); WriteBinaryLittleEndian(&file, point3D.second.XYZ()(2)); WriteBinaryLittleEndian(&file, point3D.second.Color(0)); WriteBinaryLittleEndian(&file, point3D.second.Color(1)); WriteBinaryLittleEndian(&file, point3D.second.Color(2)); WriteBinaryLittleEndian(&file, point3D.second.Error()); WriteBinaryLittleEndian(&file, point3D.second.Track().Length()); for (const auto& track_el : point3D.second.Track().Elements()) { WriteBinaryLittleEndian(&file, track_el.image_id); WriteBinaryLittleEndian(&file, track_el.point2D_idx); } } } void Reconstruction::SetObservationAsTriangulated( const image_t image_id, const point2D_t point2D_idx, const bool is_continued_point3D) { if (scene_graph_ == nullptr) { return; } const class Image& image = Image(image_id); const Point2D& point2D = image.Point2D(point2D_idx); const std::vector& corrs = scene_graph_->FindCorrespondences(image_id, point2D_idx); CHECK(image.IsRegistered()); CHECK(point2D.HasPoint3D()); for (const auto& corr : corrs) { class Image& corr_image = Image(corr.image_id); const Point2D& corr_point2D = corr_image.Point2D(corr.point2D_idx); corr_image.IncrementCorrespondenceHasPoint3D(corr.point2D_idx); // Update number of shared 3D points between image pairs and make sure to // only count the correspondences once (not twice forward and backward). if (point2D.Point3DId() == corr_point2D.Point3DId() && (is_continued_point3D || image_id < corr.image_id)) { const image_pair_t pair_id = Database::ImagePairToPairId(image_id, corr.image_id); image_pairs_[pair_id].first += 1; CHECK_LE(image_pairs_[pair_id].first, image_pairs_[pair_id].second) << "The scene graph graph must not contain duplicate matches"; } } } void Reconstruction::ResetTriObservations(const image_t image_id, const point2D_t point2D_idx, const bool is_deleted_point3D) { if (scene_graph_ == nullptr) { return; } const class Image& image = Image(image_id); const Point2D& point2D = image.Point2D(point2D_idx); const std::vector& corrs = scene_graph_->FindCorrespondences(image_id, point2D_idx); CHECK(image.IsRegistered()); CHECK(point2D.HasPoint3D()); for (const auto& corr : corrs) { class Image& corr_image = Image(corr.image_id); const Point2D& corr_point2D = corr_image.Point2D(corr.point2D_idx); corr_image.DecrementCorrespondenceHasPoint3D(corr.point2D_idx); // Update number of shared 3D points between image pairs and make sure to // only count the correspondences once (not twice forward and backward). if (point2D.Point3DId() == corr_point2D.Point3DId() && (!is_deleted_point3D || image_id < corr.image_id)) { const image_pair_t pair_id = Database::ImagePairToPairId(image_id, corr.image_id); image_pairs_[pair_id].first -= 1; CHECK_GE(image_pairs_[pair_id].first, 0) << "The scene graph graph must not contain duplicate matches"; } } } } // namespace colmap colmap-3.4/src/base/reconstruction.h000077500000000000000000000373701323400541200175750ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_RECONSTRUCTION_H_ #define COLMAP_SRC_BASE_RECONSTRUCTION_H_ #include #include #include #include #include "base/camera.h" #include "base/database_cache.h" #include "base/image.h" #include "base/point2d.h" #include "base/point3d.h" #include "base/track.h" #include "util/alignment.h" #include "util/types.h" namespace colmap { // Reconstruction class holds all information about a single reconstructed // model. It is used by the mapping and bundle adjustment classes and can be // written to and read from disk. class Reconstruction { public: Reconstruction(); // Get number of objects. inline size_t NumCameras() const; inline size_t NumImages() const; inline size_t NumRegImages() const; inline size_t NumPoints3D() const; inline size_t NumImagePairs() const; // Get const objects. inline const class Camera& Camera(const camera_t camera_id) const; inline const class Image& Image(const image_t image_id) const; inline const class Point3D& Point3D(const point3D_t point3D_id) const; inline const std::pair& ImagePair( const image_pair_t pair_id) const; inline std::pair& ImagePair(const image_t image_id1, const image_t image_id2); // Get mutable objects. inline class Camera& Camera(const camera_t camera_id); inline class Image& Image(const image_t image_id); inline class Point3D& Point3D(const point3D_t point3D_id); inline std::pair& ImagePair(const image_pair_t pair_id); inline const std::pair& ImagePair( const image_t image_id1, const image_t image_id2) const; // Get reference to all objects. inline const EIGEN_STL_UMAP(camera_t, class Camera) & Cameras() const; inline const EIGEN_STL_UMAP(image_t, class Image) & Images() const; inline const std::vector& RegImageIds() const; inline const EIGEN_STL_UMAP(point3D_t, class Point3D) & Points3D() const; inline const std::unordered_map>& ImagePairs() const; // Identifiers of all 3D points. std::unordered_set Point3DIds() const; // Check whether specific object exists. inline bool ExistsCamera(const camera_t camera_id) const; inline bool ExistsImage(const image_t image_id) const; inline bool ExistsPoint3D(const point3D_t point3D_id) const; inline bool ExistsImagePair(const image_pair_t pair_id) const; // Load data from given `DatabaseCache`. void Load(const DatabaseCache& database_cache); // Setup all relevant data structures before reconstruction. Note that the // scene graph object must live until the `TearDown` method is called. void SetUp(const SceneGraph* scene_graph); // Finalize the Reconstruction after the reconstruction has finished. // // Once a scene has been finalized, it cannot be used for reconstruction. // // This removes all not yet registered images and unused cameras, in order to // save memory. void TearDown(); // Add new camera. There is only one camera per image, while multiple images // might be taken by the same camera. void AddCamera(const class Camera& camera); // Add new image. void AddImage(const class Image& image); // Add new 3D object, and return its unique ID. point3D_t AddPoint3D(const Eigen::Vector3d& xyz, const Track& track); // Add observation to existing 3D point. void AddObservation(const point3D_t point3D_id, const TrackElement& track_el); // Merge two 3D points and return new identifier of new 3D point. // The location of the merged 3D point is a weighted average of the two // original 3D point's locations according to their track lengths. point3D_t MergePoints3D(const point3D_t point3D_id1, const point3D_t point3D_id2); // Delete a 3D point, and all its references in the observed images. void DeletePoint3D(const point3D_t point3D_id); // Delete one observation from an image and the corresponding 3D point. // Note that this deletes the entire 3D point, if the track has two elements // prior to calling this method. void DeleteObservation(const image_t image_id, const point2D_t point2D_idx); // Register an existing image. void RegisterImage(const image_t image_id); // De-register an existing image, and all its references. void DeRegisterImage(const image_t image_id); // Check if image is registered. inline bool IsImageRegistered(const image_t image_id) const; // Normalize scene by scaling and translation to avoid degenerate // visualization after bundle adjustment and to improve numerical // stability of algorithms. // // Translates scene such that the mean of the camera centers or point // locations are at the origin of the coordinate system. // // Scales scene such that the minimum and maximum camera centers are at the // given `extent`, whereas `p0` and `p1` determine the minimum and // maximum percentiles of the camera centers considered. void Normalize(const double extent = 10.0, const double p0 = 0.1, const double p1 = 0.9, const bool use_images = true); // Apply the 3D similarity transformation to all images and points. void Transform(const double scale, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec); // Merge the given reconstruction into this reconstruction by registering the // images registered in the given but not in this reconstruction and by // merging the two clouds and their tracks. The coordinate frames of the two // reconstructions are aligned using the projection centers of common // registered images. Return true if the two reconstructions could be merged. bool Merge(const Reconstruction& reconstruction, const int min_common_images); // Align the given reconstruction with a set of pre-defined camera positions. // Assuming that locations[i] gives the 3D coordinates of the center // of projection of the image with name image_names[i]. bool Align(const std::vector& image_names, const std::vector& locations, const int min_common_images); // Robust alignment using RANSAC. bool AlignRobust(const std::vector& image_names, const std::vector& locations, const int min_common_images, const RANSACOptions& ransac_options); // Find image with name. // // @param name Name of the image. // // @return Nullptr if image was not found. const class Image* FindImageWithName(const std::string& name) const; // Filter 3D points with large reprojection error, negative depth, or // insufficient triangulation angle. // // @param max_reproj_error The maximum reprojection error. // @param min_tri_angle The minimum triangulation angle. // @param point3D_ids The points to be filtered. // // @return The number of filtered observations. size_t FilterPoints3D(const double max_reproj_error, const double min_tri_angle, const std::unordered_set& point3D_ids); size_t FilterPoints3DInImages(const double max_reproj_error, const double min_tri_angle, const std::unordered_set& image_ids); size_t FilterAllPoints3D(const double max_reproj_error, const double min_tri_angle); // Filter observations that have negative depth. // // @return The number of filtered observations. size_t FilterObservationsWithNegativeDepth(); // Filter images without observations or bogus camera parameters. // // @return The identifiers of the filtered images. std::vector FilterImages(const double min_focal_length_ratio, const double max_focal_length_ratio, const double max_extra_param); // Compute statistics for scene. size_t ComputeNumObservations() const; double ComputeMeanTrackLength() const; double ComputeMeanObservationsPerRegImage() const; double ComputeMeanReprojectionError() const; // Read data from text or binary file. Prefer binary data if it exists. void Read(const std::string& path); void Write(const std::string& path) const; // Read data from binary/text file. void ReadText(const std::string& path); void ReadBinary(const std::string& path); // Write data from binary/text file. void WriteText(const std::string& path) const; void WriteBinary(const std::string& path) const; // Import from other data formats. Note that these import functions are // only intended for visualization of data and usable for reconstruction. void ImportPLY(const std::string& path); // Export to other data formats. bool ExportNVM(const std::string& path) const; bool ExportBundler(const std::string& path, const std::string& list_path) const; void ExportPLY(const std::string& path) const; void ExportVRML(const std::string& images_path, const std::string& points3D_path, const double image_scale, const Eigen::Vector3d& image_rgb) const; // Extract colors for 3D points of given image. Colors will be extracted // only for 3D points which are completely black. // // @param image_id Identifier of the image for which to extract colors. // @param path Absolute or relative path to root folder of image. // The image path is determined by concatenating the // root path and the name of the image. // // @return True if image could be read at given path. bool ExtractColorsForImage(const image_t image_id, const std::string& path); // Extract colors for all 3D points by computing the mean color of all images. // // @param path Absolute or relative path to root folder of image. // The image path is determined by concatenating the // root path and the name of the image. void ExtractColorsForAllImages(const std::string& path); // Create all image sub-directories in the given path. void CreateImageDirs(const std::string& path) const; private: size_t FilterPoints3DWithSmallTriangulationAngle( const double min_tri_angle, const std::unordered_set& point3D_ids); size_t FilterPoints3DWithLargeReprojectionError( const double max_reproj_error, const std::unordered_set& point3D_ids); void ReadCamerasText(const std::string& path); void ReadImagesText(const std::string& path); void ReadPoints3DText(const std::string& path); void ReadCamerasBinary(const std::string& path); void ReadImagesBinary(const std::string& path); void ReadPoints3DBinary(const std::string& path); void WriteCamerasText(const std::string& path) const; void WriteImagesText(const std::string& path) const; void WritePoints3DText(const std::string& path) const; void WriteCamerasBinary(const std::string& path) const; void WriteImagesBinary(const std::string& path) const; void WritePoints3DBinary(const std::string& path) const; void SetObservationAsTriangulated(const image_t image_id, const point2D_t point2D_idx, const bool is_continued_point3D); void ResetTriObservations(const image_t image_id, const point2D_t point2D_idx, const bool is_deleted_point3D); const SceneGraph* scene_graph_; EIGEN_STL_UMAP(camera_t, class Camera) cameras_; EIGEN_STL_UMAP(image_t, class Image) images_; EIGEN_STL_UMAP(point3D_t, class Point3D) points3D_; std::unordered_map> image_pairs_; // { image_id, ... } where `images_.at(image_id).registered == true`. std::vector reg_image_ids_; // Total number of added 3D points, used to generate unique identifiers. point3D_t num_added_points3D_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// size_t Reconstruction::NumCameras() const { return cameras_.size(); } size_t Reconstruction::NumImages() const { return images_.size(); } size_t Reconstruction::NumRegImages() const { return reg_image_ids_.size(); } size_t Reconstruction::NumPoints3D() const { return points3D_.size(); } size_t Reconstruction::NumImagePairs() const { return image_pairs_.size(); } const class Camera& Reconstruction::Camera(const camera_t camera_id) const { return cameras_.at(camera_id); } const class Image& Reconstruction::Image(const image_t image_id) const { return images_.at(image_id); } const class Point3D& Reconstruction::Point3D(const point3D_t point3D_id) const { return points3D_.at(point3D_id); } const std::pair& Reconstruction::ImagePair( const image_pair_t pair_id) const { return image_pairs_.at(pair_id); } const std::pair& Reconstruction::ImagePair( const image_t image_id1, const image_t image_id2) const { const auto pair_id = Database::ImagePairToPairId(image_id1, image_id2); return image_pairs_.at(pair_id); } class Camera& Reconstruction::Camera(const camera_t camera_id) { return cameras_.at(camera_id); } class Image& Reconstruction::Image(const image_t image_id) { return images_.at(image_id); } class Point3D& Reconstruction::Point3D(const point3D_t point3D_id) { return points3D_.at(point3D_id); } std::pair& Reconstruction::ImagePair( const image_pair_t pair_id) { return image_pairs_.at(pair_id); } std::pair& Reconstruction::ImagePair(const image_t image_id1, const image_t image_id2) { const auto pair_id = Database::ImagePairToPairId(image_id1, image_id2); return image_pairs_.at(pair_id); } const EIGEN_STL_UMAP(camera_t, Camera) & Reconstruction::Cameras() const { return cameras_; } const EIGEN_STL_UMAP(image_t, class Image) & Reconstruction::Images() const { return images_; } const std::vector& Reconstruction::RegImageIds() const { return reg_image_ids_; } const EIGEN_STL_UMAP(point3D_t, Point3D) & Reconstruction::Points3D() const { return points3D_; } const std::unordered_map>& Reconstruction::ImagePairs() const { return image_pairs_; } bool Reconstruction::ExistsCamera(const camera_t camera_id) const { return cameras_.find(camera_id) != cameras_.end(); } bool Reconstruction::ExistsImage(const image_t image_id) const { return images_.find(image_id) != images_.end(); } bool Reconstruction::ExistsPoint3D(const point3D_t point3D_id) const { return points3D_.find(point3D_id) != points3D_.end(); } bool Reconstruction::ExistsImagePair(const image_pair_t pair_id) const { return image_pairs_.find(pair_id) != image_pairs_.end(); } bool Reconstruction::IsImageRegistered(const image_t image_id) const { return Image(image_id).IsRegistered(); } } // namespace colmap #endif // COLMAP_SRC_BASE_RECONSTRUCTION_H_ colmap-3.4/src/base/reconstruction_manager.cc000066400000000000000000000050741323400541200214160ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/reconstruction_manager.h" #include "util/misc.h" #include "util/option_manager.h" namespace colmap { ReconstructionManager::ReconstructionManager() {} ReconstructionManager::ReconstructionManager(ReconstructionManager&& other) : ReconstructionManager() { reconstructions_ = std::move(other.reconstructions_); } ReconstructionManager& ReconstructionManager::operator=( ReconstructionManager&& other) { if (this != &other) { reconstructions_ = std::move(other.reconstructions_); } return *this; } size_t ReconstructionManager::Size() const { return reconstructions_.size(); } const Reconstruction& ReconstructionManager::Get(const size_t idx) const { return *reconstructions_.at(idx); } Reconstruction& ReconstructionManager::Get(const size_t idx) { return *reconstructions_.at(idx); } size_t ReconstructionManager::Add() { const size_t idx = Size(); reconstructions_.emplace_back(new Reconstruction()); return idx; } void ReconstructionManager::Delete(const size_t idx) { CHECK_LT(idx, reconstructions_.size()); reconstructions_.erase(reconstructions_.begin() + idx); } void ReconstructionManager::Clear() { reconstructions_.clear(); } size_t ReconstructionManager::Read(const std::string& path) { const size_t idx = Add(); reconstructions_[idx]->Read(path); return idx; } void ReconstructionManager::Write(const std::string& path, const OptionManager* options) const { for (size_t i = 0; i < reconstructions_.size(); ++i) { const std::string reconstruction_path = JoinPaths(path, std::to_string(i)); CreateDirIfNotExists(reconstruction_path); reconstructions_[i]->Write(reconstruction_path); if (options != nullptr) { options->Write(JoinPaths(reconstruction_path, "project.ini")); } } } } // namespace colmap colmap-3.4/src/base/reconstruction_manager.h000066400000000000000000000041711323400541200212550ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_RECONSTRUCTION_MANAGER_H_ #define COLMAP_SRC_BASE_RECONSTRUCTION_MANAGER_H_ #include "base/reconstruction.h" namespace colmap { class OptionManager; class ReconstructionManager { public: ReconstructionManager(); // Move constructor and assignment. ReconstructionManager(ReconstructionManager&& other); ReconstructionManager& operator=(ReconstructionManager&& other); // The number of reconstructions managed. size_t Size() const; // Get a reference to a specific reconstruction. const Reconstruction& Get(const size_t idx) const; Reconstruction& Get(const size_t idx); // Add a new empty reconstruction and return its index. size_t Add(); // Delete a specific reconstruction. void Delete(const size_t idx); // Delete all reconstructions. void Clear(); // Read and add a new reconstruction and return its index. size_t Read(const std::string& path); // Write all managed reconstructions into sub-folders "0", "1", "2", ... // If the option manager object is not null, the options are written // to each respective reconstruction folder as well. void Write(const std::string& path, const OptionManager* options) const; private: NON_COPYABLE(ReconstructionManager) std::vector> reconstructions_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_RECONSTRUCTION_MANAGER_H_ colmap-3.4/src/base/reconstruction_manager_test.cc000066400000000000000000000045031323400541200224510ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/reconstruction_manager" #include "util/testing.h" #include "base/reconstruction_manager.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEmpty) { ReconstructionManager reconstruction_manager; BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 0); } BOOST_AUTO_TEST_CASE(TestAddGet) { ReconstructionManager reconstruction_manager; BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 0); for (size_t i = 0; i < 10; ++i) { const size_t idx = reconstruction_manager.Add(); BOOST_CHECK_EQUAL(reconstruction_manager.Size(), i + 1); BOOST_CHECK_EQUAL(idx, i); BOOST_CHECK_EQUAL(reconstruction_manager.Get(idx).NumCameras(), 0); BOOST_CHECK_EQUAL(reconstruction_manager.Get(idx).NumImages(), 0); BOOST_CHECK_EQUAL(reconstruction_manager.Get(idx).NumPoints3D(), 0); } } BOOST_AUTO_TEST_CASE(TestDelete) { ReconstructionManager reconstruction_manager; BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 0); for (size_t i = 0; i < 10; ++i) { reconstruction_manager.Add(); } BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 10); for (size_t i = 0; i < 10; ++i) { reconstruction_manager.Delete(0); BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 9 - i); } } BOOST_AUTO_TEST_CASE(TestClear) { ReconstructionManager reconstruction_manager; BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 0); for (size_t i = 0; i < 10; ++i) { reconstruction_manager.Add(); } BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 10); reconstruction_manager.Clear(); BOOST_CHECK_EQUAL(reconstruction_manager.Size(), 0); } colmap-3.4/src/base/reconstruction_test.cc000077500000000000000000000574231323400541200207730ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/reconstruction" #include "util/testing.h" #include "base/pose.h" #include "base/reconstruction.h" using namespace colmap; void GenerateReconstruction(const image_t num_images, Reconstruction* reconstruction, SceneGraph* scene_graph) { const size_t kNumPoints2D = 10; Camera camera; camera.SetCameraId(1); camera.InitializeWithName("PINHOLE", 1, 1, 1); reconstruction->AddCamera(camera); for (image_t image_id = 1; image_id <= num_images; ++image_id) { Image image; image.SetImageId(image_id); image.SetCameraId(1); image.SetName("image" + std::to_string(image_id)); image.SetPoints2D( std::vector(kNumPoints2D, Eigen::Vector2d::Zero())); reconstruction->AddImage(image); reconstruction->RegisterImage(image_id); scene_graph->AddImage(image_id, kNumPoints2D); } reconstruction->SetUp(scene_graph); } BOOST_AUTO_TEST_CASE(TestEmpty) { Reconstruction reconstruction; BOOST_CHECK_EQUAL(reconstruction.NumCameras(), 0); BOOST_CHECK_EQUAL(reconstruction.NumImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); BOOST_CHECK_EQUAL(reconstruction.NumImagePairs(), 0); } BOOST_AUTO_TEST_CASE(TestAddCamera) { Reconstruction reconstruction; Camera camera; camera.SetCameraId(1); camera.InitializeWithId(SimplePinholeCameraModel::model_id, 1, 1, 1); reconstruction.AddCamera(camera); BOOST_CHECK(reconstruction.ExistsCamera(camera.CameraId())); BOOST_CHECK_EQUAL(reconstruction.Camera(camera.CameraId()).CameraId(), camera.CameraId()); BOOST_CHECK_EQUAL(reconstruction.Cameras().count(camera.CameraId()), 1); BOOST_CHECK_EQUAL(reconstruction.Cameras().size(), 1); BOOST_CHECK_EQUAL(reconstruction.NumCameras(), 1); BOOST_CHECK_EQUAL(reconstruction.NumImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); BOOST_CHECK_EQUAL(reconstruction.NumImagePairs(), 0); } BOOST_AUTO_TEST_CASE(TestAddImage) { Reconstruction reconstruction; Image image; image.SetImageId(1); reconstruction.AddImage(image); BOOST_CHECK(reconstruction.ExistsImage(1)); BOOST_CHECK_EQUAL(reconstruction.Image(1).ImageId(), 1); BOOST_CHECK_EQUAL(reconstruction.Image(1).IsRegistered(), false); BOOST_CHECK_EQUAL(reconstruction.Images().count(1), 1); BOOST_CHECK_EQUAL(reconstruction.Images().size(), 1); BOOST_CHECK_EQUAL(reconstruction.NumCameras(), 0); BOOST_CHECK_EQUAL(reconstruction.NumImages(), 1); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); BOOST_CHECK_EQUAL(reconstruction.NumImagePairs(), 0); } BOOST_AUTO_TEST_CASE(TestAddPoint3D) { Reconstruction reconstruction; const point3D_t point3D_id = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK(reconstruction.ExistsPoint3D(point3D_id)); BOOST_CHECK_EQUAL(reconstruction.Point3D(point3D_id).Track().Length(), 0); BOOST_CHECK_EQUAL(reconstruction.Points3D().count(point3D_id), 1); BOOST_CHECK_EQUAL(reconstruction.Points3D().size(), 1); BOOST_CHECK_EQUAL(reconstruction.NumCameras(), 0); BOOST_CHECK_EQUAL(reconstruction.NumImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); BOOST_CHECK_EQUAL(reconstruction.NumImagePairs(), 0); BOOST_CHECK_EQUAL(reconstruction.Point3DIds().count(point3D_id), 1); } BOOST_AUTO_TEST_CASE(TestAddObservation) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(1, &reconstruction, &scene_graph); Track track; track.AddElement(1, 0); const point3D_t point3D_id = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), track); BOOST_CHECK_EQUAL(reconstruction.Image(1).NumPoints3D(), 1); BOOST_CHECK(reconstruction.Image(1).Point2D(0).HasPoint3D()); BOOST_CHECK(!reconstruction.Image(1).Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(reconstruction.Point3D(point3D_id).Track().Length(), 1); reconstruction.AddObservation(point3D_id, TrackElement(1, 1)); BOOST_CHECK_EQUAL(reconstruction.Image(1).NumPoints3D(), 2); BOOST_CHECK(reconstruction.Image(1).Point2D(0).HasPoint3D()); BOOST_CHECK(reconstruction.Image(1).Point2D(1).HasPoint3D()); BOOST_CHECK_EQUAL(reconstruction.Point3D(point3D_id).Track().Length(), 2); } BOOST_AUTO_TEST_CASE(TestMergePoints3D) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d(0, 0, 0), Track()); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id1, TrackElement(2, 0)); reconstruction.Point3D(point3D_id1).Color() = Eigen::Matrix(0, 0, 0); const point3D_t point3D_id2 = reconstruction.AddPoint3D(Eigen::Vector3d(1, 1, 1), Track()); reconstruction.AddObservation(point3D_id2, TrackElement(1, 1)); reconstruction.AddObservation(point3D_id2, TrackElement(2, 1)); reconstruction.Point3D(point3D_id2).Color() = Eigen::Matrix(20, 20, 20); const point3D_t merged_point3D_id = reconstruction.MergePoints3D(point3D_id1, point3D_id2); BOOST_CHECK(!reconstruction.ExistsPoint3D(point3D_id1)); BOOST_CHECK(!reconstruction.ExistsPoint3D(point3D_id2)); BOOST_CHECK(reconstruction.ExistsPoint3D(merged_point3D_id)); BOOST_CHECK_EQUAL(reconstruction.Image(1).Point2D(0).Point3DId(), merged_point3D_id); BOOST_CHECK_EQUAL(reconstruction.Image(1).Point2D(1).Point3DId(), merged_point3D_id); BOOST_CHECK_EQUAL(reconstruction.Image(2).Point2D(0).Point3DId(), merged_point3D_id); BOOST_CHECK_EQUAL(reconstruction.Image(2).Point2D(1).Point3DId(), merged_point3D_id); BOOST_CHECK(reconstruction.Point3D(merged_point3D_id) .XYZ() .isApprox(Eigen::Vector3d(0.5, 0.5, 0.5))); BOOST_CHECK_EQUAL(reconstruction.Point3D(merged_point3D_id).Color(), Eigen::Vector3ub(10, 10, 10)); } BOOST_AUTO_TEST_CASE(TestDeletePoint3D) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(1, &reconstruction, &scene_graph); const point3D_t point3D_id = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); reconstruction.AddObservation(point3D_id, TrackElement(1, 0)); reconstruction.DeletePoint3D(point3D_id); BOOST_CHECK(!reconstruction.ExistsPoint3D(point3D_id)); BOOST_CHECK_EQUAL(reconstruction.Image(1).NumPoints3D(), 0); } BOOST_AUTO_TEST_CASE(TestDeleteObservation) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); const point3D_t point3D_id = reconstruction.AddPoint3D(Eigen::Vector3d(0, 0, 0), Track()); reconstruction.AddObservation(point3D_id, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id, TrackElement(1, 1)); reconstruction.AddObservation(point3D_id, TrackElement(1, 2)); reconstruction.DeleteObservation(1, 0); BOOST_CHECK_EQUAL(reconstruction.Point3D(point3D_id).Track().Length(), 2); BOOST_CHECK(!reconstruction.Image(point3D_id).Point2D(0).HasPoint3D()); reconstruction.DeleteObservation(1, 1); BOOST_CHECK(!reconstruction.ExistsPoint3D(point3D_id)); BOOST_CHECK(!reconstruction.Image(point3D_id).Point2D(1).HasPoint3D()); BOOST_CHECK(!reconstruction.Image(point3D_id).Point2D(2).HasPoint3D()); } BOOST_AUTO_TEST_CASE(TestRegisterImage) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(1, &reconstruction, &scene_graph); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 1); BOOST_CHECK_EQUAL(reconstruction.Image(1).IsRegistered(), true); BOOST_CHECK(reconstruction.IsImageRegistered(1)); reconstruction.RegisterImage(1); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 1); BOOST_CHECK_EQUAL(reconstruction.Image(1).IsRegistered(), true); BOOST_CHECK(reconstruction.IsImageRegistered(1)); reconstruction.DeRegisterImage(1); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 0); BOOST_CHECK_EQUAL(reconstruction.Image(1).IsRegistered(), false); BOOST_CHECK(!reconstruction.IsImageRegistered(1)); } BOOST_AUTO_TEST_CASE(TestNormalize) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(3, &reconstruction, &scene_graph); reconstruction.Image(1).Tvec(2) = -10.0; reconstruction.Image(2).Tvec(2) = 0.0; reconstruction.Image(3).Tvec(2) = 10.0; reconstruction.DeRegisterImage(1); reconstruction.DeRegisterImage(2); reconstruction.DeRegisterImage(3); reconstruction.Normalize(); BOOST_CHECK_LT(std::abs(reconstruction.Image(1).Tvec(2) + 10), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(2).Tvec(2)), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(3).Tvec(2) - 10), 1e-6); reconstruction.RegisterImage(1); reconstruction.RegisterImage(2); reconstruction.RegisterImage(3); reconstruction.Normalize(); BOOST_CHECK_LT(std::abs(reconstruction.Image(1).Tvec(2) + 5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(2).Tvec(2)), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(3).Tvec(2) - 5), 1e-6); reconstruction.Normalize(5); BOOST_CHECK_LT(std::abs(reconstruction.Image(1).Tvec(2) + 2.5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(2).Tvec(2)), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(3).Tvec(2) - 2.5), 1e-6); reconstruction.Normalize(10, 0.0, 1.0); BOOST_CHECK_LT(std::abs(reconstruction.Image(1).Tvec(2) + 5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(2).Tvec(2)), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(3).Tvec(2) - 5), 1e-6); reconstruction.Normalize(20); Image image; image.SetImageId(4); reconstruction.AddImage(image); reconstruction.RegisterImage(4); image.SetImageId(5); reconstruction.AddImage(image); reconstruction.RegisterImage(5); image.SetImageId(6); reconstruction.AddImage(image); reconstruction.RegisterImage(6); image.SetImageId(7); reconstruction.AddImage(image); reconstruction.RegisterImage(7); reconstruction.Image(4).Tvec(2) = -7.5; reconstruction.Image(5).Tvec(2) = -5.0; reconstruction.Image(6).Tvec(2) = 5.0; reconstruction.Image(7).Tvec(2) = 7.5; reconstruction.RegisterImage(7); reconstruction.Normalize(10, 0.0, 1.0); BOOST_CHECK_LT(std::abs(reconstruction.Image(1).Tvec(2) + 5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(2).Tvec(2)), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(3).Tvec(2) - 5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(4).Tvec(2) + 3.75), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(5).Tvec(2) + 2.5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(6).Tvec(2) - 2.5), 1e-6); BOOST_CHECK_LT(std::abs(reconstruction.Image(7).Tvec(2) - 3.75), 1e-6); } BOOST_AUTO_TEST_CASE(TestTransform) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(3, &reconstruction, &scene_graph); const point3D_t point3D_id = reconstruction.AddPoint3D(Eigen::Vector3d(1, 1, 1), Track()); reconstruction.AddObservation(point3D_id, TrackElement(1, 1)); reconstruction.AddObservation(point3D_id, TrackElement(2, 1)); reconstruction.Transform(2, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 1, 2)); BOOST_CHECK_EQUAL(reconstruction.Image(1).ProjectionCenter(), Eigen::Vector3d(0, 1, 2)); BOOST_CHECK_EQUAL(reconstruction.Point3D(point3D_id).XYZ(), Eigen::Vector3d(2, 3, 4)); } BOOST_AUTO_TEST_CASE(TestFindImageWithName) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); BOOST_CHECK_EQUAL(reconstruction.FindImageWithName("image1"), &reconstruction.Image(1)); BOOST_CHECK_EQUAL(reconstruction.FindImageWithName("image2"), &reconstruction.Image(2)); BOOST_CHECK(reconstruction.FindImageWithName("image3") == nullptr); } BOOST_AUTO_TEST_CASE(TestFilterPoints3D) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3D(0.0, 0.0, std::unordered_set{}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3D(0.0, 0.0, std::unordered_set{point3D_id1 + 1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3D(0.0, 0.0, std::unordered_set{point3D_id1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id2 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); reconstruction.AddObservation(point3D_id2, TrackElement(1, 0)); reconstruction.FilterPoints3D(0.0, 0.0, std::unordered_set{point3D_id2}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id3 = reconstruction.AddPoint3D(Eigen::Vector3d(-0.5, -0.5, 1), Track()); reconstruction.AddObservation(point3D_id3, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id3, TrackElement(2, 0)); reconstruction.FilterPoints3D(0.0, 0.0, std::unordered_set{point3D_id3}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3D(0.0, 1e-3, std::unordered_set{point3D_id3}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id4 = reconstruction.AddPoint3D(Eigen::Vector3d(-0.6, -0.5, 1), Track()); reconstruction.AddObservation(point3D_id4, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id4, TrackElement(2, 0)); reconstruction.FilterPoints3D(0.1, 0.0, std::unordered_set{point3D_id4}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3D(0.09, 0.0, std::unordered_set{point3D_id4}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); } BOOST_AUTO_TEST_CASE(TestFilterPoints3DInImages) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3DInImages(0.0, 0.0, std::unordered_set{}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3DInImages(0.0, 0.0, std::unordered_set{1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); reconstruction.FilterPoints3DInImages(0.0, 0.0, std::unordered_set{2}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3DInImages(0.0, 0.0, std::unordered_set{1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id3 = reconstruction.AddPoint3D(Eigen::Vector3d(-0.5, -0.5, 1), Track()); reconstruction.AddObservation(point3D_id3, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id3, TrackElement(2, 0)); reconstruction.FilterPoints3DInImages(0.0, 0.0, std::unordered_set{1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3DInImages(0.0, 1e-3, std::unordered_set{1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id4 = reconstruction.AddPoint3D(Eigen::Vector3d(-0.6, -0.5, 1), Track()); reconstruction.AddObservation(point3D_id4, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id4, TrackElement(2, 0)); reconstruction.FilterPoints3DInImages(0.1, 0.0, std::unordered_set{1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterPoints3DInImages(0.09, 0.0, std::unordered_set{1}); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); } BOOST_AUTO_TEST_CASE(TestFilterAllPoints) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterAllPoints3D(0.0, 0.0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id2 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); reconstruction.AddObservation(point3D_id2, TrackElement(1, 0)); reconstruction.FilterAllPoints3D(0.0, 0.0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id3 = reconstruction.AddPoint3D(Eigen::Vector3d(-0.5, -0.5, 1), Track()); reconstruction.AddObservation(point3D_id3, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id3, TrackElement(2, 0)); reconstruction.FilterAllPoints3D(0.0, 0.0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterAllPoints3D(0.0, 1e-3); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); const point3D_t point3D_id4 = reconstruction.AddPoint3D(Eigen::Vector3d(-0.6, -0.5, 1), Track()); reconstruction.AddObservation(point3D_id4, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id4, TrackElement(2, 0)); reconstruction.FilterAllPoints3D(0.1, 0.0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterAllPoints3D(0.09, 0.0); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); } BOOST_AUTO_TEST_CASE(TestFilterObservationsWithNegativeDepth) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d(0, 0, 1), Track()); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.FilterObservationsWithNegativeDepth(); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.Point3D(point3D_id1).XYZ(2) = 0.001; reconstruction.FilterObservationsWithNegativeDepth(); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.Point3D(point3D_id1).XYZ(2) = 0.0; reconstruction.FilterObservationsWithNegativeDepth(); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); reconstruction.Point3D(point3D_id1).XYZ(2) = 0.001; reconstruction.FilterObservationsWithNegativeDepth(); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 1); reconstruction.Point3D(point3D_id1).XYZ(2) = 0.0; reconstruction.FilterObservationsWithNegativeDepth(); BOOST_CHECK_EQUAL(reconstruction.NumPoints3D(), 0); } BOOST_AUTO_TEST_CASE(TestFilterImages) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(4, &reconstruction, &scene_graph); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); reconstruction.AddObservation(point3D_id1, TrackElement(2, 0)); reconstruction.AddObservation(point3D_id1, TrackElement(3, 0)); reconstruction.FilterImages(0.0, 10.0, 1.0); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 3); reconstruction.DeleteObservation(3, 0); reconstruction.FilterImages(0.0, 10.0, 1.0); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 2); reconstruction.FilterImages(0.0, 0.9, 1.0); BOOST_CHECK_EQUAL(reconstruction.NumRegImages(), 0); } BOOST_AUTO_TEST_CASE(TestComputeNumObservations) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.ComputeNumObservations(), 0); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); BOOST_CHECK_EQUAL(reconstruction.ComputeNumObservations(), 1); reconstruction.AddObservation(point3D_id1, TrackElement(1, 1)); BOOST_CHECK_EQUAL(reconstruction.ComputeNumObservations(), 2); reconstruction.AddObservation(point3D_id1, TrackElement(2, 0)); BOOST_CHECK_EQUAL(reconstruction.ComputeNumObservations(), 3); } BOOST_AUTO_TEST_CASE(TestComputeMeanTrackLength) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanTrackLength(), 0); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanTrackLength(), 0); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanTrackLength(), 1); reconstruction.AddObservation(point3D_id1, TrackElement(1, 1)); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanTrackLength(), 2); reconstruction.AddObservation(point3D_id1, TrackElement(2, 0)); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanTrackLength(), 3); } BOOST_AUTO_TEST_CASE(TestComputeMeanObservationsPerRegImage) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanObservationsPerRegImage(), 0); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanObservationsPerRegImage(), 0); reconstruction.AddObservation(point3D_id1, TrackElement(1, 0)); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanObservationsPerRegImage(), 0.5); reconstruction.AddObservation(point3D_id1, TrackElement(1, 1)); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanObservationsPerRegImage(), 1.0); reconstruction.AddObservation(point3D_id1, TrackElement(2, 0)); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanObservationsPerRegImage(), 1.5); } BOOST_AUTO_TEST_CASE(TestComputeMeanReprojectionError) { Reconstruction reconstruction; SceneGraph scene_graph; GenerateReconstruction(2, &reconstruction, &scene_graph); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanReprojectionError(), 0); const point3D_t point3D_id1 = reconstruction.AddPoint3D(Eigen::Vector3d::Random(), Track()); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanReprojectionError(), 0); reconstruction.Point3D(point3D_id1).SetError(0.0); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanReprojectionError(), 0); reconstruction.Point3D(point3D_id1).SetError(1.0); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanReprojectionError(), 1); reconstruction.Point3D(point3D_id1).SetError(2.0); BOOST_CHECK_EQUAL(reconstruction.ComputeMeanReprojectionError(), 2.0); } colmap-3.4/src/base/scene_clustering.cc000066400000000000000000000144551323400541200202020ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/scene_clustering.h" #include #include "base/database.h" #include "base/graph_cut.h" #include "util/random.h" namespace colmap { bool SceneClustering::Options::Check() const { CHECK_OPTION_GT(branching, 0); CHECK_OPTION_GE(image_overlap, 0); return true; } SceneClustering::SceneClustering(const Options& options) : options_(options) { CHECK(options_.Check()); } void SceneClustering::Partition( const std::vector>& image_pairs, const std::vector& num_inliers) { CHECK(!root_cluster_); CHECK_EQ(image_pairs.size(), num_inliers.size()); std::set image_ids; std::vector> edges; edges.reserve(image_pairs.size()); for (const auto& image_pair : image_pairs) { image_ids.insert(image_pair.first); image_ids.insert(image_pair.second); edges.emplace_back(image_pair.first, image_pair.second); } root_cluster_.reset(new Cluster()); root_cluster_->image_ids.insert(root_cluster_->image_ids.end(), image_ids.begin(), image_ids.end()); PartitionCluster(edges, num_inliers, root_cluster_.get()); } void SceneClustering::PartitionCluster( const std::vector>& edges, const std::vector& weights, Cluster* cluster) { CHECK_EQ(edges.size(), weights.size()); // If the cluster is small enough, we return from the recursive clustering. if (edges.size() == 0 || cluster->image_ids.size() <= static_cast(options_.leaf_max_num_images)) { return; } // Partition the cluster using a normalized cut on the scene graph. const auto labels = ComputeNormalizedMinGraphCut(edges, weights, options_.branching); // Assign the images to the clustered child clusters. cluster->child_clusters.resize(options_.branching); for (const auto image_id : cluster->image_ids) { if (labels.count(image_id)) { auto& child_cluster = cluster->child_clusters.at(labels.at(image_id)); child_cluster.image_ids.push_back(image_id); } } // Collect the edges based on whether they are inter or intra child clusters. std::vector>> child_edges(options_.branching); std::vector> child_weights(options_.branching); std::vector, int>>> overlapping_edges(options_.branching); for (size_t i = 0; i < edges.size(); ++i) { const int label1 = labels.at(edges[i].first); const int label2 = labels.at(edges[i].second); if (label1 == label2) { child_edges.at(label1).push_back(edges[i]); child_weights.at(label1).push_back(weights[i]); } else { overlapping_edges.at(label1).emplace_back(edges[i], weights[i]); overlapping_edges.at(label2).emplace_back(edges[i], weights[i]); } } // Recursively partition all the child clusters. for (int i = 0; i < options_.branching; ++i) { PartitionCluster(child_edges[i], child_weights[i], &cluster->child_clusters[i]); } if (options_.image_overlap > 0) { for (int i = 0; i < options_.branching; ++i) { // Sort the overlapping edges by the number of inlier matches, such // that we add overlapping images with many common observations. std::sort(overlapping_edges[i].begin(), overlapping_edges[i].end(), [](const std::pair, int>& edge1, const std::pair, int>& edge2) { return edge1.second > edge2.second; }); // Select overlapping edges at random and add image to cluster. std::set overlapping_image_ids; for (const auto& edge : overlapping_edges[i]) { if (labels.at(edge.first.first) == i) { overlapping_image_ids.insert(edge.first.second); } else { overlapping_image_ids.insert(edge.first.first); } if (overlapping_image_ids.size() >= static_cast(options_.image_overlap)) { break; } } // Recursively append the overlapping images to cluster and its children. std::function InsertOverlappingImageIds = [&](Cluster* cluster) { cluster->image_ids.insert(cluster->image_ids.end(), overlapping_image_ids.begin(), overlapping_image_ids.end()); for (auto& child_cluster : cluster->child_clusters) { InsertOverlappingImageIds(&child_cluster); } }; InsertOverlappingImageIds(&cluster->child_clusters[i]); } } } const SceneClustering::Cluster* SceneClustering::GetRootCluster() const { return root_cluster_.get(); } std::vector SceneClustering::GetLeafClusters() const { CHECK(root_cluster_); std::vector leaf_clusters; if (!root_cluster_) { return leaf_clusters; } else if (root_cluster_->child_clusters.empty()) { leaf_clusters.push_back(root_cluster_.get()); return leaf_clusters; } std::vector non_leaf_clusters; non_leaf_clusters.push_back(root_cluster_.get()); while (!non_leaf_clusters.empty()) { const auto cluster = non_leaf_clusters.back(); non_leaf_clusters.pop_back(); for (const auto& child_cluster : cluster->child_clusters) { if (child_cluster.child_clusters.empty()) { leaf_clusters.push_back(&child_cluster); } else { non_leaf_clusters.push_back(&child_cluster); } } } return leaf_clusters; } } // namespace colmap colmap-3.4/src/base/scene_clustering.h000066400000000000000000000045341323400541200200410ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_SCENE_CLUSTERING_H_ #define COLMAP_SRC_BASE_SCENE_CLUSTERING_H_ #include #include #include "util/types.h" namespace colmap { // Scene clustering approach using normalized cuts on the scene graph. The scene // is hierarchically partitioned into overlapping clusters until a maximum // number of images is in a leaf node. class SceneClustering { public: struct Options { // The branching factor of the hierarchical clustering. int branching = 2; // The number of overlapping images between child clusters. int image_overlap = 50; // The maximum number of images in a leaf node cluster, otherwise the // cluster is further partitioned using the given branching factor. Note // that a cluster leaf node will have at most `leaf_max_num_images + // overlap` images to satisfy the overlap constraint. int leaf_max_num_images = 500; bool Check() const; }; struct Cluster { std::vector image_ids; std::vector child_clusters; }; SceneClustering(const Options& options); void Partition(const std::vector>& image_pairs, const std::vector& num_inliers); const Cluster* GetRootCluster() const; std::vector GetLeafClusters() const; private: void PartitionCluster(const std::vector>& edges, const std::vector& weights, Cluster* cluster); const Options options_; std::unique_ptr root_cluster_; }; } // namespace colmap #endif // COLMAP_SRC_BASE_SCENE_CLUSTERING_H_ colmap-3.4/src/base/scene_clustering_test.cc000066400000000000000000000226051323400541200212350ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/scene_clustering" #include "util/testing.h" #include #include "base/database.h" #include "base/scene_clustering.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEmpty) { const std::vector> image_pairs; const std::vector num_inliers; SceneClustering::Options options; options.branching = 2; options.image_overlap = 0; options.leaf_max_num_images = 2; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->child_clusters.size(), 0); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 1); } BOOST_AUTO_TEST_CASE(TestOneLevel) { const std::vector> image_pairs = {{0, 1}}; const std::vector num_inliers = {10}; SceneClustering::Options options; options.branching = 2; options.image_overlap = 0; options.leaf_max_num_images = 2; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[0], 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[1], 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->child_clusters.size(), 0); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster(), scene_clustering.GetLeafClusters()[0]); } BOOST_AUTO_TEST_CASE(TestTwoLevels) { const std::vector> image_pairs = {{0, 1}}; const std::vector num_inliers = {10}; SceneClustering::Options options; options.branching = 2; options.image_overlap = 0; options.leaf_max_num_images = 1; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[0], 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[1], 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->child_clusters.size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[0]->image_ids[0], 1); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[1]->image_ids[0], 0); } BOOST_AUTO_TEST_CASE(TestThreeLevels) { const std::vector> image_pairs = {{0, 1}, {0, 2}}; const std::vector num_inliers = {10, 11}; SceneClustering::Options options; options.branching = 2; options.image_overlap = 0; options.leaf_max_num_images = 1; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 3); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[0], 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[1], 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[2], 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 3); std::set image_ids; image_ids.insert(scene_clustering.GetLeafClusters()[0]->image_ids[0]); image_ids.insert(scene_clustering.GetLeafClusters()[1]->image_ids[0]); image_ids.insert(scene_clustering.GetLeafClusters()[2]->image_ids[0]); BOOST_CHECK_EQUAL(image_ids.size(), 3); BOOST_CHECK(image_ids.count(0)); BOOST_CHECK(image_ids.count(1)); BOOST_CHECK(image_ids.count(2)); } BOOST_AUTO_TEST_CASE(TestThreeLevelsMultipleImages) { const std::vector> image_pairs = {{0, 1}, {0, 2}}; const std::vector num_inliers = {10, 11}; SceneClustering::Options options; options.branching = 2; options.image_overlap = 0; options.leaf_max_num_images = 2; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 3); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[0], 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[1], 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[2], 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[0]->image_ids.size(), 1); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[1]->image_ids.size(), 2); std::set image_ids; image_ids.insert(scene_clustering.GetLeafClusters()[0]->image_ids[0]); image_ids.insert(scene_clustering.GetLeafClusters()[1]->image_ids[0]); image_ids.insert(scene_clustering.GetLeafClusters()[1]->image_ids[1]); BOOST_CHECK_EQUAL(image_ids.size(), 3); BOOST_CHECK(image_ids.count(0)); BOOST_CHECK(image_ids.count(1)); BOOST_CHECK(image_ids.count(2)); } BOOST_AUTO_TEST_CASE(TestOneOverlap) { const std::vector> image_pairs = { {0, 1}, {0, 2}, {1, 2}, {0, 3}, {1, 3}, {2, 3}}; const std::vector num_inliers = {10, 11, 12, 13, 14, 15}; SceneClustering::Options options; options.branching = 2; options.image_overlap = 1; options.leaf_max_num_images = 3; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 4); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[0], 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[1], 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[2], 2); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[3], 3); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[0]->image_ids.size(), 3); const std::set image_ids0( scene_clustering.GetLeafClusters()[0]->image_ids.begin(), scene_clustering.GetLeafClusters()[0]->image_ids.end()); BOOST_CHECK(image_ids0.count(0)); BOOST_CHECK(image_ids0.count(1) || image_ids0.count(2)); BOOST_CHECK(image_ids0.count(3)); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[1]->image_ids.size(), 3); const std::set image_ids1( scene_clustering.GetLeafClusters()[1]->image_ids.begin(), scene_clustering.GetLeafClusters()[1]->image_ids.end()); BOOST_CHECK(image_ids1.count(1)); BOOST_CHECK(image_ids0.count(0) || image_ids0.count(2)); BOOST_CHECK(image_ids1.count(3)); } BOOST_AUTO_TEST_CASE(TestTwoOverlap) { const std::vector> image_pairs = { {0, 1}, {0, 2}, {1, 2}, {0, 3}, {1, 3}, {2, 3}}; const std::vector num_inliers = {10, 11, 12, 13, 14, 15}; SceneClustering::Options options; options.branching = 2; options.image_overlap = 2; options.leaf_max_num_images = 2; SceneClustering scene_clustering(options); BOOST_CHECK(scene_clustering.GetRootCluster() == nullptr); scene_clustering.Partition(image_pairs, num_inliers); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids.size(), 4); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[0], 0); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[1], 1); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[2], 2); BOOST_CHECK_EQUAL(scene_clustering.GetRootCluster()->image_ids[3], 3); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters().size(), 2); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[0]->image_ids.size(), 4); const std::set image_ids0( scene_clustering.GetLeafClusters()[0]->image_ids.begin(), scene_clustering.GetLeafClusters()[0]->image_ids.end()); BOOST_CHECK(image_ids0.count(0)); BOOST_CHECK(image_ids0.count(1)); BOOST_CHECK(image_ids0.count(2)); BOOST_CHECK(image_ids0.count(3)); BOOST_CHECK_EQUAL(scene_clustering.GetLeafClusters()[1]->image_ids.size(), 4); const std::set image_ids1( scene_clustering.GetLeafClusters()[1]->image_ids.begin(), scene_clustering.GetLeafClusters()[1]->image_ids.end()); BOOST_CHECK(image_ids1.count(0)); BOOST_CHECK(image_ids1.count(1)); BOOST_CHECK(image_ids1.count(2)); BOOST_CHECK(image_ids1.count(3)); } colmap-3.4/src/base/scene_graph.cc000077500000000000000000000176111323400541200171240ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/scene_graph.h" #include #include "util/string.h" namespace colmap { SceneGraph::SceneGraph() {} void SceneGraph::Finalize() { for (auto it = images_.begin(); it != images_.end();) { it->second.num_observations = 0; for (auto& corr : it->second.corrs) { corr.shrink_to_fit(); if (corr.size() > 0) { it->second.num_observations += 1; } } if (it->second.num_observations == 0) { images_.erase(it++); } else { ++it; } } } void SceneGraph::AddImage(const image_t image_id, const size_t num_points) { CHECK(!ExistsImage(image_id)); images_[image_id].corrs.resize(num_points); } void SceneGraph::AddCorrespondences(const image_t image_id1, const image_t image_id2, const FeatureMatches& matches) { // Avoid self-matches - should only happen, if user provides custom matches. if (image_id1 == image_id2) { std::cout << "WARNING: Cannot use self-matches for image_id=" << image_id1 << std::endl; return; } // Corresponding images. struct Image& image1 = images_.at(image_id1); struct Image& image2 = images_.at(image_id2); // Store number of correspondences for each image to find good initial pair. image1.num_correspondences += matches.size(); image2.num_correspondences += matches.size(); const image_pair_t pair_id = Database::ImagePairToPairId(image_id1, image_id2); point2D_t& num_correspondences = image_pairs_[pair_id]; num_correspondences += static_cast(matches.size()); // Store all matches in correspondence graph data structure. This data- // structure uses more memory than storing the raw match matrices, but is // significantly more efficient when updating the correspondences in case an // observation is triangulated. for (size_t i = 0; i < matches.size(); ++i) { const point2D_t point2D_idx1 = matches[i].point2D_idx1; const point2D_t point2D_idx2 = matches[i].point2D_idx2; const bool valid_idx1 = point2D_idx1 < image1.corrs.size(); const bool valid_idx2 = point2D_idx2 < image2.corrs.size(); if (valid_idx1 && valid_idx2) { auto& corrs1 = image1.corrs[point2D_idx1]; auto& corrs2 = image2.corrs[point2D_idx2]; const bool duplicate1 = std::find_if(corrs1.begin(), corrs1.end(), [image_id2](const Correspondence& corr) { return corr.image_id == image_id2; }) != corrs1.end(); const bool duplicate2 = std::find_if(corrs2.begin(), corrs2.end(), [image_id1](const Correspondence& corr) { return corr.image_id == image_id1; }) != corrs2.end(); if (duplicate1 || duplicate2) { image1.num_correspondences -= 1; image2.num_correspondences -= 1; num_correspondences -= 1; std::cout << StringPrintf( "WARNING: Duplicate correspondence between " "point2D_idx=%d in image_id=%d and point2D_idx=%d in " "image_id=%d", point2D_idx1, image_id1, point2D_idx2, image_id2) << std::endl; } else { corrs1.emplace_back(image_id2, point2D_idx2); corrs2.emplace_back(image_id1, point2D_idx1); } } else { image1.num_correspondences -= 1; image2.num_correspondences -= 1; num_correspondences -= 1; if (!valid_idx1) { std::cout << StringPrintf( "WARNING: point2D_idx=%d in image_id=%d does not exist", point2D_idx1, image_id1) << std::endl; } if (!valid_idx2) { std::cout << StringPrintf( "WARNING: point2D_idx=%d in image_id=%d does not exist", point2D_idx2, image_id2) << std::endl; } } } } std::vector SceneGraph::FindTransitiveCorrespondences(const image_t image_id, const point2D_t point2D_idx, const size_t transitivity) const { if (transitivity == 1) { return FindCorrespondences(image_id, point2D_idx); } std::vector found_corrs; if (!HasCorrespondences(image_id, point2D_idx)) { return found_corrs; } found_corrs.emplace_back(image_id, point2D_idx); std::unordered_map> image_corrs; image_corrs[image_id].insert(point2D_idx); size_t corr_queue_begin = 0; size_t corr_queue_end = found_corrs.size(); for (size_t t = 0; t < transitivity; ++t) { // Collect correspondences at transitive level t to all // correspondences that were collected at transitive level t - 1. for (size_t i = corr_queue_begin; i < corr_queue_end; ++i) { const Correspondence ref_corr = found_corrs[i]; const Image& image = images_.at(ref_corr.image_id); const std::vector& ref_corrs = image.corrs[ref_corr.point2D_idx]; for (const Correspondence corr : ref_corrs) { // Check if correspondence already collected, otherwise collect. auto& corr_image_corrs = image_corrs[corr.image_id]; if (corr_image_corrs.count(corr.point2D_idx) == 0) { corr_image_corrs.insert(corr.point2D_idx); found_corrs.emplace_back(corr.image_id, corr.point2D_idx); } } } // Move on to the next block of correspondences at next transitive level. corr_queue_begin = corr_queue_end; corr_queue_end = found_corrs.size(); // No new correspondences collected in last transitivity level. if (corr_queue_begin == corr_queue_end) { break; } } // Remove first element, which is the given observation by swapping it // with the last collected correspondence. if (found_corrs.size() > 1) { found_corrs.front() = found_corrs.back(); } found_corrs.pop_back(); return found_corrs; } std::vector> SceneGraph::FindCorrespondencesBetweenImages(const image_t image_id1, const image_t image_id2) const { std::vector> found_corrs; const struct Image& image1 = images_.at(image_id1); for (point2D_t point2D_idx1 = 0; point2D_idx1 < image1.corrs.size(); ++point2D_idx1) { for (const Correspondence& corr1 : image1.corrs[point2D_idx1]) { if (corr1.image_id == image_id2) { found_corrs.emplace_back(point2D_idx1, corr1.point2D_idx); } } } return found_corrs; } bool SceneGraph::IsTwoViewObservation(const image_t image_id, const point2D_t point2D_idx) const { const struct Image& image = images_.at(image_id); const std::vector& corrs = image.corrs.at(point2D_idx); if (corrs.size() != 1) { return false; } const struct Image& other_image = images_.at(corrs[0].image_id); const std::vector& other_corrs = other_image.corrs.at(corrs[0].point2D_idx); return other_corrs.size() == 1; } } // namespace colmap colmap-3.4/src/base/scene_graph.h000077500000000000000000000156351323400541200167720ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_SCENE_GRAPH_H_ #define COLMAP_SRC_BASE_SCENE_GRAPH_H_ #include #include #include "base/database.h" #include "util/types.h" namespace colmap { // Scene graph represents the graph of image to image and feature to feature // correspondences of a dataset. It should be accessed from the DatabaseCache. class SceneGraph { public: struct Correspondence { Correspondence() : image_id(kInvalidImageId), point2D_idx(kInvalidPoint2DIdx) {} Correspondence(const image_t image_id, const point2D_t point2D_idx) : image_id(image_id), point2D_idx(point2D_idx) {} // The identifier of the corresponding image. image_t image_id; // The index of the corresponding point in the corresponding image. point2D_t point2D_idx; }; SceneGraph(); // Number of added images. inline size_t NumImages() const; // Check whether image exists. inline bool ExistsImage(const image_t image_id) const; // Get the number of observations in an image. An observation is an image // point that has at least one correspondence. inline point2D_t NumObservationsForImage(const image_t image_id) const; // Get the number of correspondences per image. inline point2D_t NumCorrespondencesForImage(const image_t image_id) const; // Get the number of correspondences between a pair of images. inline point2D_t NumCorrespondencesBetweenImages( const image_t image_id1, const image_t image_id2) const; // Get the number of correspondences between all images. inline const std::unordered_map& NumCorrespondencesBetweenImages() const; // Finalize the database manager. // // - Calculates the number of observations per image by counting the number // of image points that have at least one correspondence. // - Deletes images without observations, as they are useless for SfM. // - Shrinks the correspondence vectors to their size to save memory. void Finalize(); // Add new image to the scene graph. void AddImage(const image_t image_id, const size_t num_points2D); // Add matches between images. This function ignores invalid correspondences // where the point indices are out of bounds or duplicate correspondences // between the same image points. Whenever either of the two cases occur // this function prints a warning to the standard output. void AddCorrespondences(const image_t image_id1, const image_t image_id2, const FeatureMatches& matches); // Find the correspondence of an image point to any other image. inline const std::vector& FindCorrespondences( const image_t image_id, const point2D_t point2D_idx) const; // Find correspondences to the given observation. // // Transitively collects correspondences to the given observation by first // finding correspondences to the given observation, then looking for // correspondences to the collected correspondences in the first step, and so // forth until the transitivity is exhausted or no more correspondences are // found. The returned list does not contain duplicates and contains // the given observation. std::vector FindTransitiveCorrespondences( const image_t image_id, const point2D_t point2D_idx, const size_t transitivity) const; // Find all correspondences between two images. std::vector> FindCorrespondencesBetweenImages( const image_t image_id1, const image_t image_id2) const; // Check whether the image point has correspondences. inline bool HasCorrespondences(const image_t image_id, const point2D_t point2D_idx) const; // Check whether the given observation is part of a two-view track, i.e. // it only has one correspondence and that correspondence has the given // observation as its only correspondence. bool IsTwoViewObservation(const image_t image_id, const point2D_t point2D_idx) const; private: struct Image { // Number of 2D points with at least one correspondence to another image. point2D_t num_observations = 0; // Total number of correspondences to other images. This measure is useful // to find a good initial pair, that is connected to many images. point2D_t num_correspondences = 0; // Correspondences to other images per image point. std::vector> corrs; }; // The nodes of the scene graph are images. EIGEN_STL_UMAP(image_t, Image) images_; // The number of correspondences between pairs of images. std::unordered_map image_pairs_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// size_t SceneGraph::NumImages() const { return images_.size(); } bool SceneGraph::ExistsImage(const image_t image_id) const { return images_.find(image_id) != images_.end(); } point2D_t SceneGraph::NumObservationsForImage(const image_t image_id) const { return images_.at(image_id).num_observations; } point2D_t SceneGraph::NumCorrespondencesForImage(const image_t image_id) const { return images_.at(image_id).num_correspondences; } point2D_t SceneGraph::NumCorrespondencesBetweenImages( const image_t image_id1, const image_t image_id2) const { const image_pair_t pair_id = Database::ImagePairToPairId(image_id1, image_id2); const auto it = image_pairs_.find(pair_id); if (it == image_pairs_.end()) { return 0; } else { return static_cast(it->second); } } inline const std::unordered_map& SceneGraph::NumCorrespondencesBetweenImages() const { return image_pairs_; } const std::vector& SceneGraph::FindCorrespondences( const image_t image_id, const point2D_t point2D_idx) const { return images_.at(image_id).corrs.at(point2D_idx); } bool SceneGraph::HasCorrespondences(const image_t image_id, const point2D_t point2D_idx) const { return !images_.at(image_id).corrs.at(point2D_idx).empty(); } } // namespace colmap #endif // COLMAP_SRC_BASE_SCENE_GRAPH_H_ colmap-3.4/src/base/scene_graph_test.cc000077500000000000000000000377471323400541200201770ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/scene_graph" #include "util/testing.h" #include "base/scene_graph.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDefault) { SceneGraph scene_graph; BOOST_CHECK_EQUAL(scene_graph.NumImages(), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().size(), 0); } BOOST_AUTO_TEST_CASE(TestTwoView) { SceneGraph scene_graph; scene_graph.AddImage(0, 10); scene_graph.AddImage(1, 10); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(0), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(1), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(2), false); BOOST_CHECK_EQUAL(scene_graph.NumImages(), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().size(), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages(0, 1), 0); for (size_t i = 0; i < 10; ++i) { BOOST_CHECK(!scene_graph.HasCorrespondences(0, i)); BOOST_CHECK(!scene_graph.HasCorrespondences(1, i)); BOOST_CHECK(!scene_graph.IsTwoViewObservation(0, i)); BOOST_CHECK(!scene_graph.IsTwoViewObservation(1, i)); } FeatureMatches matches(4); matches[0].point2D_idx1 = 0; matches[0].point2D_idx2 = 0; matches[1].point2D_idx1 = 1; matches[1].point2D_idx2 = 2; matches[2].point2D_idx1 = 3; matches[2].point2D_idx2 = 7; matches[3].point2D_idx1 = 4; matches[3].point2D_idx2 = 8; scene_graph.AddCorrespondences(0, 1, matches); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 4); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 4); const image_pair_t pair_id = Database::ImagePairToPairId(0, 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().size(), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().at(pair_id), 4); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(0, 0)); BOOST_CHECK(scene_graph.IsTwoViewObservation(0, 0)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).at(0).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).at(0).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(1, 0)); BOOST_CHECK(scene_graph.IsTwoViewObservation(1, 0)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).at(0).image_id, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).at(0).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 1).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(0, 1)); BOOST_CHECK(scene_graph.IsTwoViewObservation(0, 1)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 1).at(0).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 1).at(0).point2D_idx, 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 2).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(1, 2)); BOOST_CHECK(scene_graph.IsTwoViewObservation(1, 2)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 2).at(0).image_id, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 2).at(0).point2D_idx, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 4).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(0, 3)); BOOST_CHECK(scene_graph.IsTwoViewObservation(0, 4)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 3).at(0).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 3).at(0).point2D_idx, 7); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 4).at(0).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 4).at(0).point2D_idx, 8); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 7).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(1, 7)); BOOST_CHECK(scene_graph.IsTwoViewObservation(1, 7)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 7).at(0).image_id, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 7).at(0).point2D_idx, 3); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 8).size(), 1); BOOST_CHECK(scene_graph.HasCorrespondences(1, 8)); BOOST_CHECK(scene_graph.IsTwoViewObservation(1, 8)); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 8).at(0).image_id, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 8).at(0).point2D_idx, 4); for (size_t i = 0; i < 10; ++i) { BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(0, i, 0).size(), 0); BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(0, i).size(), scene_graph.FindTransitiveCorrespondences(0, i, 1).size()); BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(0, i).size(), scene_graph.FindTransitiveCorrespondences(0, i, 2).size()); BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(1, i, 0).size(), 0); BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(1, i).size(), scene_graph.FindTransitiveCorrespondences(1, i, 1).size()); BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(1, i).size(), scene_graph.FindTransitiveCorrespondences(1, i, 2).size()); } const auto corrs01 = scene_graph.FindCorrespondencesBetweenImages(0, 1); const auto corrs10 = scene_graph.FindCorrespondencesBetweenImages(1, 0); BOOST_CHECK_EQUAL(corrs01.size(), matches.size()); BOOST_CHECK_EQUAL(corrs10.size(), matches.size()); for (size_t i = 0; i < corrs01.size(); ++i) { BOOST_CHECK_EQUAL(corrs01[i].first, corrs10[i].second); BOOST_CHECK_EQUAL(corrs01[i].second, corrs10[i].first); BOOST_CHECK_EQUAL(matches[i].point2D_idx1, corrs01[i].first); BOOST_CHECK_EQUAL(matches[i].point2D_idx2, corrs01[i].second); } scene_graph.Finalize(); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 4); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 4); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 4); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 4); } BOOST_AUTO_TEST_CASE(TestThreeView) { SceneGraph scene_graph; scene_graph.AddImage(0, 10); scene_graph.AddImage(1, 10); scene_graph.AddImage(2, 10); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(0), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(1), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(2), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(3), false); BOOST_CHECK_EQUAL(scene_graph.NumImages(), 3); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().size(), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(2), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(2), 0); for (size_t i = 0; i < 10; ++i) { BOOST_CHECK(!scene_graph.HasCorrespondences(0, i)); BOOST_CHECK(!scene_graph.HasCorrespondences(1, i)); BOOST_CHECK(!scene_graph.HasCorrespondences(2, i)); BOOST_CHECK(!scene_graph.IsTwoViewObservation(0, i)); BOOST_CHECK(!scene_graph.IsTwoViewObservation(1, i)); BOOST_CHECK(!scene_graph.IsTwoViewObservation(2, i)); } FeatureMatches matches01(1); matches01[0].point2D_idx1 = 0; matches01[0].point2D_idx2 = 0; scene_graph.AddCorrespondences(0, 1, matches01); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(2), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(2), 0); FeatureMatches matches02(1); matches02[0].point2D_idx1 = 0; matches02[0].point2D_idx2 = 0; scene_graph.AddCorrespondences(0, 2, matches02); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(2), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(2), 1); FeatureMatches matches12(2); matches12[0].point2D_idx1 = 0; matches12[0].point2D_idx2 = 0; matches12[1].point2D_idx1 = 5; matches12[1].point2D_idx2 = 5; scene_graph.AddCorrespondences(1, 2, matches12); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 0); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(2), 0); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 3); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(2), 3); const image_pair_t pair_id01 = Database::ImagePairToPairId(0, 1); const image_pair_t pair_id02 = Database::ImagePairToPairId(0, 2); const image_pair_t pair_id12 = Database::ImagePairToPairId(1, 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().size(), 3); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().at(pair_id01), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().at(pair_id02), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().at(pair_id12), 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).at(0).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).at(0).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).at(1).image_id, 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(0, 0).at(1).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).at(0).image_id, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).at(0).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).at(1).image_id, 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 0).at(1).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 0).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 0).at(0).image_id, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 0).at(0).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 0).at(1).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 0).at(1).point2D_idx, 0); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 5).size(), 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 5).at(0).image_id, 2); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(1, 5).at(0).point2D_idx, 5); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 5).size(), 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 5).at(0).image_id, 1); BOOST_CHECK_EQUAL(scene_graph.FindCorrespondences(2, 5).at(0).point2D_idx, 5); for (size_t i = 0; i < 10; ++i) { BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(0, i).size(), scene_graph.FindTransitiveCorrespondences(0, i, 1).size()); BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(1, i).size(), scene_graph.FindTransitiveCorrespondences(1, i, 1).size()); BOOST_CHECK_EQUAL( scene_graph.FindCorrespondences(2, i).size(), scene_graph.FindTransitiveCorrespondences(2, i, 1).size()); } BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(0, 0, 2).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(1, 0, 2).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(2, 0, 2).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(0, 0, 3).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(1, 0, 3).size(), 2); BOOST_CHECK_EQUAL(scene_graph.FindTransitiveCorrespondences(2, 0, 3).size(), 2); scene_graph.Finalize(); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 1); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 2); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(2), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 3); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(2), 3); scene_graph.AddImage(3, 10); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(0), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(1), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(2), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(3), true); BOOST_CHECK_EQUAL(scene_graph.NumImages(), 4); scene_graph.Finalize(); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(0), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(1), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(2), true); BOOST_CHECK_EQUAL(scene_graph.ExistsImage(3), false); BOOST_CHECK_EQUAL(scene_graph.NumImages(), 3); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(0), 1); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(1), 2); BOOST_CHECK_EQUAL(scene_graph.NumObservationsForImage(2), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 2); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 3); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(2), 3); } BOOST_AUTO_TEST_CASE(TestOutOfBounds) { SceneGraph scene_graph; scene_graph.AddImage(0, 10); scene_graph.AddImage(1, 4); FeatureMatches matches(3); matches[0].point2D_idx1 = 9; matches[0].point2D_idx2 = 3; matches[1].point2D_idx1 = 10; matches[1].point2D_idx2 = 3; matches[2].point2D_idx1 = 9; matches[2].point2D_idx2 = 4; scene_graph.AddCorrespondences(0, 1, matches); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 1); const image_pair_t pair_id = Database::ImagePairToPairId(0, 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().at(pair_id), 1); } BOOST_AUTO_TEST_CASE(TestDuplicate) { SceneGraph scene_graph; scene_graph.AddImage(0, 10); scene_graph.AddImage(1, 10); FeatureMatches matches(5); matches[0].point2D_idx1 = 0; matches[0].point2D_idx2 = 0; matches[1].point2D_idx1 = 1; matches[1].point2D_idx2 = 1; matches[2].point2D_idx1 = 1; matches[2].point2D_idx2 = 1; matches[3].point2D_idx1 = 3; matches[3].point2D_idx2 = 3; matches[4].point2D_idx1 = 3; matches[4].point2D_idx2 = 4; scene_graph.AddCorrespondences(0, 1, matches); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(0), 3); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesForImage(1), 3); const image_pair_t pair_id = Database::ImagePairToPairId(0, 1); BOOST_CHECK_EQUAL(scene_graph.NumCorrespondencesBetweenImages().at(pair_id), 3); } colmap-3.4/src/base/similarity_transform.cc000077500000000000000000000074001323400541200211220ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/similarity_transform.h" #include "base/pose.h" #include "base/projection.h" #include "estimators/similarity_transform.h" namespace colmap { SimilarityTransform3::SimilarityTransform3() { SimilarityTransform3(1, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0)); } SimilarityTransform3::SimilarityTransform3(const Eigen::Matrix3x4d& matrix) { transform_.matrix().topLeftCorner<3, 4>() = matrix; } SimilarityTransform3::SimilarityTransform3( const Eigen::Transform& transform) : transform_(transform) {} SimilarityTransform3::SimilarityTransform3(const double scale, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec) { Eigen::Matrix4d matrix = Eigen::MatrixXd::Identity(4, 4); matrix.topLeftCorner<3, 4>() = ComposeProjectionMatrix(qvec, tvec); matrix.block<3, 3>(0, 0) *= scale; transform_.matrix() = matrix; } void SimilarityTransform3::Estimate(const std::vector& src, const std::vector& dst) { transform_.matrix().topLeftCorner<3, 4>() = SimilarityTransformEstimator<3>().Estimate(src, dst)[0]; } SimilarityTransform3 SimilarityTransform3::Inverse() const { return SimilarityTransform3(transform_.inverse()); } void SimilarityTransform3::TransformPoint(Eigen::Vector3d* xyz) const { *xyz = transform_ * *xyz; } void SimilarityTransform3::TransformPose(Eigen::Vector4d* qvec, Eigen::Vector3d* tvec) const { // Projection matrix P1 projects 3D object points to image plane and thus to // 2D image points in the source coordinate system: // x' = P1 * X1 // 3D object points can be transformed to the destination system by applying // the similarity transformation S: // X2 = S * X1 // To obtain the projection matrix P2 that transforms the object point in the // destination system to the 2D image points, which do not change: // x' = P2 * X2 = P2 * S * X1 = P1 * S^-1 * S * X1 = P1 * I * X1 // and thus: // P2' = P1 * S^-1 // Finally, undo the inverse scaling of the rotation matrix: // P2 = s * P2' Eigen::Matrix4d src_matrix = Eigen::MatrixXd::Identity(4, 4); src_matrix.topLeftCorner<3, 4>() = ComposeProjectionMatrix(*qvec, *tvec); Eigen::Matrix4d dst_matrix = src_matrix.matrix() * transform_.inverse().matrix(); dst_matrix *= Scale(); *qvec = RotationMatrixToQuaternion(dst_matrix.block<3, 3>(0, 0)); *tvec = dst_matrix.block<3, 1>(0, 3); } Eigen::Matrix4d SimilarityTransform3::Matrix() const { return transform_.matrix(); } double SimilarityTransform3::Scale() const { return Matrix().block<1, 3>(0, 0).norm(); } Eigen::Vector4d SimilarityTransform3::Rotation() const { return RotationMatrixToQuaternion(Matrix().block<3, 3>(0, 0) / Scale()); } Eigen::Vector3d SimilarityTransform3::Translation() const { return Matrix().block<3, 1>(0, 3); } } // namespace colmap colmap-3.4/src/base/similarity_transform.h000077500000000000000000000040751323400541200207710ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_SIMILARITY_TRANSFORM_H_ #define COLMAP_SRC_BASE_SIMILARITY_TRANSFORM_H_ #include #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // 3D similarity transformation with 7 degrees of freedom. class SimilarityTransform3 { public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW SimilarityTransform3(); explicit SimilarityTransform3(const Eigen::Matrix3x4d& matrix); explicit SimilarityTransform3( const Eigen::Transform& transform); SimilarityTransform3(const double scale, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec); void Estimate(const std::vector& src, const std::vector& dst); SimilarityTransform3 Inverse() const; void TransformPoint(Eigen::Vector3d* xyz) const; void TransformPose(Eigen::Vector4d* qvec, Eigen::Vector3d* tvec) const; Eigen::Matrix4d Matrix() const; double Scale() const; Eigen::Vector4d Rotation() const; Eigen::Vector3d Translation() const; private: Eigen::Transform transform_; }; } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::SimilarityTransform3) #endif // COLMAP_SRC_BASE_SIMILARITY_TRANSFORM_H_ colmap-3.4/src/base/similarity_transform_test.cc000077500000000000000000000044351323400541200221660ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/similarity_transform" #include "util/testing.h" #include #include "base/pose.h" #include "base/similarity_transform.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestInitialization) { const Eigen::Vector4d qvec = NormalizeQuaternion(Eigen::Vector4d(0.1, 0.3, 0.2, 0.4)); const SimilarityTransform3 tform(2, qvec, Eigen::Vector3d(100, 10, 0.5)); BOOST_CHECK_CLOSE(tform.Scale(), 2, 1e-10); BOOST_CHECK_CLOSE(tform.Rotation()(0), qvec(0), 1e-10); BOOST_CHECK_CLOSE(tform.Rotation()(1), qvec(1), 1e-10); BOOST_CHECK_CLOSE(tform.Rotation()(2), qvec(2), 1e-10); BOOST_CHECK_CLOSE(tform.Rotation()(3), qvec(3), 1e-10); BOOST_CHECK_CLOSE(tform.Translation()[0], 100, 1e-10); BOOST_CHECK_CLOSE(tform.Translation()[1], 10, 1e-10); BOOST_CHECK_CLOSE(tform.Translation()[2], 0.5, 1e-10); } void TestEstimationWithNumCoords(const size_t num_coords) { const SimilarityTransform3 orig_tform(2, Eigen::Vector4d(0.1, 0.3, 0.2, 0.4), Eigen::Vector3d(100, 10, 0.5)); std::vector src; std::vector dst; for (size_t i = 0; i < num_coords; ++i) { src.emplace_back(i, i + 2, i * i); dst.push_back(src.back()); orig_tform.TransformPoint(&dst.back()); } SimilarityTransform3 est_tform; est_tform.Estimate(src, dst); BOOST_CHECK((orig_tform.Matrix() - est_tform.Matrix()).norm() < 1e-6); } BOOST_AUTO_TEST_CASE(TestEstimation) { TestEstimationWithNumCoords(3); TestEstimationWithNumCoords(100); } colmap-3.4/src/base/track.cc000077500000000000000000000027461323400541200157550ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/track.h" namespace colmap { Track::Track() {} TrackElement::TrackElement() : image_id(kInvalidImageId), point2D_idx(kInvalidPoint2DIdx) {} TrackElement::TrackElement(const image_t image_id, const point2D_t point2D_idx) : image_id(image_id), point2D_idx(point2D_idx) {} void Track::DeleteElement(const image_t image_id, const point2D_t point2D_idx) { elements_.erase( std::remove_if(elements_.begin(), elements_.end(), [image_id, point2D_idx](const TrackElement& element) { return element.image_id == image_id && element.point2D_idx == point2D_idx; }), elements_.end()); } } // namespace colmap colmap-3.4/src/base/track.h000077500000000000000000000075661323400541200156240ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_TRACK_H_ #define COLMAP_SRC_BASE_TRACK_H_ #include #include "util/logging.h" #include "util/types.h" namespace colmap { // Track class stores all observations of a 3D point. struct TrackElement { TrackElement(); TrackElement(const image_t image_id, const point2D_t point2D_idx); // The image in which the track element is observed. image_t image_id; // The point in the image that the track element is observed. point2D_t point2D_idx; }; class Track { public: Track(); // The number of track elements. inline size_t Length() const; // Access all elements. inline const std::vector& Elements() const; inline void SetElements(const std::vector& elements); // Access specific elements. inline const TrackElement& Element(const size_t idx) const; inline TrackElement& Element(const size_t idx); inline void SetElement(const size_t idx, const TrackElement& element); // Append new elements. inline void AddElement(const TrackElement& element); inline void AddElement(const image_t image_id, const point2D_t point2D_idx); inline void AddElements(const std::vector& elements); // Delete existing element. inline void DeleteElement(const size_t idx); void DeleteElement(const image_t image_id, const point2D_t point2D_idx); // Requests that the track capacity be at least enough to contain the // specified number of elements. inline void Reserve(const size_t num_elements); // Shrink the capacity of track vector to fit its size to save memory. inline void Compress(); private: std::vector elements_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// // The number of track elements. size_t Track::Length() const { return elements_.size(); } // Access all elements. const std::vector& Track::Elements() const { return elements_; } void Track::SetElements(const std::vector& elements) { elements_ = elements; } // Access specific elements. const TrackElement& Track::Element(const size_t idx) const { return elements_.at(idx); } TrackElement& Track::Element(const size_t idx) { return elements_.at(idx); } void Track::SetElement(const size_t idx, const TrackElement& element) { elements_.at(idx) = element; } // Append new element. void Track::AddElement(const TrackElement& element) { elements_.push_back(element); } void Track::AddElement(const image_t image_id, const point2D_t point2D_idx) { elements_.emplace_back(image_id, point2D_idx); } void Track::AddElements(const std::vector& elements) { elements_.insert(elements_.end(), elements.begin(), elements.end()); } // Delete existing element. void Track::DeleteElement(const size_t idx) { CHECK_LT(idx, elements_.size()); elements_.erase(elements_.begin() + idx); } void Track::Reserve(const size_t num_elements) { elements_.reserve(num_elements); } void Track::Compress() { elements_.shrink_to_fit(); } } // namespace colmap #endif // COLMAP_SRC_BASE_TRACK_H_ colmap-3.4/src/base/track_test.cc000077500000000000000000000105401323400541200170030ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/track" #include "util/testing.h" #include "base/track.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestTrackElement) { TrackElement track_el; BOOST_CHECK_EQUAL(track_el.image_id, kInvalidImageId); BOOST_CHECK_EQUAL(track_el.point2D_idx, kInvalidPoint2DIdx); } BOOST_AUTO_TEST_CASE(TestDefault) { Track track; BOOST_CHECK_EQUAL(track.Length(), 0); BOOST_CHECK_EQUAL(track.Elements().size(), track.Length()); } BOOST_AUTO_TEST_CASE(TestSetElements) { Track track; std::vector elements; elements.emplace_back(0, 1); elements.emplace_back(0, 2); track.SetElements(elements); BOOST_CHECK_EQUAL(track.Length(), 2); BOOST_CHECK_EQUAL(track.Elements().size(), track.Length()); BOOST_CHECK_EQUAL(track.Element(0).image_id, 0); BOOST_CHECK_EQUAL(track.Element(0).point2D_idx, 1); BOOST_CHECK_EQUAL(track.Element(1).image_id, 0); BOOST_CHECK_EQUAL(track.Element(1).point2D_idx, 2); for (size_t i = 0; i < track.Length(); ++i) { BOOST_CHECK_EQUAL(track.Element(i).image_id, track.Elements()[i].image_id); BOOST_CHECK_EQUAL(track.Element(i).point2D_idx, track.Elements()[i].point2D_idx); } } BOOST_AUTO_TEST_CASE(TestAddElement) { Track track; track.AddElement(0, 1); track.AddElement(TrackElement(0, 2)); std::vector elements; elements.emplace_back(0, 1); elements.emplace_back(0, 2); track.AddElements(elements); BOOST_CHECK_EQUAL(track.Length(), 4); BOOST_CHECK_EQUAL(track.Elements().size(), track.Length()); BOOST_CHECK_EQUAL(track.Element(0).image_id, 0); BOOST_CHECK_EQUAL(track.Element(0).point2D_idx, 1); BOOST_CHECK_EQUAL(track.Element(1).image_id, 0); BOOST_CHECK_EQUAL(track.Element(1).point2D_idx, 2); BOOST_CHECK_EQUAL(track.Element(2).image_id, 0); BOOST_CHECK_EQUAL(track.Element(2).point2D_idx, 1); BOOST_CHECK_EQUAL(track.Element(3).image_id, 0); BOOST_CHECK_EQUAL(track.Element(3).point2D_idx, 2); for (size_t i = 0; i < track.Length(); ++i) { BOOST_CHECK_EQUAL(track.Element(i).image_id, track.Elements()[i].image_id); BOOST_CHECK_EQUAL(track.Element(i).point2D_idx, track.Elements()[i].point2D_idx); } } BOOST_AUTO_TEST_CASE(TestDeleteElement) { Track track; track.AddElement(0, 1); track.AddElement(0, 2); track.AddElement(0, 3); track.AddElement(0, 3); BOOST_CHECK_EQUAL(track.Length(), 4); BOOST_CHECK_EQUAL(track.Elements().size(), track.Length()); track.DeleteElement(0); BOOST_CHECK_EQUAL(track.Length(), 3); BOOST_CHECK_EQUAL(track.Elements().size(), track.Length()); BOOST_CHECK_EQUAL(track.Element(0).image_id, 0); BOOST_CHECK_EQUAL(track.Element(0).point2D_idx, 2); BOOST_CHECK_EQUAL(track.Element(1).image_id, 0); BOOST_CHECK_EQUAL(track.Element(1).point2D_idx, 3); BOOST_CHECK_EQUAL(track.Element(2).image_id, 0); BOOST_CHECK_EQUAL(track.Element(2).point2D_idx, 3); track.DeleteElement(0, 3); BOOST_CHECK_EQUAL(track.Length(), 1); BOOST_CHECK_EQUAL(track.Elements().size(), track.Length()); BOOST_CHECK_EQUAL(track.Element(0).image_id, 0); BOOST_CHECK_EQUAL(track.Element(0).point2D_idx, 2); } BOOST_AUTO_TEST_CASE(TestReserve) { Track track; track.Reserve(2); BOOST_CHECK_EQUAL(track.Elements().capacity(), 2); } BOOST_AUTO_TEST_CASE(TestCompress) { Track track; track.AddElement(0, 1); track.AddElement(0, 2); track.AddElement(0, 3); track.AddElement(0, 3); BOOST_CHECK_EQUAL(track.Elements().capacity(), 4); track.DeleteElement(0); track.DeleteElement(0); BOOST_CHECK_EQUAL(track.Elements().capacity(), 4); track.Compress(); BOOST_CHECK_EQUAL(track.Elements().capacity(), 2); } colmap-3.4/src/base/triangulation.cc000077500000000000000000000137561323400541200175340ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/triangulation.h" #include "base/essential_matrix.h" #include "base/pose.h" namespace colmap { Eigen::Vector3d TriangulatePoint(const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const Eigen::Vector2d& point1, const Eigen::Vector2d& point2) { Eigen::Matrix4d A; A.row(0) = point1(0) * proj_matrix1.row(2) - proj_matrix1.row(0); A.row(1) = point1(1) * proj_matrix1.row(2) - proj_matrix1.row(1); A.row(2) = point2(0) * proj_matrix2.row(2) - proj_matrix2.row(0); A.row(3) = point2(1) * proj_matrix2.row(2) - proj_matrix2.row(1); Eigen::JacobiSVD svd(A, Eigen::ComputeFullV); return svd.matrixV().col(3).hnormalized(); } std::vector TriangulatePoints( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); std::vector points3D(points1.size()); for (size_t i = 0; i < points3D.size(); ++i) { points3D[i] = TriangulatePoint(proj_matrix1, proj_matrix2, points1[i], points2[i]); } return points3D; } Eigen::Vector3d TriangulateMultiViewPoint( const std::vector& proj_matrices, const std::vector& points) { CHECK_EQ(proj_matrices.size(), points.size()); Eigen::Matrix4d A = Eigen::Matrix4d::Zero(); for (size_t i = 0; i < points.size(); i++) { const Eigen::Vector3d point = points[i].homogeneous().normalized(); const Eigen::Matrix3x4d term = proj_matrices[i] - point * point.transpose() * proj_matrices[i]; A += term.transpose() * term; } Eigen::SelfAdjointEigenSolver eigen_solver(A); return eigen_solver.eigenvectors().col(0).hnormalized(); } Eigen::Vector3d TriangulateOptimalPoint(const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const Eigen::Vector2d& point1, const Eigen::Vector2d& point2) { const Eigen::Matrix3d E = EssentialMatrixFromAbsolutePoses(proj_matrix1, proj_matrix2); Eigen::Vector2d optimal_point1; Eigen::Vector2d optimal_point2; FindOptimalImageObservations(E, point1, point2, &optimal_point1, &optimal_point2); return TriangulatePoint(proj_matrix1, proj_matrix2, optimal_point1, optimal_point2); } std::vector TriangulateOptimalPoints( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const std::vector& points1, const std::vector& points2) { std::vector points3D(points1.size()); for (size_t i = 0; i < points3D.size(); ++i) { points3D[i] = TriangulatePoint(proj_matrix1, proj_matrix2, points1[i], points2[i]); } return points3D; } double CalculateTriangulationAngle(const Eigen::Vector3d& proj_center1, const Eigen::Vector3d& proj_center2, const Eigen::Vector3d& point3D) { const double baseline2 = (proj_center1 - proj_center2).squaredNorm(); const double ray1 = (point3D - proj_center1).norm(); const double ray2 = (point3D - proj_center2).norm(); // Angle between rays at point within the enclosing triangle, // see "law of cosines". const double angle = std::abs( std::acos((ray1 * ray1 + ray2 * ray2 - baseline2) / (2 * ray1 * ray2))); if (IsNaN(angle)) { return 0; } else { // Triangulation is unstable for acute angles (far away points) and // obtuse angles (close points), so always compute the minimum angle // between the two intersecting rays. return std::min(angle, M_PI - angle); } } std::vector CalculateTriangulationAngles( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const std::vector& points3D) { const Eigen::Vector3d& proj_center1 = ProjectionCenterFromMatrix(proj_matrix1); const Eigen::Vector3d& proj_center2 = ProjectionCenterFromMatrix(proj_matrix2); // Baseline length between cameras. const double baseline2 = (proj_center1 - proj_center2).squaredNorm(); std::vector angles(points3D.size()); for (size_t i = 0; i < points3D.size(); ++i) { const Eigen::Vector3d& point3D = points3D[i]; // Ray lengths from cameras to point. const double ray1 = (point3D - proj_center1).norm(); const double ray2 = (point3D - proj_center2).norm(); // Angle between rays at point within the enclosing triangle, // see "law of cosines". const double angle = std::abs( std::acos((ray1 * ray1 + ray2 * ray2 - baseline2) / (2 * ray1 * ray2))); if (IsNaN(angle)) { angles[i] = 0; } else { // Triangulation is unstable for acute angles (far away points) and // obtuse angles (close points), so always compute the minimum angle // between the two intersecting rays. angles[i] = std::min(angle, M_PI - angle); } } return angles; } } // namespace colmap colmap-3.4/src/base/triangulation.h000077500000000000000000000117141323400541200173660ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_TRIANGULATION_H_ #define COLMAP_SRC_BASE_TRIANGULATION_H_ #include #include #include "base/camera.h" #include "util/alignment.h" #include "util/math.h" #include "util/types.h" namespace colmap { // Triangulate 3D point from corresponding image point observations. // // Implementation of the direct linear transform triangulation method in // R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, // Cambridge Univ. Press, 2003. // // @param proj_matrix1 Projection matrix of the first image as 3x4 matrix. // @param proj_matrix2 Projection matrix of the second image as 3x4 matrix. // @param point1 Corresponding 2D point in first image. // @param point2 Corresponding 2D point in second image. // // @return Triangulated 3D point. Eigen::Vector3d TriangulatePoint(const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const Eigen::Vector2d& point1, const Eigen::Vector2d& point2); // Triangulate multiple 3D points from multiple image correspondences. std::vector TriangulatePoints( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const std::vector& points1, const std::vector& points2); // Triangulate point from multiple views minimizing the L2 error. // // @param proj_matrices Projection matrices of multi-view observations. // @param points Image observations of multi-view observations. // // @return Estimated 3D point. Eigen::Vector3d TriangulateMultiViewPoint( const std::vector& proj_matrices, const std::vector& points); // Triangulate optimal 3D point from corresponding image point observations by // finding the optimal image observations. // // Note that camera poses should be very good in order for this method to yield // good results. Otherwise just use `TriangulatePoint`. // // Implementation of the method described in // P. Lindstrom, "Triangulation Made Easy," IEEE Computer Vision and Pattern // Recognition 2010, pp. 1554-1561, June 2010. // // @param proj_matrix1 Projection matrix of the first image as 3x4 matrix. // @param proj_matrix2 Projection matrix of the second image as 3x4 matrix. // @param point1 Corresponding 2D point in first image. // @param point2 Corresponding 2D point in second image. // // @return Triangulated optimal 3D point. Eigen::Vector3d TriangulateOptimalPoint(const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const Eigen::Vector2d& point1, const Eigen::Vector2d& point2); // Triangulate multiple optimal 3D points from multiple image correspondences. std::vector TriangulateOptimalPoints( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const std::vector& points1, const std::vector& points2); // Calculate angle between the two rays of a triangulated point. // // @param pose1 Projection center of first image. // @param pose2 Projection center of second image. // @param point3D Triangulated 3D point. // // @return Angle in radians. double CalculateTriangulationAngle(const Eigen::Vector3d& proj_center1, const Eigen::Vector3d& proj_center2, const Eigen::Vector3d& point3D); // Calculate angle between the two rays of a triangulated point. // // @param proj_matrix1 Projection matrix of the first image. // @param proj_matrix2 Projection matrix of the second image. // @param points3D Triangulated 3D points. // // @return Angle in radians. std::vector CalculateTriangulationAngles( const Eigen::Matrix3x4d& proj_matrix1, const Eigen::Matrix3x4d& proj_matrix2, const std::vector& points3D); } // namespace colmap #endif // COLMAP_SRC_BASE_TRIANGULATION_H_ colmap-3.4/src/base/triangulation_test.cc000077500000000000000000000053631323400541200205660ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/triangulation" #include "util/testing.h" #include #include "base/similarity_transform.h" #include "base/triangulation.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestTriangulatePoint) { std::vector points3D(6); points3D[0] = Eigen::Vector3d(0, 0.1, 0.1); points3D[1] = Eigen::Vector3d(0, 1, 3); points3D[2] = Eigen::Vector3d(0, 1, 2); points3D[3] = Eigen::Vector3d(0.01, 0.2, 3); points3D[4] = Eigen::Vector3d(-1, 0.1, 1); points3D[5] = Eigen::Vector3d(0.1, 0.1, 0.2); Eigen::Matrix3x4d proj_matrix1 = Eigen::MatrixXd::Identity(3, 4); for (double qz = 0; qz < 1; qz += 0.2) { for (double tx = 0; tx < 10; tx += 2) { SimilarityTransform3 tform(1, Eigen::Vector4d(0.2, 0.3, 0.4, qz), Eigen::Vector3d(tx, 2, 3)); Eigen::Matrix3x4d proj_matrix2 = tform.Matrix().topLeftCorner<3, 4>(); for (size_t i = 0; i < points3D.size(); ++i) { const Eigen::Vector3d& point3D = points3D[i]; const Eigen::Vector4d point3D1(point3D(0), point3D(1), point3D(2), 1); Eigen::Vector3d point2D1 = proj_matrix1 * point3D1; Eigen::Vector3d point2D2 = proj_matrix2 * point3D1; point2D1 /= point2D1(2); point2D2 /= point2D2(2); const Eigen::Vector2d point2D1_N(point2D1(0), point2D1(1)); const Eigen::Vector2d point2D2_N(point2D2(0), point2D2(1)); const Eigen::Vector3d tri_point3D = TriangulatePoint( proj_matrix1, proj_matrix2, point2D1_N, point2D2_N); BOOST_CHECK((point3D - tri_point3D).norm() < 1e-10); } } } } BOOST_AUTO_TEST_CASE(TestCalculateTriangulationAngle) { const Eigen::Vector3d tvec1(0, 0, 0); const Eigen::Vector3d tvec2(0, 1, 0); BOOST_CHECK_CLOSE( CalculateTriangulationAngle(tvec1, tvec2, Eigen::Vector3d(0, 0, 100)), 0.009999666687, 1e-8); BOOST_CHECK_CLOSE( CalculateTriangulationAngle(tvec1, tvec2, Eigen::Vector3d(0, 0, 50)), 0.019997333973, 1e-8); } colmap-3.4/src/base/undistortion.cc000077500000000000000000001061371323400541200174110ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/undistortion.h" #include #include "base/pose.h" #include "base/warp.h" #include "util/misc.h" namespace colmap { namespace { template void WriteMatrix(const Eigen::MatrixBase& matrix, std::ofstream* file) { typedef typename Eigen::MatrixBase::Index index_t; for (index_t r = 0; r < matrix.rows(); ++r) { for (index_t c = 0; c < matrix.cols() - 1; ++c) { *file << matrix(r, c) << " "; } *file << matrix(r, matrix.cols() - 1) << std::endl; } } // Write projection matrix P = K * [R t] to file and prepend given header. void WriteProjectionMatrix(const std::string& path, const Camera& camera, const Image& image, const std::string& header) { CHECK_EQ(camera.ModelId(), PinholeCameraModel::model_id); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; Eigen::Matrix3d calib_matrix = Eigen::Matrix3d::Identity(); calib_matrix(0, 0) = camera.FocalLengthX(); calib_matrix(1, 1) = camera.FocalLengthY(); calib_matrix(0, 2) = camera.PrincipalPointX(); calib_matrix(1, 2) = camera.PrincipalPointY(); const Eigen::Matrix3x4d proj_matrix = calib_matrix * image.ProjectionMatrix(); if (!header.empty()) { file << header << std::endl; } WriteMatrix(proj_matrix, &file); } void WriteCOLMAPCommands(const bool geometric, const std::string& workspace_path, const std::string& workspace_format, const std::string& pmvs_option_name, const std::string& output_prefix, const std::string& indent, std::ofstream* file) { if (geometric) { *file << indent << "$COLMAP_EXE_PATH/dense_stereo \\" << std::endl; *file << indent << " --workspace_path " << workspace_path << " \\" << std::endl; *file << indent << " --workspace_format " << workspace_format << " \\" << std::endl; if (workspace_format == "PMVS") { *file << indent << " --pmvs_option_name " << pmvs_option_name << " \\" << std::endl; } *file << indent << " --DenseStereo.max_image_size 2000 \\" << std::endl; *file << indent << " --DenseStereo.geom_consistency true" << std::endl; } else { *file << indent << "$COLMAP_EXE_PATH/dense_stereo \\" << std::endl; *file << indent << " --workspace_path " << workspace_path << " \\" << std::endl; *file << indent << " --workspace_format " << workspace_format << " \\" << std::endl; if (workspace_format == "PMVS") { *file << indent << " --pmvs_option_name " << pmvs_option_name << " \\" << std::endl; } *file << indent << " --DenseStereo.max_image_size 2000 \\" << std::endl; *file << indent << " --DenseStereo.geom_consistency false" << std::endl; } *file << indent << "$COLMAP_EXE_PATH/dense_fuser \\" << std::endl; *file << indent << " --workspace_path " << workspace_path << " \\" << std::endl; *file << indent << " --workspace_format " << workspace_format << " \\" << std::endl; if (workspace_format == "PMVS") { *file << indent << " --pmvs_option_name " << pmvs_option_name << " \\" << std::endl; } if (geometric) { *file << indent << " --input_type geometric \\" << std::endl; } else { *file << indent << " --input_type photometric \\" << std::endl; } *file << indent << " --output_path " << JoinPaths(workspace_path, output_prefix + "fused.ply") << std::endl; *file << indent << "$COLMAP_EXE_PATH/dense_mesher \\" << std::endl; *file << indent << " --input_path " << JoinPaths(workspace_path, output_prefix + "fused.ply") << " \\" << std::endl; *file << indent << " --output_path " << JoinPaths(workspace_path, output_prefix + "meshed.ply") << std::endl; } } // namespace COLMAPUndistorter::COLMAPUndistorter(const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path) : options_(options), image_path_(image_path), output_path_(output_path), reconstruction_(reconstruction) {} void COLMAPUndistorter::Run() { PrintHeading1("Image undistortion"); CreateDirIfNotExists(JoinPaths(output_path_, "images")); CreateDirIfNotExists(JoinPaths(output_path_, "sparse")); CreateDirIfNotExists(JoinPaths(output_path_, "stereo")); CreateDirIfNotExists(JoinPaths(output_path_, "stereo/depth_maps")); CreateDirIfNotExists(JoinPaths(output_path_, "stereo/normal_maps")); CreateDirIfNotExists(JoinPaths(output_path_, "stereo/consistency_graphs")); reconstruction_.CreateImageDirs(JoinPaths(output_path_, "images")); reconstruction_.CreateImageDirs(JoinPaths(output_path_, "stereo/depth_maps")); reconstruction_.CreateImageDirs( JoinPaths(output_path_, "stereo/normal_maps")); reconstruction_.CreateImageDirs( JoinPaths(output_path_, "stereo/consistency_graphs")); ThreadPool thread_pool; std::vector> futures; futures.reserve(reconstruction_.NumRegImages()); for (size_t i = 0; i < reconstruction_.NumRegImages(); ++i) { futures.push_back( thread_pool.AddTask(&COLMAPUndistorter::Undistort, this, i)); } for (size_t i = 0; i < futures.size(); ++i) { if (IsStopped()) { break; } std::cout << StringPrintf("Undistorting image [%d/%d]", i + 1, futures.size()) << std::endl; futures[i].get(); } std::cout << "Writing reconstruction..." << std::endl; Reconstruction undistorted_reconstruction = reconstruction_; UndistortReconstruction(options_, &undistorted_reconstruction); undistorted_reconstruction.Write(JoinPaths(output_path_, "sparse")); std::cout << "Writing configuration..." << std::endl; WritePatchMatchConfig(); WriteFusionConfig(); std::cout << "Writing scripts..." << std::endl; WriteScript(false); WriteScript(true); GetTimer().PrintMinutes(); } void COLMAPUndistorter::Undistort(const size_t reg_image_idx) const { const image_t image_id = reconstruction_.RegImageIds().at(reg_image_idx); const Image& image = reconstruction_.Image(image_id); const Camera& camera = reconstruction_.Camera(image.CameraId()); const std::string output_image_path = JoinPaths(output_path_, "images", image.Name()); Bitmap distorted_bitmap; const std::string input_image_path = JoinPaths(image_path_, image.Name()); if (!distorted_bitmap.Read(input_image_path)) { std::cerr << "ERROR: Cannot read image at path " << input_image_path << std::endl; return; } Bitmap undistorted_bitmap; Camera undistorted_camera; UndistortImage(options_, distorted_bitmap, camera, &undistorted_bitmap, &undistorted_camera); undistorted_bitmap.Write(output_image_path); } void COLMAPUndistorter::WritePatchMatchConfig() const { const auto path = JoinPaths(output_path_, "stereo/patch-match.cfg"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; for (const auto image_id : reconstruction_.RegImageIds()) { const auto& image = reconstruction_.Image(image_id); file << image.Name() << std::endl; file << "__auto__, 20" << std::endl; } } void COLMAPUndistorter::WriteFusionConfig() const { const auto path = JoinPaths(output_path_, "stereo/fusion.cfg"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; for (const auto image_id : reconstruction_.RegImageIds()) { const auto& image = reconstruction_.Image(image_id); file << image.Name() << std::endl; } } void COLMAPUndistorter::WriteScript(const bool geometric) const { const std::string path = JoinPaths(output_path_, geometric ? "run-colmap-geometric.sh" : "run-colmap-photometric.sh"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# You must set $COLMAP_EXE_PATH to " << std::endl << "# the directory containing the COLMAP executables." << std::endl; WriteCOLMAPCommands(geometric, ".", "COLMAP", "option-all", "", "", &file); } PMVSUndistorter::PMVSUndistorter(const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path) : options_(options), image_path_(image_path), output_path_(output_path), reconstruction_(reconstruction) {} void PMVSUndistorter::Run() { PrintHeading1("Image undistortion (CMVS/PMVS)"); CreateDirIfNotExists(JoinPaths(output_path_, "pmvs")); CreateDirIfNotExists(JoinPaths(output_path_, "pmvs/txt")); CreateDirIfNotExists(JoinPaths(output_path_, "pmvs/visualize")); CreateDirIfNotExists(JoinPaths(output_path_, "pmvs/models")); ThreadPool thread_pool; std::vector> futures; futures.reserve(reconstruction_.NumRegImages()); for (size_t i = 0; i < reconstruction_.NumRegImages(); ++i) { futures.push_back( thread_pool.AddTask(&PMVSUndistorter::Undistort, this, i)); } for (size_t i = 0; i < futures.size(); ++i) { if (IsStopped()) { thread_pool.Stop(); std::cout << "WARNING: Stopped the undistortion process. Image point " "locations and camera parameters for not yet processed " "images in the Bundler output file is probably wrong." << std::endl; break; } std::cout << StringPrintf("Undistorting image [%d/%d]", i + 1, futures.size()) << std::endl; futures[i].get(); } std::cout << "Writing bundle file..." << std::endl; Reconstruction undistorted_reconstruction = reconstruction_; UndistortReconstruction(options_, &undistorted_reconstruction); const std::string bundle_path = JoinPaths(output_path_, "pmvs/bundle.rd.out"); undistorted_reconstruction.ExportBundler(bundle_path, bundle_path + ".list.txt"); std::cout << "Writing visibility file..." << std::endl; WriteVisibilityData(); std::cout << "Writing option file..." << std::endl; WriteOptionFile(); std::cout << "Writing scripts..." << std::endl; WritePMVSScript(); WriteCMVSPMVSScript(); WriteCOLMAPScript(false); WriteCOLMAPScript(true); WriteCMVSCOLMAPScript(false); WriteCMVSCOLMAPScript(true); GetTimer().PrintMinutes(); } void PMVSUndistorter::Undistort(const size_t reg_image_idx) const { const std::string output_image_path = JoinPaths( output_path_, StringPrintf("pmvs/visualize/%08d.jpg", reg_image_idx)); const std::string proj_matrix_path = JoinPaths(output_path_, StringPrintf("pmvs/txt/%08d.txt", reg_image_idx)); const image_t image_id = reconstruction_.RegImageIds().at(reg_image_idx); const Image& image = reconstruction_.Image(image_id); const Camera& camera = reconstruction_.Camera(image.CameraId()); Bitmap distorted_bitmap; const std::string input_image_path = JoinPaths(image_path_, image.Name()); if (!distorted_bitmap.Read(input_image_path)) { std::cerr << StringPrintf("ERROR: Cannot read image at path %s", input_image_path.c_str()) << std::endl; return; } Bitmap undistorted_bitmap; Camera undistorted_camera; UndistortImage(options_, distorted_bitmap, camera, &undistorted_bitmap, &undistorted_camera); undistorted_bitmap.Write(output_image_path); WriteProjectionMatrix(proj_matrix_path, undistorted_camera, image, "CONTOUR"); } void PMVSUndistorter::WriteVisibilityData() const { const auto path = JoinPaths(output_path_, "pmvs/vis.dat"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "VISDATA" << std::endl; file << reconstruction_.NumRegImages() << std::endl; const std::vector& reg_image_ids = reconstruction_.RegImageIds(); for (size_t i = 0; i < reg_image_ids.size(); ++i) { const image_t image_id = reg_image_ids[i]; const Image& image = reconstruction_.Image(image_id); std::unordered_set visible_image_ids; for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { const Point2D& point2D = image.Point2D(point2D_idx); if (point2D.HasPoint3D()) { const Point3D& point3D = reconstruction_.Point3D(point2D.Point3DId()); for (const TrackElement track_el : point3D.Track().Elements()) { if (track_el.image_id != image_id) { visible_image_ids.insert(track_el.image_id); } } } } std::vector sorted_visible_image_ids(visible_image_ids.begin(), visible_image_ids.end()); std::sort(sorted_visible_image_ids.begin(), sorted_visible_image_ids.end()); file << i << " " << visible_image_ids.size(); for (const image_t visible_image_id : sorted_visible_image_ids) { file << " " << visible_image_id; } file << std::endl; } } void PMVSUndistorter::WritePMVSScript() const { const auto path = JoinPaths(output_path_, "run-pmvs.sh"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# You must set $PMVS_EXE_PATH to " << std::endl << "# the directory containing the CMVS-PMVS executables." << std::endl; file << "$PMVS_EXE_PATH/pmvs2 pmvs/ option-all" << std::endl; } void PMVSUndistorter::WriteCMVSPMVSScript() const { const auto path = JoinPaths(output_path_, "run-cmvs-pmvs.sh"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# You must set $PMVS_EXE_PATH to " << std::endl << "# the directory containing the CMVS-PMVS executables." << std::endl; file << "$PMVS_EXE_PATH/cmvs pmvs/" << std::endl; file << "$PMVS_EXE_PATH/genOption pmvs/" << std::endl; file << "find pmvs/ -iname \"option-*\" | sort | while read file_name" << std::endl; file << "do" << std::endl; file << " option_name=$(basename \"$file_name\")" << std::endl; file << " if [ \"$option_name\" = \"option-all\" ]; then" << std::endl; file << " continue" << std::endl; file << " fi" << std::endl; file << " $PMVS_EXE_PATH/pmvs2 pmvs/ $option_name" << std::endl; file << "done" << std::endl; } void PMVSUndistorter::WriteCOLMAPScript(const bool geometric) const { const std::string path = JoinPaths(output_path_, geometric ? "run-colmap-geometric.sh" : "run-colmap-photometric.sh"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# You must set $COLMAP_EXE_PATH to " << std::endl << "# the directory containing the COLMAP executables." << std::endl; WriteCOLMAPCommands(geometric, "pmvs", "PMVS", "option-all", "option-all-", "", &file); } void PMVSUndistorter::WriteCMVSCOLMAPScript(const bool geometric) const { const std::string path = JoinPaths(output_path_, geometric ? "run-cmvs-colmap-geometric.sh" : "run-cmvs-colmap-photometric.sh"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# You must set $PMVS_EXE_PATH to " << std::endl << "# the directory containing the CMVS-PMVS executables" << std::endl; file << "# and you must set $COLMAP_EXE_PATH to " << std::endl << "# the directory containing the COLMAP executables." << std::endl; file << "$PMVS_EXE_PATH/cmvs pmvs/" << std::endl; file << "$PMVS_EXE_PATH/genOption pmvs/" << std::endl; file << "find pmvs/ -iname \"option-*\" | sort | while read file_name" << std::endl; file << "do" << std::endl; file << " workspace_path=$(dirname \"$file_name\")" << std::endl; file << " option_name=$(basename \"$file_name\")" << std::endl; file << " if [ \"$option_name\" = \"option-all\" ]; then" << std::endl; file << " continue" << std::endl; file << " fi" << std::endl; file << " rm -rf \"$workspace_path/stereo\"" << std::endl; WriteCOLMAPCommands(geometric, "pmvs", "PMVS", "$option_name", "$option_name-", " ", &file); file << "done" << std::endl; } void PMVSUndistorter::WriteOptionFile() const { const auto path = JoinPaths(output_path_, "pmvs/option-all"); std::ofstream file(path, std::ios::trunc); CHECK(file.is_open()) << path; file << "# Generated by COLMAP - all images, no clustering." << std::endl; file << "level 1" << std::endl; file << "csize 2" << std::endl; file << "threshold 0.7" << std::endl; file << "wsize 7" << std::endl; file << "minImageNum 3" << std::endl; file << "CPU " << std::thread::hardware_concurrency() << std::endl; file << "setEdge 0" << std::endl; file << "useBound 0" << std::endl; file << "useVisData 1" << std::endl; file << "sequence -1" << std::endl; file << "maxAngle 10" << std::endl; file << "quad 2.0" << std::endl; file << "timages " << reconstruction_.NumRegImages(); for (size_t i = 0; i < reconstruction_.NumRegImages(); ++i) { file << " " << i; } file << std::endl; file << "oimages 0" << std::endl; } CMPMVSUndistorter::CMPMVSUndistorter(const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path) : options_(options), image_path_(image_path), output_path_(output_path), reconstruction_(reconstruction) {} void CMPMVSUndistorter::Run() { PrintHeading1("Image undistortion (CMP-MVS)"); ThreadPool thread_pool; std::vector> futures; futures.reserve(reconstruction_.NumRegImages()); for (size_t i = 0; i < reconstruction_.NumRegImages(); ++i) { futures.push_back( thread_pool.AddTask(&CMPMVSUndistorter::Undistort, this, i)); } for (size_t i = 0; i < futures.size(); ++i) { if (IsStopped()) { break; } std::cout << StringPrintf("Undistorting image [%d/%d]", i + 1, futures.size()) << std::endl; futures[i].get(); } GetTimer().PrintMinutes(); } void CMPMVSUndistorter::Undistort(const size_t reg_image_idx) const { const std::string output_image_path = JoinPaths(output_path_, StringPrintf("%05d.jpg", reg_image_idx + 1)); const std::string proj_matrix_path = JoinPaths(output_path_, StringPrintf("%05d_P.txt", reg_image_idx + 1)); const image_t image_id = reconstruction_.RegImageIds().at(reg_image_idx); const Image& image = reconstruction_.Image(image_id); const Camera& camera = reconstruction_.Camera(image.CameraId()); Bitmap distorted_bitmap; const std::string input_image_path = JoinPaths(image_path_, image.Name()); if (!distorted_bitmap.Read(input_image_path)) { std::cerr << "ERROR: Cannot read image at path " << input_image_path << std::endl; return; } Bitmap undistorted_bitmap; Camera undistorted_camera; UndistortImage(options_, distorted_bitmap, camera, &undistorted_bitmap, &undistorted_camera); undistorted_bitmap.Write(output_image_path); WriteProjectionMatrix(proj_matrix_path, undistorted_camera, image, "CONTOUR"); } StereoImageRectifier::StereoImageRectifier( const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path, const std::vector>& stereo_pairs) : options_(options), image_path_(image_path), output_path_(output_path), stereo_pairs_(stereo_pairs), reconstruction_(reconstruction) {} void StereoImageRectifier::Run() { PrintHeading1("Stereo rectification"); ThreadPool thread_pool; std::vector> futures; futures.reserve(stereo_pairs_.size()); for (const auto& stereo_pair : stereo_pairs_) { futures.push_back(thread_pool.AddTask(&StereoImageRectifier::Rectify, this, stereo_pair.first, stereo_pair.second)); } for (size_t i = 0; i < futures.size(); ++i) { if (IsStopped()) { break; } std::cout << StringPrintf("Rectifying image pair [%d/%d]", i + 1, futures.size()) << std::endl; futures[i].get(); } GetTimer().PrintMinutes(); } void StereoImageRectifier::Rectify(const image_t image_id1, const image_t image_id2) const { const Image& image1 = reconstruction_.Image(image_id1); const Image& image2 = reconstruction_.Image(image_id2); const Camera& camera1 = reconstruction_.Camera(image1.CameraId()); const Camera& camera2 = reconstruction_.Camera(image2.CameraId()); const std::string image_name1 = StringReplace(image1.Name(), "/", "-"); const std::string image_name2 = StringReplace(image2.Name(), "/", "-"); const std::string stereo_pair_name = StringPrintf("%s-%s", image_name1.c_str(), image_name2.c_str()); CreateDirIfNotExists(JoinPaths(output_path_, stereo_pair_name)); const std::string output_image1_path = JoinPaths(output_path_, stereo_pair_name, image_name1); const std::string output_image2_path = JoinPaths(output_path_, stereo_pair_name, image_name2); Bitmap distorted_bitmap1; const std::string input_image1_path = JoinPaths(image_path_, image1.Name()); if (!distorted_bitmap1.Read(input_image1_path)) { std::cerr << "ERROR: Cannot read image at path " << input_image1_path << std::endl; return; } Bitmap distorted_bitmap2; const std::string input_image2_path = JoinPaths(image_path_, image2.Name()); if (!distorted_bitmap2.Read(input_image2_path)) { std::cerr << "ERROR: Cannot read image at path " << input_image2_path << std::endl; return; } Eigen::Vector4d qvec; Eigen::Vector3d tvec; ComputeRelativePose(image1.Qvec(), image1.Tvec(), image2.Qvec(), image2.Tvec(), &qvec, &tvec); Bitmap undistorted_bitmap1; Bitmap undistorted_bitmap2; Camera undistorted_camera; Eigen::Matrix4d Q; RectifyAndUndistortStereoImages( options_, distorted_bitmap1, distorted_bitmap2, camera1, camera2, qvec, tvec, &undistorted_bitmap1, &undistorted_bitmap2, &undistorted_camera, &Q); undistorted_bitmap1.Write(output_image1_path); undistorted_bitmap2.Write(output_image2_path); const auto Q_path = JoinPaths(output_path_, stereo_pair_name, "Q.txt"); std::ofstream Q_file(Q_path, std::ios::trunc); CHECK(Q_file.is_open()) << Q_path; WriteMatrix(Q, &Q_file); } Camera UndistortCamera(const UndistortCameraOptions& options, const Camera& camera) { CHECK_GE(options.blank_pixels, 0); CHECK_LE(options.blank_pixels, 1); CHECK_GT(options.min_scale, 0.0); CHECK_LE(options.min_scale, options.max_scale); CHECK_NE(options.max_image_size, 0); Camera undistorted_camera; undistorted_camera.SetModelId(PinholeCameraModel::model_id); undistorted_camera.SetWidth(camera.Width()); undistorted_camera.SetHeight(camera.Height()); // Copy focal length parameters. const std::vector& focal_length_idxs = camera.FocalLengthIdxs(); CHECK_LE(focal_length_idxs.size(), 2) << "Not more than two focal length parameters supported."; if (focal_length_idxs.size() == 1) { undistorted_camera.SetFocalLengthX(camera.FocalLength()); undistorted_camera.SetFocalLengthY(camera.FocalLength()); } else if (focal_length_idxs.size() == 2) { undistorted_camera.SetFocalLengthX(camera.FocalLengthX()); undistorted_camera.SetFocalLengthY(camera.FocalLengthY()); } // Copy principal point parameters. undistorted_camera.SetPrincipalPointX(camera.PrincipalPointX()); undistorted_camera.SetPrincipalPointY(camera.PrincipalPointY()); // Scale the image such the the boundary of the undistorted image. if (camera.ModelId() != SimplePinholeCameraModel::model_id && camera.ModelId() != PinholeCameraModel::model_id) { // Determine min, max coordinates along top / bottom image border. double left_min_x = std::numeric_limits::max(); double left_max_x = std::numeric_limits::lowest(); double right_min_x = std::numeric_limits::max(); double right_max_x = std::numeric_limits::lowest(); for (size_t y = 0; y < camera.Height(); ++y) { // Left border. const Eigen::Vector2d world_point1 = camera.ImageToWorld(Eigen::Vector2d(0.5, y + 0.5)); const Eigen::Vector2d undistorted_point1 = undistorted_camera.WorldToImage(world_point1); left_min_x = std::min(left_min_x, undistorted_point1(0)); left_max_x = std::max(left_max_x, undistorted_point1(0)); // Right border. const Eigen::Vector2d world_point2 = camera.ImageToWorld(Eigen::Vector2d(camera.Width() - 0.5, y + 0.5)); const Eigen::Vector2d undistorted_point2 = undistorted_camera.WorldToImage(world_point2); right_min_x = std::min(right_min_x, undistorted_point2(0)); right_max_x = std::max(right_max_x, undistorted_point2(0)); } // Determine min, max coordinates along left / right image border. double top_min_y = std::numeric_limits::max(); double top_max_y = std::numeric_limits::lowest(); double bottom_min_y = std::numeric_limits::max(); double bottom_max_y = std::numeric_limits::lowest(); for (size_t x = 0; x < camera.Width(); ++x) { // Top border. const Eigen::Vector2d world_point1 = camera.ImageToWorld(Eigen::Vector2d(x + 0.5, 0.5)); const Eigen::Vector2d undistorted_point1 = undistorted_camera.WorldToImage(world_point1); top_min_y = std::min(top_min_y, undistorted_point1(1)); top_max_y = std::max(top_max_y, undistorted_point1(1)); // Bottom border. const Eigen::Vector2d world_point2 = camera.ImageToWorld(Eigen::Vector2d(x + 0.5, camera.Height() - 0.5)); const Eigen::Vector2d undistorted_point2 = undistorted_camera.WorldToImage(world_point2); bottom_min_y = std::min(bottom_min_y, undistorted_point2(1)); bottom_max_y = std::max(bottom_max_y, undistorted_point2(1)); } const double cx = undistorted_camera.PrincipalPointX(); const double cy = undistorted_camera.PrincipalPointY(); // Scale such that undistorted image contains all pixels of distorted image const double min_scale_x = std::min(cx / (cx - left_min_x), (camera.Width() - 0.5 - cx) / (right_max_x - cx)); const double min_scale_y = std::min(cy / (cy - top_min_y), (camera.Height() - 0.5 - cy) / (bottom_max_y - cy)); // Scale such that there are no blank pixels in undistorted image const double max_scale_x = std::max(cx / (cx - left_max_x), (camera.Width() - 0.5 - cx) / (right_min_x - cx)); const double max_scale_y = std::max(cy / (cy - top_max_y), (camera.Height() - 0.5 - cy) / (bottom_min_y - cy)); // Interpolate scale according to blank_pixels. double scale_x = 1.0 / (min_scale_x * options.blank_pixels + max_scale_x * (1.0 - options.blank_pixels)); double scale_y = 1.0 / (min_scale_y * options.blank_pixels + max_scale_y * (1.0 - options.blank_pixels)); // Clip the scaling factors. scale_x = Clip(scale_x, options.min_scale, options.max_scale); scale_y = Clip(scale_y, options.min_scale, options.max_scale); // Scale undistorted camera dimensions. undistorted_camera.SetWidth(static_cast( std::max(1.0, scale_x * undistorted_camera.Width()))); undistorted_camera.SetHeight(static_cast( std::max(1.0, scale_y * undistorted_camera.Height()))); // Scale the principal point according to the new dimensions of the image. undistorted_camera.SetPrincipalPointX( undistorted_camera.PrincipalPointX() * static_cast(undistorted_camera.Width()) / camera.Width()); undistorted_camera.SetPrincipalPointY( undistorted_camera.PrincipalPointY() * static_cast(undistorted_camera.Height()) / camera.Height()); } if (options.max_image_size > 0) { const double max_image_scale_x = options.max_image_size / static_cast(undistorted_camera.Width()); const double max_image_scale_y = options.max_image_size / static_cast(undistorted_camera.Height()); const double max_image_scale = std::min(max_image_scale_x, max_image_scale_y); if (max_image_scale < 1.0) { undistorted_camera.Rescale(max_image_scale); } } return undistorted_camera; } void UndistortImage(const UndistortCameraOptions& options, const Bitmap& distorted_bitmap, const Camera& distorted_camera, Bitmap* undistorted_bitmap, Camera* undistorted_camera) { CHECK_EQ(distorted_camera.Width(), distorted_bitmap.Width()); CHECK_EQ(distorted_camera.Height(), distorted_bitmap.Height()); *undistorted_camera = UndistortCamera(options, distorted_camera); undistorted_bitmap->Allocate(static_cast(undistorted_camera->Width()), static_cast(undistorted_camera->Height()), distorted_bitmap.IsRGB()); distorted_bitmap.CloneMetadata(undistorted_bitmap); WarpImageBetweenCameras(distorted_camera, *undistorted_camera, distorted_bitmap, undistorted_bitmap); } void UndistortReconstruction(const UndistortCameraOptions& options, Reconstruction* reconstruction) { const auto distorted_cameras = reconstruction->Cameras(); for (auto& camera : distorted_cameras) { reconstruction->Camera(camera.first) = UndistortCamera(options, camera.second); } for (const auto& distorted_image : reconstruction->Images()) { auto& image = reconstruction->Image(distorted_image.first); const auto& distorted_camera = distorted_cameras.at(image.CameraId()); const auto& undistorted_camera = reconstruction->Camera(image.CameraId()); for (point2D_t point2D_idx = 0; point2D_idx < image.NumPoints2D(); ++point2D_idx) { auto& point2D = image.Point2D(point2D_idx); point2D.SetXY(undistorted_camera.WorldToImage( distorted_camera.ImageToWorld(point2D.XY()))); } } } void RectifyStereoCameras(const Camera& camera1, const Camera& camera2, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, Eigen::Matrix3d* H1, Eigen::Matrix3d* H2, Eigen::Matrix4d* Q) { CHECK(camera1.ModelId() == SimplePinholeCameraModel::model_id || camera1.ModelId() == PinholeCameraModel::model_id); CHECK(camera2.ModelId() == SimplePinholeCameraModel::model_id || camera2.ModelId() == PinholeCameraModel::model_id); // Compute the average rotation between the first and the second camera. Eigen::AngleAxisd rvec( Eigen::Quaterniond(qvec(0), qvec(1), qvec(2), qvec(3))); rvec.angle() *= -0.5; Eigen::Matrix3d R2 = rvec.toRotationMatrix(); Eigen::Matrix3d R1 = R2.transpose(); // Determine the translation, such that it coincides with the X-axis. Eigen::Vector3d t = R2 * tvec; Eigen::Vector3d x_unit_vector(1, 0, 0); if (t.transpose() * x_unit_vector < 0) { x_unit_vector *= -1; } const Eigen::Vector3d rotation_axis = t.cross(x_unit_vector); Eigen::Matrix3d R_x; if (rotation_axis.norm() < std::numeric_limits::epsilon()) { R_x = Eigen::Matrix3d::Identity(); } else { const double angle = std::acos(std::abs(t.transpose() * x_unit_vector) / (t.norm() * x_unit_vector.norm())); R_x = Eigen::AngleAxisd(angle, rotation_axis.normalized()); } // Apply the X-axis correction. R1 = R_x * R1; R2 = R_x * R2; t = R_x * t; // Determine the intrinsic calibration matrix. Eigen::Matrix3d K = Eigen::Matrix3d::Identity(); K(0, 0) = std::min(camera1.MeanFocalLength(), camera2.MeanFocalLength()); K(1, 1) = K(0, 0); K(0, 2) = camera1.PrincipalPointX(); K(1, 2) = (camera1.PrincipalPointY() + camera2.PrincipalPointY()) / 2; // Compose the homographies. *H1 = K * R1 * camera1.CalibrationMatrix().inverse(); *H2 = K * R2 * camera2.CalibrationMatrix().inverse(); // Determine the inverse projection matrix that transforms disparity values // to 3D world coordinates: [x, y, disparity, 1] * Q = [X, Y, Z, 1] * w. *Q = Eigen::Matrix4d::Identity(); (*Q)(3, 0) = -K(1, 2); (*Q)(3, 1) = -K(0, 2); (*Q)(3, 2) = K(0, 0); (*Q)(2, 3) = -1 / t(0); (*Q)(3, 3) = 0; } void RectifyAndUndistortStereoImages( const UndistortCameraOptions& options, const Bitmap& distorted_image1, const Bitmap& distorted_image2, const Camera& distorted_camera1, const Camera& distorted_camera2, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, Bitmap* undistorted_image1, Bitmap* undistorted_image2, Camera* undistorted_camera, Eigen::Matrix4d* Q) { CHECK_EQ(distorted_camera1.Width(), distorted_image1.Width()); CHECK_EQ(distorted_camera1.Height(), distorted_image1.Height()); CHECK_EQ(distorted_camera2.Width(), distorted_image2.Width()); CHECK_EQ(distorted_camera2.Height(), distorted_image2.Height()); *undistorted_camera = UndistortCamera(options, distorted_camera1); undistorted_image1->Allocate(static_cast(undistorted_camera->Width()), static_cast(undistorted_camera->Height()), distorted_image1.IsRGB()); distorted_image1.CloneMetadata(undistorted_image1); undistorted_image2->Allocate(static_cast(undistorted_camera->Width()), static_cast(undistorted_camera->Height()), distorted_image2.IsRGB()); distorted_image2.CloneMetadata(undistorted_image2); Eigen::Matrix3d H1; Eigen::Matrix3d H2; RectifyStereoCameras(*undistorted_camera, *undistorted_camera, qvec, tvec, &H1, &H2, Q); WarpImageWithHomographyBetweenCameras(H1.inverse(), distorted_camera1, *undistorted_camera, distorted_image1, undistorted_image1); WarpImageWithHomographyBetweenCameras(H2.inverse(), distorted_camera2, *undistorted_camera, distorted_image2, undistorted_image2); } } // namespace colmap colmap-3.4/src/base/undistortion.h000077500000000000000000000155371323400541200172560ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_UNDISTORTION_H_ #define COLMAP_SRC_BASE_UNDISTORTION_H_ #include "base/reconstruction.h" #include "util/alignment.h" #include "util/bitmap.h" #include "util/threading.h" namespace colmap { struct UndistortCameraOptions { // The amount of blank pixels in the undistorted image in the range [0, 1]. double blank_pixels = 0.0; // Minimum and maximum scale change of camera used to satisfy the blank // pixel constraint. double min_scale = 0.2; double max_scale = 2.0; // Maximum image size in terms of width or height of the undistorted camera. int max_image_size = -1; }; // Undistort images and export undistorted cameras, as required by the // mvs::PatchMatchController class. class COLMAPUndistorter : public Thread { public: COLMAPUndistorter(const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path); private: void Run(); void Undistort(const size_t reg_image_idx) const; void WritePatchMatchConfig() const; void WriteFusionConfig() const; void WriteScript(const bool geometric) const; UndistortCameraOptions options_; std::string image_path_; std::string output_path_; const Reconstruction& reconstruction_; }; // Undistort images and prepare data for CMVS/PMVS. class PMVSUndistorter : public Thread { public: PMVSUndistorter(const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path); private: void Run(); void Undistort(const size_t reg_image_idx) const; void WriteVisibilityData() const; void WriteOptionFile() const; void WritePMVSScript() const; void WriteCMVSPMVSScript() const; void WriteCOLMAPScript(const bool geometric) const; void WriteCMVSCOLMAPScript(const bool geometric) const; UndistortCameraOptions options_; std::string image_path_; std::string output_path_; const Reconstruction& reconstruction_; }; // Undistort images and prepare data for CMP-MVS. class CMPMVSUndistorter : public Thread { public: CMPMVSUndistorter(const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path); private: void Run(); void Undistort(const size_t reg_image_idx) const; UndistortCameraOptions options_; std::string image_path_; std::string output_path_; const Reconstruction& reconstruction_; }; // Rectify stereo image pairs. class StereoImageRectifier : public Thread { public: StereoImageRectifier( const UndistortCameraOptions& options, const Reconstruction& reconstruction, const std::string& image_path, const std::string& output_path, const std::vector>& stereo_pairs); private: void Run(); void Rectify(const image_t image_id1, const image_t image_id2) const; UndistortCameraOptions options_; std::string image_path_; std::string output_path_; const std::vector>& stereo_pairs_; const Reconstruction& reconstruction_; }; // Undistort camera by resizing the image and shifting the principal point. // // The scaling factor is computed such that no blank pixels are in the // undistorted image (blank_pixels=0) or all pixels in distorted image are // contained in output image (blank_pixels=1). // // The focal length of the image is preserved and the dimensions of the // undistorted pinhole camera are adjusted such that either all pixels in // the undistorted image have a corresponding pixel in the distorted image // (i.e. no blank pixels at the borders, for `blank_pixels=0`), or all pixels // in the distorted image project have a corresponding pixel in the undistorted // image (i.e. blank pixels at the borders, for `blank_pixels=1`). Intermediate // states can be achieved by setting `blank_pixels` between 0 and 1. // // The relative location of the principal point of the distorted camera is // preserved. The scaling of the image dimensions is subject to the `min_scale`, // `max_scale`, and `max_image_size` constraints. Camera UndistortCamera(const UndistortCameraOptions& options, const Camera& camera); // Undistort image such that the viewing geometry of the undistorted image // follows a pinhole camera model. See `UndistortCamera` for more details // on the undistortion conventions. void UndistortImage(const UndistortCameraOptions& options, const Bitmap& distorted_image, const Camera& distorted_camera, Bitmap* undistorted_image, Camera* undistorted_camera); // Undistort all cameras in the reconstruction and accordingly all // observations in their corresponding images. void UndistortReconstruction(const UndistortCameraOptions& options, Reconstruction* reconstruction); // Compute stereo rectification homographies that transform two images, // such that corresponding pixels in one image lie on the same scanline in the // other image. The matrix Q transforms disparity values to world coordinates // as [x, y, disparity, 1] * Q = [X, Y, Z, 1] * w. Note that this function // assumes that the two cameras are already undistorted. void RectifyStereoCameras(const Camera& camera1, const Camera& camera2, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, Eigen::Matrix3d* H1, Eigen::Matrix3d* H2, Eigen::Matrix4d* Q); // Rectify and undistort the stereo image pair using the given geometry. void RectifyAndUndistortStereoImages( const UndistortCameraOptions& options, const Bitmap& distorted_image1, const Bitmap& distorted_image2, const Camera& distorted_camera1, const Camera& distorted_camera2, const Eigen::Vector4d& qvec, const Eigen::Vector3d& tvec, Bitmap* undistorted_image1, Bitmap* undistorted_image2, Camera* undistorted_camera, Eigen::Matrix4d* Q); } // namespace colmap #endif // COLMAP_SRC_BASE_UNDISTORTION_H_ colmap-3.4/src/base/undistortion_test.cc000077500000000000000000000201061323400541200204370ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/undistortion" #include "util/testing.h" #include "base/pose.h" #include "base/undistortion.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestUndistortCamera) { UndistortCameraOptions options; Camera distorted_camera; Camera undistorted_camera; distorted_camera.InitializeWithName("SIMPLE_PINHOLE", 1, 1, 1); undistorted_camera = UndistortCamera(options, distorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 1); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 1); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 1); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 1); distorted_camera.InitializeWithName("SIMPLE_RADIAL", 1, 1, 1); undistorted_camera = UndistortCamera(options, distorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 1); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 1); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 1); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 1); distorted_camera.InitializeWithName("SIMPLE_RADIAL", 100, 100, 100); distorted_camera.Params(3) = 0.5; undistorted_camera = UndistortCamera(options, distorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 100); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 100); BOOST_CHECK_EQUAL(undistorted_camera.PrincipalPointX(), 84.0 / 2.0); BOOST_CHECK_EQUAL(undistorted_camera.PrincipalPointY(), 84.0 / 2.0); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 84); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 84); options.blank_pixels = 1; undistorted_camera = UndistortCamera(options, distorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 100); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 100); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 90); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 90); options.max_scale = 0.75; undistorted_camera = UndistortCamera(options, distorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 100); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 100); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 75); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 75); } BOOST_AUTO_TEST_CASE(TestUndistortCameraBlankPixels) { UndistortCameraOptions options; options.blank_pixels = 1; Camera distorted_camera; distorted_camera.InitializeWithName("SIMPLE_RADIAL", 100, 100, 100); distorted_camera.Params(3) = 0.5; Bitmap distorted_image; distorted_image.Allocate(100, 100, false); distorted_image.Fill(BitmapColor(255)); Bitmap undistorted_image; Camera undistorted_camera; UndistortImage(options, distorted_image, distorted_camera, &undistorted_image, &undistorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 100); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 100); BOOST_CHECK_EQUAL(undistorted_camera.PrincipalPointX(), 90.0 / 2.0); BOOST_CHECK_EQUAL(undistorted_camera.PrincipalPointY(), 90.0 / 2.0); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 90); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 90); // Make sure that there is no blank pixel. size_t num_blank_pixels = 0; for (int y = 0; y < undistorted_image.Height(); ++y) { for (int x = 0; x < undistorted_image.Width(); ++x) { BitmapColor color; BOOST_CHECK(undistorted_image.GetPixel(x, y, &color)); if (color == BitmapColor(0)) { num_blank_pixels += 1; } } } BOOST_CHECK_GT(num_blank_pixels, 0); } BOOST_AUTO_TEST_CASE(TestUndistortCameraNoBlankPixels) { UndistortCameraOptions options; options.blank_pixels = 0; Camera distorted_camera; distorted_camera.InitializeWithName("SIMPLE_RADIAL", 100, 100, 100); distorted_camera.Params(3) = 0.5; Bitmap distorted_image; distorted_image.Allocate(100, 100, false); distorted_image.Fill(BitmapColor(255)); Bitmap undistorted_image; Camera undistorted_camera; UndistortImage(options, distorted_image, distorted_camera, &undistorted_image, &undistorted_camera); BOOST_CHECK_EQUAL(undistorted_camera.ModelName(), "PINHOLE"); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthX(), 100); BOOST_CHECK_EQUAL(undistorted_camera.FocalLengthY(), 100); BOOST_CHECK_EQUAL(undistorted_camera.PrincipalPointX(), 84.0 / 2.0); BOOST_CHECK_EQUAL(undistorted_camera.PrincipalPointY(), 84.0 / 2.0); BOOST_CHECK_EQUAL(undistorted_camera.Width(), 84); BOOST_CHECK_EQUAL(undistorted_camera.Height(), 84); // Make sure that there is no blank pixel. for (int y = 0; y < undistorted_image.Height(); ++y) { for (int x = 0; x < undistorted_image.Width(); ++x) { BitmapColor color; BOOST_CHECK(undistorted_image.GetPixel(x, y, &color)); BOOST_CHECK_NE(color.r, 0); BOOST_CHECK_EQUAL(color.g, 0); BOOST_CHECK_EQUAL(color.b, 0); } } } BOOST_AUTO_TEST_CASE(TestUndistortReconstruction) { const size_t kNumImages = 10; const size_t kNumPoints2D = 10; Reconstruction reconstruction; Camera camera; camera.SetCameraId(1); camera.InitializeWithName("OPENCV", 1, 1, 1); camera.Params(4) = 1.0; reconstruction.AddCamera(camera); for (image_t image_id = 1; image_id <= kNumImages; ++image_id) { Image image; image.SetImageId(image_id); image.SetCameraId(1); image.SetName("image" + std::to_string(image_id)); image.SetPoints2D( std::vector(kNumPoints2D, Eigen::Vector2d::Ones())); reconstruction.AddImage(image); reconstruction.RegisterImage(image_id); } UndistortCameraOptions options; UndistortReconstruction(options, &reconstruction); for (const auto& camera : reconstruction.Cameras()) { BOOST_CHECK_EQUAL(camera.second.ModelName(), "PINHOLE"); } for (const auto& image : reconstruction.Images()) { for (const auto& point2D : image.second.Points2D()) { BOOST_CHECK_NE(point2D.XY(), Eigen::Vector2d::Ones()); } } } BOOST_AUTO_TEST_CASE(TestRectifyStereoCameras) { Camera camera1; camera1.SetCameraId(1); camera1.InitializeWithName("PINHOLE", 1, 1, 1); Camera camera2; camera2.SetCameraId(1); camera2.InitializeWithName("PINHOLE", 1, 1, 1); const Eigen::Vector4d qvec = RotationMatrixToQuaternion(EulerAnglesToRotationMatrix(0.1, 0.2, 0.3)); const Eigen::Vector3d tvec(0.1, 0.2, 0.3); Camera rectified_camera1; Camera rectified_camera2; Eigen::Matrix3d H1; Eigen::Matrix3d H2; Eigen::Matrix4d Q; RectifyStereoCameras(camera1, camera2, qvec, tvec, &H1, &H2, &Q); Eigen::Matrix3d H1_ref; H1_ref << -0.202759, -0.815848, -0.897034, 0.416329, 0.733069, -0.199657, 0.910839, -0.175408, 0.942638; BOOST_CHECK(H1.isApprox(H1_ref.transpose(), 1e-5)); Eigen::Matrix3d H2_ref; H2_ref << -0.082173, -1.01288, -0.698868, 0.301854, 0.472844, -0.465336, 0.963533, 0.292411, 1.12528; BOOST_CHECK(H2.isApprox(H2_ref.transpose(), 1e-5)); Eigen::Matrix4d Q_ref; Q_ref << 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -2.67261, -0.5, -0.5, 1, 0; BOOST_CHECK(Q.isApprox(Q_ref, 1e-5)); } colmap-3.4/src/base/visibility_pyramid.cc000077500000000000000000000053531323400541200205620ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/visibility_pyramid.h" #include "util/logging.h" #include "util/math.h" namespace colmap { VisibilityPyramid::VisibilityPyramid() : VisibilityPyramid(0, 0, 0) {} VisibilityPyramid::VisibilityPyramid(const size_t num_levels, const size_t width, const size_t height) : width_(width), height_(height), score_(0), max_score_(0) { pyramid_.resize(num_levels); for (size_t level = 0; level < num_levels; ++level) { const size_t level_plus_one = level + 1; const int dim = 1 << level_plus_one; pyramid_[level].setZero(dim, dim); max_score_ += dim * dim * dim * dim; } } void VisibilityPyramid::SetPoint(const double x, const double y) { CHECK_GT(pyramid_.size(), 0); size_t cx = 0; size_t cy = 0; CellForPoint(x, y, &cx, &cy); for (int i = static_cast(pyramid_.size() - 1); i >= 0; --i) { auto& level = pyramid_[i]; level(cy, cx) += 1; if (level(cy, cx) == 1) { score_ += level.size(); } cx = cx >> 1; cy = cy >> 1; } CHECK_LE(score_, max_score_); } void VisibilityPyramid::ResetPoint(const double x, const double y) { CHECK_GT(pyramid_.size(), 0); size_t cx = 0; size_t cy = 0; CellForPoint(x, y, &cx, &cy); for (int i = static_cast(pyramid_.size() - 1); i >= 0; --i) { auto& level = pyramid_[i]; level(cy, cx) -= 1; if (level(cy, cx) == 0) { score_ -= level.size(); } cx = cx >> 1; cy = cy >> 1; } CHECK_LE(score_, max_score_); } void VisibilityPyramid::CellForPoint(const double x, const double y, size_t* cx, size_t* cy) const { CHECK_GT(width_, 0); CHECK_GT(height_, 0); const int max_dim = 1 << pyramid_.size(); *cx = Clip(static_cast(max_dim * x / width_), 0, static_cast(max_dim - 1)); *cy = Clip(static_cast(max_dim * y / height_), 0, static_cast(max_dim - 1)); } } // namespace colmap colmap-3.4/src/base/visibility_pyramid.h000077500000000000000000000057161323400541200204270ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_VISIBILITY_PYRAMID_H_ #define COLMAP_SRC_BASE_VISIBILITY_PYRAMID_H_ #include #include #include "util/alignment.h" namespace colmap { // A class that captures the distribution of points in a 2D grid. // For example, to capture the distribution of visible 3D points in an image. // // The class captures the distribution of points by a score. A higher score // corresponds to a more uniform distribution of the points in the grid. // // The score is computed by the number of populated cells in a multi-resolution // pyramid. A populated cell contributes to the overall score if it is // populated by at least one point and the contributed score is according // to its resolution in the pyramid. A cell in a higher resolution level // contributes a higher score to the overall score. class VisibilityPyramid { public: VisibilityPyramid(); VisibilityPyramid(const size_t num_levels, const size_t width, const size_t height); void SetPoint(const double x, const double y); void ResetPoint(const double x, const double y); inline size_t NumLevels() const; inline size_t Width() const; inline size_t Height() const; inline size_t Score() const; inline size_t MaxScore() const; private: void CellForPoint(const double x, const double y, size_t* cx, size_t* cy) const; // Range of the input points. size_t width_; size_t height_; // The overall visibility score. size_t score_; // The maximum score when all cells are populated. size_t max_score_; // The visibilty pyramid with multiple levels. std::vector pyramid_; }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// size_t VisibilityPyramid::NumLevels() const { return pyramid_.size(); } size_t VisibilityPyramid::Width() const { return width_; } size_t VisibilityPyramid::Height() const { return height_; } size_t VisibilityPyramid::Score() const { return score_; } size_t VisibilityPyramid::MaxScore() const { return max_score_; } } // namespace colmap #endif // COLMAP_SRC_BASE_VISIBILITY_PYRAMID_H_ colmap-3.4/src/base/visibility_pyramid_test.cc000077500000000000000000000055741323400541200216260ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/visibility_pyramid" #include "util/testing.h" #include "base/visibility_pyramid.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestDefault) { VisibilityPyramid pyramid; BOOST_CHECK_EQUAL(pyramid.NumLevels(), 0); BOOST_CHECK_EQUAL(pyramid.Width(), 0); BOOST_CHECK_EQUAL(pyramid.Height(), 0); BOOST_CHECK_EQUAL(pyramid.Score(), 0); } BOOST_AUTO_TEST_CASE(TestScore) { for (int num_levels = 1; num_levels < 8; ++num_levels) { Eigen::VectorXi scores(num_levels); size_t max_score = 0; for (int i = 1; i <= num_levels; ++i) { scores(i - 1) = (1 << i) * (1 << i); max_score += scores(i - 1) * scores(i - 1); } VisibilityPyramid pyramid(static_cast(num_levels), 4, 4); BOOST_CHECK_EQUAL(pyramid.NumLevels(), num_levels); BOOST_CHECK_EQUAL(pyramid.Width(), 4); BOOST_CHECK_EQUAL(pyramid.Height(), 4); BOOST_CHECK_EQUAL(pyramid.Score(), 0); BOOST_CHECK_EQUAL(pyramid.MaxScore(), max_score); BOOST_CHECK_EQUAL(pyramid.Score(), 0); pyramid.SetPoint(0, 0); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum()); pyramid.SetPoint(0, 0); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum()); pyramid.SetPoint(0, 1); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum() + scores.tail(scores.size() - 1).sum()); pyramid.SetPoint(0, 1); pyramid.SetPoint(0, 1); pyramid.SetPoint(1, 0); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum() + 2 * scores.tail(scores.size() - 1).sum()); pyramid.SetPoint(1, 0); pyramid.SetPoint(1, 1); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum() + 3 * scores.tail(scores.size() - 1).sum()); pyramid.ResetPoint(0, 0); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum() + 3 * scores.tail(scores.size() - 1).sum()); pyramid.ResetPoint(0, 0); BOOST_CHECK_EQUAL(pyramid.Score(), scores.sum() + 2 * scores.tail(scores.size() - 1).sum()); pyramid.SetPoint(0, 2); BOOST_CHECK_EQUAL( pyramid.Score(), 2 * scores.sum() + 2 * scores.tail(scores.size() - 1).sum()); } } colmap-3.4/src/base/warp.cc000077500000000000000000000175361323400541200156250ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "base/warp.h" #include "ext/VLFeat/imopv.h" #include "util/logging.h" namespace colmap { namespace { float GetPixelConstantBorder(const float* data, const int rows, const int cols, const int row, const int col) { if (row >= 0 && col >= 0 && row < rows && col < cols) { return data[row * cols + col]; } else { return 0; } } } // namespace void WarpImageBetweenCameras(const Camera& source_camera, const Camera& target_camera, const Bitmap& source_image, Bitmap* target_image) { CHECK_EQ(source_camera.Width(), source_image.Width()); CHECK_EQ(source_camera.Height(), source_image.Height()); CHECK_NOTNULL(target_image); target_image->Allocate(static_cast(target_camera.Width()), static_cast(target_camera.Height()), source_image.IsRGB()); Eigen::Vector2d image_point; for (int y = 0; y < target_image->Height(); ++y) { image_point.y() = y + 0.5; for (int x = 0; x < target_image->Width(); ++x) { image_point.x() = x + 0.5; // Camera models assume that the upper left pixel center is (0.5, 0.5). const Eigen::Vector2d world_point = target_camera.ImageToWorld(image_point); const Eigen::Vector2d source_point = source_camera.WorldToImage(world_point); BitmapColor color; if (source_image.InterpolateBilinear(source_point.x() - 0.5, source_point.y() - 0.5, &color)) { target_image->SetPixel(x, y, color.Cast()); } else { target_image->SetPixel(x, y, BitmapColor(0)); } } } } void WarpImageWithHomography(const Eigen::Matrix3d& H, const Bitmap& source_image, Bitmap* target_image) { CHECK_NOTNULL(target_image); CHECK_GT(target_image->Width(), 0); CHECK_GT(target_image->Height(), 0); CHECK_EQ(source_image.IsRGB(), target_image->IsRGB()); Eigen::Vector3d target_pixel(0, 0, 1); for (int y = 0; y < target_image->Height(); ++y) { target_pixel.y() = y + 0.5; for (int x = 0; x < target_image->Width(); ++x) { target_pixel.x() = x + 0.5; const Eigen::Vector2d source_pixel = (H * target_pixel).hnormalized(); BitmapColor color; if (source_image.InterpolateBilinear(source_pixel.x() - 0.5, source_pixel.y() - 0.5, &color)) { target_image->SetPixel(x, y, color.Cast()); } else { target_image->SetPixel(x, y, BitmapColor(0)); } } } } void WarpImageWithHomographyBetweenCameras(const Eigen::Matrix3d& H, const Camera& source_camera, const Camera& target_camera, const Bitmap& source_image, Bitmap* target_image) { CHECK_EQ(source_camera.Width(), source_image.Width()); CHECK_EQ(source_camera.Height(), source_image.Height()); CHECK_NOTNULL(target_image); target_image->Allocate(static_cast(target_camera.Width()), static_cast(target_camera.Height()), source_image.IsRGB()); Eigen::Vector3d image_point(0, 0, 1); for (int y = 0; y < target_image->Height(); ++y) { image_point.y() = y + 0.5; for (int x = 0; x < target_image->Width(); ++x) { image_point.x() = x + 0.5; // Camera models assume that the upper left pixel center is (0.5, 0.5). const Eigen::Vector3d warped_point = H * image_point; const Eigen::Vector2d world_point = target_camera.ImageToWorld(warped_point.hnormalized()); const Eigen::Vector2d source_point = source_camera.WorldToImage(world_point); BitmapColor color; if (source_image.InterpolateBilinear(source_point.x() - 0.5, source_point.y() - 0.5, &color)) { target_image->SetPixel(x, y, color.Cast()); } else { target_image->SetPixel(x, y, BitmapColor(0)); } } } } void ResampleImageBilinear(const float* data, const int rows, const int cols, const int new_rows, const int new_cols, float* resampled) { CHECK_NOTNULL(data); CHECK_NOTNULL(resampled); CHECK_GT(rows, 0); CHECK_GT(cols, 0); CHECK_GT(new_rows, 0); CHECK_GT(new_cols, 0); const float scale_r = static_cast(rows) / static_cast(new_rows); const float scale_c = static_cast(cols) / static_cast(new_cols); for (int r = 0; r < new_rows; ++r) { const float r_i = (r + 0.5f) * scale_r - 0.5f; const int r_i_min = std::floor(r_i); const int r_i_max = r_i_min + 1; const float d_r_min = r_i - r_i_min; const float d_r_max = r_i_max - r_i; for (int c = 0; c < new_cols; ++c) { const float c_i = (c + 0.5f) * scale_c - 0.5f; const int c_i_min = std::floor(c_i); const int c_i_max = c_i_min + 1; const float d_c_min = c_i - c_i_min; const float d_c_max = c_i_max - c_i; // Interpolation in column direction. const float value1 = d_c_max * GetPixelConstantBorder(data, rows, cols, r_i_min, c_i_min) + d_c_min * GetPixelConstantBorder(data, rows, cols, r_i_min, c_i_max); const float value2 = d_c_max * GetPixelConstantBorder(data, rows, cols, r_i_max, c_i_min) + d_c_min * GetPixelConstantBorder(data, rows, cols, r_i_max, c_i_max); // Interpolation in row direction. resampled[r * new_cols + c] = d_r_max * value1 + d_r_min * value2; } } } void SmoothImage(const float* data, const int rows, const int cols, const float sigma_r, const float sigma_c, float* smoothed) { CHECK_NOTNULL(data); CHECK_NOTNULL(smoothed); CHECK_GT(rows, 0); CHECK_GT(cols, 0); CHECK_GT(sigma_r, 0); CHECK_GT(sigma_c, 0); vl_imsmooth_f(smoothed, cols, data, cols, rows, cols, sigma_c, sigma_r); } void DownsampleImage(const float* data, const int rows, const int cols, const int new_rows, const int new_cols, float* downsampled) { CHECK_NOTNULL(data); CHECK_NOTNULL(downsampled); CHECK_LE(new_rows, rows); CHECK_LE(new_cols, cols); CHECK_GT(rows, 0); CHECK_GT(cols, 0); CHECK_GT(new_rows, 0); CHECK_GT(new_cols, 0); const float scale_c = static_cast(cols) / static_cast(new_cols); const float scale_r = static_cast(rows) / static_cast(new_rows); const float kSigmaScale = 0.5f; const float sigma_c = std::max(std::numeric_limits::epsilon(), kSigmaScale * (scale_c - 1)); const float sigma_r = std::max(std::numeric_limits::epsilon(), kSigmaScale * (scale_r - 1)); std::vector smoothed(rows * cols); SmoothImage(data, rows, cols, sigma_r, sigma_c, smoothed.data()); ResampleImageBilinear(smoothed.data(), rows, cols, new_rows, new_cols, downsampled); } } // namespace colmap colmap-3.4/src/base/warp.h000077500000000000000000000060261323400541200154570ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_WARP_H_ #define COLMAP_SRC_BASE_WARP_H_ #include "base/camera.h" #include "util/alignment.h" #include "util/bitmap.h" namespace colmap { // Warp source image to target image by projecting the pixels of the target // image up to infinity and projecting it down into the source image // (i.e. an inverse mapping). The function allocates the target image. void WarpImageBetweenCameras(const Camera& source_camera, const Camera& target_camera, const Bitmap& source_image, Bitmap* target_image); // Warp an image with the given homography, where H defines the pixel mapping // from the target to source image. Note that the pixel centers are assumed to // have coordinates (0.5, 0.5). void WarpImageWithHomography(const Eigen::Matrix3d& H, const Bitmap& source_image, Bitmap* target_image); // First, warp source image to target image by projecting the pixels of the // target image up to infinity and projecting it down into the source image // (i.e. an inverse mapping). Second, warp the coordinates from the first // warping with the given homography. The function allocates the target image. void WarpImageWithHomographyBetweenCameras(const Eigen::Matrix3d& H, const Camera& source_camera, const Camera& target_camera, const Bitmap& source_image, Bitmap* target_image); // Resample row-major image using bilinear interpolation. void ResampleImageBilinear(const float* data, const int rows, const int cols, const int new_rows, const int new_cols, float* resampled); // Smooth row-major image using a Gaussian filter kernel. void SmoothImage(const float* data, const int rows, const int cols, const float sigma_r, const float sigma_c, float* smoothed); // Downsample row-major image by first smoothing and then resampling. void DownsampleImage(const float* data, const int rows, const int cols, const int new_rows, const int new_cols, float* downsampled); } // namespace colmap #endif // COLMAP_SRC_BASE_WARP_H_ colmap-3.4/src/base/warp_test.cc000077500000000000000000000226421323400541200166560ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/warp" #include "util/testing.h" #include "base/warp.h" #include "util/random.h" using namespace colmap; namespace { void GenerateRandomBitmap(const int width, const int height, const bool as_rgb, Bitmap* bitmap) { bitmap->Allocate(width, height, as_rgb); for (int x = 0; x < width; ++x) { for (int y = 0; y < height; ++y) { BitmapColor color; color.r = RandomInteger(0, 255); color.g = RandomInteger(0, 255); color.b = RandomInteger(0, 255); bitmap->SetPixel(x, y, color); } } } // Check that the two bitmaps are equal, ignoring a 1px boundary. void CheckBitmapsEqual(const Bitmap& bitmap1, const Bitmap& bitmap2) { BOOST_REQUIRE_EQUAL(bitmap1.IsGrey(), bitmap2.IsGrey()); BOOST_REQUIRE_EQUAL(bitmap1.IsRGB(), bitmap2.IsRGB()); BOOST_REQUIRE_EQUAL(bitmap1.Width(), bitmap2.Width()); BOOST_REQUIRE_EQUAL(bitmap1.Height(), bitmap2.Height()); for (int x = 1; x < bitmap1.Width() - 1; ++x) { for (int y = 1; y < bitmap1.Height() - 1; ++y) { BitmapColor color1; BitmapColor color2; BOOST_CHECK(bitmap1.GetPixel(x, y, &color1)); BOOST_CHECK(bitmap2.GetPixel(x, y, &color2)); BOOST_CHECK_EQUAL(color1, color2); } } } // Check that the two bitmaps are equal, ignoring a 1px boundary. void CheckBitmapsTransposed(const Bitmap& bitmap1, const Bitmap& bitmap2) { BOOST_REQUIRE_EQUAL(bitmap1.IsGrey(), bitmap2.IsGrey()); BOOST_REQUIRE_EQUAL(bitmap1.IsRGB(), bitmap2.IsRGB()); BOOST_REQUIRE_EQUAL(bitmap1.Width(), bitmap2.Width()); BOOST_REQUIRE_EQUAL(bitmap1.Height(), bitmap2.Height()); for (int x = 1; x < bitmap1.Width() - 1; ++x) { for (int y = 1; y < bitmap1.Height() - 1; ++y) { BitmapColor color1; BitmapColor color2; BOOST_CHECK(bitmap1.GetPixel(x, y, &color1)); BOOST_CHECK(bitmap2.GetPixel(y, x, &color2)); BOOST_CHECK_EQUAL(color1, color2); } } } } // namespace BOOST_AUTO_TEST_CASE(TestIdenticalCameras) { Camera source_camera; source_camera.InitializeWithName("PINHOLE", 1, 100, 100); Camera target_camera = source_camera; Bitmap source_image_gray; GenerateRandomBitmap(100, 100, false, &source_image_gray); Bitmap target_image_gray; WarpImageBetweenCameras(source_camera, target_camera, source_image_gray, &target_image_gray); CheckBitmapsEqual(source_image_gray, target_image_gray); Bitmap source_image_rgb; GenerateRandomBitmap(100, 100, true, &source_image_rgb); Bitmap target_image_rgb; WarpImageBetweenCameras(source_camera, target_camera, source_image_rgb, &target_image_rgb); CheckBitmapsEqual(source_image_rgb, target_image_rgb); } BOOST_AUTO_TEST_CASE(TestShiftedCameras) { Camera source_camera; source_camera.InitializeWithName("PINHOLE", 1, 100, 100); Camera target_camera = source_camera; target_camera.SetPrincipalPointX(0.0); Bitmap source_image_gray; GenerateRandomBitmap(100, 100, true, &source_image_gray); Bitmap target_image_gray; WarpImageBetweenCameras(source_camera, target_camera, source_image_gray, &target_image_gray); for (int x = 0; x < target_image_gray.Width(); ++x) { for (int y = 0; y < target_image_gray.Height(); ++y) { BitmapColor color; BOOST_CHECK(target_image_gray.GetPixel(x, y, &color)); if (x >= 50) { BOOST_CHECK_EQUAL(color, BitmapColor(0)); } else { BitmapColor source_color; if (source_image_gray.GetPixel(x + 50, y, &source_color) && color != BitmapColor(0)) { BOOST_CHECK_EQUAL(color, source_color); } } } } } BOOST_AUTO_TEST_CASE(TestWarpImageWithHomographyIdentity) { Bitmap source_image_gray; GenerateRandomBitmap(100, 100, false, &source_image_gray); Bitmap target_image_gray; target_image_gray.Allocate(100, 100, false); WarpImageWithHomography(Eigen::Matrix3d::Identity(), source_image_gray, &target_image_gray); CheckBitmapsEqual(source_image_gray, target_image_gray); Bitmap source_image_rgb; GenerateRandomBitmap(100, 100, true, &source_image_rgb); Bitmap target_image_rgb; target_image_rgb.Allocate(100, 100, true); WarpImageWithHomography(Eigen::Matrix3d::Identity(), source_image_rgb, &target_image_rgb); CheckBitmapsEqual(source_image_rgb, target_image_rgb); } BOOST_AUTO_TEST_CASE(TestWarpImageWithHomographyTransposed) { Eigen::Matrix3d H; H << 0, 1, 0, 1, 0, 0, 0, 0, 1; Bitmap source_image_gray; GenerateRandomBitmap(100, 100, false, &source_image_gray); Bitmap target_image_gray; target_image_gray.Allocate(100, 100, false); WarpImageWithHomography(H, source_image_gray, &target_image_gray); CheckBitmapsTransposed(source_image_gray, target_image_gray); Bitmap source_image_rgb; GenerateRandomBitmap(100, 100, true, &source_image_rgb); Bitmap target_image_rgb; target_image_rgb.Allocate(100, 100, true); WarpImageWithHomography(H, source_image_rgb, &target_image_rgb); CheckBitmapsTransposed(source_image_rgb, target_image_rgb); } BOOST_AUTO_TEST_CASE(TestWarpImageWithHomographyBetweenCamerasIdentity) { Camera source_camera; source_camera.InitializeWithName("PINHOLE", 1, 100, 100); Camera target_camera = source_camera; Bitmap source_image_gray; GenerateRandomBitmap(100, 100, false, &source_image_gray); Bitmap target_image_gray; target_image_gray.Allocate(100, 100, false); WarpImageWithHomographyBetweenCameras(Eigen::Matrix3d::Identity(), source_camera, target_camera, source_image_gray, &target_image_gray); CheckBitmapsEqual(source_image_gray, target_image_gray); Bitmap source_image_rgb; GenerateRandomBitmap(100, 100, true, &source_image_rgb); Bitmap target_image_rgb; target_image_rgb.Allocate(100, 100, true); WarpImageWithHomographyBetweenCameras(Eigen::Matrix3d::Identity(), source_camera, target_camera, source_image_rgb, &target_image_rgb); CheckBitmapsEqual(source_image_rgb, target_image_rgb); } BOOST_AUTO_TEST_CASE(TestWarpImageWithHomographyBetweenCamerasTransposed) { Camera source_camera; source_camera.InitializeWithName("PINHOLE", 1, 100, 100); Camera target_camera = source_camera; Eigen::Matrix3d H; H << 0, 1, 0, 1, 0, 0, 0, 0, 1; Bitmap source_image_gray; GenerateRandomBitmap(100, 100, false, &source_image_gray); Bitmap target_image_gray; target_image_gray.Allocate(100, 100, false); WarpImageWithHomographyBetweenCameras(H, source_camera, target_camera, source_image_gray, &target_image_gray); CheckBitmapsTransposed(source_image_gray, target_image_gray); Bitmap source_image_rgb; GenerateRandomBitmap(100, 100, true, &source_image_rgb); Bitmap target_image_rgb; target_image_rgb.Allocate(100, 100, true); WarpImageWithHomographyBetweenCameras(H, source_camera, target_camera, source_image_rgb, &target_image_rgb); CheckBitmapsTransposed(source_image_rgb, target_image_rgb); } BOOST_AUTO_TEST_CASE(TestResampleImageBilinear) { std::vector image(16); for (size_t i = 0; i < image.size(); ++i) { image[i] = i; } std::vector resampled(4); ResampleImageBilinear(image.data(), 4, 4, 2, 2, resampled.data()); BOOST_CHECK_EQUAL(resampled[0], 2.5); BOOST_CHECK_EQUAL(resampled[1], 4.5); BOOST_CHECK_EQUAL(resampled[2], 10.5); BOOST_CHECK_EQUAL(resampled[3], 12.5); } BOOST_AUTO_TEST_CASE(TestSmoothImage) { std::vector image(16); for (size_t i = 0; i < image.size(); ++i) { image[i] = i; } std::vector smoothed(16); SmoothImage(image.data(), 4, 4, 1, 1, smoothed.data()); BOOST_CHECK_CLOSE(smoothed[0], 1.81673253, 1e-3); BOOST_CHECK_CLOSE(smoothed[1], 2.51182437, 1e-3); BOOST_CHECK_CLOSE(smoothed[2], 3.39494729, 1e-3); BOOST_CHECK_CLOSE(smoothed[3], 4.09003973, 1e-3); BOOST_CHECK_CLOSE(smoothed[4], 4.59710073, 1e-3); BOOST_CHECK_CLOSE(smoothed[5], 5.29219341, 1e-3); BOOST_CHECK_CLOSE(smoothed[6], 6.17531633, 1e-3); BOOST_CHECK_CLOSE(smoothed[7], 6.87040806, 1e-3); } BOOST_AUTO_TEST_CASE(TestDownsampleImage) { std::vector image(16); for (size_t i = 0; i < image.size(); ++i) { image[i] = i; } std::vector downsampled(4); DownsampleImage(image.data(), 4, 4, 2, 2, downsampled.data()); BOOST_CHECK_CLOSE(downsampled[0], 2.76810598, 1e-3); BOOST_CHECK_CLOSE(downsampled[1], 4.66086388, 1e-3); BOOST_CHECK_CLOSE(downsampled[2], 10.3391361, 1e-3); BOOST_CHECK_CLOSE(downsampled[3], 12.2318935, 1e-3); } colmap-3.4/src/controllers/000077500000000000000000000000001323400541200157625ustar00rootroot00000000000000colmap-3.4/src/controllers/CMakeLists.txt000066400000000000000000000004111323400541200205160ustar00rootroot00000000000000set(FOLDER_NAME "controllers") COLMAP_ADD_LIBRARY(controllers automatic_reconstruction.h automatic_reconstruction.cc bundle_adjustment.h bundle_adjustment.cc hierarchical_mapper.h hierarchical_mapper.cc incremental_mapper.h incremental_mapper.cc ) colmap-3.4/src/controllers/automatic_reconstruction.cc000066400000000000000000000225261323400541200234270ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "controllers/automatic_reconstruction.h" #include "base/undistortion.h" #include "controllers/incremental_mapper.h" #include "feature/extraction.h" #include "feature/matching.h" #include "mvs/fusion.h" #include "mvs/meshing.h" #include "mvs/patch_match.h" #include "util/misc.h" #include "util/option_manager.h" namespace colmap { AutomaticReconstructionController::AutomaticReconstructionController( const Options& options, ReconstructionManager* reconstruction_manager) : options_(options), reconstruction_manager_(reconstruction_manager), active_thread_(nullptr) { CHECK(ExistsDir(options_.workspace_path)); CHECK(ExistsDir(options_.image_path)); CHECK_NOTNULL(reconstruction_manager_); option_manager_.AddAllOptions(); *option_manager_.image_path = options_.image_path; *option_manager_.database_path = JoinPaths(options_.workspace_path, "database.db"); if (options_.data_type == DataType::VIDEO) { option_manager_.ModifyForVideoData(); } else if (options_.data_type == DataType::INDIVIDUAL) { option_manager_.ModifyForIndividualData(); } else if (options_.data_type == DataType::INTERNET) { option_manager_.ModifyForInternetData(); } else { LOG(FATAL) << "Data type not supported"; } CHECK(ExistsCameraModelWithName(options_.camera_model)); if (options_.quality == Quality::LOW) { option_manager_.ModifyForLowQuality(); } else if (options_.quality == Quality::MEDIUM) { option_manager_.ModifyForMediumQuality(); } else if (options_.quality == Quality::HIGH) { option_manager_.ModifyForHighQuality(); } else if (options_.quality == Quality::EXTREME) { option_manager_.ModifyForExtremeQuality(); } option_manager_.sift_extraction->num_threads = options_.num_threads; option_manager_.sift_matching->num_threads = options_.num_threads; option_manager_.mapper->num_threads = options_.num_threads; option_manager_.dense_meshing->num_threads = options_.num_threads; ImageReaderOptions reader_options = *option_manager_.image_reader; reader_options.database_path = *option_manager_.database_path; reader_options.image_path = *option_manager_.image_path; reader_options.single_camera = options_.single_camera; reader_options.camera_model = options_.camera_model; option_manager_.sift_extraction->use_gpu = options_.use_gpu; option_manager_.sift_matching->use_gpu = options_.use_gpu; option_manager_.sift_extraction->gpu_index = options_.gpu_index; option_manager_.sift_matching->gpu_index = options_.gpu_index; option_manager_.dense_stereo->gpu_index = options_.gpu_index; feature_extractor_.reset(new SiftFeatureExtractor( reader_options, *option_manager_.sift_extraction)); exhaustive_matcher_.reset(new ExhaustiveFeatureMatcher( *option_manager_.exhaustive_matching, *option_manager_.sift_matching, *option_manager_.database_path)); if (!options_.vocab_tree_path.empty()) { option_manager_.sequential_matching->loop_detection = true; option_manager_.sequential_matching->vocab_tree_path = options_.vocab_tree_path; } sequential_matcher_.reset(new SequentialFeatureMatcher( *option_manager_.sequential_matching, *option_manager_.sift_matching, *option_manager_.database_path)); if (!options_.vocab_tree_path.empty()) { option_manager_.vocab_tree_matching->vocab_tree_path = options_.vocab_tree_path; vocab_tree_matcher_.reset(new VocabTreeFeatureMatcher( *option_manager_.vocab_tree_matching, *option_manager_.sift_matching, *option_manager_.database_path)); } } void AutomaticReconstructionController::Stop() { if (active_thread_ != nullptr) { active_thread_->Stop(); } Thread::Stop(); } void AutomaticReconstructionController::Run() { if (IsStopped()) { return; } RunFeatureExtraction(); if (IsStopped()) { return; } RunFeatureMatching(); if (IsStopped()) { return; } if (options_.sparse) { RunSparseMapper(); } if (IsStopped()) { return; } if (options_.dense) { RunDenseMapper(); } } void AutomaticReconstructionController::RunFeatureExtraction() { CHECK(feature_extractor_); active_thread_ = feature_extractor_.get(); feature_extractor_->Start(); feature_extractor_->Wait(); feature_extractor_.reset(); active_thread_ = nullptr; } void AutomaticReconstructionController::RunFeatureMatching() { Thread* matcher = nullptr; if (options_.data_type == DataType::VIDEO) { matcher = sequential_matcher_.get(); } else if (options_.data_type == DataType::INDIVIDUAL || options_.data_type == DataType::INTERNET) { Database database(*option_manager_.database_path); const size_t num_images = database.NumImages(); if (options_.vocab_tree_path.empty() || num_images < 200) { matcher = exhaustive_matcher_.get(); } else { matcher = vocab_tree_matcher_.get(); } } CHECK(matcher); active_thread_ = matcher; matcher->Start(); matcher->Wait(); exhaustive_matcher_.reset(); sequential_matcher_.reset(); vocab_tree_matcher_.reset(); active_thread_ = nullptr; } void AutomaticReconstructionController::RunSparseMapper() { const auto sparse_path = JoinPaths(options_.workspace_path, "sparse"); if (ExistsDir(sparse_path)) { auto dir_list = GetDirList(sparse_path); std::sort(dir_list.begin(), dir_list.end()); if (dir_list.size() > 0) { std::cout << std::endl << "WARNING: Skipping sparse reconstruction because it is " "already computed" << std::endl; for (const auto& dir : dir_list) { reconstruction_manager_->Read(dir); } return; } } IncrementalMapperController mapper( option_manager_.mapper.get(), *option_manager_.image_path, *option_manager_.database_path, reconstruction_manager_); active_thread_ = &mapper; mapper.Start(); mapper.Wait(); active_thread_ = nullptr; CreateDirIfNotExists(sparse_path); reconstruction_manager_->Write(sparse_path, &option_manager_); } void AutomaticReconstructionController::RunDenseMapper() { #ifndef CUDA_ENABLED std::cout << std::endl << "WARNING: Skipping dense reconstruction because CUDA is not available" << std::endl; return; #endif CreateDirIfNotExists(JoinPaths(options_.workspace_path, "dense")); for (size_t i = 0; i < reconstruction_manager_->Size(); ++i) { if (IsStopped()) { return; } const std::string dense_path = JoinPaths(options_.workspace_path, "dense", std::to_string(i)); const std::string fused_path = JoinPaths(dense_path, "fused.ply"); const std::string meshed_path = JoinPaths(dense_path, "meshed.ply"); if (ExistsFile(fused_path) && ExistsFile(meshed_path)) { continue; } // Image undistortion if (!ExistsDir(dense_path)) { CreateDirIfNotExists(dense_path); UndistortCameraOptions undistortion_options; undistortion_options.max_image_size = option_manager_.dense_stereo->max_image_size; COLMAPUndistorter undistorter(undistortion_options, reconstruction_manager_->Get(i), *option_manager_.image_path, dense_path); active_thread_ = &undistorter; undistorter.Start(); undistorter.Wait(); active_thread_ = nullptr; } if (IsStopped()) { return; } // Dense stereo { mvs::PatchMatchController patch_match_controller( *option_manager_.dense_stereo, dense_path, "COLMAP", ""); active_thread_ = &patch_match_controller; patch_match_controller.Start(); patch_match_controller.Wait(); active_thread_ = nullptr; } if (IsStopped()) { return; } // Dense fusion if (!ExistsFile(fused_path)) { auto fusion_options = *option_manager_.dense_fusion; const int num_reg_images = reconstruction_manager_->Get(i).NumRegImages(); fusion_options.min_num_pixels = std::min(num_reg_images + 1, fusion_options.min_num_pixels); mvs::StereoFusion fuser( fusion_options, dense_path, "COLMAP", "", options_.quality == Quality::HIGH ? "geometric" : "photometric"); active_thread_ = &fuser; fuser.Start(); fuser.Wait(); active_thread_ = nullptr; std::cout << "Writing output: " << fused_path << std::endl; WritePlyBinary(fused_path, fuser.GetFusedPoints()); } if (IsStopped()) { return; } // Dense meshing if (!ExistsFile(meshed_path)) { mvs::PoissonReconstruction(*option_manager_.dense_meshing, fused_path, meshed_path); } } } } // namespace colmap colmap-3.4/src/controllers/automatic_reconstruction.h000066400000000000000000000062161323400541200232670ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_CONTROLLERS_AUTOMATIC_RECONSTRUCTION_H_ #define COLMAP_SRC_CONTROLLERS_AUTOMATIC_RECONSTRUCTION_H_ #include #include "base/reconstruction_manager.h" #include "util/option_manager.h" #include "util/threading.h" namespace colmap { class AutomaticReconstructionController : public Thread { public: enum class DataType { INDIVIDUAL, VIDEO, INTERNET }; enum class Quality { LOW, MEDIUM, HIGH, EXTREME }; struct Options { // The path to the workspace folder in which all results are stored. std::string workspace_path; // The path to the image folder which are used as input. std::string image_path; // The path to the vocabulary tree for feature matching. std::string vocab_tree_path; // The type of input data used to choose optimal mapper settings. DataType data_type = DataType::INDIVIDUAL; // Whether to perform low- or high-quality reconstruction. Quality quality = Quality::HIGH; // Whether to use shared intrinsics or not. bool single_camera = false; // Which camera model to use for images. std::string camera_model = "SIMPLE_RADIAL"; // Whether to perform sparse mapping. bool sparse = true; // Whether to perform dense mapping. #ifdef CUDA_ENABLED bool dense = true; #else bool dense = false; #endif // The number of threads to use in all stages. int num_threads = -1; // Whether to use the GPU in feature extraction and matching. bool use_gpu = true; // Index of the GPU used for GPU stages. For multi-GPU computation, // you should separate multiple GPU indices by comma, e.g., "0,1,2,3". // By default, all GPUs will be used in all stages. std::string gpu_index = "-1"; }; AutomaticReconstructionController( const Options& options, ReconstructionManager* reconstruction_manager); void Stop() override; private: void Run() override; void RunFeatureExtraction(); void RunFeatureMatching(); void RunSparseMapper(); void RunDenseMapper(); const Options options_; OptionManager option_manager_; ReconstructionManager* reconstruction_manager_; Thread* active_thread_; std::unique_ptr feature_extractor_; std::unique_ptr exhaustive_matcher_; std::unique_ptr sequential_matcher_; std::unique_ptr vocab_tree_matcher_; }; } // namespace colmap #endif // COLMAP_SRC_CONTROLLERS_AUTOMATIC_RECONSTRUCTION_H_ colmap-3.4/src/controllers/bundle_adjustment.cc000066400000000000000000000056301323400541200220040ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "controllers/bundle_adjustment.h" #include #include "optim/bundle_adjustment.h" #include "util/misc.h" namespace colmap { namespace { // Callback functor called after each bundle adjustment iteration. class BundleAdjustmentIterationCallback : public ceres::IterationCallback { public: explicit BundleAdjustmentIterationCallback(Thread* thread) : thread_(thread) {} virtual ceres::CallbackReturnType operator()( const ceres::IterationSummary& summary) { CHECK_NOTNULL(thread_); thread_->BlockIfPaused(); if (thread_->IsStopped()) { return ceres::SOLVER_TERMINATE_SUCCESSFULLY; } else { return ceres::SOLVER_CONTINUE; } } private: Thread* thread_; }; } // namespace BundleAdjustmentController::BundleAdjustmentController( const OptionManager& options, Reconstruction* reconstruction) : options_(options), reconstruction_(reconstruction) {} void BundleAdjustmentController::Run() { CHECK_NOTNULL(reconstruction_); PrintHeading1("Global bundle adjustment"); const std::vector& reg_image_ids = reconstruction_->RegImageIds(); if (reg_image_ids.size() < 2) { std::cout << "ERROR: Need at least two views." << std::endl; return; } // Avoid degeneracies in bundle adjustment. reconstruction_->FilterObservationsWithNegativeDepth(); BundleAdjustmentOptions ba_options = *options_.bundle_adjustment; ba_options.solver_options.minimizer_progress_to_stdout = true; BundleAdjustmentIterationCallback iteration_callback(this); ba_options.solver_options.callbacks.push_back(&iteration_callback); // Configure bundle adjustment. BundleAdjustmentConfig ba_config; for (const image_t image_id : reg_image_ids) { ba_config.AddImage(image_id); } ba_config.SetConstantPose(reg_image_ids[0]); ba_config.SetConstantTvec(reg_image_ids[1], {0}); // Run bundle adjustment. BundleAdjuster bundle_adjuster(ba_options, ba_config); bundle_adjuster.Solve(reconstruction_); // Normalize scene for numerical stability and // to avoid large scale changes in viewer. reconstruction_->Normalize(); GetTimer().PrintMinutes(); } } // namespace colmap colmap-3.4/src/controllers/bundle_adjustment.h000066400000000000000000000026111323400541200216420ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_CONTROLLERS_BUNDLE_ADJUSTMENT_H_ #define COLMAP_SRC_CONTROLLERS_BUNDLE_ADJUSTMENT_H_ #include "base/reconstruction.h" #include "util/option_manager.h" #include "util/threading.h" namespace colmap { // Class that controls the global bundle adjustment procedure. class BundleAdjustmentController : public Thread { public: BundleAdjustmentController(const OptionManager& options, Reconstruction* reconstruction); private: void Run(); const OptionManager options_; Reconstruction* reconstruction_; }; } // namespace colmap #endif // COLMAP_SRC_CONTROLLERS_BUNDLE_ADJUSTMENT_H_ colmap-3.4/src/controllers/hierarchical_mapper.cc000066400000000000000000000172241323400541200222610ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "controllers/hierarchical_mapper.h" #include "base/scene_clustering.h" #include "util/misc.h" namespace colmap { namespace { void MergeClusters( const SceneClustering::Cluster& cluster, std::unordered_map* reconstruction_managers) { // Extract all reconstructions from all child clusters. std::vector reconstructions; for (const auto& child_cluster : cluster.child_clusters) { if (!child_cluster.child_clusters.empty()) { MergeClusters(child_cluster, reconstruction_managers); } auto& reconstruction_manager = reconstruction_managers->at(&child_cluster); for (size_t i = 0; i < reconstruction_manager.Size(); ++i) { reconstructions.push_back(&reconstruction_manager.Get(i)); } } // Try to merge all child cluster reconstruction. while (reconstructions.size() > 1) { bool merge_success = false; for (size_t i = 0; i < reconstructions.size(); ++i) { for (size_t j = 0; j < i; ++j) { const int kMinCommonImages = 3; if (reconstructions[i]->Merge(*reconstructions[j], kMinCommonImages)) { reconstructions.erase(reconstructions.begin() + j); merge_success = true; break; } } if (merge_success) { break; } } if (!merge_success) { break; } } // Insert a new reconstruction manager for merged cluster. auto& reconstruction_manager = (*reconstruction_managers)[&cluster]; for (const auto& reconstruction : reconstructions) { reconstruction_manager.Add(); reconstruction_manager.Get(reconstruction_manager.Size() - 1) = *reconstruction; } // Delete all merged child cluster reconstruction managers. for (const auto& child_cluster : cluster.child_clusters) { reconstruction_managers->erase(&child_cluster); } } } // namespace bool HierarchicalMapperController::Options::Check() const { CHECK_OPTION_GT(init_num_trials, -1); CHECK_OPTION_GE(num_workers, -1); return true; } HierarchicalMapperController::HierarchicalMapperController( const Options& options, const SceneClustering::Options& clustering_options, const IncrementalMapperOptions& mapper_options, ReconstructionManager* reconstruction_manager) : options_(options), clustering_options_(clustering_options), mapper_options_(mapper_options), reconstruction_manager_(reconstruction_manager) { CHECK(options_.Check()); CHECK(clustering_options_.Check()); CHECK(mapper_options_.Check()); CHECK_EQ(clustering_options_.branching, 2); } void HierarchicalMapperController::Run() { PrintHeading1("Partitioning the scene"); ////////////////////////////////////////////////////////////////////////////// // Cluster scene ////////////////////////////////////////////////////////////////////////////// SceneClustering scene_clustering(clustering_options_); std::unordered_map image_id_to_name; { Database database(options_.database_path); std::cout << "Reading images..." << std::endl; const auto images = database.ReadAllImages(); for (const auto& image : images) { image_id_to_name.emplace(image.ImageId(), image.Name()); } std::cout << "Reading scene graph..." << std::endl; std::vector> image_pairs; std::vector num_inliers; database.ReadInlierMatchesGraph(&image_pairs, &num_inliers); std::cout << "Partitioning scene graph..." << std::endl; scene_clustering.Partition(image_pairs, num_inliers); } auto leaf_clusters = scene_clustering.GetLeafClusters(); size_t total_num_images = 0; for (size_t i = 0; i < leaf_clusters.size(); ++i) { total_num_images += leaf_clusters[i]->image_ids.size(); std::cout << StringPrintf(" Cluster %d with %d images", i + 1, leaf_clusters[i]->image_ids.size()) << std::endl; } std::cout << StringPrintf("Clusters have %d images", total_num_images) << std::endl; ////////////////////////////////////////////////////////////////////////////// // Reconstruct clusters ////////////////////////////////////////////////////////////////////////////// PrintHeading1("Reconstructing clusters"); // Determine the number of workers and threads per worker. const int kMaxNumThreads = -1; const int num_eff_threads = GetEffectiveNumThreads(kMaxNumThreads); const int kDefaultNumWorkers = 8; const int num_eff_workers = options_.num_workers < 1 ? std::min(static_cast(leaf_clusters.size()), std::min(kDefaultNumWorkers, num_eff_threads)) : options_.num_workers; const int num_threads_per_worker = std::max(1, num_eff_threads / num_eff_workers); // Function to reconstruct one cluster using incremental mapping. auto ReconstructCluster = [&, this]( const SceneClustering::Cluster& cluster, ReconstructionManager* reconstruction_manager) { if (cluster.image_ids.empty()) { return; } IncrementalMapperOptions custom_options = mapper_options_; custom_options.max_model_overlap = 3; custom_options.init_num_trials = options_.init_num_trials; custom_options.num_threads = num_threads_per_worker; for (const auto image_id : cluster.image_ids) { custom_options.image_names.insert(image_id_to_name.at(image_id)); } IncrementalMapperController mapper(&custom_options, options_.image_path, options_.database_path, reconstruction_manager); mapper.Start(); mapper.Wait(); }; // Start reconstructing the bigger clusters first for resource usage. std::sort(leaf_clusters.begin(), leaf_clusters.end(), [](const SceneClustering::Cluster* cluster1, const SceneClustering::Cluster* cluster2) { return cluster1->image_ids.size() > cluster2->image_ids.size(); }); // Start the reconstruction workers. std::unordered_map reconstruction_managers; reconstruction_managers.reserve(leaf_clusters.size()); ThreadPool thread_pool(num_eff_workers); for (const auto& cluster : leaf_clusters) { thread_pool.AddTask(ReconstructCluster, *cluster, &reconstruction_managers[cluster]); } thread_pool.Wait(); ////////////////////////////////////////////////////////////////////////////// // Merge clusters ////////////////////////////////////////////////////////////////////////////// PrintHeading1("Merging clusters"); MergeClusters(*scene_clustering.GetRootCluster(), &reconstruction_managers); CHECK_EQ(reconstruction_managers.size(), 1); *reconstruction_manager_ = std::move(reconstruction_managers.begin()->second); std::cout << std::endl; GetTimer().PrintMinutes(); } } // namespace colmap colmap-3.4/src/controllers/hierarchical_mapper.h000066400000000000000000000046101323400541200221160ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_CONTROLLERS_HIERARCHICAL_MAPPER_H_ #define COLMAP_SRC_CONTROLLERS_HIERARCHICAL_MAPPER_H_ #include "base/reconstruction_manager.h" #include "base/scene_clustering.h" #include "controllers/incremental_mapper.h" #include "util/threading.h" namespace colmap { // Hierarchical mapping first hierarchically partitions the scene into multiple // overlapping clusters, then reconstructs them separately using incremental // mapping, and finally merges them all into a globally consistent // reconstruction. This is especially useful for larger-scale scenes, since // incremental mapping becomes slow with an increasing number of images. class HierarchicalMapperController : public Thread { public: struct Options { // The path to the image folder which are used as input. std::string image_path; // The path to the database file which is used as input. std::string database_path; // The maximum number of trials to initialize a cluster. int init_num_trials = 10; // The number of workers used to reconstruct clusters in parallel. int num_workers = -1; bool Check() const; }; HierarchicalMapperController( const Options& options, const SceneClustering::Options& clustering_options, const IncrementalMapperOptions& mapper_options, ReconstructionManager* reconstruction_manager); private: void Run() override; const Options options_; const SceneClustering::Options clustering_options_; const IncrementalMapperOptions mapper_options_; ReconstructionManager* reconstruction_manager_; }; } // namespace colmap #endif // COLMAP_SRC_CONTROLLERS_HIERARCHICAL_MAPPER_H_ colmap-3.4/src/controllers/incremental_mapper.cc000066400000000000000000000551021323400541200221410ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "controllers/incremental_mapper.h" #include "util/misc.h" namespace colmap { namespace { size_t TriangulateImage(const IncrementalMapperOptions& options, const Image& image, IncrementalMapper* mapper) { std::cout << " => Continued observations: " << image.NumPoints3D() << std::endl; const size_t num_tris = mapper->TriangulateImage(options.Triangulation(), image.ImageId()); std::cout << " => Added observations: " << num_tris << std::endl; return num_tris; } void AdjustGlobalBundle(const IncrementalMapperOptions& options, IncrementalMapper* mapper) { BundleAdjustmentOptions custom_options = options.GlobalBundleAdjustment(); const size_t num_reg_images = mapper->GetReconstruction().NumRegImages(); // Use stricter convergence criteria for first registered images. const size_t kMinNumRegImages = 10; if (num_reg_images < kMinNumRegImages) { custom_options.solver_options.function_tolerance /= 10; custom_options.solver_options.gradient_tolerance /= 10; custom_options.solver_options.parameter_tolerance /= 10; custom_options.solver_options.max_num_iterations *= 2; custom_options.solver_options.max_linear_solver_iterations = 200; } PrintHeading1("Global bundle adjustment"); if (options.ba_global_use_pba && num_reg_images >= kMinNumRegImages && ParallelBundleAdjuster::IsSupported(custom_options, mapper->GetReconstruction())) { mapper->AdjustParallelGlobalBundle( custom_options, options.ParallelGlobalBundleAdjustment()); } else { mapper->AdjustGlobalBundle(custom_options); } } void IterativeLocalRefinement(const IncrementalMapperOptions& options, const image_t image_id, IncrementalMapper* mapper) { auto ba_options = options.LocalBundleAdjustment(); for (int i = 0; i < options.ba_local_max_refinements; ++i) { const auto report = mapper->AdjustLocalBundle( options.Mapper(), ba_options, options.Triangulation(), image_id, mapper->GetModifiedPoints3D()); std::cout << " => Merged observations: " << report.num_merged_observations << std::endl; std::cout << " => Completed observations: " << report.num_completed_observations << std::endl; std::cout << " => Filtered observations: " << report.num_filtered_observations << std::endl; const double changed = (report.num_merged_observations + report.num_completed_observations + report.num_filtered_observations) / static_cast(report.num_adjusted_observations); std::cout << StringPrintf(" => Changed observations: %.6f", changed) << std::endl; if (changed < options.ba_local_max_refinement_change) { break; } // Only use robust cost function for first iteration. ba_options.loss_function_type = BundleAdjustmentOptions::LossFunctionType::TRIVIAL; } mapper->ClearModifiedPoints3D(); } void IterativeGlobalRefinement(const IncrementalMapperOptions& options, IncrementalMapper* mapper) { PrintHeading1("Retriangulation"); CompleteAndMergeTracks(options, mapper); std::cout << " => Retriangulated observations: " << mapper->Retriangulate(options.Triangulation()) << std::endl; for (int i = 0; i < options.ba_global_max_refinements; ++i) { const size_t num_observations = mapper->GetReconstruction().ComputeNumObservations(); size_t num_changed_observations = 0; AdjustGlobalBundle(options, mapper); num_changed_observations += CompleteAndMergeTracks(options, mapper); num_changed_observations += FilterPoints(options, mapper); const double changed = static_cast(num_changed_observations) / num_observations; std::cout << StringPrintf(" => Changed observations: %.6f", changed) << std::endl; if (changed < options.ba_global_max_refinement_change) { break; } } FilterImages(options, mapper); } void ExtractColors(const std::string& image_path, const image_t image_id, Reconstruction* reconstruction) { if (!reconstruction->ExtractColorsForImage(image_id, image_path)) { std::cout << StringPrintf("WARNING: Could not read image %s at path %s.", reconstruction->Image(image_id).Name().c_str(), image_path.c_str()) << std::endl; } } void WriteSnapshot(const Reconstruction& reconstruction, const std::string& snapshot_path) { PrintHeading1("Creating snapshot"); // Get the current timestamp in milliseconds. const size_t timestamp = std::chrono::duration_cast( std::chrono::high_resolution_clock::now().time_since_epoch()) .count(); // Write reconstruction to unique path with current timestamp. const std::string path = JoinPaths(snapshot_path, StringPrintf("%010d", timestamp)); CreateDirIfNotExists(path); std::cout << " => Writing to " << path << std::endl; reconstruction.Write(path); } } // namespace size_t FilterPoints(const IncrementalMapperOptions& options, IncrementalMapper* mapper) { const size_t num_filtered_observations = mapper->FilterPoints(options.Mapper()); std::cout << " => Filtered observations: " << num_filtered_observations << std::endl; return num_filtered_observations; } size_t FilterImages(const IncrementalMapperOptions& options, IncrementalMapper* mapper) { const size_t num_filtered_images = mapper->FilterImages(options.Mapper()); std::cout << " => Filtered images: " << num_filtered_images << std::endl; return num_filtered_images; } size_t CompleteAndMergeTracks(const IncrementalMapperOptions& options, IncrementalMapper* mapper) { const size_t num_completed_observations = mapper->CompleteTracks(options.Triangulation()); std::cout << " => Merged observations: " << num_completed_observations << std::endl; const size_t num_merged_observations = mapper->MergeTracks(options.Triangulation()); std::cout << " => Completed observations: " << num_merged_observations << std::endl; return num_completed_observations + num_merged_observations; } IncrementalMapper::Options IncrementalMapperOptions::Mapper() const { IncrementalMapper::Options options = mapper; options.abs_pose_refine_focal_length = ba_refine_focal_length; options.abs_pose_refine_extra_params = ba_refine_extra_params; options.min_focal_length_ratio = min_focal_length_ratio; options.max_focal_length_ratio = max_focal_length_ratio; options.max_extra_param = max_extra_param; options.num_threads = num_threads; return options; } IncrementalTriangulator::Options IncrementalMapperOptions::Triangulation() const { IncrementalTriangulator::Options options = triangulation; options.min_focal_length_ratio = min_focal_length_ratio; options.max_focal_length_ratio = max_focal_length_ratio; options.max_extra_param = max_extra_param; return options; } BundleAdjustmentOptions IncrementalMapperOptions::LocalBundleAdjustment() const { BundleAdjustmentOptions options; options.solver_options.function_tolerance = 0.0; options.solver_options.gradient_tolerance = 10.0; options.solver_options.parameter_tolerance = 0.0; options.solver_options.max_num_iterations = ba_local_max_num_iterations; options.solver_options.max_linear_solver_iterations = 100; options.solver_options.minimizer_progress_to_stdout = false; options.solver_options.num_threads = num_threads; options.solver_options.num_linear_solver_threads = num_threads; options.print_summary = true; options.refine_focal_length = ba_refine_focal_length; options.refine_principal_point = ba_refine_principal_point; options.refine_extra_params = ba_refine_extra_params; options.loss_function_scale = 1.0; options.loss_function_type = BundleAdjustmentOptions::LossFunctionType::CAUCHY; return options; } BundleAdjustmentOptions IncrementalMapperOptions::GlobalBundleAdjustment() const { BundleAdjustmentOptions options; options.solver_options.function_tolerance = 0.0; options.solver_options.gradient_tolerance = 1.0; options.solver_options.parameter_tolerance = 0.0; options.solver_options.max_num_iterations = ba_global_max_num_iterations; options.solver_options.max_linear_solver_iterations = 100; options.solver_options.minimizer_progress_to_stdout = true; options.solver_options.num_threads = num_threads; options.solver_options.num_linear_solver_threads = num_threads; options.print_summary = true; options.refine_focal_length = ba_refine_focal_length; options.refine_principal_point = ba_refine_principal_point; options.refine_extra_params = ba_refine_extra_params; options.loss_function_type = BundleAdjustmentOptions::LossFunctionType::TRIVIAL; return options; } ParallelBundleAdjuster::Options IncrementalMapperOptions::ParallelGlobalBundleAdjustment() const { ParallelBundleAdjuster::Options options; options.max_num_iterations = ba_global_max_num_iterations; options.print_summary = true; options.gpu_index = ba_global_pba_gpu_index; options.num_threads = num_threads; return options; } bool IncrementalMapperOptions::Check() const { CHECK_OPTION_GT(min_num_matches, 0); CHECK_OPTION_GT(max_num_models, 0); CHECK_OPTION_GT(max_model_overlap, 0); CHECK_OPTION_GE(min_model_size, 0); CHECK_OPTION_GT(init_num_trials, 0); CHECK_OPTION_GT(min_focal_length_ratio, 0); CHECK_OPTION_GT(max_focal_length_ratio, 0); CHECK_OPTION_GE(max_extra_param, 0); CHECK_OPTION_GE(ba_local_num_images, 2); CHECK_OPTION_GE(ba_local_max_num_iterations, 0); CHECK_OPTION_GT(ba_global_images_ratio, 1.0); CHECK_OPTION_GT(ba_global_points_ratio, 1.0); CHECK_OPTION_GT(ba_global_images_freq, 0); CHECK_OPTION_GT(ba_global_points_freq, 0); CHECK_OPTION_GT(ba_global_max_num_iterations, 0); CHECK_OPTION_GT(ba_local_max_refinements, 0); CHECK_OPTION_GE(ba_local_max_refinement_change, 0); CHECK_OPTION_GT(ba_global_max_refinements, 0); CHECK_OPTION_GE(ba_global_max_refinement_change, 0); CHECK_OPTION_GE(snapshot_images_freq, 0); CHECK_OPTION(Mapper().Check()); CHECK_OPTION(Triangulation().Check()); return true; } IncrementalMapperController::IncrementalMapperController( const IncrementalMapperOptions* options, const std::string& image_path, const std::string& database_path, ReconstructionManager* reconstruction_manager) : options_(options), image_path_(image_path), database_path_(database_path), reconstruction_manager_(reconstruction_manager) { CHECK(options_->Check()); RegisterCallback(INITIAL_IMAGE_PAIR_REG_CALLBACK); RegisterCallback(NEXT_IMAGE_REG_CALLBACK); RegisterCallback(LAST_IMAGE_REG_CALLBACK); } void IncrementalMapperController::Run() { if (!LoadDatabase()) { return; } IncrementalMapper::Options init_mapper_options = options_->Mapper(); Reconstruct(init_mapper_options); const size_t kNumInitRelaxations = 2; for (size_t i = 0; i < kNumInitRelaxations; ++i) { if (reconstruction_manager_->Size() > 0 || IsStopped()) { break; } std::cout << " => Relaxing the initialization constraints." << std::endl; init_mapper_options.init_min_num_inliers /= 2; Reconstruct(init_mapper_options); if (reconstruction_manager_->Size() > 0 || IsStopped()) { break; } std::cout << " => Relaxing the initialization constraints." << std::endl; init_mapper_options.init_min_tri_angle /= 2; Reconstruct(init_mapper_options); } std::cout << std::endl; GetTimer().PrintMinutes(); } bool IncrementalMapperController::LoadDatabase() { PrintHeading1("Loading database"); Database database(database_path_); Timer timer; timer.Start(); const size_t min_num_matches = static_cast(options_->min_num_matches); database_cache_.Load(database, min_num_matches, options_->ignore_watermarks, options_->image_names); std::cout << std::endl; timer.PrintMinutes(); std::cout << std::endl; if (database_cache_.NumImages() == 0) { std::cout << "WARNING: No images with matches found in the database." << std::endl << std::endl; return false; } return true; } void IncrementalMapperController::Reconstruct( const IncrementalMapper::Options& init_mapper_options) { const bool kDiscardReconstruction = true; ////////////////////////////////////////////////////////////////////////////// // Main loop ////////////////////////////////////////////////////////////////////////////// IncrementalMapper mapper(&database_cache_); // Is there a sub-model before we start the reconstruction? I.e. the user // has imported an existing reconstruction. const bool initial_reconstruction_given = reconstruction_manager_->Size() > 0; CHECK_LE(reconstruction_manager_->Size(), 1) << "Can only resume from a " "single reconstruction, but " "multiple are given."; for (int num_trials = 0; num_trials < options_->init_num_trials; ++num_trials) { BlockIfPaused(); if (IsStopped()) { break; } size_t reconstruction_idx; if (!initial_reconstruction_given || num_trials > 0) { reconstruction_idx = reconstruction_manager_->Add(); } else { reconstruction_idx = 0; } Reconstruction& reconstruction = reconstruction_manager_->Get(reconstruction_idx); mapper.BeginReconstruction(&reconstruction); //////////////////////////////////////////////////////////////////////////// // Register initial pair //////////////////////////////////////////////////////////////////////////// if (reconstruction.NumRegImages() == 0) { image_t image_id1 = static_cast(options_->init_image_id1); image_t image_id2 = static_cast(options_->init_image_id2); // Try to find good initial pair. if (options_->init_image_id1 == -1 || options_->init_image_id2 == -1) { const bool find_init_success = mapper.FindInitialImagePair( init_mapper_options, &image_id1, &image_id2); if (!find_init_success) { std::cout << " => No good initial image pair found." << std::endl; mapper.EndReconstruction(kDiscardReconstruction); reconstruction_manager_->Delete(reconstruction_idx); break; } } else { if (!reconstruction.ExistsImage(image_id1) || !reconstruction.ExistsImage(image_id2)) { std::cout << StringPrintf( " => Initial image pair #%d and #%d do not exist.", image_id1, image_id2) << std::endl; mapper.EndReconstruction(kDiscardReconstruction); reconstruction_manager_->Delete(reconstruction_idx); return; } } PrintHeading1(StringPrintf("Initializing with image pair #%d and #%d", image_id1, image_id2)); const bool reg_init_success = mapper.RegisterInitialImagePair( init_mapper_options, image_id1, image_id2); if (!reg_init_success) { std::cout << " => Initialization failed - possible solutions:" << std::endl << " - try to relax the initialization constraints" << std::endl << " - manually select an initial image pair" << std::endl; mapper.EndReconstruction(kDiscardReconstruction); reconstruction_manager_->Delete(reconstruction_idx); break; } AdjustGlobalBundle(*options_, &mapper); FilterPoints(*options_, &mapper); FilterImages(*options_, &mapper); // Initial image pair failed to register. if (reconstruction.NumRegImages() == 0 || reconstruction.NumPoints3D() == 0) { mapper.EndReconstruction(kDiscardReconstruction); reconstruction_manager_->Delete(reconstruction_idx); // If both initial images are manually specified, there is no need for // further initialization trials. if (options_->init_image_id1 != -1 && options_->init_image_id2 != -1) { break; } else { continue; } } if (options_->extract_colors) { ExtractColors(image_path_, image_id1, &reconstruction); } } Callback(INITIAL_IMAGE_PAIR_REG_CALLBACK); //////////////////////////////////////////////////////////////////////////// // Incremental mapping //////////////////////////////////////////////////////////////////////////// size_t snapshot_prev_num_reg_images = reconstruction.NumRegImages(); size_t ba_prev_num_reg_images = reconstruction.NumRegImages(); size_t ba_prev_num_points = reconstruction.NumPoints3D(); bool reg_next_success = true; bool prev_reg_next_success = true; while (reg_next_success) { BlockIfPaused(); if (IsStopped()) { break; } reg_next_success = false; const std::vector next_images = mapper.FindNextImages(options_->Mapper()); if (next_images.empty()) { break; } for (size_t reg_trial = 0; reg_trial < next_images.size(); ++reg_trial) { const image_t next_image_id = next_images[reg_trial]; const Image& next_image = reconstruction.Image(next_image_id); PrintHeading1(StringPrintf("Registering image #%d (%d)", next_image_id, reconstruction.NumRegImages() + 1)); std::cout << StringPrintf(" => Image sees %d / %d points", next_image.NumVisiblePoints3D(), next_image.NumObservations()) << std::endl; reg_next_success = mapper.RegisterNextImage(options_->Mapper(), next_image_id); if (reg_next_success) { TriangulateImage(*options_, next_image, &mapper); IterativeLocalRefinement(*options_, next_image_id, &mapper); if (reconstruction.NumRegImages() >= options_->ba_global_images_ratio * ba_prev_num_reg_images || reconstruction.NumRegImages() >= options_->ba_global_images_freq + ba_prev_num_reg_images || reconstruction.NumPoints3D() >= options_->ba_global_points_ratio * ba_prev_num_points || reconstruction.NumPoints3D() >= options_->ba_global_points_freq + ba_prev_num_points) { IterativeGlobalRefinement(*options_, &mapper); ba_prev_num_points = reconstruction.NumPoints3D(); ba_prev_num_reg_images = reconstruction.NumRegImages(); } if (options_->extract_colors) { ExtractColors(image_path_, next_image_id, &reconstruction); } if (options_->snapshot_images_freq > 0 && reconstruction.NumRegImages() >= options_->snapshot_images_freq + snapshot_prev_num_reg_images) { snapshot_prev_num_reg_images = reconstruction.NumRegImages(); WriteSnapshot(reconstruction, options_->snapshot_path); } Callback(NEXT_IMAGE_REG_CALLBACK); break; } else { std::cout << " => Could not register, trying another image." << std::endl; // If initial pair fails to continue for some time, // abort and try different initial pair. const size_t kMinNumInitialRegTrials = 30; if (reg_trial >= kMinNumInitialRegTrials && reconstruction.NumRegImages() < static_cast(options_->min_model_size)) { break; } } } const size_t max_model_overlap = static_cast(options_->max_model_overlap); if (mapper.NumSharedRegImages() >= max_model_overlap) { break; } // If no image could be registered, try a single final global iterative // bundle adjustment and try again to register one image. If this fails // once, then exit the incremental mapping. if (!reg_next_success && prev_reg_next_success) { reg_next_success = true; prev_reg_next_success = false; IterativeGlobalRefinement(*options_, &mapper); } else { prev_reg_next_success = reg_next_success; } } if (IsStopped()) { const bool kDiscardReconstruction = false; mapper.EndReconstruction(kDiscardReconstruction); break; } // Only run final global BA, if last incremental BA was not global. if (reconstruction.NumRegImages() >= 2 && reconstruction.NumRegImages() != ba_prev_num_reg_images && reconstruction.NumPoints3D() != ba_prev_num_points) { IterativeGlobalRefinement(*options_, &mapper); } // If the total number of images is small then do not enforce the minimum // model size so that we can reconstruct small image collections. const size_t min_model_size = std::min(database_cache_.NumImages(), static_cast(options_->min_model_size)); if ((options_->multiple_models && reconstruction.NumRegImages() < min_model_size) || reconstruction.NumRegImages() == 0) { mapper.EndReconstruction(kDiscardReconstruction); reconstruction_manager_->Delete(reconstruction_idx); } else { const bool kDiscardReconstruction = false; mapper.EndReconstruction(kDiscardReconstruction); } Callback(LAST_IMAGE_REG_CALLBACK); const size_t max_num_models = static_cast(options_->max_num_models); if (initial_reconstruction_given || !options_->multiple_models || reconstruction_manager_->Size() >= max_num_models || mapper.NumTotalRegImages() >= database_cache_.NumImages() - 1) { break; } } } } // namespace colmap colmap-3.4/src/controllers/incremental_mapper.h000066400000000000000000000140431323400541200220020ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_CONTROLLERS_INCREMENTAL_MAPPER_H_ #define COLMAP_SRC_CONTROLLERS_INCREMENTAL_MAPPER_H_ #include "base/reconstruction_manager.h" #include "sfm/incremental_mapper.h" #include "util/threading.h" namespace colmap { struct IncrementalMapperOptions { public: // The minimum number of matches for inlier matches to be considered. int min_num_matches = 15; // Whether to ignore the inlier matches of watermark image pairs. bool ignore_watermarks = false; // Whether to reconstruct multiple sub-models. bool multiple_models = true; // The number of sub-models to reconstruct. int max_num_models = 50; // The maximum number of overlapping images between sub-models. If the // current sub-models shares more than this number of images with another // model, then the reconstruction is stopped. int max_model_overlap = 20; // The minimum number of registered images of a sub-model, otherwise the // sub-model is discarded. int min_model_size = 10; // The image identifiers used to initialize the reconstruction. Note that // only one or both image identifiers can be specified. In the former case, // the second image is automatically determined. int init_image_id1 = -1; int init_image_id2 = -1; // The number of trials to initialize the reconstruction. int init_num_trials = 200; // Whether to extract colors for reconstructed points. bool extract_colors = true; // The number of threads to use during reconstruction. int num_threads = -1; // Thresholds for filtering images with degenerate intrinsics. double min_focal_length_ratio = 0.1; double max_focal_length_ratio = 10.0; double max_extra_param = 1.0; // Which intrinsic parameters to optimize during the reconstruction. bool ba_refine_focal_length = true; bool ba_refine_principal_point = false; bool ba_refine_extra_params = true; // The number of images to optimize in local bundle adjustment. int ba_local_num_images = 6; // The maximum number of local bundle adjustment iterations. int ba_local_max_num_iterations = 25; // Whether to use PBA in global bundle adjustment. bool ba_global_use_pba = true; // The GPU index for PBA bundle adjustment. int ba_global_pba_gpu_index = -1; // The growth rates after which to perform global bundle adjustment. double ba_global_images_ratio = 1.1; double ba_global_points_ratio = 1.1; int ba_global_images_freq = 500; int ba_global_points_freq = 250000; // The maximum number of global bundle adjustment iterations. int ba_global_max_num_iterations = 50; // The thresholds for iterative bundle adjustment refinements. int ba_local_max_refinements = 2; double ba_local_max_refinement_change = 0.001; int ba_global_max_refinements = 5; double ba_global_max_refinement_change = 0.0005; // Path to a folder with reconstruction snapshots during incremental // reconstruction. Snapshots will be saved according to the specified // frequency of registered images. std::string snapshot_path = ""; int snapshot_images_freq = 0; // Which images to reconstruct. If no images are specified, all images will // be reconstructed by default. std::set image_names; IncrementalMapper::Options Mapper() const; IncrementalTriangulator::Options Triangulation() const; BundleAdjustmentOptions LocalBundleAdjustment() const; BundleAdjustmentOptions GlobalBundleAdjustment() const; ParallelBundleAdjuster::Options ParallelGlobalBundleAdjustment() const; bool Check() const; private: friend class OptionManager; friend class MapperGeneralOptionsWidget; friend class MapperTriangulationOptionsWidget; friend class MapperRegistrationOptionsWidget; friend class MapperInitializationOptionsWidget; friend class MapperBundleAdjustmentOptionsWidget; friend class MapperFilteringOptionsWidget; friend class ReconstructionOptionsWidget; IncrementalMapper::Options mapper; IncrementalTriangulator::Options triangulation; }; // Class that controls the incremental mapping procedure by iteratively // initializing reconstructions from the same scene graph. class IncrementalMapperController : public Thread { public: enum { INITIAL_IMAGE_PAIR_REG_CALLBACK, NEXT_IMAGE_REG_CALLBACK, LAST_IMAGE_REG_CALLBACK, }; IncrementalMapperController(const IncrementalMapperOptions* options, const std::string& image_path, const std::string& database_path, ReconstructionManager* reconstruction_manager); private: void Run(); bool LoadDatabase(); void Reconstruct(const IncrementalMapper::Options& init_mapper_options); const IncrementalMapperOptions* options_; const std::string image_path_; const std::string database_path_; ReconstructionManager* reconstruction_manager_; DatabaseCache database_cache_; }; // Globally filter points and images in mapper. size_t FilterPoints(const IncrementalMapperOptions& options, IncrementalMapper* mapper); size_t FilterImages(const IncrementalMapperOptions& options, IncrementalMapper* mapper); // Globally complete and merge tracks in mapper. size_t CompleteAndMergeTracks( const IncrementalMapperOptions& options, IncrementalMapper* mapper); } // namespace colmap #endif // COLMAP_SRC_CONTROLLERS_INCREMENTAL_MAPPER_H_ colmap-3.4/src/estimators/000077500000000000000000000000001323400541200156065ustar00rootroot00000000000000colmap-3.4/src/estimators/CMakeLists.txt000077500000000000000000000025651323400541200203610ustar00rootroot00000000000000set(FOLDER_NAME "estimators") COLMAP_ADD_LIBRARY(estimators absolute_pose.h absolute_pose.cc affine_transform.h affine_transform.cc coordinate_frame.h coordinate_frame.cc essential_matrix.h essential_matrix.cc euclidean_transform.h fundamental_matrix.h fundamental_matrix.cc generalized_absolute_pose.h generalized_absolute_pose.cc generalized_absolute_pose_coeffs.h generalized_absolute_pose_coeffs.cc generalized_relative_pose.h generalized_relative_pose.cc homography_matrix.h homography_matrix.cc pose.h pose.cc similarity_transform.h translation_transform.h triangulation.h triangulation.cc two_view_geometry.h two_view_geometry.cc utils.h utils.cc ) COLMAP_ADD_TEST(absolute_pose_test absolute_pose_test.cc) COLMAP_ADD_TEST(affine_transform_test affine_transform_test.cc) COLMAP_ADD_TEST(coordinate_frame_test coordinate_frame_test.cc) COLMAP_ADD_TEST(essential_matrix_test essential_matrix_test.cc) COLMAP_ADD_TEST(estimators_utils_test utils_test.cc) COLMAP_ADD_TEST(fundamental_matrix_test fundamental_matrix_test.cc) COLMAP_ADD_TEST(generalized_absolute_pose_test generalized_absolute_pose_test.cc) COLMAP_ADD_TEST(generalized_relative_pose_test generalized_relative_pose_test.cc) COLMAP_ADD_TEST(homography_matrix_test homography_matrix_test.cc) COLMAP_ADD_TEST(translation_transform_test translation_transform_test.cc) colmap-3.4/src/estimators/absolute_pose.cc000077500000000000000000000473331323400541200207760ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/absolute_pose.h" #include "base/polynomial.h" #include "estimators/utils.h" #include "util/logging.h" namespace colmap { namespace { Eigen::Vector3d LiftImagePoint(const Eigen::Vector2d& point) { return point.homogeneous() / std::sqrt(point.squaredNorm() + 1); } } // namespace std::vector P3PEstimator::Estimate( const std::vector& points2D, const std::vector& points3D) { CHECK_EQ(points2D.size(), 3); CHECK_EQ(points3D.size(), 3); Eigen::Matrix3d points3D_world; points3D_world.col(0) = points3D[0]; points3D_world.col(1) = points3D[1]; points3D_world.col(2) = points3D[2]; const Eigen::Vector3d u = LiftImagePoint(points2D[0]); const Eigen::Vector3d v = LiftImagePoint(points2D[1]); const Eigen::Vector3d w = LiftImagePoint(points2D[2]); // Angles between 2D points. const double cos_uv = u.transpose() * v; const double cos_uw = u.transpose() * w; const double cos_vw = v.transpose() * w; // Distances between 2D points. const double dist_AB_2 = (points3D[0] - points3D[1]).squaredNorm(); const double dist_AC_2 = (points3D[0] - points3D[2]).squaredNorm(); const double dist_BC_2 = (points3D[1] - points3D[2]).squaredNorm(); const double dist_AB = std::sqrt(dist_AB_2); const double a = dist_BC_2 / dist_AB_2; const double b = dist_AC_2 / dist_AB_2; // Helper variables for calculation of coefficients. const double a2 = a * a; const double b2 = b * b; const double p = 2 * cos_vw; const double q = 2 * cos_uw; const double r = 2 * cos_uv; const double p2 = p * p; const double p3 = p2 * p; const double q2 = q * q; const double r2 = r * r; const double r3 = r2 * r; const double r4 = r3 * r; const double r5 = r4 * r; // Build polynomial coefficients: a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0 = 0. Eigen::Matrix coeffs; coeffs(0) = -2 * b + b2 + a2 + 1 + a * b * (2 - r2) - 2 * a; coeffs(1) = -2 * q * a2 - r * p * b2 + 4 * q * a + (2 * q + p * r) * b + (r2 * q - 2 * q + r * p) * a * b - 2 * q; coeffs(2) = (2 + q2) * a2 + (p2 + r2 - 2) * b2 - (4 + 2 * q2) * a - (p * q * r + p2) * b - (p * q * r + r2) * a * b + q2 + 2; coeffs(3) = -2 * q * a2 - r * p * b2 + 4 * q * a + (p * r + q * p2 - 2 * q) * b + (r * p + 2 * q) * a * b - 2 * q; coeffs(4) = a2 + b2 - 2 * a + (2 - p2) * b - 2 * a * b + 1; Eigen::VectorXd roots_real; Eigen::VectorXd roots_imag; if (!FindPolynomialRootsCompanionMatrix(coeffs, &roots_real, &roots_imag)) { return std::vector({}); } std::vector models; models.reserve(roots_real.size()); for (Eigen::VectorXd::Index i = 0; i < roots_real.size(); ++i) { const double kMaxRootImag = 1e-10; if (std::abs(roots_imag(i)) > kMaxRootImag) { continue; } const double x = roots_real(i); if (x < 0) { continue; } const double x2 = x * x; const double x3 = x2 * x; // Build polynomial coefficients: b1*y + b0 = 0. const double bb1 = (p2 - p * q * r + r2) * a + (p2 - r2) * b - p2 + p * q * r - r2; const double b1 = b * bb1 * bb1; const double b0 = ((1 - a - b) * x2 + (a - 1) * q * x - a + b + 1) * (r3 * (a2 + b2 - 2 * a - 2 * b + (2 - r2) * a * b + 1) * x3 + r2 * (p + p * a2 - 2 * r * q * a * b + 2 * r * q * b - 2 * r * q - 2 * p * a - 2 * p * b + p * r2 * b + 4 * r * q * a + q * r3 * a * b - 2 * r * q * a2 + 2 * p * a * b + p * b2 - r2 * p * b2) * x2 + (r5 * (b2 - a * b) - r4 * p * q * b + r3 * (q2 - 4 * a - 2 * q2 * a + q2 * a2 + 2 * a2 - 2 * b2 + 2) + r2 * (4 * p * q * a - 2 * p * q * a * b + 2 * p * q * b - 2 * p * q - 2 * p * q * a2) + r * (p2 * b2 - 2 * p2 * b + 2 * p2 * a * b - 2 * p2 * a + p2 + p2 * a2)) * x + (2 * p * r2 - 2 * r3 * q + p3 - 2 * p2 * q * r + p * q2 * r2) * a2 + (p3 - 2 * p * r2) * b2 + (4 * q * r3 - 4 * p * r2 - 2 * p3 + 4 * p2 * q * r - 2 * p * q2 * r2) * a + (-2 * q * r3 + p * r4 + 2 * p2 * q * r - 2 * p3) * b + (2 * p3 + 2 * q * r3 - 2 * p2 * q * r) * a * b + p * q2 * r2 - 2 * p2 * q * r + 2 * p * r2 + p3 - 2 * r3 * q); // Solve for y. const double y = b0 / b1; const double y2 = y * y; const double nu = x2 + y2 - 2 * x * y * cos_uv; const double dist_PC = dist_AB / std::sqrt(nu); const double dist_PB = y * dist_PC; const double dist_PA = x * dist_PC; Eigen::Matrix3d points3D_camera; points3D_camera.col(0) = u * dist_PA; // A' points3D_camera.col(1) = v * dist_PB; // B' points3D_camera.col(2) = w * dist_PC; // C' // Find transformation from the world to the camera system. const Eigen::Matrix4d transform = Eigen::umeyama(points3D_world, points3D_camera, false); models.push_back(transform.topLeftCorner<3, 4>()); } return models; } void P3PEstimator::Residuals(const std::vector& points2D, const std::vector& points3D, const M_t& proj_matrix, std::vector* residuals) { ComputeSquaredReprojectionError(points2D, points3D, proj_matrix, residuals); } std::vector EPNPEstimator::Estimate( const std::vector& points2D, const std::vector& points3D) { CHECK_GE(points2D.size(), 4); CHECK_EQ(points2D.size(), points3D.size()); EPNPEstimator epnp; M_t proj_matrix; if (!epnp.ComputePose(points2D, points3D, &proj_matrix)) { return std::vector({}); } return std::vector({proj_matrix}); } void EPNPEstimator::Residuals(const std::vector& points2D, const std::vector& points3D, const M_t& proj_matrix, std::vector* residuals) { ComputeSquaredReprojectionError(points2D, points3D, proj_matrix, residuals); } bool EPNPEstimator::ComputePose(const std::vector& points2D, const std::vector& points3D, Eigen::Matrix3x4d* proj_matrix) { points2D_ = points2D; points3D_ = points3D; ChooseControlPoints(); if (!ComputeBarycentricCoordinates()) { return false; } const Eigen::Matrix M = ComputeM(); const Eigen::Matrix MtM = M.transpose() * M; Eigen::JacobiSVD> svd( MtM, Eigen::ComputeFullV | Eigen::ComputeFullU); const Eigen::Matrix Ut = svd.matrixU().transpose(); const Eigen::Matrix L6x10 = ComputeL6x10(Ut); const Eigen::Matrix rho = ComputeRho(); Eigen::Vector4d betas[4]; std::array reproj_errors; std::array Rs; std::array ts; FindBetasApprox1(L6x10, rho, &betas[1]); RunGaussNewton(L6x10, rho, &betas[1]); reproj_errors[1] = ComputeRT(Ut, betas[1], &Rs[1], &ts[1]); FindBetasApprox2(L6x10, rho, &betas[2]); RunGaussNewton(L6x10, rho, &betas[2]); reproj_errors[2] = ComputeRT(Ut, betas[2], &Rs[2], &ts[2]); FindBetasApprox3(L6x10, rho, &betas[3]); RunGaussNewton(L6x10, rho, &betas[3]); reproj_errors[3] = ComputeRT(Ut, betas[3], &Rs[3], &ts[3]); int best_idx = 1; if (reproj_errors[2] < reproj_errors[1]) { best_idx = 2; } if (reproj_errors[3] < reproj_errors[best_idx]) { best_idx = 3; } proj_matrix->leftCols<3>() = Rs[best_idx]; proj_matrix->rightCols<1>() = ts[best_idx]; return true; } void EPNPEstimator::ChooseControlPoints() { // Take C0 as the reference points centroid: cws_[0].setZero(); for (size_t i = 0; i < points3D_.size(); ++i) { cws_[0] += points3D_[i]; } cws_[0] /= points3D_.size(); Eigen::Matrix PW0(points3D_.size(), 3); for (size_t i = 0; i < points3D_.size(); ++i) { PW0.row(i) = points3D_[i] - cws_[0]; } const Eigen::Matrix3d PW0tPW0 = PW0.transpose() * PW0; Eigen::JacobiSVD svd( PW0tPW0, Eigen::ComputeFullV | Eigen::ComputeFullU); const Eigen::Vector3d D = svd.singularValues(); const Eigen::Matrix3d Ut = svd.matrixU().transpose(); for (int i = 1; i < 4; ++i) { const double k = std::sqrt(D(i - 1) / points3D_.size()); cws_[i] = cws_[0] + k * Ut.row(i - 1).transpose(); } } bool EPNPEstimator::ComputeBarycentricCoordinates() { Eigen::Matrix3d CC; for (int i = 0; i < 3; ++i) { for (int j = 1; j < 4; ++j) { CC(i, j - 1) = cws_[j][i] - cws_[0][i]; } } if (CC.colPivHouseholderQr().rank() < 3) { return false; } const Eigen::Matrix3d CC_inv = CC.inverse(); alphas_.resize(points2D_.size()); for (size_t i = 0; i < points3D_.size(); ++i) { for (int j = 0; j < 3; ++j) { alphas_[i][1 + j] = CC_inv(j, 0) * (points3D_[i][0] - cws_[0][0]) + CC_inv(j, 1) * (points3D_[i][1] - cws_[0][1]) + CC_inv(j, 2) * (points3D_[i][2] - cws_[0][2]); } alphas_[i][0] = 1.0 - alphas_[i][1] - alphas_[i][2] - alphas_[i][3]; } return true; } Eigen::Matrix EPNPEstimator::ComputeM() { Eigen::Matrix M(2 * points2D_.size(), 12); for (size_t i = 0; i < points3D_.size(); ++i) { for (size_t j = 0; j < 4; ++j) { M(2 * i, 3 * j) = alphas_[i][j]; M(2 * i, 3 * j + 1) = 0.0; M(2 * i, 3 * j + 2) = -alphas_[i][j] * points2D_[i].x(); M(2 * i + 1, 3 * j) = 0.0; M(2 * i + 1, 3 * j + 1) = alphas_[i][j]; M(2 * i + 1, 3 * j + 2) = -alphas_[i][j] * points2D_[i].y(); } } return M; } Eigen::Matrix EPNPEstimator::ComputeL6x10( const Eigen::Matrix& Ut) { Eigen::Matrix L6x10; std::array, 4> dv; for (int i = 0; i < 4; ++i) { int a = 0, b = 1; for (int j = 0; j < 6; ++j) { dv[i][j][0] = Ut(11 - i, 3 * a) - Ut(11 - i, 3 * b); dv[i][j][1] = Ut(11 - i, 3 * a + 1) - Ut(11 - i, 3 * b + 1); dv[i][j][2] = Ut(11 - i, 3 * a + 2) - Ut(11 - i, 3 * b + 2); b += 1; if (b > 3) { a += 1; b = a + 1; } } } for (int i = 0; i < 6; ++i) { L6x10(i, 0) = dv[0][i].transpose() * dv[0][i]; L6x10(i, 1) = 2.0 * dv[0][i].transpose() * dv[1][i]; L6x10(i, 2) = dv[1][i].transpose() * dv[1][i]; L6x10(i, 3) = 2.0 * dv[0][i].transpose() * dv[2][i]; L6x10(i, 4) = 2.0 * dv[1][i].transpose() * dv[2][i]; L6x10(i, 5) = dv[2][i].transpose() * dv[2][i]; L6x10(i, 6) = 2.0 * dv[0][i].transpose() * dv[3][i]; L6x10(i, 7) = 2.0 * dv[1][i].transpose() * dv[3][i]; L6x10(i, 8) = 2.0 * dv[2][i].transpose() * dv[3][i]; L6x10(i, 9) = dv[3][i].transpose() * dv[3][i]; } return L6x10; } Eigen::Matrix EPNPEstimator::ComputeRho() { Eigen::Matrix rho; rho[0] = (cws_[0] - cws_[1]).squaredNorm(); rho[1] = (cws_[0] - cws_[2]).squaredNorm(); rho[2] = (cws_[0] - cws_[3]).squaredNorm(); rho[3] = (cws_[1] - cws_[2]).squaredNorm(); rho[4] = (cws_[1] - cws_[3]).squaredNorm(); rho[5] = (cws_[2] - cws_[3]).squaredNorm(); return rho; } // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44] // betas_approx_1 = [B11 B12 B13 B14] void EPNPEstimator::FindBetasApprox1(const Eigen::Matrix& L6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas) { Eigen::Matrix L_6x4; for (int i = 0; i < 6; ++i) { L_6x4(i, 0) = L6x10(i, 0); L_6x4(i, 1) = L6x10(i, 1); L_6x4(i, 2) = L6x10(i, 3); L_6x4(i, 3) = L6x10(i, 6); } Eigen::JacobiSVD> svd( L_6x4, Eigen::ComputeFullV | Eigen::ComputeFullU); Eigen::Matrix Rho_temp = rho; const Eigen::Matrix b4 = svd.solve(Rho_temp); if (b4[0] < 0) { (*betas)[0] = std::sqrt(-b4[0]); (*betas)[1] = -b4[1] / (*betas)[0]; (*betas)[2] = -b4[2] / (*betas)[0]; (*betas)[3] = -b4[3] / (*betas)[0]; } else { (*betas)[0] = std::sqrt(b4[0]); (*betas)[1] = b4[1] / (*betas)[0]; (*betas)[2] = b4[2] / (*betas)[0]; (*betas)[3] = b4[3] / (*betas)[0]; } } // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44] // betas_approx_2 = [B11 B12 B22 ] void EPNPEstimator::FindBetasApprox2(const Eigen::Matrix& L6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas) { Eigen::Matrix L_6x3(6, 3); for (int i = 0; i < 6; ++i) { L_6x3(i, 0) = L6x10(i, 0); L_6x3(i, 1) = L6x10(i, 1); L_6x3(i, 2) = L6x10(i, 2); } Eigen::JacobiSVD> svd( L_6x3, Eigen::ComputeFullV | Eigen::ComputeFullU); Eigen::Matrix Rho_temp = rho; const Eigen::Matrix b3 = svd.solve(Rho_temp); if (b3[0] < 0) { (*betas)[0] = std::sqrt(-b3[0]); (*betas)[1] = (b3[2] < 0) ? std::sqrt(-b3[2]) : 0.0; } else { (*betas)[0] = std::sqrt(b3[0]); (*betas)[1] = (b3[2] > 0) ? std::sqrt(b3[2]) : 0.0; } if (b3[1] < 0) { (*betas)[0] = -(*betas)[0]; } (*betas)[2] = 0.0; (*betas)[3] = 0.0; } // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44] // betas_approx_3 = [B11 B12 B22 B13 B23 ] void EPNPEstimator::FindBetasApprox3(const Eigen::Matrix& L6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas) { Eigen::JacobiSVD> svd( L6x10.leftCols<5>(), Eigen::ComputeFullV | Eigen::ComputeFullU); Eigen::Matrix Rho_temp = rho; const Eigen::Matrix b5 = svd.solve(Rho_temp); if (b5[0] < 0) { (*betas)[0] = std::sqrt(-b5[0]); (*betas)[1] = (b5[2] < 0) ? std::sqrt(-b5[2]) : 0.0; } else { (*betas)[0] = std::sqrt(b5[0]); (*betas)[1] = (b5[2] > 0) ? std::sqrt(b5[2]) : 0.0; } if (b5[1] < 0) { (*betas)[0] = -(*betas)[0]; } (*betas)[2] = b5[3] / (*betas)[0]; (*betas)[3] = 0.0; } void EPNPEstimator::RunGaussNewton(const Eigen::Matrix& L6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas) { Eigen::Matrix A; Eigen::Matrix b; const int kNumIterations = 5; for (int k = 0; k < kNumIterations; ++k) { for (int i = 0; i < 6; ++i) { A(i, 0) = 2 * L6x10(i, 0) * (*betas)[0] + L6x10(i, 1) * (*betas)[1] + L6x10(i, 3) * (*betas)[2] + L6x10(i, 6) * (*betas)[3]; A(i, 1) = L6x10(i, 1) * (*betas)[0] + 2 * L6x10(i, 2) * (*betas)[1] + L6x10(i, 4) * (*betas)[2] + L6x10(i, 7) * (*betas)[3]; A(i, 2) = L6x10(i, 3) * (*betas)[0] + L6x10(i, 4) * (*betas)[1] + 2 * L6x10(i, 5) * (*betas)[2] + L6x10(i, 8) * (*betas)[3]; A(i, 3) = L6x10(i, 6) * (*betas)[0] + L6x10(i, 7) * (*betas)[1] + L6x10(i, 8) * (*betas)[2] + 2 * L6x10(i, 9) * (*betas)[3]; b(i) = rho[i] - (L6x10(i, 0) * (*betas)[0] * (*betas)[0] + L6x10(i, 1) * (*betas)[0] * (*betas)[1] + L6x10(i, 2) * (*betas)[1] * (*betas)[1] + L6x10(i, 3) * (*betas)[0] * (*betas)[2] + L6x10(i, 4) * (*betas)[1] * (*betas)[2] + L6x10(i, 5) * (*betas)[2] * (*betas)[2] + L6x10(i, 6) * (*betas)[0] * (*betas)[3] + L6x10(i, 7) * (*betas)[1] * (*betas)[3] + L6x10(i, 8) * (*betas)[2] * (*betas)[3] + L6x10(i, 9) * (*betas)[3] * (*betas)[3]); } const Eigen::Vector4d x = A.colPivHouseholderQr().solve(b); (*betas) += x; } } double EPNPEstimator::ComputeRT(const Eigen::Matrix& Ut, const Eigen::Vector4d& betas, Eigen::Matrix3d* R, Eigen::Vector3d* t) { ComputeCcs(betas, Ut); ComputePcs(); SolveForSign(); EstimateRT(R, t); return ComputeTotalReprojectionError(*R, *t); } void EPNPEstimator::ComputeCcs(const Eigen::Vector4d& betas, const Eigen::Matrix& Ut) { for (int i = 0; i < 4; ++i) { ccs_[i][0] = ccs_[i][1] = ccs_[i][2] = 0.0; } for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) { for (int k = 0; k < 3; ++k) { ccs_[j][k] += betas[i] * Ut(11 - i, 3 * j + k); } } } } void EPNPEstimator::ComputePcs() { pcs_.resize(points2D_.size()); for (size_t i = 0; i < points3D_.size(); ++i) { for (int j = 0; j < 3; ++j) { pcs_[i][j] = alphas_[i][0] * ccs_[0][j] + alphas_[i][1] * ccs_[1][j] + alphas_[i][2] * ccs_[2][j] + alphas_[i][3] * ccs_[3][j]; } } } void EPNPEstimator::SolveForSign() { if (pcs_[0][2] < 0.0 || pcs_[0][2] > 0.0) { for (int i = 0; i < 4; ++i) { ccs_[i] = -ccs_[i]; } for (size_t i = 0; i < points3D_.size(); ++i) { pcs_[i] = -pcs_[i]; } } } void EPNPEstimator::EstimateRT(Eigen::Matrix3d* R, Eigen::Vector3d* t) { Eigen::Vector3d pc0 = Eigen::Vector3d::Zero(); Eigen::Vector3d pw0 = Eigen::Vector3d::Zero(); for (size_t i = 0; i < points3D_.size(); ++i) { pc0 += pcs_[i]; pw0 += points3D_[i]; } pc0 /= points3D_.size(); pw0 /= points3D_.size(); Eigen::Matrix3d abt = Eigen::Matrix3d::Zero(); for (size_t i = 0; i < points3D_.size(); ++i) { for (int j = 0; j < 3; ++j) { abt(j, 0) += (pcs_[i][j] - pc0[j]) * (points3D_[i][0] - pw0[0]); abt(j, 1) += (pcs_[i][j] - pc0[j]) * (points3D_[i][1] - pw0[1]); abt(j, 2) += (pcs_[i][j] - pc0[j]) * (points3D_[i][2] - pw0[2]); } } Eigen::JacobiSVD svd( abt, Eigen::ComputeFullV | Eigen::ComputeFullU); const Eigen::Matrix3d abt_U = svd.matrixU(); const Eigen::Matrix3d abt_V = svd.matrixV(); for (int i = 0; i < 3; ++i) { for (int j = 0; j < 3; ++j) { (*R)(i, j) = abt_U.row(i) * abt_V.row(j).transpose(); } } if (R->determinant() < 0) { Eigen::Matrix3d Abt_v_prime = abt_V; Abt_v_prime.col(2) = -abt_V.col(2); for (int i = 0; i < 3; ++i) { for (int j = 0; j < 3; ++j) { (*R)(i, j) = abt_U.row(i) * Abt_v_prime.row(j).transpose(); } } } *t = pc0 - *R * pw0; } double EPNPEstimator::ComputeTotalReprojectionError(const Eigen::Matrix3d& R, const Eigen::Vector3d& t) { Eigen::Matrix3x4d proj_matrix; proj_matrix.leftCols<3>() = R; proj_matrix.rightCols<1>() = t; std::vector residuals; ComputeSquaredReprojectionError(points2D_, points3D_, proj_matrix, &residuals); double reproj_error = 0.0; for (const double residual : residuals) { reproj_error += std::sqrt(residual); } return reproj_error; } } // namespace colmap colmap-3.4/src/estimators/absolute_pose.h000077500000000000000000000147321323400541200206350ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_ABSOLUTE_POSE_H_ #define COLMAP_SRC_ESTIMATORS_ABSOLUTE_POSE_H_ #include #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Analytic solver for the P3P (Perspective-Three-Point) problem. // // The algorithm is based on the following paper: // // X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang. Complete Solution // Classification for the Perspective-Three-Point Problem. // http://www.mmrc.iss.ac.cn/~xgao/paper/ieee.pdf class P3PEstimator { public: // The 2D image feature observations. typedef Eigen::Vector2d X_t; // The observed 3D features in the world frame. typedef Eigen::Vector3d Y_t; // The transformation from the world to the camera frame. typedef Eigen::Matrix3x4d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 3; // Estimate the most probable solution of the P3P problem from a set of // three 2D-3D point correspondences. // // @param points2D Normalized 2D image points as 3x2 matrix. // @param points3D 3D world points as 3x3 matrix. // // @return Most probable pose as length-1 vector of a 3x4 matrix. static std::vector Estimate(const std::vector& points2D, const std::vector& points3D); // Calculate the squared reprojection error given a set of 2D-3D point // correspondences and a projection matrix. // // @param points2D Normalized 2D image points as Nx2 matrix. // @param points3D 3D world points as Nx3 matrix. // @param proj_matrix 3x4 projection matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points2D, const std::vector& points3D, const M_t& proj_matrix, std::vector* residuals); }; // EPNP solver for the PNP (Perspective-N-Point) problem. The solver needs a // minimum of 4 2D-3D correspondences. // // The algorithm is based on the following paper: // // Lepetit, Vincent, Francesc Moreno-Noguer, and Pascal Fua. // "Epnp: An accurate o (n) solution to the pnp problem." // International journal of computer vision 81.2 (2009): 155-166. // // The implementation is based on their original open-source release, but is // ported to Eigen and contains several improvements over the original code. class EPNPEstimator { public: // The 2D image feature observations. typedef Eigen::Vector2d X_t; // The observed 3D features in the world frame. typedef Eigen::Vector3d Y_t; // The transformation from the world to the camera frame. typedef Eigen::Matrix3x4d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 4; // Estimate the most probable solution of the P3P problem from a set of // three 2D-3D point correspondences. // // @param points2D Normalized 2D image points as 3x2 matrix. // @param points3D 3D world points as 3x3 matrix. // // @return Most probable pose as length-1 vector of a 3x4 matrix. static std::vector Estimate(const std::vector& points2D, const std::vector& points3D); // Calculate the squared reprojection error given a set of 2D-3D point // correspondences and a projection matrix. // // @param points2D Normalized 2D image points as Nx2 matrix. // @param points3D 3D world points as Nx3 matrix. // @param proj_matrix 3x4 projection matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points2D, const std::vector& points3D, const M_t& proj_matrix, std::vector* residuals); private: bool ComputePose(const std::vector& points2D, const std::vector& points3D, Eigen::Matrix3x4d* proj_matrix); void ChooseControlPoints(); bool ComputeBarycentricCoordinates(); Eigen::Matrix ComputeM(); Eigen::Matrix ComputeL6x10( const Eigen::Matrix& Ut); Eigen::Matrix ComputeRho(); void FindBetasApprox1(const Eigen::Matrix& L_6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas); void FindBetasApprox2(const Eigen::Matrix& L_6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas); void FindBetasApprox3(const Eigen::Matrix& L_6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas); void RunGaussNewton(const Eigen::Matrix& L_6x10, const Eigen::Matrix& rho, Eigen::Vector4d* betas); double ComputeRT(const Eigen::Matrix& Ut, const Eigen::Vector4d& betas, Eigen::Matrix3d* R, Eigen::Vector3d* t); void ComputeCcs(const Eigen::Vector4d& betas, const Eigen::Matrix& Ut); void ComputePcs(); void SolveForSign(); void EstimateRT(Eigen::Matrix3d* R, Eigen::Vector3d* t); double ComputeTotalReprojectionError(const Eigen::Matrix3d& R, const Eigen::Vector3d& t); std::vector points2D_; std::vector points3D_; std::vector pcs_; std::vector alphas_; std::array cws_; std::array ccs_; }; } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_ABSOLUTE_POSE_H_ colmap-3.4/src/estimators/absolute_pose_test.cc000077500000000000000000000120041323400541200220200ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/absolute_pose" #include "util/testing.h" #include #include "base/pose.h" #include "base/similarity_transform.h" #include "estimators/absolute_pose.h" #include "estimators/essential_matrix.h" #include "optim/ransac.h" #include "util/random.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestP3P) { SetPRNGSeed(0); std::vector points3D; points3D.emplace_back(1, 1, 1); points3D.emplace_back(0, 1, 1); points3D.emplace_back(3, 1.0, 4); points3D.emplace_back(3, 1.1, 4); points3D.emplace_back(3, 1.2, 4); points3D.emplace_back(3, 1.3, 4); points3D.emplace_back(3, 1.4, 4); points3D.emplace_back(2, 1, 7); auto points3D_faulty = points3D; for (size_t i = 0; i < points3D.size(); ++i) { points3D_faulty[i](0) = 20; } for (double qx = 0; qx < 1; qx += 0.2) { for (double tx = 0; tx < 1; tx += 0.1) { const SimilarityTransform3 orig_tform(1, Eigen::Vector4d(1, qx, 0, 0), Eigen::Vector3d(tx, 0, 0)); // Project points to camera coordinate system. std::vector points2D; for (size_t i = 0; i < points3D.size(); ++i) { Eigen::Vector3d point3D_camera = points3D[i]; orig_tform.TransformPoint(&point3D_camera); points2D.push_back(point3D_camera.hnormalized()); } RANSACOptions options; options.max_error = 1e-5; RANSAC ransac(options); const auto report = ransac.Estimate(points2D, points3D); BOOST_CHECK_EQUAL(report.success, true); // Test if correct transformation has been determined. const double matrix_diff = (orig_tform.Matrix().topLeftCorner<3, 4>() - report.model).norm(); BOOST_CHECK(matrix_diff < 1e-2); // Test residuals of exact points. std::vector residuals; P3PEstimator::Residuals(points2D, points3D, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] < 1e-3); } // Test residuals of faulty points. P3PEstimator::Residuals(points2D, points3D_faulty, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] > 0.1); } } } } BOOST_AUTO_TEST_CASE(TestEPNP) { SetPRNGSeed(0); std::vector points3D; points3D.emplace_back(1, 1, 1); points3D.emplace_back(0, 1, 1); points3D.emplace_back(3, 1.0, 4); points3D.emplace_back(3, 1.1, 4); points3D.emplace_back(3, 1.2, 4); points3D.emplace_back(3, 1.3, 4); points3D.emplace_back(3, 1.4, 4); points3D.emplace_back(2, 1, 7); auto points3D_faulty = points3D; for (size_t i = 0; i < points3D.size(); ++i) { points3D_faulty[i](0) = 20; } for (double qx = 0; qx < 1; qx += 0.2) { for (double tx = 0; tx < 1; tx += 0.1) { const SimilarityTransform3 orig_tform(1, Eigen::Vector4d(1, qx, 0, 0), Eigen::Vector3d(tx, 0, 0)); // Project points to camera coordinate system. std::vector points2D; for (size_t i = 0; i < points3D.size(); ++i) { Eigen::Vector3d point3D_camera = points3D[i]; orig_tform.TransformPoint(&point3D_camera); points2D.push_back(point3D_camera.hnormalized()); } RANSACOptions options; options.max_error = 1e-5; RANSAC ransac(options); const auto report = ransac.Estimate(points2D, points3D); BOOST_CHECK_EQUAL(report.success, true); // Test if correct transformation has been determined. const double matrix_diff = (orig_tform.Matrix().topLeftCorner<3, 4>() - report.model).norm(); BOOST_CHECK(matrix_diff < 1e-3); // Test residuals of exact points. std::vector residuals; EPNPEstimator::Residuals(points2D, points3D, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] < 1e-3); } // Test residuals of faulty points. EPNPEstimator::Residuals(points2D, points3D_faulty, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] > 0.1); } } } } colmap-3.4/src/estimators/affine_transform.cc000066400000000000000000000060041323400541200214400ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/affine_transform.h" #include #include "util/logging.h" namespace colmap { std::vector AffineTransformEstimator::Estimate( const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); CHECK_GE(points1.size(), 3); // Sets up the linear system that we solve to obtain a least squared solution // for the affine transformation. Eigen::MatrixXd C(2 * points1.size(), 6); C.setZero(); Eigen::VectorXd b(2 * points1.size(), 1); for (size_t i = 0; i < points1.size(); ++i) { const Eigen::Vector2d& x1 = points1[i]; const Eigen::Vector2d& x2 = points2[i]; C(2 * i, 0) = x1(0); C(2 * i, 1) = x1(1); C(2 * i, 2) = 1.0f; b(2 * i) = x2(0); C(2 * i + 1, 3) = x1(0); C(2 * i + 1, 4) = x1(1); C(2 * i + 1, 5) = 1.0f; b(2 * i + 1) = x2(1); } const Eigen::VectorXd nullspace = C.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(b); Eigen::Map> A_t(nullspace.data()); const std::vector models = {A_t.transpose()}; return models; } void AffineTransformEstimator::Residuals(const std::vector& points1, const std::vector& points2, const M_t& A, std::vector* residuals) { CHECK_EQ(points1.size(), points2.size()); residuals->resize(points1.size()); // Note that this code might not be as nice as Eigen expressions, // but it is significantly faster in various tests. const double A_00 = A(0, 0); const double A_01 = A(0, 1); const double A_02 = A(0, 2); const double A_10 = A(1, 0); const double A_11 = A(1, 1); const double A_12 = A(1, 2); for (size_t i = 0; i < points1.size(); ++i) { const double s_0 = points1[i](0); const double s_1 = points1[i](1); const double d_0 = points2[i](0); const double d_1 = points2[i](1); const double pd_0 = A_00 * s_0 + A_01 * s_1 + A_02; const double pd_1 = A_10 * s_0 + A_11 * s_1 + A_12; const double dd_0 = d_0 - pd_0; const double dd_1 = d_1 - pd_1; (*residuals)[i] = dd_0 * dd_0 + dd_1 * dd_1; } } } // namespace colmap colmap-3.4/src/estimators/affine_transform.h000066400000000000000000000033501323400541200213030ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_AFFINE_TRANSFORM_H_ #define COLMAP_SRC_ESTIMATORS_AFFINE_TRANSFORM_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { class AffineTransformEstimator { public: typedef Eigen::Vector2d X_t; typedef Eigen::Vector2d Y_t; typedef Eigen::Matrix M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 3; // Estimate the affine transformation from at least 3 correspondences. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Compute the squared transformation error. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& E, std::vector* residuals); }; } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_AFFINE_TRANSFORM_H_ colmap-3.4/src/estimators/affine_transform_test.cc000066400000000000000000000032361323400541200225030ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/affine_transform" #include "util/testing.h" #include "estimators/affine_transform.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestAffineTransform) { for (double x = 0; x < 1; x += 0.1) { Eigen::Matrix A; A << x, 0.2, 0.3, 30, 0.2, 0.1; std::vector src; src.emplace_back(x, 0); src.emplace_back(1, 0); src.emplace_back(2, 1); std::vector dst; for (size_t i = 0; i < 3; ++i) { dst.push_back(A * src[i].homogeneous()); } AffineTransformEstimator estimator; const auto models = estimator.Estimate(src, dst); BOOST_CHECK_EQUAL(models.size(), 1); std::vector residuals; estimator.Residuals(src, dst, models[0], &residuals); BOOST_CHECK_EQUAL(residuals.size(), 3); for (size_t i = 0; i < 3; ++i) { BOOST_CHECK_LT(residuals[i], 1e-6); } } } colmap-3.4/src/estimators/coordinate_frame.cc000066400000000000000000000246471323400541200214330ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/coordinate_frame.h" #include "base/line.h" #include "base/pose.h" #include "base/undistortion.h" #include "estimators/utils.h" #include "optim/ransac.h" #include "util/logging.h" #include "util/misc.h" namespace colmap { namespace { struct VanishingPointEstimator { // The line segments. typedef LineSegment X_t; // The line representation of the segments. typedef Eigen::Vector3d Y_t; // The vanishing point. typedef Eigen::Vector3d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 2; // Estimate the vanishing point from at least two line segments. static std::vector Estimate(const std::vector& line_segments, const std::vector& lines) { CHECK_EQ(line_segments.size(), 2); CHECK_EQ(lines.size(), 2); return {lines[0].cross(lines[1])}; } // Calculate the squared distance of each line segment's end point to the line // connecting the vanishing point and the midpoint of the line segment. static void Residuals(const std::vector& line_segments, const std::vector& lines, const M_t& vanishing_point, std::vector* residuals) { residuals->resize(line_segments.size()); // Check if vanishing point is at infinity. if (vanishing_point[2] == 0) { std::fill(residuals->begin(), residuals->end(), std::numeric_limits::max()); return; } for (size_t i = 0; i < lines.size(); ++i) { const Eigen::Vector3d midpoint = (0.5 * (line_segments[i].start + line_segments[i].end)).homogeneous(); const Eigen::Vector3d connecting_line = midpoint.cross(vanishing_point); const double signed_distance = connecting_line.dot(line_segments[i].end.homogeneous()) / connecting_line.head<2>().norm(); (*residuals)[i] = signed_distance * signed_distance; } } }; Eigen::Vector3d FindBestConsensusAxis(const std::vector& axes, const double max_distance) { if (axes.empty()) { return Eigen::Vector3d::Zero(); } std::vector inlier_idxs; inlier_idxs.reserve(axes.size()); std::vector best_inlier_idxs; best_inlier_idxs.reserve(axes.size()); double best_inlier_distance_sum = std::numeric_limits::max(); for (size_t i = 0; i < axes.size(); ++i) { const Eigen::Vector3d ref_axis = axes[i]; double inlier_distance_sum = 0; inlier_idxs.clear(); for (size_t j = 0; j < axes.size(); ++j) { if (i == j) { inlier_idxs.push_back(j); } else { const double distance = 1 - ref_axis.dot(axes[j]); if (distance <= max_distance) { inlier_distance_sum += distance; inlier_idxs.push_back(j); } } } if (inlier_idxs.size() > best_inlier_idxs.size() || (inlier_idxs.size() == best_inlier_idxs.size() && inlier_distance_sum < best_inlier_distance_sum)) { best_inlier_distance_sum = inlier_distance_sum; best_inlier_idxs = inlier_idxs; } } if (best_inlier_idxs.empty()) { return Eigen::Vector3d::Zero(); } Eigen::Vector3d best_axis(0, 0, 0); for (const auto idx : best_inlier_idxs) { best_axis += axes[idx]; } best_axis /= best_inlier_idxs.size(); return best_axis; } } // namespace Eigen::Vector3d EstimateGravityVectorFromImageOrientation( const Reconstruction& reconstruction, const double max_axis_distance) { std::vector downward_axes; downward_axes.reserve(reconstruction.NumRegImages()); for (const auto image_id : reconstruction.RegImageIds()) { const auto& image = reconstruction.Image(image_id); downward_axes.push_back(image.RotationMatrix().row(1)); } return FindBestConsensusAxis(downward_axes, max_axis_distance); } Eigen::Matrix3d EstimateManhattanWorldFrame( const ManhattanWorldFrameEstimationOptions& options, const Reconstruction& reconstruction, const std::string& image_path) { std::vector rightward_axes; std::vector downward_axes; for (size_t i = 0; i < reconstruction.NumRegImages(); ++i) { const auto image_id = reconstruction.RegImageIds()[i]; const auto& image = reconstruction.Image(image_id); const auto& camera = reconstruction.Camera(image.CameraId()); PrintHeading1(StringPrintf("Processing image %s (%d / %d)", image.Name().c_str(), i + 1, reconstruction.NumRegImages())); std::cout << "Reading image..." << std::endl; colmap::Bitmap bitmap; CHECK(bitmap.Read(colmap::JoinPaths(image_path, image.Name()))); std::cout << "Undistorting image..." << std::endl; UndistortCameraOptions undistortion_options; undistortion_options.max_image_size = options.max_image_size; Bitmap undistorted_bitmap; Camera undistorted_camera; UndistortImage(undistortion_options, bitmap, camera, &undistorted_bitmap, &undistorted_camera); std::cout << "Detecting lines..."; const std::vector line_segments = DetectLineSegments(undistorted_bitmap, options.min_line_length); const std::vector line_orientations = ClassifyLineSegmentOrientations(line_segments, options.line_orientation_tolerance); std::cout << StringPrintf(" %d", line_segments.size()); std::vector horizontal_line_segments; std::vector vertical_line_segments; std::vector horizontal_lines; std::vector vertical_lines; for (size_t i = 0; i < line_segments.size(); ++i) { const auto line_segment = line_segments[i]; const Eigen::Vector3d line_segment_start = line_segment.start.homogeneous(); const Eigen::Vector3d line_segment_end = line_segment.end.homogeneous(); const Eigen::Vector3d line = line_segment_start.cross(line_segment_end); if (line_orientations[i] == LineSegmentOrientation::HORIZONTAL) { horizontal_line_segments.push_back(line_segment); horizontal_lines.push_back(line); } else if (line_orientations[i] == LineSegmentOrientation::VERTICAL) { vertical_line_segments.push_back(line_segment); vertical_lines.push_back(line); } } std::cout << StringPrintf(" (%d horizontal, %d vertical)", horizontal_lines.size(), vertical_lines.size()) << std::endl; std::cout << "Estimating vanishing points..."; RANSACOptions ransac_options; ransac_options.max_error = options.max_line_vp_distance; RANSAC ransac(ransac_options); const auto horizontal_report = ransac.Estimate(horizontal_line_segments, horizontal_lines); const auto vertical_report = ransac.Estimate(vertical_line_segments, vertical_lines); std::cout << StringPrintf(" (%d horizontal inliers, %d vertical inliers)", horizontal_report.support.num_inliers, vertical_report.support.num_inliers) << std::endl; std::cout << "Composing coordinate axes..." << std::endl; const Eigen::Matrix3d inv_calib_matrix = undistorted_camera.CalibrationMatrix().inverse(); const Eigen::Vector4d inv_qvec = InvertQuaternion(image.Qvec()); if (horizontal_report.success) { const Eigen::Vector3d horizontal_camera_axis = (inv_calib_matrix * horizontal_report.model).normalized(); Eigen::Vector3d horizontal_axis = QuaternionRotatePoint(inv_qvec, horizontal_camera_axis).normalized(); // Make sure all axes point into the same direction. if (rightward_axes.size() > 0 && rightward_axes[0].dot(horizontal_axis) < 0) { horizontal_axis = -horizontal_axis; } rightward_axes.push_back(horizontal_axis); std::cout << " Horizontal: " << horizontal_axis.transpose() << std::endl; } if (vertical_report.success) { const Eigen::Vector3d vertical_camera_axis = (inv_calib_matrix * vertical_report.model).normalized(); Eigen::Vector3d vertical_axis = QuaternionRotatePoint(inv_qvec, vertical_camera_axis).normalized(); // Make sure axis points downwards in the image, assuming that the image // was taken in upright orientation. if (vertical_camera_axis.dot(Eigen::Vector3d(0, 1, 0)) < 0) { vertical_axis = -vertical_axis; } downward_axes.push_back(vertical_axis); std::cout << " Vertical: " << vertical_axis.transpose() << std::endl; } } PrintHeading1("Computing coordinate frame"); Eigen::Matrix3d frame = Eigen::Matrix3d::Zero(); if (rightward_axes.size() > 0) { frame.col(0) = FindBestConsensusAxis(rightward_axes, options.max_axis_distance); } std::cout << "Found rightward axis: " << frame.col(0).transpose() << std::endl; if (downward_axes.size() > 0) { frame.col(1) = FindBestConsensusAxis(downward_axes, options.max_axis_distance); } std::cout << "Found downward axis: " << frame.col(1).transpose() << std::endl; if (rightward_axes.size() > 0 && downward_axes.size() > 0) { frame.col(2) = frame.col(0).cross(frame.col(1)); Eigen::JacobiSVD svd( frame, Eigen::ComputeFullV | Eigen::ComputeFullU); const Eigen::Matrix3d orthonormal_frame = svd.matrixU() * Eigen::Matrix3d::Identity() * svd.matrixV().transpose(); frame = orthonormal_frame; } std::cout << "Found orthonormal frame: " << std::endl; std::cout << frame << std::endl; return frame; } } // namespace colmap colmap-3.4/src/estimators/coordinate_frame.h000066400000000000000000000051131323400541200212600ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_COORDINATE_AXES_H_ #define COLMAP_SRC_ESTIMATORS_COORDINATE_AXES_H_ #include #include "base/reconstruction.h" namespace colmap { struct ManhattanWorldFrameEstimationOptions { // The maximum image size for line detection. int max_image_size = 1024; // The minimum length of line segments in pixels. double min_line_length = 3; // The tolerance for classifying lines into horizontal/vertical. double line_orientation_tolerance = 0.2; // The maximum distance in pixels between lines and the vanishing points. double max_line_vp_distance = 0.5; // The maximum cosine distance between estimated axes to be inliers. double max_axis_distance = 0.05; }; // Estimate gravity vector by assuming gravity-aligned image orientation, i.e. // the majority of images is assumed to have the gravity vector aligned with an // upright image plane. Eigen::Vector3d EstimateGravityVectorFromImageOrientation( const Reconstruction& reconstruction, const double max_axis_distance = 0.05); // Estimate the coordinate frame of the reconstruction assuming a Manhattan // world by finding the major vanishing points in each image. This function // assumes that the majority of images is taken in upright direction, i.e. // people are standing upright in the image. The orthonormal axes of the // estimated coordinate frame will be given in the columns of the returned // matrix. If one axis could not be determined, the respective column will be // zero. The axes are specified in the world coordinate system in the order // rightward, downward, forward. Eigen::Matrix3d EstimateManhattanWorldFrame( const ManhattanWorldFrameEstimationOptions& options, const Reconstruction& reconstruction, const std::string& image_path); } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_COORDINATE_AXES_H_ colmap-3.4/src/estimators/coordinate_frame_test.cc000066400000000000000000000026611323400541200224620ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/coordinate_frame" #include "util/testing.h" #include "estimators/coordinate_frame.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEstimateGravityVectorFromImageOrientation) { Reconstruction reconstruction; BOOST_CHECK_EQUAL(EstimateGravityVectorFromImageOrientation(reconstruction), Eigen::Vector3d::Zero()); } BOOST_AUTO_TEST_CASE(TestEstimateManhattanWorldFrame) { Reconstruction reconstruction; std::string image_path; BOOST_CHECK_EQUAL( EstimateManhattanWorldFrame(ManhattanWorldFrameEstimationOptions(), reconstruction, image_path), Eigen::Matrix3d::Zero()); } colmap-3.4/src/estimators/essential_matrix.cc000077500000000000000000000162341323400541200215010ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/essential_matrix.h" #include #include #include #include #include "base/polynomial.h" #include "estimators/utils.h" #include "util/logging.h" #include "util/math.h" namespace colmap { std::vector EssentialMatrixFivePointEstimator::Estimate(const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); // Step 1: Extraction of the nullspace x, y, z, w. Eigen::Matrix Q(points1.size(), 9); for (size_t i = 0; i < points1.size(); ++i) { const double x1_0 = points1[i](0); const double x1_1 = points1[i](1); const double x2_0 = points2[i](0); const double x2_1 = points2[i](1); Q(i, 0) = x1_0 * x2_0; Q(i, 1) = x1_1 * x2_0; Q(i, 2) = x2_0; Q(i, 3) = x1_0 * x2_1; Q(i, 4) = x1_1 * x2_1; Q(i, 5) = x2_1; Q(i, 6) = x1_0; Q(i, 7) = x1_1; Q(i, 8) = 1; } // Extract the 4 Eigen vectors corresponding to the smallest singular values. const Eigen::JacobiSVD> svd( Q, Eigen::ComputeFullV); const Eigen::Matrix E = svd.matrixV().block<9, 4>(0, 5); // Step 3: Gauss-Jordan elimination with partial pivoting on A. Eigen::Matrix A; #include "estimators/essential_matrix_poly.h" Eigen::Matrix AA = A.block<10, 10>(0, 0).partialPivLu().solve(A.block<10, 10>(0, 10)); // Step 4: Expansion of the determinant polynomial of the 3x3 polynomial // matrix B to obtain the tenth degree polynomial. Eigen::Matrix B; for (size_t i = 0; i < 3; ++i) { B(0, i) = 0; B(4, i) = 0; B(8, i) = 0; B.block<3, 1>(1, i) = AA.block<1, 3>(i * 2 + 4, 0); B.block<3, 1>(5, i) = AA.block<1, 3>(i * 2 + 4, 3); B.block<4, 1>(9, i) = AA.block<1, 4>(i * 2 + 4, 6); B.block<3, 1>(0, i) -= AA.block<1, 3>(i * 2 + 5, 0); B.block<3, 1>(4, i) -= AA.block<1, 3>(i * 2 + 5, 3); B.block<4, 1>(8, i) -= AA.block<1, 4>(i * 2 + 5, 6); } // Step 5: Extraction of roots from the degree 10 polynomial. Eigen::Matrix coeffs; #include "estimators/essential_matrix_coeffs.h" Eigen::VectorXd roots_real; Eigen::VectorXd roots_imag; if (!FindPolynomialRootsCompanionMatrix(coeffs, &roots_real, &roots_imag)) { return {}; } std::vector models; models.reserve(roots_real.size()); for (Eigen::VectorXd::Index i = 0; i < roots_imag.size(); ++i) { const double kMaxRootImag = 1e-10; if (std::abs(roots_imag(i)) > kMaxRootImag) { continue; } const double z1 = roots_real(i); const double z2 = z1 * z1; const double z3 = z2 * z1; const double z4 = z3 * z1; Eigen::Matrix3d Bz; for (size_t j = 0; j < 3; ++j) { Bz(j, 0) = B(0, j) * z3 + B(1, j) * z2 + B(2, j) * z1 + B(3, j); Bz(j, 1) = B(4, j) * z3 + B(5, j) * z2 + B(6, j) * z1 + B(7, j); Bz(j, 2) = B(8, j) * z4 + B(9, j) * z3 + B(10, j) * z2 + B(11, j) * z1 + B(12, j); } const Eigen::JacobiSVD svd(Bz, Eigen::ComputeFullV); const Eigen::Vector3d X = svd.matrixV().block<3, 1>(0, 2); const double kMaxX3 = 1e-10; if (std::abs(X(2)) < kMaxX3) { continue; } Eigen::MatrixXd essential_vec = E.col(0) * (X(0) / X(2)) + E.col(1) * (X(1) / X(2)) + E.col(2) * z1 + E.col(3); essential_vec /= essential_vec.norm(); const Eigen::Matrix3d essential_matrix = Eigen::Map>( essential_vec.data()); models.push_back(essential_matrix); } return models; } void EssentialMatrixFivePointEstimator::Residuals( const std::vector& points1, const std::vector& points2, const M_t& E, std::vector* residuals) { ComputeSquaredSampsonError(points1, points2, E, residuals); } std::vector EssentialMatrixEightPointEstimator::Estimate(const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); // Center and normalize image points for better numerical stability. std::vector normed_points1; std::vector normed_points2; Eigen::Matrix3d points1_norm_matrix; Eigen::Matrix3d points2_norm_matrix; CenterAndNormalizeImagePoints(points1, &normed_points1, &points1_norm_matrix); CenterAndNormalizeImagePoints(points2, &normed_points2, &points2_norm_matrix); // Setup homogeneous linear equation as x2' * F * x1 = 0. Eigen::Matrix cmatrix(points1.size(), 9); for (size_t i = 0; i < points1.size(); ++i) { cmatrix.block<1, 3>(i, 0) = normed_points1[i].homogeneous(); cmatrix.block<1, 3>(i, 0) *= normed_points2[i].x(); cmatrix.block<1, 3>(i, 3) = normed_points1[i].homogeneous(); cmatrix.block<1, 3>(i, 3) *= normed_points2[i].y(); cmatrix.block<1, 3>(i, 6) = normed_points1[i].homogeneous(); } // Solve for the nullspace of the constraint matrix. Eigen::JacobiSVD> cmatrix_svd( cmatrix, Eigen::ComputeFullV); const Eigen::VectorXd ematrix_nullspace = cmatrix_svd.matrixV().col(8); const Eigen::Map ematrix_t(ematrix_nullspace.data()); // Enforcing the internal constraint that two singular values must be equal // and one must be zero. Eigen::JacobiSVD ematrix_svd( ematrix_t.transpose(), Eigen::ComputeFullU | Eigen::ComputeFullV); Eigen::Vector3d singular_values = ematrix_svd.singularValues(); singular_values(0) = (singular_values(0) + singular_values(1)) / 2.0; singular_values(1) = singular_values(0); singular_values(2) = 0.0; const Eigen::Matrix3d E = ematrix_svd.matrixU() * singular_values.asDiagonal() * ematrix_svd.matrixV().transpose(); const std::vector models = {points2_norm_matrix.transpose() * E * points1_norm_matrix}; return models; } void EssentialMatrixEightPointEstimator::Residuals( const std::vector& points1, const std::vector& points2, const M_t& E, std::vector* residuals) { ComputeSquaredSampsonError(points1, points2, E, residuals); } } // namespace colmap colmap-3.4/src/estimators/essential_matrix.h000077500000000000000000000101451323400541200213360ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_ESSENTIAL_MATRIX_H_ #define COLMAP_SRC_ESTIMATORS_ESSENTIAL_MATRIX_H_ #include #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Essential matrix estimator from corresponding normalized point pairs. // // This algorithm solves the 5-Point problem based on the following paper: // // D. Nister, An efficient solution to the five-point relative pose problem, // IEEE-T-PAMI, 26(6), 2004. // http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.8769 class EssentialMatrixFivePointEstimator { public: typedef Eigen::Vector2d X_t; typedef Eigen::Vector2d Y_t; typedef Eigen::Matrix3d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 5; // Estimate up to 10 possible essential matrix solutions from a set of // corresponding points. // // The number of corresponding points must be at least 5. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // // @return Up to 10 solutions as a vector of 3x3 essential matrices. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the residuals of a set of corresponding points and a given // essential matrix. // // Residuals are defined as the squared Sampson error. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param E 3x3 essential matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& E, std::vector* residuals); }; // Essential matrix estimator from corresponding normalized point pairs. // // This algorithm solves the 8-Point problem based on the following paper: // // Hartley and Zisserman, Multiple View Geometry, algorithm 11.1, page 282. class EssentialMatrixEightPointEstimator { public: typedef Eigen::Vector2d X_t; typedef Eigen::Vector2d Y_t; typedef Eigen::Matrix3d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 8; // Estimate essential matrix solutions from set of corresponding points. // // The number of corresponding points must be at least 8. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the residuals of a set of corresponding points and a given // essential matrix. // // Residuals are defined as the squared Sampson error. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param E 3x3 essential matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& E, std::vector* residuals); }; } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_ESSENTIAL_MATRIX_H_ colmap-3.4/src/estimators/essential_matrix_coeffs.h000077500000000000000000000314431323400541200226670ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . { const double* b = B.data(); coeffs(0) = b[0] * b[17] * b[34] + b[26] * b[4] * b[21] - b[26] * b[17] * b[8] - b[13] * b[4] * b[34] - b[0] * b[21] * b[30] + b[13] * b[30] * b[8]; coeffs(1) = b[26] * b[4] * b[22] + b[14] * b[30] * b[8] + b[13] * b[31] * b[8] + b[1] * b[17] * b[34] - b[13] * b[5] * b[34] + b[26] * b[5] * b[21] - b[0] * b[21] * b[31] - b[26] * b[17] * b[9] - b[1] * b[21] * b[30] + b[27] * b[4] * b[21] + b[0] * b[17] * b[35] - b[0] * b[22] * b[30] + b[13] * b[30] * b[9] + b[0] * b[18] * b[34] - b[27] * b[17] * b[8] - b[14] * b[4] * b[34] - b[13] * b[4] * b[35] - b[26] * b[18] * b[8]; coeffs(2) = b[14] * b[30] * b[9] + b[14] * b[31] * b[8] + b[13] * b[31] * b[9] - b[13] * b[4] * b[36] - b[13] * b[5] * b[35] + b[15] * b[30] * b[8] - b[13] * b[6] * b[34] + b[13] * b[30] * b[10] + b[13] * b[32] * b[8] - b[14] * b[4] * b[35] - b[14] * b[5] * b[34] + b[26] * b[4] * b[23] + b[26] * b[5] * b[22] + b[26] * b[6] * b[21] - b[26] * b[17] * b[10] - b[15] * b[4] * b[34] - b[26] * b[18] * b[9] - b[26] * b[19] * b[8] + b[27] * b[4] * b[22] + b[27] * b[5] * b[21] - b[27] * b[17] * b[9] - b[27] * b[18] * b[8] - b[1] * b[21] * b[31] - b[0] * b[23] * b[30] - b[0] * b[21] * b[32] + b[28] * b[4] * b[21] - b[28] * b[17] * b[8] + b[2] * b[17] * b[34] + b[0] * b[18] * b[35] - b[0] * b[22] * b[31] + b[0] * b[17] * b[36] + b[0] * b[19] * b[34] - b[1] * b[22] * b[30] + b[1] * b[18] * b[34] + b[1] * b[17] * b[35] - b[2] * b[21] * b[30]; coeffs(3) = b[14] * b[30] * b[10] + b[14] * b[32] * b[8] - b[3] * b[21] * b[30] + b[3] * b[17] * b[34] + b[13] * b[32] * b[9] + b[13] * b[33] * b[8] - b[13] * b[4] * b[37] - b[13] * b[5] * b[36] + b[15] * b[30] * b[9] + b[15] * b[31] * b[8] - b[16] * b[4] * b[34] - b[13] * b[6] * b[35] - b[13] * b[7] * b[34] + b[13] * b[30] * b[11] + b[13] * b[31] * b[10] + b[14] * b[31] * b[9] - b[14] * b[4] * b[36] - b[14] * b[5] * b[35] - b[14] * b[6] * b[34] + b[16] * b[30] * b[8] - b[26] * b[20] * b[8] + b[26] * b[4] * b[24] + b[26] * b[5] * b[23] + b[26] * b[6] * b[22] + b[26] * b[7] * b[21] - b[26] * b[17] * b[11] - b[15] * b[4] * b[35] - b[15] * b[5] * b[34] - b[26] * b[18] * b[10] - b[26] * b[19] * b[9] + b[27] * b[4] * b[23] + b[27] * b[5] * b[22] + b[27] * b[6] * b[21] - b[27] * b[17] * b[10] - b[27] * b[18] * b[9] - b[27] * b[19] * b[8] + b[0] * b[17] * b[37] - b[0] * b[23] * b[31] - b[0] * b[24] * b[30] - b[0] * b[21] * b[33] - b[29] * b[17] * b[8] + b[28] * b[4] * b[22] + b[28] * b[5] * b[21] - b[28] * b[17] * b[9] - b[28] * b[18] * b[8] + b[29] * b[4] * b[21] + b[1] * b[19] * b[34] - b[2] * b[21] * b[31] + b[0] * b[20] * b[34] + b[0] * b[19] * b[35] + b[0] * b[18] * b[36] - b[0] * b[22] * b[32] - b[1] * b[23] * b[30] - b[1] * b[21] * b[32] + b[1] * b[18] * b[35] - b[1] * b[22] * b[31] - b[2] * b[22] * b[30] + b[2] * b[17] * b[35] + b[1] * b[17] * b[36] + b[2] * b[18] * b[34]; coeffs(4) = -b[14] * b[6] * b[35] - b[14] * b[7] * b[34] - b[3] * b[22] * b[30] - b[3] * b[21] * b[31] + b[3] * b[17] * b[35] + b[3] * b[18] * b[34] + b[13] * b[32] * b[10] + b[13] * b[33] * b[9] - b[13] * b[4] * b[38] - b[13] * b[5] * b[37] - b[15] * b[6] * b[34] + b[15] * b[30] * b[10] + b[15] * b[32] * b[8] - b[16] * b[4] * b[35] - b[13] * b[6] * b[36] - b[13] * b[7] * b[35] + b[13] * b[31] * b[11] + b[13] * b[30] * b[12] + b[14] * b[32] * b[9] + b[14] * b[33] * b[8] - b[14] * b[4] * b[37] - b[14] * b[5] * b[36] + b[16] * b[30] * b[9] + b[16] * b[31] * b[8] - b[26] * b[20] * b[9] + b[26] * b[4] * b[25] + b[26] * b[5] * b[24] + b[26] * b[6] * b[23] + b[26] * b[7] * b[22] - b[26] * b[17] * b[12] + b[14] * b[30] * b[11] + b[14] * b[31] * b[10] + b[15] * b[31] * b[9] - b[15] * b[4] * b[36] - b[15] * b[5] * b[35] - b[26] * b[18] * b[11] - b[26] * b[19] * b[10] - b[27] * b[20] * b[8] + b[27] * b[4] * b[24] + b[27] * b[5] * b[23] + b[27] * b[6] * b[22] + b[27] * b[7] * b[21] - b[27] * b[17] * b[11] - b[27] * b[18] * b[10] - b[27] * b[19] * b[9] - b[16] * b[5] * b[34] - b[29] * b[17] * b[9] - b[29] * b[18] * b[8] + b[28] * b[4] * b[23] + b[28] * b[5] * b[22] + b[28] * b[6] * b[21] - b[28] * b[17] * b[10] - b[28] * b[18] * b[9] - b[28] * b[19] * b[8] + b[29] * b[4] * b[22] + b[29] * b[5] * b[21] - b[2] * b[23] * b[30] + b[2] * b[18] * b[35] - b[1] * b[22] * b[32] - b[2] * b[21] * b[32] + b[2] * b[19] * b[34] + b[0] * b[19] * b[36] - b[0] * b[22] * b[33] + b[0] * b[20] * b[35] - b[0] * b[23] * b[32] - b[0] * b[25] * b[30] + b[0] * b[17] * b[38] + b[0] * b[18] * b[37] - b[0] * b[24] * b[31] + b[1] * b[17] * b[37] - b[1] * b[23] * b[31] - b[1] * b[24] * b[30] - b[1] * b[21] * b[33] + b[1] * b[20] * b[34] + b[1] * b[19] * b[35] + b[1] * b[18] * b[36] + b[2] * b[17] * b[36] - b[2] * b[22] * b[31]; coeffs(5) = -b[14] * b[6] * b[36] - b[14] * b[7] * b[35] + b[14] * b[31] * b[11] - b[3] * b[23] * b[30] - b[3] * b[21] * b[32] + b[3] * b[18] * b[35] - b[3] * b[22] * b[31] + b[3] * b[17] * b[36] + b[3] * b[19] * b[34] + b[13] * b[32] * b[11] + b[13] * b[33] * b[10] - b[13] * b[5] * b[38] - b[15] * b[6] * b[35] - b[15] * b[7] * b[34] + b[15] * b[30] * b[11] + b[15] * b[31] * b[10] + b[16] * b[31] * b[9] - b[13] * b[6] * b[37] - b[13] * b[7] * b[36] + b[13] * b[31] * b[12] + b[14] * b[32] * b[10] + b[14] * b[33] * b[9] - b[14] * b[4] * b[38] - b[14] * b[5] * b[37] - b[16] * b[6] * b[34] + b[16] * b[30] * b[10] + b[16] * b[32] * b[8] - b[26] * b[20] * b[10] + b[26] * b[5] * b[25] + b[26] * b[6] * b[24] + b[26] * b[7] * b[23] + b[14] * b[30] * b[12] + b[15] * b[32] * b[9] + b[15] * b[33] * b[8] - b[15] * b[4] * b[37] - b[15] * b[5] * b[36] + b[29] * b[5] * b[22] + b[29] * b[6] * b[21] - b[26] * b[18] * b[12] - b[26] * b[19] * b[11] - b[27] * b[20] * b[9] + b[27] * b[4] * b[25] + b[27] * b[5] * b[24] + b[27] * b[6] * b[23] + b[27] * b[7] * b[22] - b[27] * b[17] * b[12] - b[27] * b[18] * b[11] - b[27] * b[19] * b[10] - b[28] * b[20] * b[8] - b[16] * b[4] * b[36] - b[16] * b[5] * b[35] - b[29] * b[17] * b[10] - b[29] * b[18] * b[9] - b[29] * b[19] * b[8] + b[28] * b[4] * b[24] + b[28] * b[5] * b[23] + b[28] * b[6] * b[22] + b[28] * b[7] * b[21] - b[28] * b[17] * b[11] - b[28] * b[18] * b[10] - b[28] * b[19] * b[9] + b[29] * b[4] * b[23] - b[2] * b[22] * b[32] - b[2] * b[21] * b[33] - b[1] * b[24] * b[31] + b[0] * b[18] * b[38] - b[0] * b[24] * b[32] + b[0] * b[19] * b[37] + b[0] * b[20] * b[36] - b[0] * b[25] * b[31] - b[0] * b[23] * b[33] + b[1] * b[19] * b[36] - b[1] * b[22] * b[33] + b[1] * b[20] * b[35] + b[2] * b[19] * b[35] - b[2] * b[24] * b[30] - b[2] * b[23] * b[31] + b[2] * b[20] * b[34] + b[2] * b[17] * b[37] - b[1] * b[25] * b[30] + b[1] * b[18] * b[37] + b[1] * b[17] * b[38] - b[1] * b[23] * b[32] + b[2] * b[18] * b[36]; coeffs(6) = -b[14] * b[6] * b[37] - b[14] * b[7] * b[36] + b[14] * b[31] * b[12] + b[3] * b[17] * b[37] - b[3] * b[23] * b[31] - b[3] * b[24] * b[30] - b[3] * b[21] * b[33] + b[3] * b[20] * b[34] + b[3] * b[19] * b[35] + b[3] * b[18] * b[36] - b[3] * b[22] * b[32] + b[13] * b[32] * b[12] + b[13] * b[33] * b[11] - b[15] * b[6] * b[36] - b[15] * b[7] * b[35] + b[15] * b[31] * b[11] + b[15] * b[30] * b[12] + b[16] * b[32] * b[9] + b[16] * b[33] * b[8] - b[13] * b[6] * b[38] - b[13] * b[7] * b[37] + b[14] * b[32] * b[11] + b[14] * b[33] * b[10] - b[14] * b[5] * b[38] - b[16] * b[6] * b[35] - b[16] * b[7] * b[34] + b[16] * b[30] * b[11] + b[16] * b[31] * b[10] - b[26] * b[19] * b[12] - b[26] * b[20] * b[11] + b[26] * b[6] * b[25] + b[26] * b[7] * b[24] + b[15] * b[32] * b[10] + b[15] * b[33] * b[9] - b[15] * b[4] * b[38] - b[15] * b[5] * b[37] + b[29] * b[5] * b[23] + b[29] * b[6] * b[22] + b[29] * b[7] * b[21] - b[27] * b[20] * b[10] + b[27] * b[5] * b[25] + b[27] * b[6] * b[24] + b[27] * b[7] * b[23] - b[27] * b[18] * b[12] - b[27] * b[19] * b[11] - b[28] * b[20] * b[9] - b[16] * b[4] * b[37] - b[16] * b[5] * b[36] + b[0] * b[19] * b[38] - b[0] * b[24] * b[33] + b[0] * b[20] * b[37] - b[29] * b[17] * b[11] - b[29] * b[18] * b[10] - b[29] * b[19] * b[9] + b[28] * b[4] * b[25] + b[28] * b[5] * b[24] + b[28] * b[6] * b[23] + b[28] * b[7] * b[22] - b[28] * b[17] * b[12] - b[28] * b[18] * b[11] - b[28] * b[19] * b[10] - b[29] * b[20] * b[8] + b[29] * b[4] * b[24] + b[2] * b[18] * b[37] - b[0] * b[25] * b[32] + b[1] * b[18] * b[38] - b[1] * b[24] * b[32] + b[1] * b[19] * b[37] + b[1] * b[20] * b[36] - b[1] * b[25] * b[31] + b[2] * b[17] * b[38] + b[2] * b[19] * b[36] - b[2] * b[24] * b[31] - b[2] * b[22] * b[33] - b[2] * b[23] * b[32] + b[2] * b[20] * b[35] - b[1] * b[23] * b[33] - b[2] * b[25] * b[30]; coeffs(7) = -b[14] * b[6] * b[38] - b[14] * b[7] * b[37] + b[3] * b[19] * b[36] - b[3] * b[22] * b[33] + b[3] * b[20] * b[35] - b[3] * b[23] * b[32] - b[3] * b[25] * b[30] + b[3] * b[17] * b[38] + b[3] * b[18] * b[37] - b[3] * b[24] * b[31] - b[15] * b[6] * b[37] - b[15] * b[7] * b[36] + b[15] * b[31] * b[12] + b[16] * b[32] * b[10] + b[16] * b[33] * b[9] + b[13] * b[33] * b[12] - b[13] * b[7] * b[38] + b[14] * b[32] * b[12] + b[14] * b[33] * b[11] - b[16] * b[6] * b[36] - b[16] * b[7] * b[35] + b[16] * b[31] * b[11] + b[16] * b[30] * b[12] + b[15] * b[32] * b[11] + b[15] * b[33] * b[10] - b[15] * b[5] * b[38] + b[29] * b[5] * b[24] + b[29] * b[6] * b[23] - b[26] * b[20] * b[12] + b[26] * b[7] * b[25] - b[27] * b[19] * b[12] - b[27] * b[20] * b[11] + b[27] * b[6] * b[25] + b[27] * b[7] * b[24] - b[28] * b[20] * b[10] - b[16] * b[4] * b[38] - b[16] * b[5] * b[37] + b[29] * b[7] * b[22] - b[29] * b[17] * b[12] - b[29] * b[18] * b[11] - b[29] * b[19] * b[10] + b[28] * b[5] * b[25] + b[28] * b[6] * b[24] + b[28] * b[7] * b[23] - b[28] * b[18] * b[12] - b[28] * b[19] * b[11] - b[29] * b[20] * b[9] + b[29] * b[4] * b[25] - b[2] * b[24] * b[32] + b[0] * b[20] * b[38] - b[0] * b[25] * b[33] + b[1] * b[19] * b[38] - b[1] * b[24] * b[33] + b[1] * b[20] * b[37] - b[2] * b[25] * b[31] + b[2] * b[20] * b[36] - b[1] * b[25] * b[32] + b[2] * b[19] * b[37] + b[2] * b[18] * b[38] - b[2] * b[23] * b[33]; coeffs(8) = b[3] * b[18] * b[38] - b[3] * b[24] * b[32] + b[3] * b[19] * b[37] + b[3] * b[20] * b[36] - b[3] * b[25] * b[31] - b[3] * b[23] * b[33] - b[15] * b[6] * b[38] - b[15] * b[7] * b[37] + b[16] * b[32] * b[11] + b[16] * b[33] * b[10] - b[16] * b[5] * b[38] - b[16] * b[6] * b[37] - b[16] * b[7] * b[36] + b[16] * b[31] * b[12] + b[14] * b[33] * b[12] - b[14] * b[7] * b[38] + b[15] * b[32] * b[12] + b[15] * b[33] * b[11] + b[29] * b[5] * b[25] + b[29] * b[6] * b[24] - b[27] * b[20] * b[12] + b[27] * b[7] * b[25] - b[28] * b[19] * b[12] - b[28] * b[20] * b[11] + b[29] * b[7] * b[23] - b[29] * b[18] * b[12] - b[29] * b[19] * b[11] + b[28] * b[6] * b[25] + b[28] * b[7] * b[24] - b[29] * b[20] * b[10] + b[2] * b[19] * b[38] - b[1] * b[25] * b[33] + b[2] * b[20] * b[37] - b[2] * b[24] * b[33] - b[2] * b[25] * b[32] + b[1] * b[20] * b[38]; coeffs(9) = b[29] * b[7] * b[24] - b[29] * b[20] * b[11] + b[2] * b[20] * b[38] - b[2] * b[25] * b[33] - b[28] * b[20] * b[12] + b[28] * b[7] * b[25] - b[29] * b[19] * b[12] - b[3] * b[24] * b[33] + b[15] * b[33] * b[12] + b[3] * b[19] * b[38] - b[16] * b[6] * b[38] + b[3] * b[20] * b[37] + b[16] * b[32] * b[12] + b[29] * b[6] * b[25] - b[16] * b[7] * b[37] - b[3] * b[25] * b[32] - b[15] * b[7] * b[38] + b[16] * b[33] * b[11]; coeffs(10) = -b[29] * b[20] * b[12] + b[29] * b[7] * b[25] + b[16] * b[33] * b[12] - b[16] * b[7] * b[38] + b[3] * b[20] * b[38] - b[3] * b[25] * b[33]; } colmap-3.4/src/estimators/essential_matrix_poly.h000077500000000000000000004476741323400541200224260ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . { double* a = A.data(); const double* e = E.data(); double e2[36]; double e3[36]; for (size_t i = 0; i < 36; ++i) { e2[i] = e[i] * e[i]; e3[i] = e2[i] * e[i]; } a[190] = e[33] * e[28] * e[32] - e[33] * e[31] * e[29] + e[30] * e[34] * e[29] - e[30] * e[28] * e[35] - e[27] * e[32] * e[34] + e[27] * e[31] * e[35]; a[7] = 0.5 * e[6] * e2[8] - 0.5 * e[6] * e2[5] + 0.5 * e3[6] + 0.5 * e[6] * e2[7] - 0.5 * e[6] * e2[4] + e[0] * e[2] * e[8] + e[3] * e[4] * e[7] + e[3] * e[5] * e[8] + e[0] * e[1] * e[7] - 0.5 * e[6] * e2[1] - 0.5 * e[6] * e2[2] + 0.5 * e2[0] * e[6] + 0.5 * e2[3] * e[6]; a[120] = e[30] * e[34] * e[2] + e[33] * e[1] * e[32] - e[3] * e[28] * e[35] + e[0] * e[31] * e[35] + e[3] * e[34] * e[29] - e[30] * e[1] * e[35] + e[27] * e[31] * e[8] - e[27] * e[32] * e[7] - e[30] * e[28] * e[8] - e[33] * e[31] * e[2] - e[0] * e[32] * e[34] + e[6] * e[28] * e[32] - e[33] * e[4] * e[29] + e[33] * e[28] * e[5] + e[30] * e[7] * e[29] + e[27] * e[4] * e[35] - e[27] * e[5] * e[34] - e[6] * e[31] * e[29]; a[77] = e[9] * e[27] * e[15] + e[9] * e[29] * e[17] + e[9] * e[11] * e[35] + e[9] * e[28] * e[16] + e[9] * e[10] * e[34] + e[27] * e[11] * e[17] + e[27] * e[10] * e[16] + e[12] * e[30] * e[15] + e[12] * e[32] * e[17] + e[12] * e[14] * e[35] + e[12] * e[31] * e[16] + e[12] * e[13] * e[34] + e[30] * e[14] * e[17] + e[30] * e[13] * e[16] + e[15] * e[35] * e[17] + e[15] * e[34] * e[16] - e[15] * e[28] * e[10] - e[15] * e[31] * e[13] - e[15] * e[32] * e[14] - e[15] * e[29] * e[11] + 0.5 * e2[9] * e[33] + 0.5 * e[33] * e2[16] - 0.5 * e[33] * e2[11] + 0.5 * e[33] * e2[12] + 1.5 * e[33] * e2[15] + 0.5 * e[33] * e2[17] - 0.5 * e[33] * e2[10] - 0.5 * e[33] * e2[14] - 0.5 * e[33] * e2[13]; a[180] = -e[33] * e[22] * e[29] - e[33] * e[31] * e[20] - e[27] * e[32] * e[25] + e[27] * e[22] * e[35] - e[27] * e[23] * e[34] + e[27] * e[31] * e[26] + e[33] * e[28] * e[23] - e[21] * e[28] * e[35] + e[30] * e[25] * e[29] + e[24] * e[28] * e[32] - e[24] * e[31] * e[29] + e[18] * e[31] * e[35] - e[30] * e[28] * e[26] - e[30] * e[19] * e[35] + e[21] * e[34] * e[29] + e[33] * e[19] * e[32] - e[18] * e[32] * e[34] + e[30] * e[34] * e[20]; a[87] = e[18] * e[2] * e[17] + e[3] * e[21] * e[15] + e[3] * e[12] * e[24] + e[3] * e[23] * e[17] + e[3] * e[14] * e[26] + e[3] * e[22] * e[16] + e[3] * e[13] * e[25] + 3. * e[6] * e[24] * e[15] + e[6] * e[26] * e[17] + e[6] * e[25] * e[16] + e[0] * e[20] * e[17] + e[0] * e[11] * e[26] + e[0] * e[19] * e[16] + e[0] * e[10] * e[25] + e[15] * e[26] * e[8] - e[15] * e[20] * e[2] - e[15] * e[19] * e[1] - e[15] * e[22] * e[4] + e[15] * e[25] * e[7] - e[15] * e[23] * e[5] + e[12] * e[21] * e[6] + e[12] * e[22] * e[7] + e[12] * e[4] * e[25] + e[12] * e[23] * e[8] + e[12] * e[5] * e[26] - e[24] * e[11] * e[2] - e[24] * e[10] * e[1] - e[24] * e[13] * e[4] + e[24] * e[16] * e[7] - e[24] * e[14] * e[5] + e[24] * e[17] * e[8] + e[21] * e[13] * e[7] + e[21] * e[4] * e[16] + e[21] * e[14] * e[8] + e[21] * e[5] * e[17] - e[6] * e[23] * e[14] - e[6] * e[20] * e[11] - e[6] * e[19] * e[10] - e[6] * e[22] * e[13] + e[9] * e[18] * e[6] + e[9] * e[0] * e[24] + e[9] * e[19] * e[7] + e[9] * e[1] * e[25] + e[9] * e[20] * e[8] + e[9] * e[2] * e[26] + e[18] * e[0] * e[15] + e[18] * e[10] * e[7] + e[18] * e[1] * e[16] + e[18] * e[11] * e[8]; a[150] = e[33] * e[10] * e[32] + e[33] * e[28] * e[14] - e[33] * e[13] * e[29] - e[33] * e[31] * e[11] + e[9] * e[31] * e[35] - e[9] * e[32] * e[34] + e[27] * e[13] * e[35] - e[27] * e[32] * e[16] + e[27] * e[31] * e[17] - e[27] * e[14] * e[34] + e[12] * e[34] * e[29] - e[12] * e[28] * e[35] + e[30] * e[34] * e[11] + e[30] * e[16] * e[29] - e[30] * e[10] * e[35] - e[30] * e[28] * e[17] + e[15] * e[28] * e[32] - e[15] * e[31] * e[29]; a[57] = e[0] * e[27] * e[6] + e[0] * e[28] * e[7] + e[0] * e[1] * e[34] + e[0] * e[29] * e[8] + e[0] * e[2] * e[35] + e[6] * e[34] * e[7] - e[6] * e[32] * e[5] + e[6] * e[30] * e[3] + e[6] * e[35] * e[8] - e[6] * e[29] * e[2] - e[6] * e[28] * e[1] - e[6] * e[31] * e[4] + e[27] * e[1] * e[7] + e[27] * e[2] * e[8] + e[3] * e[31] * e[7] + e[3] * e[4] * e[34] + e[3] * e[32] * e[8] + e[3] * e[5] * e[35] + e[30] * e[4] * e[7] + e[30] * e[5] * e[8] + 0.5 * e2[0] * e[33] + 1.5 * e[33] * e2[6] - 0.5 * e[33] * e2[4] - 0.5 * e[33] * e2[5] - 0.5 * e[33] * e2[1] + 0.5 * e[33] * e2[7] + 0.5 * e[33] * e2[3] - 0.5 * e[33] * e2[2] + 0.5 * e[33] * e2[8]; a[80] = -e[0] * e[23] * e[16] + e[9] * e[4] * e[26] + e[9] * e[22] * e[8] - e[9] * e[5] * e[25] - e[9] * e[23] * e[7] + e[18] * e[4] * e[17] + e[18] * e[13] * e[8] - e[18] * e[5] * e[16] - e[18] * e[14] * e[7] + e[3] * e[16] * e[20] + e[3] * e[25] * e[11] - e[3] * e[10] * e[26] - e[3] * e[19] * e[17] + e[12] * e[7] * e[20] + e[12] * e[25] * e[2] - e[12] * e[1] * e[26] - e[12] * e[19] * e[8] + e[21] * e[7] * e[11] + e[21] * e[16] * e[2] - e[21] * e[1] * e[17] - e[21] * e[10] * e[8] + e[6] * e[10] * e[23] + e[6] * e[19] * e[14] - e[6] * e[13] * e[20] - e[6] * e[22] * e[11] + e[15] * e[1] * e[23] + e[15] * e[19] * e[5] - e[15] * e[4] * e[20] - e[15] * e[22] * e[2] + e[24] * e[1] * e[14] + e[24] * e[10] * e[5] - e[24] * e[4] * e[11] - e[24] * e[13] * e[2] + e[0] * e[13] * e[26] + e[0] * e[22] * e[17] - e[0] * e[14] * e[25]; a[167] = e[18] * e[19] * e[25] + 0.5 * e3[24] - 0.5 * e[24] * e2[23] + e[18] * e[20] * e[26] + e[21] * e[22] * e[25] + e[21] * e[23] * e[26] - 0.5 * e[24] * e2[19] + 0.5 * e2[21] * e[24] + 0.5 * e[24] * e2[26] - 0.5 * e[24] * e2[20] + 0.5 * e2[18] * e[24] - 0.5 * e[24] * e2[22] + 0.5 * e[24] * e2[25]; a[50] = -e[3] * e[1] * e[35] - e[0] * e[32] * e[7] + e[27] * e[4] * e[8] + e[33] * e[1] * e[5] - e[33] * e[4] * e[2] + e[0] * e[4] * e[35] + e[3] * e[34] * e[2] - e[30] * e[1] * e[8] + e[30] * e[7] * e[2] - e[6] * e[4] * e[29] + e[3] * e[7] * e[29] + e[6] * e[1] * e[32] - e[0] * e[5] * e[34] - e[3] * e[28] * e[8] + e[0] * e[31] * e[8] + e[6] * e[28] * e[5] - e[6] * e[31] * e[2] - e[27] * e[5] * e[7]; a[97] = e[33] * e[16] * e[7] - e[33] * e[14] * e[5] + e[33] * e[17] * e[8] + e[30] * e[13] * e[7] + e[30] * e[4] * e[16] + e[30] * e[14] * e[8] + e[30] * e[5] * e[17] + e[6] * e[27] * e[9] - e[6] * e[28] * e[10] - e[6] * e[31] * e[13] - e[6] * e[32] * e[14] - e[6] * e[29] * e[11] + e[9] * e[28] * e[7] + e[9] * e[1] * e[34] + e[9] * e[29] * e[8] + e[9] * e[2] * e[35] + e[27] * e[10] * e[7] + e[27] * e[1] * e[16] + e[27] * e[11] * e[8] + e[27] * e[2] * e[17] + e[3] * e[30] * e[15] + e[3] * e[12] * e[33] + e[3] * e[32] * e[17] + e[3] * e[14] * e[35] + e[3] * e[31] * e[16] + e[3] * e[13] * e[34] + 3. * e[6] * e[33] * e[15] + e[6] * e[35] * e[17] + e[6] * e[34] * e[16] + e[0] * e[27] * e[15] + e[0] * e[9] * e[33] + e[0] * e[29] * e[17] + e[0] * e[11] * e[35] + e[0] * e[28] * e[16] + e[0] * e[10] * e[34] + e[15] * e[34] * e[7] - e[15] * e[32] * e[5] + e[15] * e[35] * e[8] - e[15] * e[29] * e[2] - e[15] * e[28] * e[1] - e[15] * e[31] * e[4] + e[12] * e[30] * e[6] + e[12] * e[31] * e[7] + e[12] * e[4] * e[34] + e[12] * e[32] * e[8] + e[12] * e[5] * e[35] - e[33] * e[11] * e[2] - e[33] * e[10] * e[1] - e[33] * e[13] * e[4]; a[0] = e[6] * e[1] * e[5] - e[6] * e[4] * e[2] + e[3] * e[7] * e[2] + e[0] * e[4] * e[8] - e[0] * e[5] * e[7] - e[3] * e[1] * e[8]; a[17] = 0.5 * e3[15] + e[9] * e[10] * e[16] - 0.5 * e[15] * e2[11] + e[9] * e[11] * e[17] + 0.5 * e2[12] * e[15] + 0.5 * e[15] * e2[16] + 0.5 * e[15] * e2[17] - 0.5 * e[15] * e2[13] + 0.5 * e2[9] * e[15] + e[12] * e[14] * e[17] - 0.5 * e[15] * e2[10] - 0.5 * e[15] * e2[14] + e[12] * e[13] * e[16]; a[70] = e[15] * e[28] * e[14] - e[15] * e[13] * e[29] - e[15] * e[31] * e[11] + e[33] * e[10] * e[14] - e[33] * e[13] * e[11] + e[9] * e[13] * e[35] - e[9] * e[32] * e[16] + e[9] * e[31] * e[17] - e[9] * e[14] * e[34] + e[27] * e[13] * e[17] - e[27] * e[14] * e[16] + e[12] * e[34] * e[11] + e[12] * e[16] * e[29] - e[12] * e[10] * e[35] - e[12] * e[28] * e[17] + e[30] * e[16] * e[11] - e[30] * e[10] * e[17] + e[15] * e[10] * e[32]; a[177] = e[18] * e[27] * e[24] + e[18] * e[28] * e[25] + e[18] * e[19] * e[34] + e[18] * e[29] * e[26] + e[18] * e[20] * e[35] + e[27] * e[19] * e[25] + e[27] * e[20] * e[26] + e[21] * e[30] * e[24] + e[21] * e[31] * e[25] + e[21] * e[22] * e[34] + e[21] * e[32] * e[26] + e[21] * e[23] * e[35] + e[30] * e[22] * e[25] + e[30] * e[23] * e[26] + e[24] * e[34] * e[25] + e[24] * e[35] * e[26] - e[24] * e[29] * e[20] - e[24] * e[31] * e[22] - e[24] * e[32] * e[23] - e[24] * e[28] * e[19] + 1.5 * e[33] * e2[24] + 0.5 * e[33] * e2[25] + 0.5 * e[33] * e2[26] - 0.5 * e[33] * e2[23] - 0.5 * e[33] * e2[19] - 0.5 * e[33] * e2[20] - 0.5 * e[33] * e2[22] + 0.5 * e2[18] * e[33] + 0.5 * e2[21] * e[33]; a[170] = e[21] * e[25] * e[29] - e[27] * e[23] * e[25] + e[24] * e[19] * e[32] - e[21] * e[28] * e[26] - e[21] * e[19] * e[35] + e[18] * e[31] * e[26] - e[30] * e[19] * e[26] - e[24] * e[31] * e[20] + e[24] * e[28] * e[23] + e[27] * e[22] * e[26] + e[30] * e[25] * e[20] - e[33] * e[22] * e[20] + e[33] * e[19] * e[23] + e[21] * e[34] * e[20] - e[18] * e[23] * e[34] - e[24] * e[22] * e[29] - e[18] * e[32] * e[25] + e[18] * e[22] * e[35]; a[37] = e[12] * e[14] * e[8] + e[12] * e[5] * e[17] + e[15] * e[16] * e[7] + e[15] * e[17] * e[8] + e[0] * e[11] * e[17] + e[0] * e[9] * e[15] + e[0] * e[10] * e[16] + e[3] * e[14] * e[17] + e[3] * e[13] * e[16] + e[9] * e[10] * e[7] + e[9] * e[1] * e[16] + e[9] * e[11] * e[8] + e[9] * e[2] * e[17] - e[15] * e[11] * e[2] - e[15] * e[10] * e[1] - e[15] * e[13] * e[4] - e[15] * e[14] * e[5] + e[12] * e[3] * e[15] + e[12] * e[13] * e[7] + e[12] * e[4] * e[16] + 0.5 * e2[12] * e[6] + 1.5 * e2[15] * e[6] + 0.5 * e[6] * e2[17] + 0.5 * e[6] * e2[16] + 0.5 * e[6] * e2[9] - 0.5 * e[6] * e2[11] - 0.5 * e[6] * e2[10] - 0.5 * e[6] * e2[14] - 0.5 * e[6] * e2[13]; a[10] = -e[9] * e[14] * e[16] - e[12] * e[10] * e[17] + e[9] * e[13] * e[17] - e[15] * e[13] * e[11] + e[15] * e[10] * e[14] + e[12] * e[16] * e[11]; a[67] = e[21] * e[14] * e[17] + e[21] * e[13] * e[16] + e[15] * e[26] * e[17] + e[15] * e[25] * e[16] - e[15] * e[23] * e[14] - e[15] * e[20] * e[11] - e[15] * e[19] * e[10] - e[15] * e[22] * e[13] + e[9] * e[20] * e[17] + e[9] * e[11] * e[26] + e[9] * e[19] * e[16] + e[9] * e[10] * e[25] + 0.5 * e2[12] * e[24] + 1.5 * e[24] * e2[15] + 0.5 * e[24] * e2[17] + 0.5 * e[24] * e2[16] + 0.5 * e2[9] * e[24] - 0.5 * e[24] * e2[11] - 0.5 * e[24] * e2[10] - 0.5 * e[24] * e2[14] - 0.5 * e[24] * e2[13] + e[18] * e[11] * e[17] + e[18] * e[9] * e[15] + e[18] * e[10] * e[16] + e[12] * e[21] * e[15] + e[12] * e[23] * e[17] + e[12] * e[14] * e[26] + e[12] * e[22] * e[16] + e[12] * e[13] * e[25]; a[90] = -e[9] * e[5] * e[34] + e[9] * e[31] * e[8] - e[9] * e[32] * e[7] + e[27] * e[4] * e[17] + e[27] * e[13] * e[8] - e[27] * e[5] * e[16] - e[27] * e[14] * e[7] + e[0] * e[13] * e[35] - e[0] * e[32] * e[16] + e[0] * e[31] * e[17] - e[0] * e[14] * e[34] + e[9] * e[4] * e[35] + e[6] * e[10] * e[32] + e[6] * e[28] * e[14] - e[6] * e[13] * e[29] - e[6] * e[31] * e[11] + e[15] * e[1] * e[32] + e[3] * e[34] * e[11] + e[3] * e[16] * e[29] - e[3] * e[10] * e[35] - e[3] * e[28] * e[17] - e[12] * e[1] * e[35] + e[12] * e[7] * e[29] + e[12] * e[34] * e[2] - e[12] * e[28] * e[8] + e[15] * e[28] * e[5] - e[15] * e[4] * e[29] - e[15] * e[31] * e[2] + e[33] * e[1] * e[14] + e[33] * e[10] * e[5] - e[33] * e[4] * e[11] - e[33] * e[13] * e[2] + e[30] * e[7] * e[11] + e[30] * e[16] * e[2] - e[30] * e[1] * e[17] - e[30] * e[10] * e[8]; a[117] = e[21] * e[31] * e[7] + e[21] * e[4] * e[34] + e[21] * e[32] * e[8] + e[21] * e[5] * e[35] + e[30] * e[22] * e[7] + e[30] * e[4] * e[25] + e[30] * e[23] * e[8] + e[30] * e[5] * e[26] + 3. * e[24] * e[33] * e[6] + e[24] * e[34] * e[7] + e[24] * e[35] * e[8] + e[33] * e[25] * e[7] + e[33] * e[26] * e[8] + e[0] * e[27] * e[24] + e[0] * e[18] * e[33] + e[0] * e[28] * e[25] + e[0] * e[19] * e[34] + e[0] * e[29] * e[26] + e[0] * e[20] * e[35] + e[18] * e[27] * e[6] + e[18] * e[28] * e[7] + e[18] * e[1] * e[34] + e[18] * e[29] * e[8] + e[18] * e[2] * e[35] + e[27] * e[19] * e[7] + e[27] * e[1] * e[25] + e[27] * e[20] * e[8] + e[27] * e[2] * e[26] + e[3] * e[30] * e[24] + e[3] * e[21] * e[33] + e[3] * e[31] * e[25] + e[3] * e[22] * e[34] + e[3] * e[32] * e[26] + e[3] * e[23] * e[35] + e[6] * e[30] * e[21] - e[6] * e[29] * e[20] + e[6] * e[35] * e[26] - e[6] * e[31] * e[22] - e[6] * e[32] * e[23] - e[6] * e[28] * e[19] + e[6] * e[34] * e[25] - e[24] * e[32] * e[5] - e[24] * e[29] * e[2] - e[24] * e[28] * e[1] - e[24] * e[31] * e[4] - e[33] * e[20] * e[2] - e[33] * e[19] * e[1] - e[33] * e[22] * e[4] - e[33] * e[23] * e[5]; a[160] = e[21] * e[25] * e[20] - e[21] * e[19] * e[26] + e[18] * e[22] * e[26] - e[18] * e[23] * e[25] - e[24] * e[22] * e[20] + e[24] * e[19] * e[23]; a[47] = e[3] * e[4] * e[25] + e[3] * e[23] * e[8] + e[3] * e[5] * e[26] + e[21] * e[4] * e[7] + e[21] * e[5] * e[8] + e[6] * e[25] * e[7] + e[6] * e[26] * e[8] + e[0] * e[19] * e[7] + e[0] * e[1] * e[25] + e[0] * e[20] * e[8] + e[0] * e[2] * e[26] - e[6] * e[20] * e[2] - e[6] * e[19] * e[1] - e[6] * e[22] * e[4] - e[6] * e[23] * e[5] + e[18] * e[1] * e[7] + e[18] * e[0] * e[6] + e[18] * e[2] * e[8] + e[3] * e[21] * e[6] + e[3] * e[22] * e[7] - 0.5 * e[24] * e2[4] + 0.5 * e[24] * e2[0] + 1.5 * e[24] * e2[6] - 0.5 * e[24] * e2[5] - 0.5 * e[24] * e2[1] + 0.5 * e[24] * e2[7] + 0.5 * e[24] * e2[3] - 0.5 * e[24] * e2[2] + 0.5 * e[24] * e2[8]; a[110] = e[6] * e[28] * e[23] - e[6] * e[22] * e[29] - e[6] * e[31] * e[20] - e[3] * e[19] * e[35] + e[3] * e[34] * e[20] + e[3] * e[25] * e[29] - e[21] * e[1] * e[35] + e[21] * e[7] * e[29] + e[21] * e[34] * e[2] + e[24] * e[1] * e[32] + e[24] * e[28] * e[5] - e[24] * e[4] * e[29] - e[24] * e[31] * e[2] + e[33] * e[1] * e[23] + e[33] * e[19] * e[5] - e[33] * e[4] * e[20] - e[33] * e[22] * e[2] - e[21] * e[28] * e[8] + e[30] * e[7] * e[20] + e[30] * e[25] * e[2] - e[30] * e[1] * e[26] + e[18] * e[4] * e[35] - e[18] * e[5] * e[34] + e[18] * e[31] * e[8] - e[18] * e[32] * e[7] + e[27] * e[4] * e[26] + e[27] * e[22] * e[8] - e[27] * e[5] * e[25] - e[27] * e[23] * e[7] - e[3] * e[28] * e[26] - e[0] * e[32] * e[25] + e[0] * e[22] * e[35] - e[0] * e[23] * e[34] + e[0] * e[31] * e[26] - e[30] * e[19] * e[8] + e[6] * e[19] * e[32]; a[107] = 0.5 * e2[18] * e[6] + 0.5 * e2[21] * e[6] + 1.5 * e2[24] * e[6] + 0.5 * e[6] * e2[26] - 0.5 * e[6] * e2[23] - 0.5 * e[6] * e2[19] - 0.5 * e[6] * e2[20] - 0.5 * e[6] * e2[22] + 0.5 * e[6] * e2[25] + e[21] * e[3] * e[24] + e[18] * e[20] * e[8] + e[21] * e[4] * e[25] + e[18] * e[19] * e[7] + e[18] * e[1] * e[25] + e[21] * e[22] * e[7] + e[21] * e[23] * e[8] + e[18] * e[0] * e[24] + e[18] * e[2] * e[26] + e[21] * e[5] * e[26] + e[24] * e[26] * e[8] - e[24] * e[20] * e[2] - e[24] * e[19] * e[1] - e[24] * e[22] * e[4] + e[24] * e[25] * e[7] - e[24] * e[23] * e[5] + e[0] * e[19] * e[25] + e[0] * e[20] * e[26] + e[3] * e[22] * e[25] + e[3] * e[23] * e[26]; a[40] = e[18] * e[4] * e[8] + e[3] * e[7] * e[20] + e[3] * e[25] * e[2] - e[3] * e[1] * e[26] - e[18] * e[5] * e[7] + e[6] * e[1] * e[23] + e[6] * e[19] * e[5] - e[6] * e[4] * e[20] - e[6] * e[22] * e[2] + e[21] * e[7] * e[2] - e[21] * e[1] * e[8] + e[24] * e[1] * e[5] - e[24] * e[4] * e[2] - e[3] * e[19] * e[8] + e[0] * e[4] * e[26] + e[0] * e[22] * e[8] - e[0] * e[5] * e[25] - e[0] * e[23] * e[7]; a[27] = e[9] * e[1] * e[7] + e[9] * e[0] * e[6] + e[9] * e[2] * e[8] + e[3] * e[12] * e[6] + e[3] * e[13] * e[7] + e[3] * e[4] * e[16] + e[3] * e[14] * e[8] + e[3] * e[5] * e[17] + e[12] * e[4] * e[7] + e[12] * e[5] * e[8] + e[6] * e[16] * e[7] + e[6] * e[17] * e[8] - e[6] * e[11] * e[2] - e[6] * e[10] * e[1] - e[6] * e[13] * e[4] - e[6] * e[14] * e[5] + e[0] * e[10] * e[7] + e[0] * e[1] * e[16] + e[0] * e[11] * e[8] + e[0] * e[2] * e[17] + 0.5 * e2[3] * e[15] + 1.5 * e[15] * e2[6] + 0.5 * e[15] * e2[7] + 0.5 * e[15] * e2[8] + 0.5 * e2[0] * e[15] - 0.5 * e[15] * e2[4] - 0.5 * e[15] * e2[5] - 0.5 * e[15] * e2[1] - 0.5 * e[15] * e2[2]; a[30] = -e[15] * e[13] * e[2] - e[6] * e[13] * e[11] - e[15] * e[4] * e[11] + e[12] * e[16] * e[2] - e[3] * e[10] * e[17] + e[3] * e[16] * e[11] + e[0] * e[13] * e[17] - e[0] * e[14] * e[16] + e[15] * e[1] * e[14] - e[12] * e[10] * e[8] + e[9] * e[4] * e[17] + e[9] * e[13] * e[8] - e[9] * e[5] * e[16] - e[9] * e[14] * e[7] + e[15] * e[10] * e[5] + e[12] * e[7] * e[11] + e[6] * e[10] * e[14] - e[12] * e[1] * e[17]; a[147] = e[12] * e[30] * e[24] + e[12] * e[21] * e[33] + e[12] * e[31] * e[25] + e[12] * e[22] * e[34] + e[12] * e[32] * e[26] + e[12] * e[23] * e[35] + e[9] * e[27] * e[24] + e[9] * e[18] * e[33] + e[9] * e[28] * e[25] + e[9] * e[19] * e[34] + e[9] * e[29] * e[26] + e[9] * e[20] * e[35] + e[21] * e[30] * e[15] + e[21] * e[32] * e[17] + e[21] * e[14] * e[35] + e[21] * e[31] * e[16] + e[21] * e[13] * e[34] + e[30] * e[23] * e[17] + e[30] * e[14] * e[26] + e[30] * e[22] * e[16] + e[30] * e[13] * e[25] + e[15] * e[27] * e[18] + 3. * e[15] * e[33] * e[24] - e[15] * e[29] * e[20] + e[15] * e[35] * e[26] - e[15] * e[31] * e[22] - e[15] * e[32] * e[23] - e[15] * e[28] * e[19] + e[15] * e[34] * e[25] + e[18] * e[29] * e[17] + e[18] * e[11] * e[35] + e[18] * e[28] * e[16] + e[18] * e[10] * e[34] + e[27] * e[20] * e[17] + e[27] * e[11] * e[26] + e[27] * e[19] * e[16] + e[27] * e[10] * e[25] - e[24] * e[28] * e[10] - e[24] * e[31] * e[13] - e[24] * e[32] * e[14] + e[24] * e[34] * e[16] + e[24] * e[35] * e[17] - e[24] * e[29] * e[11] - e[33] * e[23] * e[14] + e[33] * e[25] * e[16] + e[33] * e[26] * e[17] - e[33] * e[20] * e[11] - e[33] * e[19] * e[10] - e[33] * e[22] * e[13]; a[60] = e[18] * e[13] * e[17] + e[9] * e[13] * e[26] + e[9] * e[22] * e[17] - e[9] * e[14] * e[25] - e[18] * e[14] * e[16] - e[15] * e[13] * e[20] - e[15] * e[22] * e[11] + e[12] * e[16] * e[20] + e[12] * e[25] * e[11] - e[12] * e[10] * e[26] - e[12] * e[19] * e[17] + e[21] * e[16] * e[11] - e[21] * e[10] * e[17] - e[9] * e[23] * e[16] + e[24] * e[10] * e[14] - e[24] * e[13] * e[11] + e[15] * e[10] * e[23] + e[15] * e[19] * e[14]; a[137] = e[21] * e[12] * e[24] + e[21] * e[23] * e[17] + e[21] * e[14] * e[26] + e[21] * e[22] * e[16] + e[21] * e[13] * e[25] + e[24] * e[26] * e[17] + e[24] * e[25] * e[16] + e[9] * e[19] * e[25] + e[9] * e[18] * e[24] + e[9] * e[20] * e[26] + e[12] * e[22] * e[25] + e[12] * e[23] * e[26] + e[18] * e[20] * e[17] + e[18] * e[11] * e[26] + e[18] * e[19] * e[16] + e[18] * e[10] * e[25] - e[24] * e[23] * e[14] - e[24] * e[20] * e[11] - e[24] * e[19] * e[10] - e[24] * e[22] * e[13] + 0.5 * e2[21] * e[15] + 1.5 * e2[24] * e[15] + 0.5 * e[15] * e2[25] + 0.5 * e[15] * e2[26] + 0.5 * e[15] * e2[18] - 0.5 * e[15] * e2[23] - 0.5 * e[15] * e2[19] - 0.5 * e[15] * e2[20] - 0.5 * e[15] * e2[22]; a[20] = e[6] * e[1] * e[14] + e[15] * e[1] * e[5] - e[0] * e[5] * e[16] - e[0] * e[14] * e[7] + e[0] * e[13] * e[8] - e[15] * e[4] * e[2] + e[12] * e[7] * e[2] + e[6] * e[10] * e[5] + e[3] * e[7] * e[11] - e[6] * e[4] * e[11] + e[3] * e[16] * e[2] - e[6] * e[13] * e[2] - e[3] * e[1] * e[17] - e[9] * e[5] * e[7] - e[3] * e[10] * e[8] - e[12] * e[1] * e[8] + e[0] * e[4] * e[17] + e[9] * e[4] * e[8]; a[16] = -0.5 * e[14] * e2[16] - 0.5 * e[14] * e2[10] - 0.5 * e[14] * e2[9] + e[11] * e[9] * e[12] + 0.5 * e3[14] + e[17] * e[13] * e[16] + 0.5 * e[14] * e2[12] + e[11] * e[10] * e[13] - 0.5 * e[14] * e2[15] + 0.5 * e[14] * e2[17] + e[17] * e[12] * e[15] + 0.5 * e2[11] * e[14] + 0.5 * e[14] * e2[13]; a[100] = -e[21] * e[19] * e[8] + e[18] * e[4] * e[26] - e[18] * e[5] * e[25] - e[18] * e[23] * e[7] + e[21] * e[25] * e[2] - e[21] * e[1] * e[26] + e[6] * e[19] * e[23] + e[18] * e[22] * e[8] - e[0] * e[23] * e[25] - e[6] * e[22] * e[20] + e[24] * e[1] * e[23] + e[24] * e[19] * e[5] - e[24] * e[4] * e[20] - e[24] * e[22] * e[2] + e[3] * e[25] * e[20] - e[3] * e[19] * e[26] + e[0] * e[22] * e[26] + e[21] * e[7] * e[20]; a[176] = 0.5 * e2[20] * e[32] + 1.5 * e[32] * e2[23] + 0.5 * e[32] * e2[22] + 0.5 * e[32] * e2[21] + 0.5 * e[32] * e2[26] - 0.5 * e[32] * e2[18] - 0.5 * e[32] * e2[19] - 0.5 * e[32] * e2[24] - 0.5 * e[32] * e2[25] + e[20] * e[27] * e[21] + e[20] * e[18] * e[30] + e[20] * e[28] * e[22] + e[20] * e[19] * e[31] + e[20] * e[29] * e[23] + e[29] * e[19] * e[22] + e[29] * e[18] * e[21] + e[23] * e[30] * e[21] + e[23] * e[31] * e[22] + e[26] * e[30] * e[24] + e[26] * e[21] * e[33] + e[26] * e[31] * e[25] + e[26] * e[22] * e[34] + e[26] * e[23] * e[35] + e[35] * e[22] * e[25] + e[35] * e[21] * e[24] - e[23] * e[27] * e[18] - e[23] * e[33] * e[24] - e[23] * e[28] * e[19] - e[23] * e[34] * e[25]; a[130] = -e[9] * e[23] * e[25] - e[21] * e[10] * e[26] - e[21] * e[19] * e[17] - e[18] * e[23] * e[16] + e[18] * e[13] * e[26] + e[12] * e[25] * e[20] - e[12] * e[19] * e[26] - e[15] * e[22] * e[20] + e[21] * e[16] * e[20] + e[21] * e[25] * e[11] + e[24] * e[10] * e[23] + e[24] * e[19] * e[14] - e[24] * e[13] * e[20] - e[24] * e[22] * e[11] + e[18] * e[22] * e[17] - e[18] * e[14] * e[25] + e[9] * e[22] * e[26] + e[15] * e[19] * e[23]; a[166] = 0.5 * e[23] * e2[21] + e[20] * e[19] * e[22] + e[20] * e[18] * e[21] + 0.5 * e3[23] + e[26] * e[22] * e[25] + 0.5 * e[23] * e2[26] - 0.5 * e[23] * e2[18] + 0.5 * e[23] * e2[22] - 0.5 * e[23] * e2[19] + e[26] * e[21] * e[24] + 0.5 * e2[20] * e[23] - 0.5 * e[23] * e2[24] - 0.5 * e[23] * e2[25]; a[140] = e[18] * e[13] * e[35] - e[18] * e[32] * e[16] + e[18] * e[31] * e[17] - e[18] * e[14] * e[34] + e[27] * e[13] * e[26] + e[27] * e[22] * e[17] - e[27] * e[14] * e[25] - e[27] * e[23] * e[16] - e[9] * e[32] * e[25] + e[9] * e[22] * e[35] - e[9] * e[23] * e[34] + e[9] * e[31] * e[26] + e[15] * e[19] * e[32] + e[15] * e[28] * e[23] - e[15] * e[22] * e[29] - e[15] * e[31] * e[20] + e[24] * e[10] * e[32] + e[24] * e[28] * e[14] - e[24] * e[13] * e[29] - e[24] * e[31] * e[11] + e[33] * e[10] * e[23] + e[33] * e[19] * e[14] - e[33] * e[13] * e[20] - e[33] * e[22] * e[11] + e[21] * e[16] * e[29] - e[21] * e[10] * e[35] - e[21] * e[28] * e[17] + e[30] * e[16] * e[20] + e[30] * e[25] * e[11] - e[30] * e[10] * e[26] - e[30] * e[19] * e[17] - e[12] * e[28] * e[26] - e[12] * e[19] * e[35] + e[12] * e[34] * e[20] + e[12] * e[25] * e[29] + e[21] * e[34] * e[11]; a[96] = -e[32] * e[10] * e[1] + e[32] * e[13] * e[4] - e[32] * e[16] * e[7] - e[32] * e[15] * e[6] - e[32] * e[9] * e[0] + e[32] * e[12] * e[3] + e[17] * e[30] * e[6] + e[17] * e[3] * e[33] + e[17] * e[31] * e[7] + e[17] * e[4] * e[34] + e[17] * e[5] * e[35] - e[5] * e[27] * e[9] - e[5] * e[28] * e[10] - e[5] * e[33] * e[15] - e[5] * e[34] * e[16] + e[5] * e[29] * e[11] + e[35] * e[12] * e[6] + e[35] * e[3] * e[15] + e[35] * e[13] * e[7] + e[35] * e[4] * e[16] + e[11] * e[27] * e[3] + e[11] * e[0] * e[30] + e[11] * e[28] * e[4] + e[11] * e[1] * e[31] + e[29] * e[9] * e[3] + e[29] * e[0] * e[12] + e[29] * e[10] * e[4] + e[29] * e[1] * e[13] + e[5] * e[30] * e[12] + 3. * e[5] * e[32] * e[14] + e[5] * e[31] * e[13] + e[8] * e[30] * e[15] + e[8] * e[12] * e[33] + e[8] * e[32] * e[17] + e[8] * e[14] * e[35] + e[8] * e[31] * e[16] + e[8] * e[13] * e[34] + e[2] * e[27] * e[12] + e[2] * e[9] * e[30] + e[2] * e[29] * e[14] + e[2] * e[11] * e[32] + e[2] * e[28] * e[13] + e[2] * e[10] * e[31] - e[14] * e[27] * e[0] - e[14] * e[34] * e[7] - e[14] * e[33] * e[6] + e[14] * e[30] * e[3] - e[14] * e[28] * e[1] + e[14] * e[31] * e[4]; a[181] = 0.5 * e[18] * e2[29] + 0.5 * e[18] * e2[28] + 0.5 * e[18] * e2[30] + 0.5 * e[18] * e2[33] - 0.5 * e[18] * e2[32] - 0.5 * e[18] * e2[31] - 0.5 * e[18] * e2[34] - 0.5 * e[18] * e2[35] + 1.5 * e[18] * e2[27] + e[27] * e[28] * e[19] + e[27] * e[29] * e[20] + e[21] * e[27] * e[30] + e[21] * e[29] * e[32] + e[21] * e[28] * e[31] + e[30] * e[28] * e[22] + e[30] * e[19] * e[31] + e[30] * e[29] * e[23] + e[30] * e[20] * e[32] + e[24] * e[27] * e[33] + e[24] * e[29] * e[35] + e[24] * e[28] * e[34] + e[33] * e[28] * e[25] + e[33] * e[19] * e[34] + e[33] * e[29] * e[26] + e[33] * e[20] * e[35] - e[27] * e[35] * e[26] - e[27] * e[31] * e[22] - e[27] * e[32] * e[23] - e[27] * e[34] * e[25]; a[46] = e[20] * e[1] * e[4] + e[20] * e[0] * e[3] + e[20] * e[2] * e[5] + e[5] * e[21] * e[3] + e[5] * e[22] * e[4] + e[8] * e[21] * e[6] + e[8] * e[3] * e[24] + e[8] * e[22] * e[7] + e[8] * e[4] * e[25] + e[8] * e[5] * e[26] + e[26] * e[4] * e[7] + e[26] * e[3] * e[6] + e[2] * e[18] * e[3] + e[2] * e[0] * e[21] + e[2] * e[19] * e[4] + e[2] * e[1] * e[22] - e[5] * e[19] * e[1] - e[5] * e[18] * e[0] - e[5] * e[25] * e[7] - e[5] * e[24] * e[6] + 0.5 * e[23] * e2[4] - 0.5 * e[23] * e2[0] - 0.5 * e[23] * e2[6] + 1.5 * e[23] * e2[5] - 0.5 * e[23] * e2[1] - 0.5 * e[23] * e2[7] + 0.5 * e[23] * e2[3] + 0.5 * e[23] * e2[2] + 0.5 * e[23] * e2[8]; a[151] = 1.5 * e[9] * e2[27] + 0.5 * e[9] * e2[29] + 0.5 * e[9] * e2[28] - 0.5 * e[9] * e2[32] - 0.5 * e[9] * e2[31] + 0.5 * e[9] * e2[33] + 0.5 * e[9] * e2[30] - 0.5 * e[9] * e2[34] - 0.5 * e[9] * e2[35] + e[33] * e[27] * e[15] + e[33] * e[29] * e[17] + e[33] * e[11] * e[35] + e[33] * e[28] * e[16] + e[33] * e[10] * e[34] + e[27] * e[29] * e[11] + e[27] * e[28] * e[10] + e[27] * e[30] * e[12] - e[27] * e[31] * e[13] - e[27] * e[32] * e[14] - e[27] * e[34] * e[16] - e[27] * e[35] * e[17] + e[30] * e[29] * e[14] + e[30] * e[11] * e[32] + e[30] * e[28] * e[13] + e[30] * e[10] * e[31] + e[12] * e[29] * e[32] + e[12] * e[28] * e[31] + e[15] * e[29] * e[35] + e[15] * e[28] * e[34]; a[116] = -e[32] * e[24] * e[6] + e[8] * e[30] * e[24] + e[8] * e[21] * e[33] + e[8] * e[31] * e[25] + e[8] * e[22] * e[34] + e[26] * e[30] * e[6] + e[26] * e[3] * e[33] + e[26] * e[31] * e[7] + e[26] * e[4] * e[34] + e[26] * e[32] * e[8] + e[26] * e[5] * e[35] + e[35] * e[21] * e[6] + e[35] * e[3] * e[24] + e[35] * e[22] * e[7] + e[35] * e[4] * e[25] + e[35] * e[23] * e[8] + e[2] * e[27] * e[21] + e[2] * e[18] * e[30] + e[2] * e[28] * e[22] + e[2] * e[19] * e[31] + e[2] * e[29] * e[23] + e[2] * e[20] * e[32] + e[20] * e[27] * e[3] + e[20] * e[0] * e[30] + e[20] * e[28] * e[4] + e[20] * e[1] * e[31] + e[20] * e[29] * e[5] + e[29] * e[18] * e[3] + e[29] * e[0] * e[21] + e[29] * e[19] * e[4] + e[29] * e[1] * e[22] + e[5] * e[30] * e[21] + e[5] * e[31] * e[22] + 3. * e[5] * e[32] * e[23] - e[5] * e[27] * e[18] - e[5] * e[33] * e[24] - e[5] * e[28] * e[19] - e[5] * e[34] * e[25] - e[23] * e[27] * e[0] - e[23] * e[34] * e[7] - e[23] * e[33] * e[6] + e[23] * e[30] * e[3] - e[23] * e[28] * e[1] + e[23] * e[31] * e[4] + e[32] * e[21] * e[3] - e[32] * e[19] * e[1] + e[32] * e[22] * e[4] - e[32] * e[18] * e[0] - e[32] * e[25] * e[7]; a[191] = 0.5 * e[27] * e2[33] - 0.5 * e[27] * e2[32] - 0.5 * e[27] * e2[31] - 0.5 * e[27] * e2[34] - 0.5 * e[27] * e2[35] + e[33] * e[29] * e[35] + 0.5 * e[27] * e2[29] + e[30] * e[29] * e[32] + e[30] * e[28] * e[31] + e[33] * e[28] * e[34] + 0.5 * e[27] * e2[28] + 0.5 * e[27] * e2[30] + 0.5 * e3[27]; a[66] = e[14] * e[21] * e[12] + e[14] * e[22] * e[13] + e[17] * e[21] * e[15] + e[17] * e[12] * e[24] + e[17] * e[14] * e[26] + e[17] * e[22] * e[16] + e[17] * e[13] * e[25] + e[26] * e[12] * e[15] + e[26] * e[13] * e[16] - e[14] * e[24] * e[15] - e[14] * e[25] * e[16] - e[14] * e[18] * e[9] - e[14] * e[19] * e[10] + e[11] * e[18] * e[12] + e[11] * e[9] * e[21] + e[11] * e[19] * e[13] + e[11] * e[10] * e[22] + e[20] * e[11] * e[14] + e[20] * e[9] * e[12] + e[20] * e[10] * e[13] + 1.5 * e[23] * e2[14] + 0.5 * e[23] * e2[12] + 0.5 * e[23] * e2[13] + 0.5 * e[23] * e2[17] + 0.5 * e2[11] * e[23] - 0.5 * e[23] * e2[16] - 0.5 * e[23] * e2[9] - 0.5 * e[23] * e2[15] - 0.5 * e[23] * e2[10]; a[121] = 1.5 * e[0] * e2[27] + 0.5 * e[0] * e2[29] + 0.5 * e[0] * e2[28] + 0.5 * e[0] * e2[30] - 0.5 * e[0] * e2[32] - 0.5 * e[0] * e2[31] + 0.5 * e[0] * e2[33] - 0.5 * e[0] * e2[34] - 0.5 * e[0] * e2[35] - e[27] * e[31] * e[4] + e[3] * e[27] * e[30] + e[3] * e[29] * e[32] + e[3] * e[28] * e[31] + e[30] * e[28] * e[4] + e[30] * e[1] * e[31] + e[30] * e[29] * e[5] + e[30] * e[2] * e[32] + e[6] * e[27] * e[33] + e[6] * e[29] * e[35] + e[6] * e[28] * e[34] + e[27] * e[28] * e[1] + e[27] * e[29] * e[2] + e[33] * e[28] * e[7] + e[33] * e[1] * e[34] + e[33] * e[29] * e[8] + e[33] * e[2] * e[35] - e[27] * e[34] * e[7] - e[27] * e[32] * e[5] - e[27] * e[35] * e[8]; a[36] = e[14] * e[12] * e[3] + e[14] * e[13] * e[4] + e[17] * e[12] * e[6] + e[17] * e[3] * e[15] + e[17] * e[13] * e[7] + e[17] * e[4] * e[16] + e[17] * e[14] * e[8] + e[8] * e[12] * e[15] + e[8] * e[13] * e[16] + e[2] * e[11] * e[14] + e[2] * e[9] * e[12] + e[2] * e[10] * e[13] + e[11] * e[9] * e[3] + e[11] * e[0] * e[12] + e[11] * e[10] * e[4] + e[11] * e[1] * e[13] - e[14] * e[10] * e[1] - e[14] * e[16] * e[7] - e[14] * e[15] * e[6] - e[14] * e[9] * e[0] - 0.5 * e[5] * e2[16] - 0.5 * e[5] * e2[9] + 0.5 * e[5] * e2[11] + 0.5 * e[5] * e2[12] - 0.5 * e[5] * e2[15] - 0.5 * e[5] * e2[10] + 0.5 * e[5] * e2[13] + 1.5 * e2[14] * e[5] + 0.5 * e[5] * e2[17]; a[71] = 1.5 * e[27] * e2[9] - 0.5 * e[27] * e2[16] + 0.5 * e[27] * e2[11] + 0.5 * e[27] * e2[12] + 0.5 * e[27] * e2[15] - 0.5 * e[27] * e2[17] + 0.5 * e[27] * e2[10] - 0.5 * e[27] * e2[14] - 0.5 * e[27] * e2[13] + e[12] * e[10] * e[31] + e[30] * e[11] * e[14] + e[30] * e[10] * e[13] + e[15] * e[9] * e[33] + e[15] * e[29] * e[17] + e[15] * e[11] * e[35] + e[15] * e[28] * e[16] + e[15] * e[10] * e[34] + e[33] * e[11] * e[17] + e[33] * e[10] * e[16] - e[9] * e[31] * e[13] - e[9] * e[32] * e[14] - e[9] * e[34] * e[16] - e[9] * e[35] * e[17] + e[9] * e[29] * e[11] + e[9] * e[28] * e[10] + e[12] * e[9] * e[30] + e[12] * e[29] * e[14] + e[12] * e[11] * e[32] + e[12] * e[28] * e[13]; a[146] = e[29] * e[18] * e[12] + e[29] * e[9] * e[21] + e[29] * e[19] * e[13] + e[29] * e[10] * e[22] + e[17] * e[30] * e[24] + e[17] * e[21] * e[33] + e[17] * e[31] * e[25] + e[17] * e[22] * e[34] + e[17] * e[32] * e[26] + e[17] * e[23] * e[35] - e[23] * e[27] * e[9] - e[23] * e[28] * e[10] - e[23] * e[33] * e[15] - e[23] * e[34] * e[16] - e[32] * e[24] * e[15] - e[32] * e[25] * e[16] - e[32] * e[18] * e[9] - e[32] * e[19] * e[10] + e[26] * e[30] * e[15] + e[26] * e[12] * e[33] + e[26] * e[31] * e[16] + e[26] * e[13] * e[34] + e[35] * e[21] * e[15] + e[35] * e[12] * e[24] + e[35] * e[22] * e[16] + e[35] * e[13] * e[25] + e[14] * e[30] * e[21] + e[14] * e[31] * e[22] + 3. * e[14] * e[32] * e[23] + e[11] * e[27] * e[21] + e[11] * e[18] * e[30] + e[11] * e[28] * e[22] + e[11] * e[19] * e[31] + e[11] * e[29] * e[23] + e[11] * e[20] * e[32] + e[23] * e[30] * e[12] + e[23] * e[31] * e[13] + e[32] * e[21] * e[12] + e[32] * e[22] * e[13] - e[14] * e[27] * e[18] - e[14] * e[33] * e[24] + e[14] * e[29] * e[20] + e[14] * e[35] * e[26] - e[14] * e[28] * e[19] - e[14] * e[34] * e[25] + e[20] * e[27] * e[12] + e[20] * e[9] * e[30] + e[20] * e[28] * e[13] + e[20] * e[10] * e[31]; a[1] = 0.5 * e[0] * e2[1] + 0.5 * e[0] * e2[2] + e[6] * e[2] * e[8] + e[6] * e[1] * e[7] + 0.5 * e[0] * e2[3] + e[3] * e[1] * e[4] + 0.5 * e[0] * e2[6] + e[3] * e[2] * e[5] - 0.5 * e[0] * e2[5] - 0.5 * e[0] * e2[8] + 0.5 * e3[0] - 0.5 * e[0] * e2[7] - 0.5 * e[0] * e2[4]; a[136] = 1.5 * e2[23] * e[14] + 0.5 * e[14] * e2[26] - 0.5 * e[14] * e2[18] - 0.5 * e[14] * e2[19] + 0.5 * e[14] * e2[20] + 0.5 * e[14] * e2[22] - 0.5 * e[14] * e2[24] + 0.5 * e[14] * e2[21] - 0.5 * e[14] * e2[25] + e[23] * e[21] * e[12] + e[23] * e[22] * e[13] + e[26] * e[21] * e[15] + e[26] * e[12] * e[24] + e[26] * e[23] * e[17] + e[26] * e[22] * e[16] + e[26] * e[13] * e[25] + e[17] * e[22] * e[25] + e[17] * e[21] * e[24] + e[11] * e[19] * e[22] + e[11] * e[18] * e[21] + e[11] * e[20] * e[23] + e[20] * e[18] * e[12] + e[20] * e[9] * e[21] + e[20] * e[19] * e[13] + e[20] * e[10] * e[22] - e[23] * e[24] * e[15] - e[23] * e[25] * e[16] - e[23] * e[18] * e[9] - e[23] * e[19] * e[10]; a[51] = 1.5 * e[27] * e2[0] - 0.5 * e[27] * e2[4] + 0.5 * e[27] * e2[6] - 0.5 * e[27] * e2[5] + 0.5 * e[27] * e2[1] - 0.5 * e[27] * e2[7] + 0.5 * e[27] * e2[3] + 0.5 * e[27] * e2[2] - 0.5 * e[27] * e2[8] + e[0] * e[33] * e[6] + e[0] * e[30] * e[3] - e[0] * e[35] * e[8] - e[0] * e[31] * e[4] + e[3] * e[28] * e[4] + e[3] * e[1] * e[31] + e[3] * e[29] * e[5] + e[3] * e[2] * e[32] + e[30] * e[1] * e[4] + e[30] * e[2] * e[5] + e[6] * e[28] * e[7] + e[6] * e[1] * e[34] + e[6] * e[29] * e[8] + e[6] * e[2] * e[35] + e[33] * e[1] * e[7] + e[33] * e[2] * e[8] + e[0] * e[28] * e[1] + e[0] * e[29] * e[2] - e[0] * e[34] * e[7] - e[0] * e[32] * e[5]; a[106] = e[8] * e[22] * e[25] + e[8] * e[21] * e[24] + e[20] * e[18] * e[3] + e[20] * e[0] * e[21] + e[20] * e[19] * e[4] + e[20] * e[1] * e[22] + e[20] * e[2] * e[23] + e[23] * e[21] * e[3] + e[23] * e[22] * e[4] + e[23] * e[26] * e[8] - e[23] * e[19] * e[1] - e[23] * e[18] * e[0] - e[23] * e[25] * e[7] - e[23] * e[24] * e[6] + e[2] * e[19] * e[22] + e[2] * e[18] * e[21] + e[26] * e[21] * e[6] + e[26] * e[3] * e[24] + e[26] * e[22] * e[7] + e[26] * e[4] * e[25] + 0.5 * e2[20] * e[5] + 1.5 * e2[23] * e[5] + 0.5 * e[5] * e2[22] + 0.5 * e[5] * e2[21] + 0.5 * e[5] * e2[26] - 0.5 * e[5] * e2[18] - 0.5 * e[5] * e2[19] - 0.5 * e[5] * e2[24] - 0.5 * e[5] * e2[25]; a[81] = e[24] * e[11] * e[8] + e[24] * e[2] * e[17] + 3. * e[9] * e[18] * e[0] + e[9] * e[19] * e[1] + e[9] * e[20] * e[2] + e[18] * e[10] * e[1] + e[18] * e[11] * e[2] + e[3] * e[18] * e[12] + e[3] * e[9] * e[21] + e[3] * e[20] * e[14] + e[3] * e[11] * e[23] + e[3] * e[19] * e[13] + e[3] * e[10] * e[22] + e[6] * e[18] * e[15] + e[6] * e[9] * e[24] + e[6] * e[20] * e[17] + e[6] * e[11] * e[26] + e[6] * e[19] * e[16] + e[6] * e[10] * e[25] + e[0] * e[20] * e[11] + e[0] * e[19] * e[10] - e[9] * e[26] * e[8] - e[9] * e[22] * e[4] - e[9] * e[25] * e[7] - e[9] * e[23] * e[5] + e[12] * e[0] * e[21] + e[12] * e[19] * e[4] + e[12] * e[1] * e[22] + e[12] * e[20] * e[5] + e[12] * e[2] * e[23] - e[18] * e[13] * e[4] - e[18] * e[16] * e[7] - e[18] * e[14] * e[5] - e[18] * e[17] * e[8] + e[21] * e[10] * e[4] + e[21] * e[1] * e[13] + e[21] * e[11] * e[5] + e[21] * e[2] * e[14] + e[15] * e[0] * e[24] + e[15] * e[19] * e[7] + e[15] * e[1] * e[25] + e[15] * e[20] * e[8] + e[15] * e[2] * e[26] - e[0] * e[23] * e[14] - e[0] * e[25] * e[16] - e[0] * e[26] * e[17] - e[0] * e[22] * e[13] + e[24] * e[10] * e[7] + e[24] * e[1] * e[16]; a[26] = e[11] * e[1] * e[4] + e[11] * e[0] * e[3] + e[11] * e[2] * e[5] + e[5] * e[12] * e[3] + e[5] * e[13] * e[4] + e[8] * e[12] * e[6] + e[8] * e[3] * e[15] + e[8] * e[13] * e[7] + e[8] * e[4] * e[16] + e[8] * e[5] * e[17] + e[17] * e[4] * e[7] + e[17] * e[3] * e[6] - e[5] * e[10] * e[1] - e[5] * e[16] * e[7] - e[5] * e[15] * e[6] - e[5] * e[9] * e[0] + e[2] * e[9] * e[3] + e[2] * e[0] * e[12] + e[2] * e[10] * e[4] + e[2] * e[1] * e[13] + 0.5 * e2[2] * e[14] - 0.5 * e[14] * e2[0] - 0.5 * e[14] * e2[6] - 0.5 * e[14] * e2[1] - 0.5 * e[14] * e2[7] + 1.5 * e[14] * e2[5] + 0.5 * e[14] * e2[4] + 0.5 * e[14] * e2[3] + 0.5 * e[14] * e2[8]; a[91] = e[3] * e[27] * e[12] + e[3] * e[9] * e[30] + e[3] * e[29] * e[14] + e[3] * e[11] * e[32] + e[3] * e[28] * e[13] + e[3] * e[10] * e[31] + e[6] * e[27] * e[15] + e[6] * e[9] * e[33] + e[6] * e[29] * e[17] + e[6] * e[11] * e[35] + e[6] * e[28] * e[16] + e[6] * e[10] * e[34] + 3. * e[0] * e[27] * e[9] + e[0] * e[29] * e[11] + e[0] * e[28] * e[10] - e[9] * e[34] * e[7] - e[9] * e[32] * e[5] - e[9] * e[35] * e[8] + e[9] * e[29] * e[2] + e[9] * e[28] * e[1] - e[9] * e[31] * e[4] + e[12] * e[0] * e[30] + e[12] * e[28] * e[4] + e[12] * e[1] * e[31] + e[12] * e[29] * e[5] + e[12] * e[2] * e[32] + e[27] * e[11] * e[2] + e[27] * e[10] * e[1] - e[27] * e[13] * e[4] - e[27] * e[16] * e[7] - e[27] * e[14] * e[5] - e[27] * e[17] * e[8] + e[30] * e[10] * e[4] + e[30] * e[1] * e[13] + e[30] * e[11] * e[5] + e[30] * e[2] * e[14] + e[15] * e[0] * e[33] + e[15] * e[28] * e[7] + e[15] * e[1] * e[34] + e[15] * e[29] * e[8] + e[15] * e[2] * e[35] - e[0] * e[31] * e[13] - e[0] * e[32] * e[14] - e[0] * e[34] * e[16] - e[0] * e[35] * e[17] + e[33] * e[10] * e[7] + e[33] * e[1] * e[16] + e[33] * e[11] * e[8] + e[33] * e[2] * e[17]; a[127] = 0.5 * e2[30] * e[6] + 0.5 * e[6] * e2[27] - 0.5 * e[6] * e2[32] - 0.5 * e[6] * e2[28] - 0.5 * e[6] * e2[29] - 0.5 * e[6] * e2[31] + 1.5 * e[6] * e2[33] + 0.5 * e[6] * e2[34] + 0.5 * e[6] * e2[35] + e[0] * e[27] * e[33] + e[0] * e[29] * e[35] + e[0] * e[28] * e[34] + e[3] * e[30] * e[33] + e[3] * e[32] * e[35] + e[3] * e[31] * e[34] + e[30] * e[31] * e[7] + e[30] * e[4] * e[34] + e[30] * e[32] * e[8] + e[30] * e[5] * e[35] + e[27] * e[28] * e[7] + e[27] * e[1] * e[34] + e[27] * e[29] * e[8] + e[27] * e[2] * e[35] + e[33] * e[34] * e[7] + e[33] * e[35] * e[8] - e[33] * e[32] * e[5] - e[33] * e[29] * e[2] - e[33] * e[28] * e[1] - e[33] * e[31] * e[4]; a[161] = e[24] * e[20] * e[26] + e[21] * e[19] * e[22] - 0.5 * e[18] * e2[22] - 0.5 * e[18] * e2[25] + 0.5 * e3[18] + 0.5 * e[18] * e2[21] + e[21] * e[20] * e[23] + 0.5 * e[18] * e2[20] + 0.5 * e[18] * e2[19] + 0.5 * e[18] * e2[24] + e[24] * e[19] * e[25] - 0.5 * e[18] * e2[23] - 0.5 * e[18] * e2[26]; a[197] = 0.5 * e[33] * e2[35] + 0.5 * e3[33] + 0.5 * e2[27] * e[33] + 0.5 * e2[30] * e[33] - 0.5 * e[33] * e2[29] + 0.5 * e[33] * e2[34] - 0.5 * e[33] * e2[32] - 0.5 * e[33] * e2[28] + e[30] * e[32] * e[35] - 0.5 * e[33] * e2[31] + e[27] * e[29] * e[35] + e[27] * e[28] * e[34] + e[30] * e[31] * e[34]; a[171] = 1.5 * e[27] * e2[18] + 0.5 * e[27] * e2[19] + 0.5 * e[27] * e2[20] + 0.5 * e[27] * e2[21] + 0.5 * e[27] * e2[24] - 0.5 * e[27] * e2[26] - 0.5 * e[27] * e2[23] - 0.5 * e[27] * e2[22] - 0.5 * e[27] * e2[25] + e[33] * e[20] * e[26] - e[18] * e[35] * e[26] - e[18] * e[31] * e[22] - e[18] * e[32] * e[23] - e[18] * e[34] * e[25] + e[18] * e[28] * e[19] + e[18] * e[29] * e[20] + e[21] * e[18] * e[30] + e[21] * e[28] * e[22] + e[21] * e[19] * e[31] + e[21] * e[29] * e[23] + e[21] * e[20] * e[32] + e[30] * e[19] * e[22] + e[30] * e[20] * e[23] + e[24] * e[18] * e[33] + e[24] * e[28] * e[25] + e[24] * e[19] * e[34] + e[24] * e[29] * e[26] + e[24] * e[20] * e[35] + e[33] * e[19] * e[25]; a[157] = e[9] * e[27] * e[33] + e[9] * e[29] * e[35] + e[9] * e[28] * e[34] + e[33] * e[35] * e[17] + e[33] * e[34] * e[16] + e[27] * e[29] * e[17] + e[27] * e[11] * e[35] + e[27] * e[28] * e[16] + e[27] * e[10] * e[34] + e[33] * e[30] * e[12] - e[33] * e[28] * e[10] - e[33] * e[31] * e[13] - e[33] * e[32] * e[14] - e[33] * e[29] * e[11] + e[30] * e[32] * e[17] + e[30] * e[14] * e[35] + e[30] * e[31] * e[16] + e[30] * e[13] * e[34] + e[12] * e[32] * e[35] + e[12] * e[31] * e[34] + 0.5 * e[15] * e2[27] - 0.5 * e[15] * e2[32] - 0.5 * e[15] * e2[28] - 0.5 * e[15] * e2[29] - 0.5 * e[15] * e2[31] + 1.5 * e[15] * e2[33] + 0.5 * e[15] * e2[30] + 0.5 * e[15] * e2[34] + 0.5 * e[15] * e2[35]; a[11] = 0.5 * e[9] * e2[12] - 0.5 * e[9] * e2[16] + 0.5 * e[9] * e2[10] - 0.5 * e[9] * e2[17] - 0.5 * e[9] * e2[13] + e[15] * e[10] * e[16] + e[12] * e[11] * e[14] + 0.5 * e[9] * e2[11] + 0.5 * e[9] * e2[15] - 0.5 * e[9] * e2[14] + e[15] * e[11] * e[17] + 0.5 * e3[9] + e[12] * e[10] * e[13]; a[187] = e[18] * e[27] * e[33] + e[18] * e[29] * e[35] + e[18] * e[28] * e[34] + e[27] * e[28] * e[25] + e[27] * e[19] * e[34] + e[27] * e[29] * e[26] + e[27] * e[20] * e[35] + e[21] * e[30] * e[33] + e[21] * e[32] * e[35] + e[21] * e[31] * e[34] + e[30] * e[31] * e[25] + e[30] * e[22] * e[34] + e[30] * e[32] * e[26] + e[30] * e[23] * e[35] + e[33] * e[34] * e[25] + e[33] * e[35] * e[26] - e[33] * e[29] * e[20] - e[33] * e[31] * e[22] - e[33] * e[32] * e[23] - e[33] * e[28] * e[19] + 0.5 * e2[27] * e[24] + 0.5 * e2[30] * e[24] + 1.5 * e[24] * e2[33] + 0.5 * e[24] * e2[35] + 0.5 * e[24] * e2[34] - 0.5 * e[24] * e2[32] - 0.5 * e[24] * e2[28] - 0.5 * e[24] * e2[29] - 0.5 * e[24] * e2[31]; a[131] = 0.5 * e[9] * e2[21] + 0.5 * e[9] * e2[24] + 0.5 * e[9] * e2[19] + 1.5 * e[9] * e2[18] + 0.5 * e[9] * e2[20] - 0.5 * e[9] * e2[26] - 0.5 * e[9] * e2[23] - 0.5 * e[9] * e2[22] - 0.5 * e[9] * e2[25] + e[21] * e[18] * e[12] + e[21] * e[20] * e[14] + e[21] * e[11] * e[23] + e[21] * e[19] * e[13] + e[21] * e[10] * e[22] + e[24] * e[18] * e[15] + e[24] * e[20] * e[17] + e[24] * e[11] * e[26] + e[24] * e[19] * e[16] + e[24] * e[10] * e[25] + e[15] * e[19] * e[25] + e[15] * e[20] * e[26] + e[12] * e[19] * e[22] + e[12] * e[20] * e[23] + e[18] * e[20] * e[11] + e[18] * e[19] * e[10] - e[18] * e[23] * e[14] - e[18] * e[25] * e[16] - e[18] * e[26] * e[17] - e[18] * e[22] * e[13]; a[189] = 0.5 * e2[29] * e[26] + 0.5 * e2[32] * e[26] + 0.5 * e[26] * e2[33] + 1.5 * e[26] * e2[35] + 0.5 * e[26] * e2[34] - 0.5 * e[26] * e2[27] - 0.5 * e[26] * e2[28] - 0.5 * e[26] * e2[31] - 0.5 * e[26] * e2[30] + e[20] * e[27] * e[33] + e[20] * e[29] * e[35] + e[20] * e[28] * e[34] + e[29] * e[27] * e[24] + e[29] * e[18] * e[33] + e[29] * e[28] * e[25] + e[29] * e[19] * e[34] + e[23] * e[30] * e[33] + e[23] * e[32] * e[35] + e[23] * e[31] * e[34] + e[32] * e[30] * e[24] + e[32] * e[21] * e[33] + e[32] * e[31] * e[25] + e[32] * e[22] * e[34] + e[35] * e[33] * e[24] + e[35] * e[34] * e[25] - e[35] * e[27] * e[18] - e[35] * e[30] * e[21] - e[35] * e[31] * e[22] - e[35] * e[28] * e[19]; a[141] = e[12] * e[19] * e[31] + e[12] * e[29] * e[23] + e[12] * e[20] * e[32] + 3. * e[9] * e[27] * e[18] + e[9] * e[28] * e[19] + e[9] * e[29] * e[20] + e[21] * e[9] * e[30] + e[21] * e[29] * e[14] + e[21] * e[11] * e[32] + e[21] * e[28] * e[13] + e[21] * e[10] * e[31] + e[30] * e[20] * e[14] + e[30] * e[11] * e[23] + e[30] * e[19] * e[13] + e[30] * e[10] * e[22] + e[9] * e[33] * e[24] - e[9] * e[35] * e[26] - e[9] * e[31] * e[22] - e[9] * e[32] * e[23] - e[9] * e[34] * e[25] + e[18] * e[29] * e[11] + e[18] * e[28] * e[10] + e[27] * e[20] * e[11] + e[27] * e[19] * e[10] + e[15] * e[27] * e[24] + e[15] * e[18] * e[33] + e[15] * e[28] * e[25] + e[15] * e[19] * e[34] + e[15] * e[29] * e[26] + e[15] * e[20] * e[35] - e[18] * e[31] * e[13] - e[18] * e[32] * e[14] - e[18] * e[34] * e[16] - e[18] * e[35] * e[17] - e[27] * e[23] * e[14] - e[27] * e[25] * e[16] - e[27] * e[26] * e[17] - e[27] * e[22] * e[13] + e[24] * e[29] * e[17] + e[24] * e[11] * e[35] + e[24] * e[28] * e[16] + e[24] * e[10] * e[34] + e[33] * e[20] * e[17] + e[33] * e[11] * e[26] + e[33] * e[19] * e[16] + e[33] * e[10] * e[25] + e[12] * e[27] * e[21] + e[12] * e[18] * e[30] + e[12] * e[28] * e[22]; a[159] = -0.5 * e[17] * e2[27] + 0.5 * e[17] * e2[32] - 0.5 * e[17] * e2[28] + 0.5 * e[17] * e2[29] - 0.5 * e[17] * e2[31] + 0.5 * e[17] * e2[33] - 0.5 * e[17] * e2[30] + 0.5 * e[17] * e2[34] + 1.5 * e[17] * e2[35] + e[32] * e[30] * e[15] + e[32] * e[12] * e[33] + e[32] * e[31] * e[16] + e[32] * e[13] * e[34] + e[14] * e[30] * e[33] + e[14] * e[31] * e[34] + e[11] * e[27] * e[33] + e[11] * e[29] * e[35] + e[11] * e[28] * e[34] + e[35] * e[33] * e[15] + e[35] * e[34] * e[16] + e[29] * e[27] * e[15] + e[29] * e[9] * e[33] + e[29] * e[28] * e[16] + e[29] * e[10] * e[34] - e[35] * e[27] * e[9] - e[35] * e[30] * e[12] - e[35] * e[28] * e[10] - e[35] * e[31] * e[13] + e[35] * e[32] * e[14]; a[21] = 0.5 * e[9] * e2[1] + 1.5 * e[9] * e2[0] + 0.5 * e[9] * e2[2] + 0.5 * e[9] * e2[3] + 0.5 * e[9] * e2[6] - 0.5 * e[9] * e2[4] - 0.5 * e[9] * e2[5] - 0.5 * e[9] * e2[7] - 0.5 * e[9] * e2[8] + e[6] * e[0] * e[15] + e[6] * e[10] * e[7] + e[6] * e[1] * e[16] + e[6] * e[11] * e[8] + e[6] * e[2] * e[17] + e[15] * e[1] * e[7] + e[15] * e[2] * e[8] + e[0] * e[11] * e[2] + e[0] * e[10] * e[1] - e[0] * e[13] * e[4] - e[0] * e[16] * e[7] - e[0] * e[14] * e[5] - e[0] * e[17] * e[8] + e[3] * e[0] * e[12] + e[3] * e[10] * e[4] + e[3] * e[1] * e[13] + e[3] * e[11] * e[5] + e[3] * e[2] * e[14] + e[12] * e[1] * e[4] + e[12] * e[2] * e[5]; a[199] = 0.5 * e[35] * e2[33] + 0.5 * e[35] * e2[34] - 0.5 * e[35] * e2[27] - 0.5 * e[35] * e2[28] - 0.5 * e[35] * e2[31] - 0.5 * e[35] * e2[30] + e[32] * e[31] * e[34] + 0.5 * e2[29] * e[35] + 0.5 * e2[32] * e[35] + e[29] * e[28] * e[34] + e[32] * e[30] * e[33] + 0.5 * e3[35] + e[29] * e[27] * e[33]; a[101] = 0.5 * e[0] * e2[19] + 0.5 * e[0] * e2[20] + 0.5 * e[0] * e2[24] - 0.5 * e[0] * e2[26] - 0.5 * e[0] * e2[23] - 0.5 * e[0] * e2[22] - 0.5 * e[0] * e2[25] + 1.5 * e2[18] * e[0] + 0.5 * e[0] * e2[21] + e[18] * e[19] * e[1] + e[18] * e[20] * e[2] + e[21] * e[18] * e[3] + e[21] * e[19] * e[4] + e[21] * e[1] * e[22] + e[21] * e[20] * e[5] + e[21] * e[2] * e[23] - e[18] * e[26] * e[8] - e[18] * e[22] * e[4] - e[18] * e[25] * e[7] - e[18] * e[23] * e[5] + e[18] * e[24] * e[6] + e[3] * e[19] * e[22] + e[3] * e[20] * e[23] + e[24] * e[19] * e[7] + e[24] * e[1] * e[25] + e[24] * e[20] * e[8] + e[24] * e[2] * e[26] + e[6] * e[19] * e[25] + e[6] * e[20] * e[26]; a[129] = 0.5 * e2[32] * e[8] - 0.5 * e[8] * e2[27] - 0.5 * e[8] * e2[28] + 0.5 * e[8] * e2[29] - 0.5 * e[8] * e2[31] + 0.5 * e[8] * e2[33] - 0.5 * e[8] * e2[30] + 0.5 * e[8] * e2[34] + 1.5 * e[8] * e2[35] + e[2] * e[27] * e[33] + e[2] * e[29] * e[35] + e[2] * e[28] * e[34] + e[5] * e[30] * e[33] + e[5] * e[32] * e[35] + e[5] * e[31] * e[34] + e[32] * e[30] * e[6] + e[32] * e[3] * e[33] + e[32] * e[31] * e[7] + e[32] * e[4] * e[34] + e[29] * e[27] * e[6] + e[29] * e[0] * e[33] + e[29] * e[28] * e[7] + e[29] * e[1] * e[34] + e[35] * e[33] * e[6] + e[35] * e[34] * e[7] - e[35] * e[27] * e[0] - e[35] * e[30] * e[3] - e[35] * e[28] * e[1] - e[35] * e[31] * e[4]; a[41] = -0.5 * e[18] * e2[4] + 1.5 * e[18] * e2[0] + 0.5 * e[18] * e2[6] - 0.5 * e[18] * e2[5] + 0.5 * e[18] * e2[1] - 0.5 * e[18] * e2[7] + 0.5 * e[18] * e2[3] + 0.5 * e[18] * e2[2] - 0.5 * e[18] * e2[8] + e[3] * e[0] * e[21] + e[3] * e[19] * e[4] + e[3] * e[1] * e[22] + e[3] * e[20] * e[5] + e[3] * e[2] * e[23] + e[21] * e[1] * e[4] + e[21] * e[2] * e[5] + e[6] * e[0] * e[24] + e[6] * e[19] * e[7] + e[6] * e[1] * e[25] + e[6] * e[20] * e[8] + e[6] * e[2] * e[26] + e[24] * e[1] * e[7] + e[24] * e[2] * e[8] + e[0] * e[19] * e[1] + e[0] * e[20] * e[2] - e[0] * e[26] * e[8] - e[0] * e[22] * e[4] - e[0] * e[25] * e[7] - e[0] * e[23] * e[5]; a[28] = e[10] * e[1] * e[7] + e[10] * e[0] * e[6] + e[10] * e[2] * e[8] + e[4] * e[12] * e[6] + e[4] * e[3] * e[15] + e[4] * e[13] * e[7] + e[4] * e[14] * e[8] + e[4] * e[5] * e[17] + e[13] * e[3] * e[6] + e[13] * e[5] * e[8] + e[7] * e[15] * e[6] + e[7] * e[17] * e[8] - e[7] * e[11] * e[2] - e[7] * e[9] * e[0] - e[7] * e[14] * e[5] - e[7] * e[12] * e[3] + e[1] * e[9] * e[6] + e[1] * e[0] * e[15] + e[1] * e[11] * e[8] + e[1] * e[2] * e[17] + 1.5 * e[16] * e2[7] + 0.5 * e[16] * e2[6] + 0.5 * e[16] * e2[8] + 0.5 * e2[1] * e[16] - 0.5 * e[16] * e2[0] - 0.5 * e[16] * e2[5] - 0.5 * e[16] * e2[3] - 0.5 * e[16] * e2[2] + 0.5 * e2[4] * e[16]; a[111] = e[0] * e[30] * e[21] - e[0] * e[35] * e[26] - e[0] * e[31] * e[22] - e[0] * e[32] * e[23] - e[0] * e[34] * e[25] - e[18] * e[34] * e[7] - e[18] * e[32] * e[5] - e[18] * e[35] * e[8] - e[18] * e[31] * e[4] - e[27] * e[26] * e[8] - e[27] * e[22] * e[4] - e[27] * e[25] * e[7] - e[27] * e[23] * e[5] + e[6] * e[28] * e[25] + e[6] * e[19] * e[34] + e[6] * e[29] * e[26] + e[6] * e[20] * e[35] + e[21] * e[28] * e[4] + e[21] * e[1] * e[31] + e[21] * e[29] * e[5] + e[21] * e[2] * e[32] + e[30] * e[19] * e[4] + e[30] * e[1] * e[22] + e[30] * e[20] * e[5] + e[30] * e[2] * e[23] + e[24] * e[27] * e[6] + e[24] * e[0] * e[33] + e[24] * e[28] * e[7] + e[24] * e[1] * e[34] + e[24] * e[29] * e[8] + e[24] * e[2] * e[35] + e[33] * e[18] * e[6] + e[33] * e[19] * e[7] + e[33] * e[1] * e[25] + e[33] * e[20] * e[8] + e[33] * e[2] * e[26] + 3. * e[0] * e[27] * e[18] + e[0] * e[28] * e[19] + e[0] * e[29] * e[20] + e[18] * e[28] * e[1] + e[18] * e[29] * e[2] + e[27] * e[19] * e[1] + e[27] * e[20] * e[2] + e[3] * e[27] * e[21] + e[3] * e[18] * e[30] + e[3] * e[28] * e[22] + e[3] * e[19] * e[31] + e[3] * e[29] * e[23] + e[3] * e[20] * e[32]; a[108] = e[19] * e[18] * e[6] + e[19] * e[0] * e[24] + e[19] * e[1] * e[25] + e[19] * e[20] * e[8] + e[19] * e[2] * e[26] + e[22] * e[21] * e[6] + e[22] * e[3] * e[24] + e[22] * e[4] * e[25] + e[22] * e[23] * e[8] + e[22] * e[5] * e[26] - e[25] * e[21] * e[3] + e[25] * e[26] * e[8] - e[25] * e[20] * e[2] - e[25] * e[18] * e[0] - e[25] * e[23] * e[5] + e[25] * e[24] * e[6] + e[1] * e[18] * e[24] + e[1] * e[20] * e[26] + e[4] * e[21] * e[24] + e[4] * e[23] * e[26] + 0.5 * e2[19] * e[7] + 0.5 * e2[22] * e[7] + 1.5 * e2[25] * e[7] + 0.5 * e[7] * e2[26] - 0.5 * e[7] * e2[18] - 0.5 * e[7] * e2[23] - 0.5 * e[7] * e2[20] + 0.5 * e[7] * e2[24] - 0.5 * e[7] * e2[21]; a[61] = 0.5 * e[18] * e2[11] + 1.5 * e[18] * e2[9] + 0.5 * e[18] * e2[10] + 0.5 * e[18] * e2[12] + 0.5 * e[18] * e2[15] - 0.5 * e[18] * e2[16] - 0.5 * e[18] * e2[17] - 0.5 * e[18] * e2[14] - 0.5 * e[18] * e2[13] + e[12] * e[9] * e[21] + e[12] * e[20] * e[14] + e[12] * e[11] * e[23] + e[12] * e[19] * e[13] + e[12] * e[10] * e[22] + e[21] * e[11] * e[14] + e[21] * e[10] * e[13] + e[15] * e[9] * e[24] + e[15] * e[20] * e[17] + e[15] * e[11] * e[26] + e[15] * e[19] * e[16] + e[15] * e[10] * e[25] + e[24] * e[11] * e[17] + e[24] * e[10] * e[16] - e[9] * e[23] * e[14] - e[9] * e[25] * e[16] - e[9] * e[26] * e[17] + e[9] * e[20] * e[11] + e[9] * e[19] * e[10] - e[9] * e[22] * e[13]; a[138] = e[13] * e[21] * e[24] + e[13] * e[23] * e[26] + e[19] * e[18] * e[15] + e[19] * e[9] * e[24] + e[19] * e[20] * e[17] + e[19] * e[11] * e[26] - e[25] * e[23] * e[14] - e[25] * e[20] * e[11] - e[25] * e[18] * e[9] - e[25] * e[21] * e[12] + e[22] * e[21] * e[15] + e[22] * e[12] * e[24] + e[22] * e[23] * e[17] + e[22] * e[14] * e[26] + e[22] * e[13] * e[25] + e[25] * e[24] * e[15] + e[25] * e[26] * e[17] + e[10] * e[19] * e[25] + e[10] * e[18] * e[24] + e[10] * e[20] * e[26] - 0.5 * e[16] * e2[18] - 0.5 * e[16] * e2[23] + 0.5 * e[16] * e2[19] - 0.5 * e[16] * e2[20] - 0.5 * e[16] * e2[21] + 0.5 * e2[22] * e[16] + 1.5 * e2[25] * e[16] + 0.5 * e[16] * e2[24] + 0.5 * e[16] * e2[26]; a[31] = 0.5 * e[0] * e2[12] + 0.5 * e[0] * e2[15] + 0.5 * e[0] * e2[11] + 1.5 * e[0] * e2[9] + 0.5 * e[0] * e2[10] - 0.5 * e[0] * e2[16] - 0.5 * e[0] * e2[17] - 0.5 * e[0] * e2[14] - 0.5 * e[0] * e2[13] + e[12] * e[9] * e[3] + e[12] * e[10] * e[4] + e[12] * e[1] * e[13] + e[12] * e[11] * e[5] + e[12] * e[2] * e[14] + e[15] * e[9] * e[6] + e[15] * e[10] * e[7] + e[15] * e[1] * e[16] + e[15] * e[11] * e[8] + e[15] * e[2] * e[17] + e[6] * e[11] * e[17] + e[6] * e[10] * e[16] + e[3] * e[11] * e[14] + e[3] * e[10] * e[13] + e[9] * e[10] * e[1] + e[9] * e[11] * e[2] - e[9] * e[13] * e[4] - e[9] * e[16] * e[7] - e[9] * e[14] * e[5] - e[9] * e[17] * e[8]; a[148] = e[19] * e[11] * e[35] + e[28] * e[18] * e[15] + e[28] * e[9] * e[24] + e[28] * e[20] * e[17] + e[28] * e[11] * e[26] - e[25] * e[27] * e[9] - e[25] * e[30] * e[12] - e[25] * e[32] * e[14] + e[25] * e[33] * e[15] + e[25] * e[35] * e[17] - e[25] * e[29] * e[11] - e[34] * e[23] * e[14] + e[34] * e[24] * e[15] + e[34] * e[26] * e[17] - e[34] * e[20] * e[11] - e[34] * e[18] * e[9] - e[34] * e[21] * e[12] + e[13] * e[30] * e[24] + e[13] * e[21] * e[33] + e[13] * e[31] * e[25] + e[13] * e[22] * e[34] + e[13] * e[32] * e[26] + e[13] * e[23] * e[35] + e[10] * e[27] * e[24] + e[10] * e[18] * e[33] + e[10] * e[28] * e[25] + e[10] * e[19] * e[34] + e[10] * e[29] * e[26] + e[10] * e[20] * e[35] + e[22] * e[30] * e[15] + e[22] * e[12] * e[33] + e[22] * e[32] * e[17] + e[22] * e[14] * e[35] + e[22] * e[31] * e[16] + e[31] * e[21] * e[15] + e[31] * e[12] * e[24] + e[31] * e[23] * e[17] + e[31] * e[14] * e[26] - e[16] * e[27] * e[18] + e[16] * e[33] * e[24] - e[16] * e[30] * e[21] - e[16] * e[29] * e[20] + e[16] * e[35] * e[26] - e[16] * e[32] * e[23] + e[16] * e[28] * e[19] + 3. * e[16] * e[34] * e[25] + e[19] * e[27] * e[15] + e[19] * e[9] * e[33] + e[19] * e[29] * e[17]; a[52] = e[4] * e[27] * e[3] + e[4] * e[0] * e[30] + e[4] * e[29] * e[5] + e[4] * e[2] * e[32] + e[31] * e[0] * e[3] + e[31] * e[2] * e[5] + e[7] * e[27] * e[6] + e[7] * e[0] * e[33] + e[7] * e[29] * e[8] + e[7] * e[2] * e[35] + e[34] * e[0] * e[6] + e[34] * e[2] * e[8] + e[1] * e[27] * e[0] + e[1] * e[29] * e[2] + e[1] * e[34] * e[7] - e[1] * e[32] * e[5] - e[1] * e[33] * e[6] - e[1] * e[30] * e[3] - e[1] * e[35] * e[8] + e[1] * e[31] * e[4] + 1.5 * e[28] * e2[1] + 0.5 * e[28] * e2[4] + 0.5 * e[28] * e2[0] - 0.5 * e[28] * e2[6] - 0.5 * e[28] * e2[5] + 0.5 * e[28] * e2[7] - 0.5 * e[28] * e2[3] + 0.5 * e[28] * e2[2] - 0.5 * e[28] * e2[8]; a[99] = -e[35] * e[10] * e[1] - e[35] * e[13] * e[4] + e[35] * e[16] * e[7] + e[35] * e[15] * e[6] - e[35] * e[9] * e[0] - e[35] * e[12] * e[3] + e[32] * e[12] * e[6] + e[32] * e[3] * e[15] + e[32] * e[13] * e[7] + e[32] * e[4] * e[16] - e[8] * e[27] * e[9] - e[8] * e[30] * e[12] - e[8] * e[28] * e[10] - e[8] * e[31] * e[13] + e[8] * e[29] * e[11] + e[11] * e[27] * e[6] + e[11] * e[0] * e[33] + e[11] * e[28] * e[7] + e[11] * e[1] * e[34] + e[29] * e[9] * e[6] + e[29] * e[0] * e[15] + e[29] * e[10] * e[7] + e[29] * e[1] * e[16] + e[5] * e[30] * e[15] + e[5] * e[12] * e[33] + e[5] * e[32] * e[17] + e[5] * e[14] * e[35] + e[5] * e[31] * e[16] + e[5] * e[13] * e[34] + e[8] * e[33] * e[15] + 3. * e[8] * e[35] * e[17] + e[8] * e[34] * e[16] + e[2] * e[27] * e[15] + e[2] * e[9] * e[33] + e[2] * e[29] * e[17] + e[2] * e[11] * e[35] + e[2] * e[28] * e[16] + e[2] * e[10] * e[34] - e[17] * e[27] * e[0] + e[17] * e[34] * e[7] + e[17] * e[33] * e[6] - e[17] * e[30] * e[3] - e[17] * e[28] * e[1] - e[17] * e[31] * e[4] + e[14] * e[30] * e[6] + e[14] * e[3] * e[33] + e[14] * e[31] * e[7] + e[14] * e[4] * e[34] + e[14] * e[32] * e[8]; a[82] = e[19] * e[11] * e[2] + e[4] * e[18] * e[12] + e[4] * e[9] * e[21] + e[4] * e[20] * e[14] + e[4] * e[11] * e[23] + e[4] * e[19] * e[13] + e[4] * e[10] * e[22] + e[7] * e[18] * e[15] + e[7] * e[9] * e[24] + e[7] * e[20] * e[17] + e[7] * e[11] * e[26] + e[7] * e[19] * e[16] + e[7] * e[10] * e[25] + e[1] * e[18] * e[9] + e[1] * e[20] * e[11] - e[10] * e[21] * e[3] - e[10] * e[26] * e[8] - e[10] * e[23] * e[5] - e[10] * e[24] * e[6] + e[13] * e[18] * e[3] + e[13] * e[0] * e[21] + e[13] * e[1] * e[22] + e[13] * e[20] * e[5] + e[13] * e[2] * e[23] - e[19] * e[15] * e[6] - e[19] * e[14] * e[5] - e[19] * e[12] * e[3] - e[19] * e[17] * e[8] + e[22] * e[9] * e[3] + e[22] * e[0] * e[12] + e[22] * e[11] * e[5] + e[22] * e[2] * e[14] + e[16] * e[18] * e[6] + e[16] * e[0] * e[24] + e[16] * e[1] * e[25] + e[16] * e[20] * e[8] + e[16] * e[2] * e[26] - e[1] * e[23] * e[14] - e[1] * e[24] * e[15] - e[1] * e[26] * e[17] - e[1] * e[21] * e[12] + e[25] * e[9] * e[6] + e[25] * e[0] * e[15] + e[25] * e[11] * e[8] + e[25] * e[2] * e[17] + e[10] * e[18] * e[0] + 3. * e[10] * e[19] * e[1] + e[10] * e[20] * e[2] + e[19] * e[9] * e[0]; a[169] = 0.5 * e2[23] * e[26] + 0.5 * e[26] * e2[25] + 0.5 * e2[20] * e[26] - 0.5 * e[26] * e2[18] + 0.5 * e3[26] + 0.5 * e[26] * e2[24] + e[20] * e[19] * e[25] - 0.5 * e[26] * e2[19] - 0.5 * e[26] * e2[21] + e[20] * e[18] * e[24] - 0.5 * e[26] * e2[22] + e[23] * e[21] * e[24] + e[23] * e[22] * e[25]; a[72] = e[16] * e[9] * e[33] + e[16] * e[29] * e[17] + e[16] * e[11] * e[35] + e[16] * e[10] * e[34] + e[34] * e[11] * e[17] + e[34] * e[9] * e[15] - e[10] * e[30] * e[12] - e[10] * e[32] * e[14] - e[10] * e[33] * e[15] - e[10] * e[35] * e[17] + e[10] * e[27] * e[9] + e[10] * e[29] * e[11] + e[13] * e[27] * e[12] + e[13] * e[9] * e[30] + e[13] * e[29] * e[14] + e[13] * e[11] * e[32] + e[13] * e[10] * e[31] + e[31] * e[11] * e[14] + e[31] * e[9] * e[12] + e[16] * e[27] * e[15] + 1.5 * e[28] * e2[10] + 0.5 * e[28] * e2[16] + 0.5 * e[28] * e2[9] + 0.5 * e[28] * e2[11] - 0.5 * e[28] * e2[12] - 0.5 * e[28] * e2[15] - 0.5 * e[28] * e2[17] - 0.5 * e[28] * e2[14] + 0.5 * e[28] * e2[13]; a[179] = 0.5 * e2[20] * e[35] + 0.5 * e2[23] * e[35] + 1.5 * e[35] * e2[26] + 0.5 * e[35] * e2[25] + 0.5 * e[35] * e2[24] - 0.5 * e[35] * e2[18] - 0.5 * e[35] * e2[19] - 0.5 * e[35] * e2[22] - 0.5 * e[35] * e2[21] + e[20] * e[27] * e[24] + e[20] * e[18] * e[33] + e[20] * e[28] * e[25] + e[20] * e[19] * e[34] + e[20] * e[29] * e[26] + e[29] * e[19] * e[25] + e[29] * e[18] * e[24] + e[23] * e[30] * e[24] + e[23] * e[21] * e[33] + e[23] * e[31] * e[25] + e[23] * e[22] * e[34] + e[23] * e[32] * e[26] + e[32] * e[22] * e[25] + e[32] * e[21] * e[24] + e[26] * e[33] * e[24] + e[26] * e[34] * e[25] - e[26] * e[27] * e[18] - e[26] * e[30] * e[21] - e[26] * e[31] * e[22] - e[26] * e[28] * e[19]; a[2] = e[4] * e[2] * e[5] + 0.5 * e[1] * e2[0] - 0.5 * e[1] * e2[6] + e[7] * e[0] * e[6] + 0.5 * e[1] * e2[7] + 0.5 * e[1] * e2[4] - 0.5 * e[1] * e2[8] + 0.5 * e[1] * e2[2] - 0.5 * e[1] * e2[3] + 0.5 * e3[1] + e[7] * e[2] * e[8] - 0.5 * e[1] * e2[5] + e[4] * e[0] * e[3]; a[19] = -0.5 * e[17] * e2[13] - 0.5 * e[17] * e2[9] + 0.5 * e[17] * e2[16] + 0.5 * e[17] * e2[15] + 0.5 * e3[17] - 0.5 * e[17] * e2[10] + e[14] * e[13] * e[16] + e[14] * e[12] * e[15] + 0.5 * e2[14] * e[17] + e[11] * e[10] * e[16] - 0.5 * e[17] * e2[12] + 0.5 * e2[11] * e[17] + e[11] * e[9] * e[15]; a[122] = e[4] * e[27] * e[30] + e[4] * e[29] * e[32] + e[4] * e[28] * e[31] + e[31] * e[27] * e[3] + e[31] * e[0] * e[30] + e[31] * e[29] * e[5] + e[31] * e[2] * e[32] + e[7] * e[27] * e[33] + e[7] * e[29] * e[35] + e[7] * e[28] * e[34] + e[28] * e[27] * e[0] + e[28] * e[29] * e[2] + e[34] * e[27] * e[6] + e[34] * e[0] * e[33] + e[34] * e[29] * e[8] + e[34] * e[2] * e[35] - e[28] * e[32] * e[5] - e[28] * e[33] * e[6] - e[28] * e[30] * e[3] - e[28] * e[35] * e[8] + 0.5 * e[1] * e2[27] + 0.5 * e[1] * e2[29] + 1.5 * e[1] * e2[28] + 0.5 * e[1] * e2[31] - 0.5 * e[1] * e2[32] - 0.5 * e[1] * e2[33] - 0.5 * e[1] * e2[30] + 0.5 * e[1] * e2[34] - 0.5 * e[1] * e2[35]; a[79] = 0.5 * e2[11] * e[35] + 0.5 * e[35] * e2[16] - 0.5 * e[35] * e2[9] - 0.5 * e[35] * e2[12] + 0.5 * e[35] * e2[15] + 1.5 * e[35] * e2[17] - 0.5 * e[35] * e2[10] + 0.5 * e[35] * e2[14] - 0.5 * e[35] * e2[13] + e[11] * e[27] * e[15] + e[11] * e[9] * e[33] + e[11] * e[29] * e[17] + e[11] * e[28] * e[16] + e[11] * e[10] * e[34] + e[29] * e[9] * e[15] + e[29] * e[10] * e[16] + e[14] * e[30] * e[15] + e[14] * e[12] * e[33] + e[14] * e[32] * e[17] + e[14] * e[31] * e[16] + e[14] * e[13] * e[34] + e[32] * e[12] * e[15] + e[32] * e[13] * e[16] + e[17] * e[33] * e[15] + e[17] * e[34] * e[16] - e[17] * e[27] * e[9] - e[17] * e[30] * e[12] - e[17] * e[28] * e[10] - e[17] * e[31] * e[13]; a[192] = e[34] * e[27] * e[33] + e[34] * e[29] * e[35] - 0.5 * e[28] * e2[30] - 0.5 * e[28] * e2[35] + 0.5 * e3[28] + 0.5 * e[28] * e2[27] + 0.5 * e[28] * e2[29] + e[31] * e[27] * e[30] + e[31] * e[29] * e[32] - 0.5 * e[28] * e2[32] - 0.5 * e[28] * e2[33] + 0.5 * e[28] * e2[31] + 0.5 * e[28] * e2[34]; a[9] = 0.5 * e2[5] * e[8] + e[2] * e[0] * e[6] + 0.5 * e2[2] * e[8] + 0.5 * e3[8] - 0.5 * e[8] * e2[0] + e[5] * e[4] * e[7] + e[5] * e[3] * e[6] + 0.5 * e[8] * e2[7] + e[2] * e[1] * e[7] - 0.5 * e[8] * e2[1] - 0.5 * e[8] * e2[4] - 0.5 * e[8] * e2[3] + 0.5 * e[8] * e2[6]; a[152] = e[28] * e[27] * e[9] + e[28] * e[29] * e[11] - e[28] * e[30] * e[12] + e[28] * e[31] * e[13] - e[28] * e[32] * e[14] - e[28] * e[33] * e[15] - e[28] * e[35] * e[17] + e[31] * e[27] * e[12] + e[31] * e[9] * e[30] + e[31] * e[29] * e[14] + e[31] * e[11] * e[32] + e[13] * e[27] * e[30] + e[13] * e[29] * e[32] + e[16] * e[27] * e[33] + e[16] * e[29] * e[35] + e[34] * e[27] * e[15] + e[34] * e[9] * e[33] + e[34] * e[29] * e[17] + e[34] * e[11] * e[35] + e[34] * e[28] * e[16] + 0.5 * e[10] * e2[27] + 0.5 * e[10] * e2[29] + 1.5 * e[10] * e2[28] - 0.5 * e[10] * e2[32] + 0.5 * e[10] * e2[31] - 0.5 * e[10] * e2[33] - 0.5 * e[10] * e2[30] + 0.5 * e[10] * e2[34] - 0.5 * e[10] * e2[35]; a[59] = -0.5 * e[35] * e2[1] + 0.5 * e[35] * e2[7] - 0.5 * e[35] * e2[3] + 0.5 * e2[2] * e[35] + 1.5 * e[35] * e2[8] - 0.5 * e[35] * e2[4] - 0.5 * e[35] * e2[0] + 0.5 * e[35] * e2[6] + 0.5 * e[35] * e2[5] + e[2] * e[27] * e[6] + e[2] * e[0] * e[33] + e[2] * e[28] * e[7] + e[2] * e[1] * e[34] + e[2] * e[29] * e[8] - e[8] * e[27] * e[0] + e[8] * e[34] * e[7] + e[8] * e[32] * e[5] + e[8] * e[33] * e[6] - e[8] * e[30] * e[3] - e[8] * e[28] * e[1] - e[8] * e[31] * e[4] + e[29] * e[1] * e[7] + e[29] * e[0] * e[6] + e[5] * e[30] * e[6] + e[5] * e[3] * e[33] + e[5] * e[31] * e[7] + e[5] * e[4] * e[34] + e[32] * e[4] * e[7] + e[32] * e[3] * e[6]; a[182] = e[28] * e[27] * e[18] + e[28] * e[29] * e[20] + e[22] * e[27] * e[30] + e[22] * e[29] * e[32] + e[22] * e[28] * e[31] + e[31] * e[27] * e[21] + e[31] * e[18] * e[30] + e[31] * e[29] * e[23] + e[31] * e[20] * e[32] + e[25] * e[27] * e[33] + e[25] * e[29] * e[35] + e[25] * e[28] * e[34] + e[34] * e[27] * e[24] + e[34] * e[18] * e[33] + e[34] * e[29] * e[26] + e[34] * e[20] * e[35] - e[28] * e[33] * e[24] - e[28] * e[30] * e[21] - e[28] * e[35] * e[26] - e[28] * e[32] * e[23] - 0.5 * e[19] * e2[33] - 0.5 * e[19] * e2[30] - 0.5 * e[19] * e2[35] + 0.5 * e[19] * e2[27] + 0.5 * e[19] * e2[29] + 1.5 * e[19] * e2[28] + 0.5 * e[19] * e2[31] + 0.5 * e[19] * e2[34] - 0.5 * e[19] * e2[32]; a[89] = e[23] * e[3] * e[15] - e[17] * e[19] * e[1] - e[17] * e[22] * e[4] - e[17] * e[18] * e[0] + e[17] * e[25] * e[7] + e[17] * e[24] * e[6] + e[14] * e[21] * e[6] + e[14] * e[3] * e[24] + e[14] * e[22] * e[7] + e[14] * e[4] * e[25] + e[14] * e[23] * e[8] - e[26] * e[10] * e[1] - e[26] * e[13] * e[4] + e[26] * e[16] * e[7] + e[26] * e[15] * e[6] - e[26] * e[9] * e[0] - e[26] * e[12] * e[3] + e[23] * e[12] * e[6] + e[11] * e[18] * e[6] + e[11] * e[0] * e[24] + e[11] * e[19] * e[7] + e[11] * e[1] * e[25] + e[11] * e[20] * e[8] + e[11] * e[2] * e[26] + e[20] * e[9] * e[6] + e[20] * e[0] * e[15] + e[20] * e[10] * e[7] + e[20] * e[1] * e[16] + e[20] * e[2] * e[17] + e[5] * e[21] * e[15] + e[5] * e[12] * e[24] + e[5] * e[23] * e[17] + e[5] * e[14] * e[26] + e[5] * e[22] * e[16] + e[5] * e[13] * e[25] + e[8] * e[24] * e[15] + 3. * e[8] * e[26] * e[17] + e[8] * e[25] * e[16] + e[2] * e[18] * e[15] + e[2] * e[9] * e[24] + e[2] * e[19] * e[16] + e[2] * e[10] * e[25] - e[17] * e[21] * e[3] + e[23] * e[4] * e[16] + e[23] * e[13] * e[7] - e[8] * e[18] * e[9] - e[8] * e[21] * e[12] - e[8] * e[19] * e[10] - e[8] * e[22] * e[13]; a[62] = e[13] * e[18] * e[12] + e[13] * e[9] * e[21] + e[13] * e[20] * e[14] + e[13] * e[11] * e[23] + e[13] * e[10] * e[22] + e[22] * e[11] * e[14] + e[22] * e[9] * e[12] + e[16] * e[18] * e[15] + e[16] * e[9] * e[24] + e[16] * e[20] * e[17] + e[16] * e[11] * e[26] + e[16] * e[10] * e[25] + e[25] * e[11] * e[17] + e[25] * e[9] * e[15] - e[10] * e[23] * e[14] - e[10] * e[24] * e[15] - e[10] * e[26] * e[17] + e[10] * e[20] * e[11] + e[10] * e[18] * e[9] - e[10] * e[21] * e[12] + 0.5 * e[19] * e2[11] + 0.5 * e[19] * e2[9] + 1.5 * e[19] * e2[10] + 0.5 * e[19] * e2[13] + 0.5 * e[19] * e2[16] - 0.5 * e[19] * e2[12] - 0.5 * e[19] * e2[15] - 0.5 * e[19] * e2[17] - 0.5 * e[19] * e2[14]; a[88] = e[10] * e[18] * e[6] + e[10] * e[0] * e[24] + e[10] * e[19] * e[7] + e[10] * e[1] * e[25] + e[10] * e[20] * e[8] + e[10] * e[2] * e[26] + e[19] * e[9] * e[6] + e[19] * e[0] * e[15] + e[19] * e[1] * e[16] + e[19] * e[11] * e[8] + e[19] * e[2] * e[17] + e[4] * e[21] * e[15] + e[4] * e[12] * e[24] + e[4] * e[23] * e[17] + e[4] * e[14] * e[26] + e[4] * e[22] * e[16] + e[4] * e[13] * e[25] + e[7] * e[24] * e[15] + e[7] * e[26] * e[17] + 3. * e[7] * e[25] * e[16] + e[1] * e[18] * e[15] + e[1] * e[9] * e[24] + e[1] * e[20] * e[17] + e[1] * e[11] * e[26] - e[16] * e[21] * e[3] + e[16] * e[26] * e[8] - e[16] * e[20] * e[2] - e[16] * e[18] * e[0] - e[16] * e[23] * e[5] + e[16] * e[24] * e[6] + e[13] * e[21] * e[6] + e[13] * e[3] * e[24] + e[13] * e[22] * e[7] + e[13] * e[23] * e[8] + e[13] * e[5] * e[26] - e[25] * e[11] * e[2] + e[25] * e[15] * e[6] - e[25] * e[9] * e[0] - e[25] * e[14] * e[5] - e[25] * e[12] * e[3] + e[25] * e[17] * e[8] + e[22] * e[12] * e[6] + e[22] * e[3] * e[15] + e[22] * e[14] * e[8] + e[22] * e[5] * e[17] - e[7] * e[23] * e[14] - e[7] * e[20] * e[11] - e[7] * e[18] * e[9] - e[7] * e[21] * e[12]; a[32] = e[13] * e[9] * e[3] + e[13] * e[0] * e[12] + e[13] * e[10] * e[4] + e[13] * e[11] * e[5] + e[13] * e[2] * e[14] + e[16] * e[9] * e[6] + e[16] * e[0] * e[15] + e[16] * e[10] * e[7] + e[16] * e[11] * e[8] + e[16] * e[2] * e[17] + e[7] * e[11] * e[17] + e[7] * e[9] * e[15] + e[4] * e[11] * e[14] + e[4] * e[9] * e[12] + e[10] * e[9] * e[0] + e[10] * e[11] * e[2] - e[10] * e[15] * e[6] - e[10] * e[14] * e[5] - e[10] * e[12] * e[3] - e[10] * e[17] * e[8] + 0.5 * e[1] * e2[11] + 0.5 * e[1] * e2[9] + 1.5 * e[1] * e2[10] - 0.5 * e[1] * e2[12] - 0.5 * e[1] * e2[15] - 0.5 * e[1] * e2[17] - 0.5 * e[1] * e2[14] + 0.5 * e[1] * e2[13] + 0.5 * e[1] * e2[16]; a[58] = e[1] * e[27] * e[6] + e[1] * e[0] * e[33] + e[1] * e[28] * e[7] + e[1] * e[29] * e[8] + e[1] * e[2] * e[35] - e[7] * e[27] * e[0] - e[7] * e[32] * e[5] + e[7] * e[33] * e[6] - e[7] * e[30] * e[3] + e[7] * e[35] * e[8] - e[7] * e[29] * e[2] + e[7] * e[31] * e[4] + e[28] * e[0] * e[6] + e[28] * e[2] * e[8] + e[4] * e[30] * e[6] + e[4] * e[3] * e[33] + e[4] * e[32] * e[8] + e[4] * e[5] * e[35] + e[31] * e[3] * e[6] + e[31] * e[5] * e[8] + 0.5 * e2[1] * e[34] + 1.5 * e[34] * e2[7] + 0.5 * e[34] * e2[4] - 0.5 * e[34] * e2[0] + 0.5 * e[34] * e2[6] - 0.5 * e[34] * e2[5] - 0.5 * e[34] * e2[3] - 0.5 * e[34] * e2[2] + 0.5 * e[34] * e2[8]; a[42] = e[4] * e[18] * e[3] + e[4] * e[0] * e[21] + e[4] * e[1] * e[22] + e[4] * e[20] * e[5] + e[4] * e[2] * e[23] + e[22] * e[0] * e[3] + e[22] * e[2] * e[5] + e[7] * e[18] * e[6] + e[7] * e[0] * e[24] + e[7] * e[1] * e[25] + e[7] * e[20] * e[8] + e[7] * e[2] * e[26] + e[25] * e[0] * e[6] + e[25] * e[2] * e[8] + e[1] * e[18] * e[0] + e[1] * e[20] * e[2] - e[1] * e[21] * e[3] - e[1] * e[26] * e[8] - e[1] * e[23] * e[5] - e[1] * e[24] * e[6] + 0.5 * e[19] * e2[4] + 0.5 * e[19] * e2[0] - 0.5 * e[19] * e2[6] - 0.5 * e[19] * e2[5] + 1.5 * e[19] * e2[1] + 0.5 * e[19] * e2[7] - 0.5 * e[19] * e2[3] + 0.5 * e[19] * e2[2] - 0.5 * e[19] * e2[8]; a[8] = -0.5 * e[7] * e2[0] + e[4] * e[5] * e[8] + 0.5 * e2[4] * e[7] - 0.5 * e[7] * e2[2] + 0.5 * e[7] * e2[8] - 0.5 * e[7] * e2[5] + 0.5 * e[7] * e2[6] + e[1] * e[0] * e[6] + 0.5 * e3[7] + e[4] * e[3] * e[6] + e[1] * e[2] * e[8] - 0.5 * e[7] * e2[3] + 0.5 * e2[1] * e[7]; a[112] = -e[1] * e[32] * e[23] - e[19] * e[32] * e[5] - e[19] * e[33] * e[6] - e[19] * e[30] * e[3] - e[19] * e[35] * e[8] - e[28] * e[21] * e[3] - e[28] * e[26] * e[8] - e[28] * e[23] * e[5] - e[28] * e[24] * e[6] + e[7] * e[27] * e[24] + e[7] * e[18] * e[33] + e[7] * e[29] * e[26] + e[7] * e[20] * e[35] + e[22] * e[27] * e[3] + e[22] * e[0] * e[30] + e[22] * e[29] * e[5] + e[22] * e[2] * e[32] + e[31] * e[18] * e[3] + e[31] * e[0] * e[21] + e[31] * e[20] * e[5] + e[31] * e[2] * e[23] + e[25] * e[27] * e[6] + e[25] * e[0] * e[33] + e[25] * e[28] * e[7] + e[25] * e[1] * e[34] + e[25] * e[29] * e[8] + e[25] * e[2] * e[35] + e[34] * e[18] * e[6] + e[34] * e[0] * e[24] + e[34] * e[19] * e[7] + e[34] * e[20] * e[8] + e[34] * e[2] * e[26] + e[1] * e[27] * e[18] + 3. * e[1] * e[28] * e[19] + e[1] * e[29] * e[20] + e[19] * e[27] * e[0] + e[19] * e[29] * e[2] + e[28] * e[18] * e[0] + e[28] * e[20] * e[2] + e[4] * e[27] * e[21] + e[4] * e[18] * e[30] + e[4] * e[28] * e[22] + e[4] * e[19] * e[31] + e[4] * e[29] * e[23] + e[4] * e[20] * e[32] - e[1] * e[33] * e[24] - e[1] * e[30] * e[21] - e[1] * e[35] * e[26] + e[1] * e[31] * e[22]; a[78] = e[10] * e[27] * e[15] + e[10] * e[9] * e[33] + e[10] * e[29] * e[17] + e[10] * e[11] * e[35] + e[10] * e[28] * e[16] + e[28] * e[11] * e[17] + e[28] * e[9] * e[15] + e[13] * e[30] * e[15] + e[13] * e[12] * e[33] + e[13] * e[32] * e[17] + e[13] * e[14] * e[35] + e[13] * e[31] * e[16] + e[31] * e[14] * e[17] + e[31] * e[12] * e[15] + e[16] * e[33] * e[15] + e[16] * e[35] * e[17] - e[16] * e[27] * e[9] - e[16] * e[30] * e[12] - e[16] * e[32] * e[14] - e[16] * e[29] * e[11] + 0.5 * e2[10] * e[34] + 1.5 * e[34] * e2[16] - 0.5 * e[34] * e2[9] - 0.5 * e[34] * e2[11] - 0.5 * e[34] * e2[12] + 0.5 * e[34] * e2[15] + 0.5 * e[34] * e2[17] - 0.5 * e[34] * e2[14] + 0.5 * e[34] * e2[13]; a[162] = 0.5 * e[19] * e2[18] + 0.5 * e[19] * e2[25] + 0.5 * e[19] * e2[22] + e[25] * e[20] * e[26] - 0.5 * e[19] * e2[21] + 0.5 * e[19] * e2[20] - 0.5 * e[19] * e2[26] - 0.5 * e[19] * e2[23] - 0.5 * e[19] * e2[24] + 0.5 * e3[19] + e[22] * e[20] * e[23] + e[25] * e[18] * e[24] + e[22] * e[18] * e[21]; a[198] = 0.5 * e[34] * e2[33] + 0.5 * e[34] * e2[35] - 0.5 * e[34] * e2[27] - 0.5 * e[34] * e2[32] - 0.5 * e[34] * e2[29] - 0.5 * e[34] * e2[30] + 0.5 * e2[28] * e[34] + e[31] * e[30] * e[33] + e[31] * e[32] * e[35] + e[28] * e[27] * e[33] + 0.5 * e3[34] + e[28] * e[29] * e[35] + 0.5 * e2[31] * e[34]; a[92] = e[4] * e[28] * e[13] + e[4] * e[10] * e[31] + e[7] * e[27] * e[15] + e[7] * e[9] * e[33] + e[7] * e[29] * e[17] + e[7] * e[11] * e[35] + e[7] * e[28] * e[16] + e[7] * e[10] * e[34] + e[1] * e[27] * e[9] + e[1] * e[29] * e[11] + 3. * e[1] * e[28] * e[10] + e[10] * e[27] * e[0] - e[10] * e[32] * e[5] - e[10] * e[33] * e[6] - e[10] * e[30] * e[3] - e[10] * e[35] * e[8] + e[10] * e[29] * e[2] + e[13] * e[27] * e[3] + e[13] * e[0] * e[30] + e[13] * e[1] * e[31] + e[13] * e[29] * e[5] + e[13] * e[2] * e[32] + e[28] * e[11] * e[2] - e[28] * e[15] * e[6] + e[28] * e[9] * e[0] - e[28] * e[14] * e[5] - e[28] * e[12] * e[3] - e[28] * e[17] * e[8] + e[31] * e[9] * e[3] + e[31] * e[0] * e[12] + e[31] * e[11] * e[5] + e[31] * e[2] * e[14] + e[16] * e[27] * e[6] + e[16] * e[0] * e[33] + e[16] * e[1] * e[34] + e[16] * e[29] * e[8] + e[16] * e[2] * e[35] - e[1] * e[30] * e[12] - e[1] * e[32] * e[14] - e[1] * e[33] * e[15] - e[1] * e[35] * e[17] + e[34] * e[9] * e[6] + e[34] * e[0] * e[15] + e[34] * e[11] * e[8] + e[34] * e[2] * e[17] + e[4] * e[27] * e[12] + e[4] * e[9] * e[30] + e[4] * e[29] * e[14] + e[4] * e[11] * e[32]; a[128] = e[4] * e[30] * e[33] + e[4] * e[32] * e[35] + e[4] * e[31] * e[34] + e[31] * e[30] * e[6] + e[31] * e[3] * e[33] + e[31] * e[32] * e[8] + e[31] * e[5] * e[35] + e[28] * e[27] * e[6] + e[28] * e[0] * e[33] + e[28] * e[29] * e[8] + e[28] * e[2] * e[35] + e[34] * e[33] * e[6] + e[34] * e[35] * e[8] - e[34] * e[27] * e[0] - e[34] * e[32] * e[5] - e[34] * e[30] * e[3] - e[34] * e[29] * e[2] + e[1] * e[27] * e[33] + e[1] * e[29] * e[35] + e[1] * e[28] * e[34] + 0.5 * e2[31] * e[7] - 0.5 * e[7] * e2[27] - 0.5 * e[7] * e2[32] + 0.5 * e[7] * e2[28] - 0.5 * e[7] * e2[29] + 0.5 * e[7] * e2[33] - 0.5 * e[7] * e2[30] + 1.5 * e[7] * e2[34] + 0.5 * e[7] * e2[35]; a[12] = -0.5 * e[10] * e2[14] - 0.5 * e[10] * e2[17] - 0.5 * e[10] * e2[15] + e[13] * e[11] * e[14] + e[16] * e[11] * e[17] + 0.5 * e[10] * e2[13] + e[13] * e[9] * e[12] - 0.5 * e[10] * e2[12] + 0.5 * e3[10] + e[16] * e[9] * e[15] + 0.5 * e[10] * e2[16] + 0.5 * e[10] * e2[11] + 0.5 * e[10] * e2[9]; a[188] = e[22] * e[32] * e[35] + e[22] * e[31] * e[34] + e[31] * e[30] * e[24] + e[31] * e[21] * e[33] + e[31] * e[32] * e[26] + e[31] * e[23] * e[35] + e[34] * e[33] * e[24] + e[34] * e[35] * e[26] - e[34] * e[27] * e[18] - e[34] * e[30] * e[21] - e[34] * e[29] * e[20] - e[34] * e[32] * e[23] + e[19] * e[27] * e[33] + e[19] * e[29] * e[35] + e[19] * e[28] * e[34] + e[28] * e[27] * e[24] + e[28] * e[18] * e[33] + e[28] * e[29] * e[26] + e[28] * e[20] * e[35] + e[22] * e[30] * e[33] + 0.5 * e2[28] * e[25] + 0.5 * e2[31] * e[25] + 0.5 * e[25] * e2[33] + 0.5 * e[25] * e2[35] + 1.5 * e[25] * e2[34] - 0.5 * e[25] * e2[27] - 0.5 * e[25] * e2[32] - 0.5 * e[25] * e2[29] - 0.5 * e[25] * e2[30]; a[172] = -e[19] * e[35] * e[26] - e[19] * e[32] * e[23] + e[19] * e[27] * e[18] + e[19] * e[29] * e[20] + e[22] * e[27] * e[21] + e[22] * e[18] * e[30] + e[22] * e[19] * e[31] + e[22] * e[29] * e[23] + e[22] * e[20] * e[32] + e[31] * e[18] * e[21] + e[31] * e[20] * e[23] + e[25] * e[27] * e[24] + e[25] * e[18] * e[33] + e[25] * e[19] * e[34] + e[25] * e[29] * e[26] + e[25] * e[20] * e[35] + e[34] * e[18] * e[24] + e[34] * e[20] * e[26] - e[19] * e[33] * e[24] - e[19] * e[30] * e[21] + 1.5 * e[28] * e2[19] + 0.5 * e[28] * e2[18] + 0.5 * e[28] * e2[20] + 0.5 * e[28] * e2[22] + 0.5 * e[28] * e2[25] - 0.5 * e[28] * e2[26] - 0.5 * e[28] * e2[23] - 0.5 * e[28] * e2[24] - 0.5 * e[28] * e2[21]; a[158] = e[10] * e[27] * e[33] + e[10] * e[29] * e[35] + e[10] * e[28] * e[34] + e[34] * e[33] * e[15] + e[34] * e[35] * e[17] + e[28] * e[27] * e[15] + e[28] * e[9] * e[33] + e[28] * e[29] * e[17] + e[28] * e[11] * e[35] - e[34] * e[27] * e[9] - e[34] * e[30] * e[12] + e[34] * e[31] * e[13] - e[34] * e[32] * e[14] - e[34] * e[29] * e[11] + e[31] * e[30] * e[15] + e[31] * e[12] * e[33] + e[31] * e[32] * e[17] + e[31] * e[14] * e[35] + e[13] * e[30] * e[33] + e[13] * e[32] * e[35] - 0.5 * e[16] * e2[27] - 0.5 * e[16] * e2[32] + 0.5 * e[16] * e2[28] - 0.5 * e[16] * e2[29] + 0.5 * e[16] * e2[31] + 0.5 * e[16] * e2[33] - 0.5 * e[16] * e2[30] + 1.5 * e[16] * e2[34] + 0.5 * e[16] * e2[35]; a[153] = e[29] * e[32] * e[14] - e[29] * e[33] * e[15] - e[29] * e[34] * e[16] + e[32] * e[27] * e[12] + e[32] * e[9] * e[30] + e[32] * e[28] * e[13] + e[32] * e[10] * e[31] + e[14] * e[27] * e[30] + e[14] * e[28] * e[31] + e[17] * e[27] * e[33] + e[17] * e[28] * e[34] + e[35] * e[27] * e[15] + e[35] * e[9] * e[33] + e[35] * e[29] * e[17] + e[35] * e[28] * e[16] + e[35] * e[10] * e[34] + e[29] * e[27] * e[9] + e[29] * e[28] * e[10] - e[29] * e[30] * e[12] - e[29] * e[31] * e[13] + 0.5 * e[11] * e2[27] + 1.5 * e[11] * e2[29] + 0.5 * e[11] * e2[28] + 0.5 * e[11] * e2[32] - 0.5 * e[11] * e2[31] - 0.5 * e[11] * e2[33] - 0.5 * e[11] * e2[30] - 0.5 * e[11] * e2[34] + 0.5 * e[11] * e2[35]; a[118] = e[1] * e[20] * e[35] + e[19] * e[27] * e[6] + e[19] * e[0] * e[33] + e[19] * e[28] * e[7] + e[19] * e[29] * e[8] + e[19] * e[2] * e[35] + e[28] * e[18] * e[6] + e[28] * e[0] * e[24] + e[28] * e[20] * e[8] + e[28] * e[2] * e[26] + e[4] * e[30] * e[24] + e[4] * e[21] * e[33] + e[4] * e[31] * e[25] + e[4] * e[22] * e[34] + e[4] * e[32] * e[26] + e[4] * e[23] * e[35] - e[7] * e[27] * e[18] + e[7] * e[33] * e[24] - e[7] * e[30] * e[21] - e[7] * e[29] * e[20] + e[7] * e[35] * e[26] + e[7] * e[31] * e[22] - e[7] * e[32] * e[23] - e[25] * e[27] * e[0] - e[25] * e[32] * e[5] - e[25] * e[30] * e[3] - e[25] * e[29] * e[2] - e[34] * e[21] * e[3] - e[34] * e[20] * e[2] - e[34] * e[18] * e[0] - e[34] * e[23] * e[5] + e[22] * e[30] * e[6] + e[22] * e[3] * e[33] + e[22] * e[32] * e[8] + e[22] * e[5] * e[35] + e[31] * e[21] * e[6] + e[31] * e[3] * e[24] + e[31] * e[23] * e[8] + e[31] * e[5] * e[26] + e[34] * e[26] * e[8] + e[1] * e[27] * e[24] + e[1] * e[18] * e[33] + e[1] * e[28] * e[25] + e[1] * e[19] * e[34] + e[1] * e[29] * e[26] + e[34] * e[24] * e[6] + e[25] * e[33] * e[6] + 3. * e[25] * e[34] * e[7] + e[25] * e[35] * e[8]; a[183] = 0.5 * e[20] * e2[27] + 1.5 * e[20] * e2[29] + 0.5 * e[20] * e2[28] + 0.5 * e[20] * e2[32] + 0.5 * e[20] * e2[35] - 0.5 * e[20] * e2[31] - 0.5 * e[20] * e2[33] - 0.5 * e[20] * e2[30] - 0.5 * e[20] * e2[34] + e[29] * e[27] * e[18] + e[29] * e[28] * e[19] + e[23] * e[27] * e[30] + e[23] * e[29] * e[32] + e[23] * e[28] * e[31] + e[32] * e[27] * e[21] + e[32] * e[18] * e[30] + e[32] * e[28] * e[22] + e[32] * e[19] * e[31] + e[26] * e[27] * e[33] + e[26] * e[29] * e[35] + e[26] * e[28] * e[34] + e[35] * e[27] * e[24] + e[35] * e[18] * e[33] + e[35] * e[28] * e[25] + e[35] * e[19] * e[34] - e[29] * e[33] * e[24] - e[29] * e[30] * e[21] - e[29] * e[31] * e[22] - e[29] * e[34] * e[25]; a[48] = e[19] * e[1] * e[7] + e[19] * e[0] * e[6] + e[19] * e[2] * e[8] + e[4] * e[21] * e[6] + e[4] * e[3] * e[24] + e[4] * e[22] * e[7] + e[4] * e[23] * e[8] + e[4] * e[5] * e[26] + e[22] * e[3] * e[6] + e[22] * e[5] * e[8] + e[7] * e[24] * e[6] + e[7] * e[26] * e[8] + e[1] * e[18] * e[6] + e[1] * e[0] * e[24] + e[1] * e[20] * e[8] + e[1] * e[2] * e[26] - e[7] * e[21] * e[3] - e[7] * e[20] * e[2] - e[7] * e[18] * e[0] - e[7] * e[23] * e[5] + 0.5 * e[25] * e2[4] - 0.5 * e[25] * e2[0] + 0.5 * e[25] * e2[6] - 0.5 * e[25] * e2[5] + 0.5 * e[25] * e2[1] + 1.5 * e[25] * e2[7] - 0.5 * e[25] * e2[3] - 0.5 * e[25] * e2[2] + 0.5 * e[25] * e2[8]; a[123] = e[5] * e[27] * e[30] + e[5] * e[29] * e[32] + e[5] * e[28] * e[31] + e[32] * e[27] * e[3] + e[32] * e[0] * e[30] + e[32] * e[28] * e[4] + e[32] * e[1] * e[31] + e[8] * e[27] * e[33] + e[8] * e[29] * e[35] + e[8] * e[28] * e[34] + e[29] * e[27] * e[0] + e[29] * e[28] * e[1] + e[35] * e[27] * e[6] + e[35] * e[0] * e[33] + e[35] * e[28] * e[7] + e[35] * e[1] * e[34] - e[29] * e[34] * e[7] - e[29] * e[33] * e[6] - e[29] * e[30] * e[3] - e[29] * e[31] * e[4] + 0.5 * e[2] * e2[27] + 1.5 * e[2] * e2[29] + 0.5 * e[2] * e2[28] + 0.5 * e[2] * e2[32] - 0.5 * e[2] * e2[31] - 0.5 * e[2] * e2[33] - 0.5 * e[2] * e2[30] - 0.5 * e[2] * e2[34] + 0.5 * e[2] * e2[35]; a[38] = e[13] * e[12] * e[6] + e[13] * e[3] * e[15] + e[13] * e[4] * e[16] + e[13] * e[14] * e[8] + e[13] * e[5] * e[17] + e[16] * e[15] * e[6] + e[16] * e[17] * e[8] + e[1] * e[11] * e[17] + e[1] * e[9] * e[15] + e[1] * e[10] * e[16] + e[4] * e[14] * e[17] + e[4] * e[12] * e[15] + e[10] * e[9] * e[6] + e[10] * e[0] * e[15] + e[10] * e[11] * e[8] + e[10] * e[2] * e[17] - e[16] * e[11] * e[2] - e[16] * e[9] * e[0] - e[16] * e[14] * e[5] - e[16] * e[12] * e[3] + 0.5 * e2[13] * e[7] + 1.5 * e2[16] * e[7] + 0.5 * e[7] * e2[17] + 0.5 * e[7] * e2[15] - 0.5 * e[7] * e2[9] - 0.5 * e[7] * e2[11] - 0.5 * e[7] * e2[12] + 0.5 * e[7] * e2[10] - 0.5 * e[7] * e2[14]; a[193] = 0.5 * e[29] * e2[32] + 0.5 * e[29] * e2[35] - 0.5 * e[29] * e2[31] - 0.5 * e[29] * e2[33] - 0.5 * e[29] * e2[30] - 0.5 * e[29] * e2[34] + e[32] * e[27] * e[30] + 0.5 * e3[29] + 0.5 * e[29] * e2[28] + e[35] * e[28] * e[34] + 0.5 * e[29] * e2[27] + e[35] * e[27] * e[33] + e[32] * e[28] * e[31]; a[68] = -e[16] * e[21] * e[12] + e[10] * e[18] * e[15] + e[10] * e[9] * e[24] + e[10] * e[20] * e[17] + e[10] * e[11] * e[26] + e[19] * e[11] * e[17] + e[19] * e[9] * e[15] + e[19] * e[10] * e[16] + e[13] * e[21] * e[15] + e[13] * e[12] * e[24] + e[13] * e[23] * e[17] + e[13] * e[14] * e[26] + e[13] * e[22] * e[16] + e[22] * e[14] * e[17] + e[22] * e[12] * e[15] + e[16] * e[24] * e[15] + e[16] * e[26] * e[17] - e[16] * e[23] * e[14] - e[16] * e[20] * e[11] - e[16] * e[18] * e[9] + 0.5 * e2[13] * e[25] + 1.5 * e[25] * e2[16] + 0.5 * e[25] * e2[17] + 0.5 * e[25] * e2[15] + 0.5 * e2[10] * e[25] - 0.5 * e[25] * e2[9] - 0.5 * e[25] * e2[11] - 0.5 * e[25] * e2[12] - 0.5 * e[25] * e2[14]; a[102] = e[19] * e[20] * e[2] + e[22] * e[18] * e[3] + e[22] * e[0] * e[21] + e[22] * e[19] * e[4] + e[22] * e[20] * e[5] + e[22] * e[2] * e[23] - e[19] * e[21] * e[3] - e[19] * e[26] * e[8] + e[19] * e[25] * e[7] - e[19] * e[23] * e[5] - e[19] * e[24] * e[6] + e[4] * e[18] * e[21] + e[4] * e[20] * e[23] + e[25] * e[18] * e[6] + e[25] * e[0] * e[24] + e[25] * e[20] * e[8] + e[25] * e[2] * e[26] + e[7] * e[18] * e[24] + e[7] * e[20] * e[26] + e[19] * e[18] * e[0] + 1.5 * e2[19] * e[1] + 0.5 * e[1] * e2[22] + 0.5 * e[1] * e2[18] + 0.5 * e[1] * e2[20] + 0.5 * e[1] * e2[25] - 0.5 * e[1] * e2[26] - 0.5 * e[1] * e2[23] - 0.5 * e[1] * e2[24] - 0.5 * e[1] * e2[21]; a[178] = e[19] * e[27] * e[24] + e[19] * e[18] * e[33] + e[19] * e[28] * e[25] + e[19] * e[29] * e[26] + e[19] * e[20] * e[35] + e[28] * e[18] * e[24] + e[28] * e[20] * e[26] + e[22] * e[30] * e[24] + e[22] * e[21] * e[33] + e[22] * e[31] * e[25] + e[22] * e[32] * e[26] + e[22] * e[23] * e[35] + e[31] * e[21] * e[24] + e[31] * e[23] * e[26] + e[25] * e[33] * e[24] + e[25] * e[35] * e[26] - e[25] * e[27] * e[18] - e[25] * e[30] * e[21] - e[25] * e[29] * e[20] - e[25] * e[32] * e[23] - 0.5 * e[34] * e2[18] - 0.5 * e[34] * e2[23] - 0.5 * e[34] * e2[20] - 0.5 * e[34] * e2[21] + 0.5 * e2[19] * e[34] + 0.5 * e2[22] * e[34] + 1.5 * e[34] * e2[25] + 0.5 * e[34] * e2[24] + 0.5 * e[34] * e2[26]; a[22] = e[16] * e[0] * e[6] + e[16] * e[2] * e[8] + e[1] * e[11] * e[2] - e[1] * e[15] * e[6] + e[1] * e[9] * e[0] - e[1] * e[14] * e[5] - e[1] * e[12] * e[3] - e[1] * e[17] * e[8] + e[4] * e[9] * e[3] + e[4] * e[0] * e[12] + e[4] * e[1] * e[13] + e[4] * e[11] * e[5] + e[4] * e[2] * e[14] + e[13] * e[0] * e[3] + e[13] * e[2] * e[5] + e[7] * e[9] * e[6] + e[7] * e[0] * e[15] + e[7] * e[1] * e[16] + e[7] * e[11] * e[8] + e[7] * e[2] * e[17] - 0.5 * e[10] * e2[6] - 0.5 * e[10] * e2[5] - 0.5 * e[10] * e2[3] - 0.5 * e[10] * e2[8] + 1.5 * e[10] * e2[1] + 0.5 * e[10] * e2[0] + 0.5 * e[10] * e2[2] + 0.5 * e[10] * e2[4] + 0.5 * e[10] * e2[7]; a[18] = e[13] * e[14] * e[17] + e[13] * e[12] * e[15] + e[10] * e[9] * e[15] + 0.5 * e[16] * e2[15] - 0.5 * e[16] * e2[11] - 0.5 * e[16] * e2[12] - 0.5 * e[16] * e2[14] + e[10] * e[11] * e[17] + 0.5 * e2[10] * e[16] + 0.5 * e3[16] - 0.5 * e[16] * e2[9] + 0.5 * e[16] * e2[17] + 0.5 * e2[13] * e[16]; a[142] = e[10] * e[29] * e[20] + e[22] * e[27] * e[12] + e[22] * e[9] * e[30] + e[22] * e[29] * e[14] + e[22] * e[11] * e[32] + e[22] * e[10] * e[31] + e[31] * e[18] * e[12] + e[31] * e[9] * e[21] + e[31] * e[20] * e[14] + e[31] * e[11] * e[23] - e[10] * e[33] * e[24] - e[10] * e[30] * e[21] - e[10] * e[35] * e[26] - e[10] * e[32] * e[23] + e[10] * e[34] * e[25] + e[19] * e[27] * e[9] + e[19] * e[29] * e[11] + e[28] * e[18] * e[9] + e[28] * e[20] * e[11] + e[16] * e[27] * e[24] + e[16] * e[18] * e[33] + e[16] * e[28] * e[25] + e[16] * e[19] * e[34] + e[16] * e[29] * e[26] + e[16] * e[20] * e[35] - e[19] * e[30] * e[12] - e[19] * e[32] * e[14] - e[19] * e[33] * e[15] - e[19] * e[35] * e[17] - e[28] * e[23] * e[14] - e[28] * e[24] * e[15] - e[28] * e[26] * e[17] - e[28] * e[21] * e[12] + e[25] * e[27] * e[15] + e[25] * e[9] * e[33] + e[25] * e[29] * e[17] + e[25] * e[11] * e[35] + e[34] * e[18] * e[15] + e[34] * e[9] * e[24] + e[34] * e[20] * e[17] + e[34] * e[11] * e[26] + e[13] * e[27] * e[21] + e[13] * e[18] * e[30] + e[13] * e[28] * e[22] + e[13] * e[19] * e[31] + e[13] * e[29] * e[23] + e[13] * e[20] * e[32] + e[10] * e[27] * e[18] + 3. * e[10] * e[28] * e[19]; a[98] = e[4] * e[30] * e[15] + e[4] * e[12] * e[33] + e[4] * e[32] * e[17] + e[4] * e[14] * e[35] + e[4] * e[31] * e[16] + e[4] * e[13] * e[34] + e[7] * e[33] * e[15] + e[7] * e[35] * e[17] + 3. * e[7] * e[34] * e[16] + e[1] * e[27] * e[15] + e[1] * e[9] * e[33] + e[1] * e[29] * e[17] + e[1] * e[11] * e[35] + e[1] * e[28] * e[16] + e[1] * e[10] * e[34] - e[16] * e[27] * e[0] - e[16] * e[32] * e[5] + e[16] * e[33] * e[6] - e[16] * e[30] * e[3] + e[16] * e[35] * e[8] - e[16] * e[29] * e[2] + e[13] * e[30] * e[6] + e[13] * e[3] * e[33] + e[13] * e[31] * e[7] + e[13] * e[32] * e[8] + e[13] * e[5] * e[35] - e[34] * e[11] * e[2] + e[34] * e[15] * e[6] - e[34] * e[9] * e[0] - e[34] * e[14] * e[5] - e[34] * e[12] * e[3] + e[34] * e[17] * e[8] + e[31] * e[12] * e[6] + e[31] * e[3] * e[15] + e[31] * e[14] * e[8] + e[31] * e[5] * e[17] - e[7] * e[27] * e[9] - e[7] * e[30] * e[12] + e[7] * e[28] * e[10] - e[7] * e[32] * e[14] + e[10] * e[27] * e[6] + e[10] * e[0] * e[33] + e[10] * e[29] * e[8] + e[10] * e[2] * e[35] + e[28] * e[9] * e[6] + e[28] * e[0] * e[15] + e[28] * e[11] * e[8] + e[28] * e[2] * e[17] - e[7] * e[29] * e[11]; a[132] = e[22] * e[18] * e[12] + e[22] * e[9] * e[21] + e[22] * e[20] * e[14] + e[22] * e[11] * e[23] + e[22] * e[19] * e[13] + e[25] * e[18] * e[15] + e[25] * e[9] * e[24] + e[25] * e[20] * e[17] + e[25] * e[11] * e[26] + e[25] * e[19] * e[16] + e[16] * e[18] * e[24] + e[16] * e[20] * e[26] + e[13] * e[18] * e[21] + e[13] * e[20] * e[23] + e[19] * e[18] * e[9] + e[19] * e[20] * e[11] - e[19] * e[23] * e[14] - e[19] * e[24] * e[15] - e[19] * e[26] * e[17] - e[19] * e[21] * e[12] + 0.5 * e[10] * e2[22] + 0.5 * e[10] * e2[25] + 1.5 * e[10] * e2[19] + 0.5 * e[10] * e2[18] + 0.5 * e[10] * e2[20] - 0.5 * e[10] * e2[26] - 0.5 * e[10] * e2[23] - 0.5 * e[10] * e2[24] - 0.5 * e[10] * e2[21]; a[168] = e[19] * e[20] * e[26] - 0.5 * e[25] * e2[20] + e[22] * e[21] * e[24] + e[19] * e[18] * e[24] + 0.5 * e2[22] * e[25] - 0.5 * e[25] * e2[21] - 0.5 * e[25] * e2[23] + 0.5 * e2[19] * e[25] - 0.5 * e[25] * e2[18] + 0.5 * e[25] * e2[24] + 0.5 * e[25] * e2[26] + 0.5 * e3[25] + e[22] * e[23] * e[26]; a[113] = -e[20] * e[33] * e[6] - e[20] * e[30] * e[3] - e[20] * e[31] * e[4] - e[29] * e[21] * e[3] - e[29] * e[22] * e[4] - e[29] * e[25] * e[7] - e[29] * e[24] * e[6] + e[8] * e[27] * e[24] + e[8] * e[18] * e[33] + e[8] * e[28] * e[25] + e[8] * e[19] * e[34] + e[23] * e[27] * e[3] + e[23] * e[0] * e[30] + e[23] * e[28] * e[4] + e[23] * e[1] * e[31] + e[32] * e[18] * e[3] + e[32] * e[0] * e[21] + e[32] * e[19] * e[4] + e[32] * e[1] * e[22] + e[26] * e[27] * e[6] + e[26] * e[0] * e[33] + e[26] * e[28] * e[7] + e[26] * e[1] * e[34] + e[26] * e[29] * e[8] + e[26] * e[2] * e[35] + e[35] * e[18] * e[6] + e[35] * e[0] * e[24] + e[35] * e[19] * e[7] + e[35] * e[1] * e[25] + e[35] * e[20] * e[8] + e[2] * e[27] * e[18] + e[2] * e[28] * e[19] + 3. * e[2] * e[29] * e[20] + e[20] * e[27] * e[0] + e[20] * e[28] * e[1] + e[29] * e[18] * e[0] + e[29] * e[19] * e[1] + e[5] * e[27] * e[21] + e[5] * e[18] * e[30] + e[5] * e[28] * e[22] + e[5] * e[19] * e[31] + e[5] * e[29] * e[23] + e[5] * e[20] * e[32] - e[2] * e[33] * e[24] - e[2] * e[30] * e[21] - e[2] * e[31] * e[22] + e[2] * e[32] * e[23] - e[2] * e[34] * e[25] - e[20] * e[34] * e[7]; a[43] = e[5] * e[18] * e[3] + e[5] * e[0] * e[21] + e[5] * e[19] * e[4] + e[5] * e[1] * e[22] + e[5] * e[2] * e[23] + e[23] * e[1] * e[4] + e[23] * e[0] * e[3] + e[8] * e[18] * e[6] + e[8] * e[0] * e[24] + e[8] * e[19] * e[7] + e[8] * e[1] * e[25] + e[8] * e[2] * e[26] + e[26] * e[1] * e[7] + e[26] * e[0] * e[6] + e[2] * e[18] * e[0] + e[2] * e[19] * e[1] - e[2] * e[21] * e[3] - e[2] * e[22] * e[4] - e[2] * e[25] * e[7] - e[2] * e[24] * e[6] - 0.5 * e[20] * e2[4] + 0.5 * e[20] * e2[0] - 0.5 * e[20] * e2[6] + 0.5 * e[20] * e2[5] + 0.5 * e[20] * e2[1] - 0.5 * e[20] * e2[7] - 0.5 * e[20] * e2[3] + 1.5 * e[20] * e2[2] + 0.5 * e[20] * e2[8]; a[33] = e[14] * e[9] * e[3] + e[14] * e[0] * e[12] + e[14] * e[10] * e[4] + e[14] * e[1] * e[13] + e[14] * e[11] * e[5] + e[17] * e[9] * e[6] + e[17] * e[0] * e[15] + e[17] * e[10] * e[7] + e[17] * e[1] * e[16] + e[17] * e[11] * e[8] + e[8] * e[9] * e[15] + e[8] * e[10] * e[16] + e[5] * e[9] * e[12] + e[5] * e[10] * e[13] + e[11] * e[9] * e[0] + e[11] * e[10] * e[1] - e[11] * e[13] * e[4] - e[11] * e[16] * e[7] - e[11] * e[15] * e[6] - e[11] * e[12] * e[3] + 0.5 * e[2] * e2[14] + 0.5 * e[2] * e2[17] + 1.5 * e[2] * e2[11] + 0.5 * e[2] * e2[9] + 0.5 * e[2] * e2[10] - 0.5 * e[2] * e2[16] - 0.5 * e[2] * e2[12] - 0.5 * e[2] * e2[15] - 0.5 * e[2] * e2[13]; a[63] = e[14] * e[18] * e[12] + e[14] * e[9] * e[21] + e[14] * e[11] * e[23] + e[14] * e[19] * e[13] + e[14] * e[10] * e[22] + e[23] * e[9] * e[12] + e[23] * e[10] * e[13] + e[17] * e[18] * e[15] + e[17] * e[9] * e[24] + e[17] * e[11] * e[26] + e[17] * e[19] * e[16] + e[17] * e[10] * e[25] + e[26] * e[9] * e[15] + e[26] * e[10] * e[16] - e[11] * e[24] * e[15] - e[11] * e[25] * e[16] + e[11] * e[18] * e[9] - e[11] * e[21] * e[12] + e[11] * e[19] * e[10] - e[11] * e[22] * e[13] + 1.5 * e[20] * e2[11] + 0.5 * e[20] * e2[9] + 0.5 * e[20] * e2[10] + 0.5 * e[20] * e2[14] + 0.5 * e[20] * e2[17] - 0.5 * e[20] * e2[16] - 0.5 * e[20] * e2[12] - 0.5 * e[20] * e2[15] - 0.5 * e[20] * e2[13]; a[143] = e[23] * e[10] * e[31] + e[32] * e[18] * e[12] + e[32] * e[9] * e[21] + e[32] * e[19] * e[13] + e[32] * e[10] * e[22] - e[11] * e[33] * e[24] - e[11] * e[30] * e[21] + e[11] * e[35] * e[26] - e[11] * e[31] * e[22] - e[11] * e[34] * e[25] + e[20] * e[27] * e[9] + e[20] * e[28] * e[10] + e[29] * e[18] * e[9] + e[29] * e[19] * e[10] + e[17] * e[27] * e[24] + e[17] * e[18] * e[33] + e[17] * e[28] * e[25] + e[17] * e[19] * e[34] + e[17] * e[29] * e[26] + e[17] * e[20] * e[35] - e[20] * e[30] * e[12] - e[20] * e[31] * e[13] - e[20] * e[33] * e[15] - e[20] * e[34] * e[16] - e[29] * e[24] * e[15] - e[29] * e[25] * e[16] - e[29] * e[21] * e[12] - e[29] * e[22] * e[13] + e[26] * e[27] * e[15] + e[26] * e[9] * e[33] + e[26] * e[28] * e[16] + e[26] * e[10] * e[34] + e[35] * e[18] * e[15] + e[35] * e[9] * e[24] + e[35] * e[19] * e[16] + e[35] * e[10] * e[25] + e[14] * e[27] * e[21] + e[14] * e[18] * e[30] + e[14] * e[28] * e[22] + e[14] * e[19] * e[31] + e[14] * e[29] * e[23] + e[14] * e[20] * e[32] + e[11] * e[27] * e[18] + e[11] * e[28] * e[19] + 3. * e[11] * e[29] * e[20] + e[23] * e[27] * e[12] + e[23] * e[9] * e[30] + e[23] * e[11] * e[32] + e[23] * e[28] * e[13]; a[133] = e[23] * e[18] * e[12] + e[23] * e[9] * e[21] + e[23] * e[20] * e[14] + e[23] * e[19] * e[13] + e[23] * e[10] * e[22] + e[26] * e[18] * e[15] + e[26] * e[9] * e[24] + e[26] * e[20] * e[17] + e[26] * e[19] * e[16] + e[26] * e[10] * e[25] + e[17] * e[19] * e[25] + e[17] * e[18] * e[24] + e[14] * e[19] * e[22] + e[14] * e[18] * e[21] + e[20] * e[18] * e[9] + e[20] * e[19] * e[10] - e[20] * e[24] * e[15] - e[20] * e[25] * e[16] - e[20] * e[21] * e[12] - e[20] * e[22] * e[13] + 0.5 * e[11] * e2[23] + 0.5 * e[11] * e2[26] + 0.5 * e[11] * e2[19] + 0.5 * e[11] * e2[18] + 1.5 * e[11] * e2[20] - 0.5 * e[11] * e2[22] - 0.5 * e[11] * e2[24] - 0.5 * e[11] * e2[21] - 0.5 * e[11] * e2[25]; a[103] = -e[20] * e[21] * e[3] + e[20] * e[26] * e[8] - e[20] * e[22] * e[4] - e[20] * e[25] * e[7] - e[20] * e[24] * e[6] + e[5] * e[19] * e[22] + e[5] * e[18] * e[21] + e[26] * e[18] * e[6] + e[26] * e[0] * e[24] + e[26] * e[19] * e[7] + e[26] * e[1] * e[25] + e[8] * e[19] * e[25] + e[8] * e[18] * e[24] + e[20] * e[18] * e[0] + e[20] * e[19] * e[1] + e[23] * e[18] * e[3] + e[23] * e[0] * e[21] + e[23] * e[19] * e[4] + e[23] * e[1] * e[22] + e[23] * e[20] * e[5] + 1.5 * e2[20] * e[2] + 0.5 * e[2] * e2[23] + 0.5 * e[2] * e2[19] + 0.5 * e[2] * e2[18] + 0.5 * e[2] * e2[26] - 0.5 * e[2] * e2[22] - 0.5 * e[2] * e2[24] - 0.5 * e[2] * e2[21] - 0.5 * e[2] * e2[25]; a[23] = -e[2] * e[15] * e[6] + e[2] * e[9] * e[0] - e[2] * e[12] * e[3] + e[5] * e[9] * e[3] + e[5] * e[0] * e[12] + e[5] * e[10] * e[4] + e[5] * e[1] * e[13] + e[5] * e[2] * e[14] + e[14] * e[1] * e[4] + e[14] * e[0] * e[3] + e[8] * e[9] * e[6] + e[8] * e[0] * e[15] + e[8] * e[10] * e[7] + e[8] * e[1] * e[16] + e[8] * e[2] * e[17] + e[17] * e[1] * e[7] + e[17] * e[0] * e[6] + e[2] * e[10] * e[1] - e[2] * e[13] * e[4] - e[2] * e[16] * e[7] + 0.5 * e[11] * e2[1] + 0.5 * e[11] * e2[0] + 1.5 * e[11] * e2[2] + 0.5 * e[11] * e2[5] + 0.5 * e[11] * e2[8] - 0.5 * e[11] * e2[4] - 0.5 * e[11] * e2[6] - 0.5 * e[11] * e2[7] - 0.5 * e[11] * e2[3]; a[83] = e[5] * e[19] * e[13] + e[5] * e[10] * e[22] + e[8] * e[18] * e[15] + e[8] * e[9] * e[24] + e[8] * e[20] * e[17] + e[8] * e[11] * e[26] + e[8] * e[19] * e[16] + e[8] * e[10] * e[25] + e[2] * e[18] * e[9] + e[2] * e[19] * e[10] - e[11] * e[21] * e[3] - e[11] * e[22] * e[4] - e[11] * e[25] * e[7] - e[11] * e[24] * e[6] + e[14] * e[18] * e[3] + e[14] * e[0] * e[21] + e[14] * e[19] * e[4] + e[14] * e[1] * e[22] + e[14] * e[2] * e[23] - e[20] * e[13] * e[4] - e[20] * e[16] * e[7] - e[20] * e[15] * e[6] - e[20] * e[12] * e[3] + e[23] * e[9] * e[3] + e[23] * e[0] * e[12] + e[23] * e[10] * e[4] + e[23] * e[1] * e[13] + e[17] * e[18] * e[6] + e[17] * e[0] * e[24] + e[17] * e[19] * e[7] + e[17] * e[1] * e[25] + e[17] * e[2] * e[26] - e[2] * e[24] * e[15] - e[2] * e[25] * e[16] - e[2] * e[21] * e[12] - e[2] * e[22] * e[13] + e[26] * e[9] * e[6] + e[26] * e[0] * e[15] + e[26] * e[10] * e[7] + e[26] * e[1] * e[16] + e[11] * e[18] * e[0] + e[11] * e[19] * e[1] + 3. * e[11] * e[20] * e[2] + e[20] * e[9] * e[0] + e[20] * e[10] * e[1] + e[5] * e[18] * e[12] + e[5] * e[9] * e[21] + e[5] * e[20] * e[14] + e[5] * e[11] * e[23]; a[53] = e[32] * e[1] * e[4] + e[32] * e[0] * e[3] + e[8] * e[27] * e[6] + e[8] * e[0] * e[33] + e[8] * e[28] * e[7] + e[8] * e[1] * e[34] + e[35] * e[1] * e[7] + e[35] * e[0] * e[6] + e[2] * e[27] * e[0] + e[2] * e[28] * e[1] - e[2] * e[34] * e[7] + e[2] * e[32] * e[5] - e[2] * e[33] * e[6] - e[2] * e[30] * e[3] + e[2] * e[35] * e[8] - e[2] * e[31] * e[4] + e[5] * e[27] * e[3] + e[5] * e[0] * e[30] + e[5] * e[28] * e[4] + e[5] * e[1] * e[31] + 1.5 * e[29] * e2[2] - 0.5 * e[29] * e2[4] + 0.5 * e[29] * e2[0] - 0.5 * e[29] * e2[6] + 0.5 * e[29] * e2[5] + 0.5 * e[29] * e2[1] - 0.5 * e[29] * e2[7] - 0.5 * e[29] * e2[3] + 0.5 * e[29] * e2[8]; a[3] = e[5] * e[0] * e[3] + e[8] * e[1] * e[7] + e[8] * e[0] * e[6] + e[5] * e[1] * e[4] - 0.5 * e[2] * e2[4] + 0.5 * e3[2] + 0.5 * e[2] * e2[1] - 0.5 * e[2] * e2[3] + 0.5 * e[2] * e2[0] + 0.5 * e[2] * e2[8] + 0.5 * e[2] * e2[5] - 0.5 * e[2] * e2[6] - 0.5 * e[2] * e2[7]; a[73] = e[35] * e[9] * e[15] + e[35] * e[10] * e[16] - e[11] * e[30] * e[12] - e[11] * e[31] * e[13] - e[11] * e[33] * e[15] - e[11] * e[34] * e[16] + e[11] * e[27] * e[9] + e[11] * e[28] * e[10] + e[14] * e[27] * e[12] + e[14] * e[9] * e[30] + e[14] * e[11] * e[32] + e[14] * e[28] * e[13] + e[14] * e[10] * e[31] + e[32] * e[9] * e[12] + e[32] * e[10] * e[13] + e[17] * e[27] * e[15] + e[17] * e[9] * e[33] + e[17] * e[11] * e[35] + e[17] * e[28] * e[16] + e[17] * e[10] * e[34] + 1.5 * e[29] * e2[11] - 0.5 * e[29] * e2[16] + 0.5 * e[29] * e2[9] - 0.5 * e[29] * e2[12] - 0.5 * e[29] * e2[15] + 0.5 * e[29] * e2[17] + 0.5 * e[29] * e2[10] + 0.5 * e[29] * e2[14] - 0.5 * e[29] * e2[13]; a[13] = e[14] * e[9] * e[12] + e[17] * e[10] * e[16] + e[17] * e[9] * e[15] + 0.5 * e3[11] + e[14] * e[10] * e[13] + 0.5 * e[11] * e2[10] - 0.5 * e[11] * e2[15] + 0.5 * e[11] * e2[14] - 0.5 * e[11] * e2[13] - 0.5 * e[11] * e2[12] + 0.5 * e[11] * e2[9] - 0.5 * e[11] * e2[16] + 0.5 * e[11] * e2[17]; a[173] = e[20] * e[27] * e[18] + e[20] * e[28] * e[19] + e[23] * e[27] * e[21] + e[23] * e[18] * e[30] + e[23] * e[28] * e[22] + e[23] * e[19] * e[31] + e[23] * e[20] * e[32] + e[32] * e[19] * e[22] + e[32] * e[18] * e[21] + e[26] * e[27] * e[24] + e[26] * e[18] * e[33] + e[26] * e[28] * e[25] + e[26] * e[19] * e[34] + e[26] * e[20] * e[35] + e[35] * e[19] * e[25] + e[35] * e[18] * e[24] - e[20] * e[33] * e[24] - e[20] * e[30] * e[21] - e[20] * e[31] * e[22] - e[20] * e[34] * e[25] + 0.5 * e[29] * e2[23] + 0.5 * e[29] * e2[26] - 0.5 * e[29] * e2[22] - 0.5 * e[29] * e2[24] - 0.5 * e[29] * e2[21] - 0.5 * e[29] * e2[25] + 1.5 * e[29] * e2[20] + 0.5 * e[29] * e2[19] + 0.5 * e[29] * e2[18]; a[163] = 0.5 * e[20] * e2[26] + 0.5 * e[20] * e2[18] + 0.5 * e3[20] + 0.5 * e[20] * e2[19] + e[26] * e[18] * e[24] + 0.5 * e[20] * e2[23] - 0.5 * e[20] * e2[25] + e[23] * e[19] * e[22] - 0.5 * e[20] * e2[24] - 0.5 * e[20] * e2[21] - 0.5 * e[20] * e2[22] + e[23] * e[18] * e[21] + e[26] * e[19] * e[25]; a[93] = e[8] * e[28] * e[16] + e[8] * e[10] * e[34] + e[2] * e[27] * e[9] + 3. * e[2] * e[29] * e[11] + e[2] * e[28] * e[10] + e[11] * e[27] * e[0] - e[11] * e[34] * e[7] - e[11] * e[33] * e[6] - e[11] * e[30] * e[3] + e[11] * e[28] * e[1] - e[11] * e[31] * e[4] + e[14] * e[27] * e[3] + e[14] * e[0] * e[30] + e[14] * e[28] * e[4] + e[14] * e[1] * e[31] + e[14] * e[2] * e[32] + e[29] * e[10] * e[1] - e[29] * e[13] * e[4] - e[29] * e[16] * e[7] - e[29] * e[15] * e[6] + e[29] * e[9] * e[0] - e[29] * e[12] * e[3] + e[32] * e[9] * e[3] + e[32] * e[0] * e[12] + e[32] * e[10] * e[4] + e[32] * e[1] * e[13] + e[17] * e[27] * e[6] + e[17] * e[0] * e[33] + e[17] * e[28] * e[7] + e[17] * e[1] * e[34] + e[17] * e[2] * e[35] - e[2] * e[30] * e[12] - e[2] * e[31] * e[13] - e[2] * e[33] * e[15] - e[2] * e[34] * e[16] + e[35] * e[9] * e[6] + e[35] * e[0] * e[15] + e[35] * e[10] * e[7] + e[35] * e[1] * e[16] + e[5] * e[27] * e[12] + e[5] * e[9] * e[30] + e[5] * e[29] * e[14] + e[5] * e[11] * e[32] + e[5] * e[28] * e[13] + e[5] * e[10] * e[31] + e[8] * e[27] * e[15] + e[8] * e[9] * e[33] + e[8] * e[29] * e[17] + e[8] * e[11] * e[35]; a[94] = -e[12] * e[34] * e[7] + e[12] * e[32] * e[5] - e[12] * e[35] * e[8] - e[12] * e[29] * e[2] - e[12] * e[28] * e[1] + e[12] * e[31] * e[4] - e[30] * e[11] * e[2] - e[30] * e[10] * e[1] + e[30] * e[13] * e[4] - e[30] * e[16] * e[7] + e[30] * e[14] * e[5] - e[30] * e[17] * e[8] + e[15] * e[3] * e[33] + e[15] * e[31] * e[7] + e[15] * e[4] * e[34] + e[15] * e[32] * e[8] + e[15] * e[5] * e[35] + e[3] * e[27] * e[9] - e[3] * e[28] * e[10] - e[3] * e[34] * e[16] - e[3] * e[35] * e[17] - e[3] * e[29] * e[11] + e[33] * e[13] * e[7] + e[33] * e[4] * e[16] + e[33] * e[14] * e[8] + e[33] * e[5] * e[17] + e[9] * e[28] * e[4] + e[9] * e[1] * e[31] + e[9] * e[29] * e[5] + e[9] * e[2] * e[32] + e[27] * e[10] * e[4] + e[27] * e[1] * e[13] + e[27] * e[11] * e[5] + e[27] * e[2] * e[14] + 3. * e[3] * e[30] * e[12] + e[3] * e[32] * e[14] + e[3] * e[31] * e[13] + e[6] * e[30] * e[15] + e[6] * e[12] * e[33] + e[6] * e[32] * e[17] + e[6] * e[14] * e[35] + e[6] * e[31] * e[16] + e[6] * e[13] * e[34] + e[0] * e[27] * e[12] + e[0] * e[9] * e[30] + e[0] * e[29] * e[14] + e[0] * e[11] * e[32] + e[0] * e[28] * e[13] + e[0] * e[10] * e[31]; a[164] = 0.5 * e[21] * e2[24] - 0.5 * e[21] * e2[25] + 0.5 * e[21] * e2[23] - 0.5 * e[21] * e2[26] + 0.5 * e2[18] * e[21] + 0.5 * e[21] * e2[22] - 0.5 * e[21] * e2[20] + e[24] * e[22] * e[25] + e[24] * e[23] * e[26] - 0.5 * e[21] * e2[19] + e[18] * e[19] * e[22] + e[18] * e[20] * e[23] + 0.5 * e3[21]; a[174] = -0.5 * e[30] * e2[26] - 0.5 * e[30] * e2[19] - 0.5 * e[30] * e2[20] - 0.5 * e[30] * e2[25] + 0.5 * e2[18] * e[30] + 1.5 * e[30] * e2[21] + 0.5 * e[30] * e2[22] + 0.5 * e[30] * e2[23] + 0.5 * e[30] * e2[24] + e[18] * e[27] * e[21] + e[18] * e[28] * e[22] + e[18] * e[19] * e[31] + e[18] * e[29] * e[23] + e[18] * e[20] * e[32] + e[27] * e[19] * e[22] + e[27] * e[20] * e[23] + e[21] * e[31] * e[22] + e[21] * e[32] * e[23] + e[24] * e[21] * e[33] + e[24] * e[31] * e[25] + e[24] * e[22] * e[34] + e[24] * e[32] * e[26] + e[24] * e[23] * e[35] + e[33] * e[22] * e[25] + e[33] * e[23] * e[26] - e[21] * e[29] * e[20] - e[21] * e[35] * e[26] - e[21] * e[28] * e[19] - e[21] * e[34] * e[25]; a[14] = 0.5 * e[12] * e2[15] - 0.5 * e[12] * e2[17] + e[15] * e[13] * e[16] - 0.5 * e[12] * e2[10] + e[15] * e[14] * e[17] - 0.5 * e[12] * e2[16] - 0.5 * e[12] * e2[11] + e[9] * e[10] * e[13] + 0.5 * e[12] * e2[13] + 0.5 * e2[9] * e[12] + 0.5 * e3[12] + e[9] * e[11] * e[14] + 0.5 * e[12] * e2[14]; a[34] = e[12] * e[13] * e[4] + e[12] * e[14] * e[5] + e[15] * e[12] * e[6] + e[15] * e[13] * e[7] + e[15] * e[4] * e[16] + e[15] * e[14] * e[8] + e[15] * e[5] * e[17] + e[6] * e[14] * e[17] + e[6] * e[13] * e[16] + e[0] * e[11] * e[14] + e[0] * e[9] * e[12] + e[0] * e[10] * e[13] + e[9] * e[10] * e[4] + e[9] * e[1] * e[13] + e[9] * e[11] * e[5] + e[9] * e[2] * e[14] - e[12] * e[11] * e[2] - e[12] * e[10] * e[1] - e[12] * e[16] * e[7] - e[12] * e[17] * e[8] + 1.5 * e2[12] * e[3] + 0.5 * e[3] * e2[15] - 0.5 * e[3] * e2[16] + 0.5 * e[3] * e2[9] - 0.5 * e[3] * e2[11] - 0.5 * e[3] * e2[17] - 0.5 * e[3] * e2[10] + 0.5 * e[3] * e2[14] + 0.5 * e[3] * e2[13]; a[64] = e[18] * e[11] * e[14] + e[18] * e[9] * e[12] + e[18] * e[10] * e[13] + e[12] * e[23] * e[14] + e[12] * e[22] * e[13] + e[15] * e[12] * e[24] + e[15] * e[23] * e[17] + e[15] * e[14] * e[26] + e[15] * e[22] * e[16] + e[15] * e[13] * e[25] + e[24] * e[14] * e[17] + e[24] * e[13] * e[16] - e[12] * e[25] * e[16] - e[12] * e[26] * e[17] - e[12] * e[20] * e[11] - e[12] * e[19] * e[10] + e[9] * e[20] * e[14] + e[9] * e[11] * e[23] + e[9] * e[19] * e[13] + e[9] * e[10] * e[22] + 0.5 * e2[9] * e[21] - 0.5 * e[21] * e2[16] - 0.5 * e[21] * e2[11] - 0.5 * e[21] * e2[17] - 0.5 * e[21] * e2[10] + 1.5 * e[21] * e2[12] + 0.5 * e[21] * e2[14] + 0.5 * e[21] * e2[13] + 0.5 * e[21] * e2[15]; a[114] = -e[21] * e[35] * e[8] - e[21] * e[29] * e[2] - e[21] * e[28] * e[1] + e[21] * e[31] * e[4] - e[30] * e[26] * e[8] - e[30] * e[20] * e[2] - e[30] * e[19] * e[1] + e[30] * e[22] * e[4] - e[30] * e[25] * e[7] + e[30] * e[23] * e[5] + e[6] * e[31] * e[25] + e[6] * e[22] * e[34] + e[6] * e[32] * e[26] + e[6] * e[23] * e[35] + e[24] * e[30] * e[6] + e[24] * e[3] * e[33] + e[24] * e[31] * e[7] + e[24] * e[4] * e[34] + e[24] * e[32] * e[8] + e[24] * e[5] * e[35] + e[33] * e[21] * e[6] + e[33] * e[22] * e[7] + e[33] * e[4] * e[25] + e[33] * e[23] * e[8] + e[33] * e[5] * e[26] + e[0] * e[27] * e[21] + e[0] * e[18] * e[30] + e[0] * e[28] * e[22] + e[0] * e[19] * e[31] + e[0] * e[29] * e[23] + e[0] * e[20] * e[32] + e[18] * e[27] * e[3] + e[18] * e[28] * e[4] + e[18] * e[1] * e[31] + e[18] * e[29] * e[5] + e[18] * e[2] * e[32] + e[27] * e[19] * e[4] + e[27] * e[1] * e[22] + e[27] * e[20] * e[5] + e[27] * e[2] * e[23] + 3. * e[3] * e[30] * e[21] + e[3] * e[31] * e[22] + e[3] * e[32] * e[23] - e[3] * e[29] * e[20] - e[3] * e[35] * e[26] - e[3] * e[28] * e[19] - e[3] * e[34] * e[25] - e[21] * e[34] * e[7] + e[21] * e[32] * e[5]; a[44] = e[18] * e[1] * e[4] + e[18] * e[0] * e[3] + e[18] * e[2] * e[5] + e[3] * e[22] * e[4] + e[3] * e[23] * e[5] + e[6] * e[3] * e[24] + e[6] * e[22] * e[7] + e[6] * e[4] * e[25] + e[6] * e[23] * e[8] + e[6] * e[5] * e[26] + e[24] * e[4] * e[7] + e[24] * e[5] * e[8] + e[0] * e[19] * e[4] + e[0] * e[1] * e[22] + e[0] * e[20] * e[5] + e[0] * e[2] * e[23] - e[3] * e[26] * e[8] - e[3] * e[20] * e[2] - e[3] * e[19] * e[1] - e[3] * e[25] * e[7] + 0.5 * e[21] * e2[4] + 0.5 * e[21] * e2[0] + 0.5 * e[21] * e2[6] + 0.5 * e[21] * e2[5] - 0.5 * e[21] * e2[1] - 0.5 * e[21] * e2[7] + 1.5 * e[21] * e2[3] - 0.5 * e[21] * e2[2] - 0.5 * e[21] * e2[8]; a[184] = 0.5 * e2[27] * e[21] + 1.5 * e[21] * e2[30] + 0.5 * e[21] * e2[32] + 0.5 * e[21] * e2[31] + 0.5 * e[21] * e2[33] - 0.5 * e[21] * e2[28] - 0.5 * e[21] * e2[29] - 0.5 * e[21] * e2[34] - 0.5 * e[21] * e2[35] + e[18] * e[27] * e[30] + e[18] * e[29] * e[32] + e[18] * e[28] * e[31] + e[27] * e[28] * e[22] + e[27] * e[19] * e[31] + e[27] * e[29] * e[23] + e[27] * e[20] * e[32] + e[30] * e[31] * e[22] + e[30] * e[32] * e[23] + e[24] * e[30] * e[33] + e[24] * e[32] * e[35] + e[24] * e[31] * e[34] + e[33] * e[31] * e[25] + e[33] * e[22] * e[34] + e[33] * e[32] * e[26] + e[33] * e[23] * e[35] - e[30] * e[29] * e[20] - e[30] * e[35] * e[26] - e[30] * e[28] * e[19] - e[30] * e[34] * e[25]; a[49] = -0.5 * e[26] * e2[4] - 0.5 * e[26] * e2[0] + 0.5 * e[26] * e2[6] + 0.5 * e[26] * e2[5] - 0.5 * e[26] * e2[1] + 0.5 * e[26] * e2[7] - 0.5 * e[26] * e2[3] + 0.5 * e[26] * e2[2] + 1.5 * e[26] * e2[8] + e[20] * e[0] * e[6] + e[20] * e[2] * e[8] + e[5] * e[21] * e[6] + e[5] * e[3] * e[24] + e[5] * e[22] * e[7] + e[5] * e[4] * e[25] + e[5] * e[23] * e[8] + e[23] * e[4] * e[7] + e[23] * e[3] * e[6] + e[8] * e[24] * e[6] + e[8] * e[25] * e[7] + e[2] * e[18] * e[6] + e[2] * e[0] * e[24] + e[2] * e[19] * e[7] + e[2] * e[1] * e[25] - e[8] * e[21] * e[3] - e[8] * e[19] * e[1] - e[8] * e[22] * e[4] - e[8] * e[18] * e[0] + e[20] * e[1] * e[7]; a[154] = e[9] * e[27] * e[30] + e[9] * e[29] * e[32] + e[9] * e[28] * e[31] + e[33] * e[30] * e[15] + e[33] * e[32] * e[17] + e[33] * e[14] * e[35] + e[33] * e[31] * e[16] + e[33] * e[13] * e[34] + e[27] * e[29] * e[14] + e[27] * e[11] * e[32] + e[27] * e[28] * e[13] + e[27] * e[10] * e[31] - e[30] * e[28] * e[10] + e[30] * e[31] * e[13] + e[30] * e[32] * e[14] - e[30] * e[34] * e[16] - e[30] * e[35] * e[17] - e[30] * e[29] * e[11] + e[15] * e[32] * e[35] + e[15] * e[31] * e[34] - 0.5 * e[12] * e2[34] - 0.5 * e[12] * e2[35] + 0.5 * e[12] * e2[27] + 0.5 * e[12] * e2[32] - 0.5 * e[12] * e2[28] - 0.5 * e[12] * e2[29] + 0.5 * e[12] * e2[31] + 0.5 * e[12] * e2[33] + 1.5 * e[12] * e2[30]; a[119] = e[23] * e[30] * e[6] + e[23] * e[3] * e[33] + e[23] * e[31] * e[7] + e[23] * e[4] * e[34] + e[32] * e[21] * e[6] + e[32] * e[3] * e[24] + e[32] * e[22] * e[7] + e[32] * e[4] * e[25] + e[26] * e[33] * e[6] + e[26] * e[34] * e[7] + 3. * e[26] * e[35] * e[8] + e[35] * e[24] * e[6] + e[35] * e[25] * e[7] + e[2] * e[27] * e[24] + e[2] * e[18] * e[33] + e[2] * e[28] * e[25] + e[2] * e[19] * e[34] + e[2] * e[29] * e[26] + e[2] * e[20] * e[35] + e[20] * e[27] * e[6] + e[20] * e[0] * e[33] + e[20] * e[28] * e[7] + e[20] * e[1] * e[34] + e[20] * e[29] * e[8] + e[29] * e[18] * e[6] + e[29] * e[0] * e[24] + e[29] * e[19] * e[7] + e[29] * e[1] * e[25] + e[5] * e[30] * e[24] + e[5] * e[21] * e[33] + e[5] * e[31] * e[25] + e[5] * e[22] * e[34] + e[5] * e[32] * e[26] + e[5] * e[23] * e[35] - e[8] * e[27] * e[18] + e[8] * e[33] * e[24] - e[8] * e[30] * e[21] - e[8] * e[31] * e[22] + e[8] * e[32] * e[23] - e[8] * e[28] * e[19] + e[8] * e[34] * e[25] - e[26] * e[27] * e[0] - e[26] * e[30] * e[3] - e[26] * e[28] * e[1] - e[26] * e[31] * e[4] - e[35] * e[21] * e[3] - e[35] * e[19] * e[1] - e[35] * e[22] * e[4] - e[35] * e[18] * e[0]; a[194] = e[27] * e[29] * e[32] + e[27] * e[28] * e[31] + e[33] * e[32] * e[35] + e[33] * e[31] * e[34] + 0.5 * e3[30] - 0.5 * e[30] * e2[28] - 0.5 * e[30] * e2[29] - 0.5 * e[30] * e2[34] + 0.5 * e[30] * e2[33] + 0.5 * e2[27] * e[30] + 0.5 * e[30] * e2[32] + 0.5 * e[30] * e2[31] - 0.5 * e[30] * e2[35]; a[69] = 0.5 * e2[14] * e[26] + 1.5 * e[26] * e2[17] + 0.5 * e[26] * e2[15] + 0.5 * e[26] * e2[16] + 0.5 * e2[11] * e[26] - 0.5 * e[26] * e2[9] - 0.5 * e[26] * e2[12] - 0.5 * e[26] * e2[10] - 0.5 * e[26] * e2[13] + e[20] * e[11] * e[17] + e[20] * e[9] * e[15] + e[20] * e[10] * e[16] + e[14] * e[21] * e[15] + e[14] * e[12] * e[24] + e[14] * e[23] * e[17] + e[14] * e[22] * e[16] + e[14] * e[13] * e[25] + e[23] * e[12] * e[15] + e[23] * e[13] * e[16] + e[17] * e[24] * e[15] + e[17] * e[25] * e[16] - e[17] * e[18] * e[9] - e[17] * e[21] * e[12] - e[17] * e[19] * e[10] - e[17] * e[22] * e[13] + e[11] * e[18] * e[15] + e[11] * e[9] * e[24] + e[11] * e[19] * e[16] + e[11] * e[10] * e[25]; a[124] = e[0] * e[27] * e[30] + e[0] * e[29] * e[32] + e[0] * e[28] * e[31] + e[30] * e[31] * e[4] + e[30] * e[32] * e[5] + e[6] * e[30] * e[33] + e[6] * e[32] * e[35] + e[6] * e[31] * e[34] + e[27] * e[28] * e[4] + e[27] * e[1] * e[31] + e[27] * e[29] * e[5] + e[27] * e[2] * e[32] + e[33] * e[31] * e[7] + e[33] * e[4] * e[34] + e[33] * e[32] * e[8] + e[33] * e[5] * e[35] - e[30] * e[34] * e[7] - e[30] * e[35] * e[8] - e[30] * e[29] * e[2] - e[30] * e[28] * e[1] + 1.5 * e[3] * e2[30] + 0.5 * e[3] * e2[32] + 0.5 * e[3] * e2[31] + 0.5 * e[3] * e2[27] - 0.5 * e[3] * e2[28] - 0.5 * e[3] * e2[29] + 0.5 * e[3] * e2[33] - 0.5 * e[3] * e2[34] - 0.5 * e[3] * e2[35]; a[39] = 0.5 * e2[14] * e[8] + 1.5 * e2[17] * e[8] + 0.5 * e[8] * e2[15] + 0.5 * e[8] * e2[16] - 0.5 * e[8] * e2[9] + 0.5 * e[8] * e2[11] - 0.5 * e[8] * e2[12] - 0.5 * e[8] * e2[10] - 0.5 * e[8] * e2[13] + e[14] * e[12] * e[6] + e[14] * e[3] * e[15] + e[14] * e[13] * e[7] + e[14] * e[4] * e[16] + e[14] * e[5] * e[17] + e[17] * e[15] * e[6] + e[17] * e[16] * e[7] + e[2] * e[11] * e[17] + e[2] * e[9] * e[15] + e[2] * e[10] * e[16] + e[5] * e[12] * e[15] + e[5] * e[13] * e[16] + e[11] * e[9] * e[6] + e[11] * e[0] * e[15] + e[11] * e[10] * e[7] + e[11] * e[1] * e[16] - e[17] * e[10] * e[1] - e[17] * e[13] * e[4] - e[17] * e[9] * e[0] - e[17] * e[12] * e[3]; a[4] = -0.5 * e[3] * e2[1] - 0.5 * e[3] * e2[7] + 0.5 * e3[3] - 0.5 * e[3] * e2[8] + e[0] * e[2] * e[5] + 0.5 * e[3] * e2[6] + 0.5 * e[3] * e2[4] - 0.5 * e[3] * e2[2] + e[0] * e[1] * e[4] + e[6] * e[4] * e[7] + 0.5 * e2[0] * e[3] + 0.5 * e[3] * e2[5] + e[6] * e[5] * e[8]; a[139] = 0.5 * e2[23] * e[17] + 1.5 * e2[26] * e[17] + 0.5 * e[17] * e2[25] + 0.5 * e[17] * e2[24] - 0.5 * e[17] * e2[18] - 0.5 * e[17] * e2[19] + 0.5 * e[17] * e2[20] - 0.5 * e[17] * e2[22] - 0.5 * e[17] * e2[21] + e[23] * e[21] * e[15] + e[23] * e[12] * e[24] + e[23] * e[14] * e[26] + e[23] * e[22] * e[16] + e[23] * e[13] * e[25] + e[26] * e[24] * e[15] + e[26] * e[25] * e[16] + e[11] * e[19] * e[25] + e[11] * e[18] * e[24] + e[11] * e[20] * e[26] + e[14] * e[22] * e[25] + e[14] * e[21] * e[24] + e[20] * e[18] * e[15] + e[20] * e[9] * e[24] + e[20] * e[19] * e[16] + e[20] * e[10] * e[25] - e[26] * e[18] * e[9] - e[26] * e[21] * e[12] - e[26] * e[19] * e[10] - e[26] * e[22] * e[13]; a[74] = -e[12] * e[34] * e[16] - e[12] * e[35] * e[17] - e[12] * e[29] * e[11] + e[9] * e[27] * e[12] + e[9] * e[29] * e[14] + e[9] * e[11] * e[32] + e[9] * e[28] * e[13] + e[9] * e[10] * e[31] + e[27] * e[11] * e[14] + e[27] * e[10] * e[13] + e[12] * e[32] * e[14] + e[12] * e[31] * e[13] + e[15] * e[12] * e[33] + e[15] * e[32] * e[17] + e[15] * e[14] * e[35] + e[15] * e[31] * e[16] + e[15] * e[13] * e[34] + e[33] * e[14] * e[17] + e[33] * e[13] * e[16] - e[12] * e[28] * e[10] + 0.5 * e2[9] * e[30] - 0.5 * e[30] * e2[16] - 0.5 * e[30] * e2[11] + 1.5 * e[30] * e2[12] + 0.5 * e[30] * e2[15] - 0.5 * e[30] * e2[17] - 0.5 * e[30] * e2[10] + 0.5 * e[30] * e2[14] + 0.5 * e[30] * e2[13]; a[149] = e[32] * e[22] * e[16] + e[32] * e[13] * e[25] - e[17] * e[27] * e[18] + e[17] * e[33] * e[24] - e[17] * e[30] * e[21] + e[17] * e[29] * e[20] + 3. * e[17] * e[35] * e[26] - e[17] * e[31] * e[22] - e[17] * e[28] * e[19] + e[17] * e[34] * e[25] + e[20] * e[27] * e[15] + e[20] * e[9] * e[33] + e[20] * e[28] * e[16] + e[20] * e[10] * e[34] + e[29] * e[18] * e[15] + e[29] * e[9] * e[24] + e[29] * e[19] * e[16] + e[29] * e[10] * e[25] - e[26] * e[27] * e[9] - e[26] * e[30] * e[12] - e[26] * e[28] * e[10] - e[26] * e[31] * e[13] + e[26] * e[33] * e[15] + e[26] * e[34] * e[16] + e[35] * e[24] * e[15] + e[35] * e[25] * e[16] - e[35] * e[18] * e[9] - e[35] * e[21] * e[12] - e[35] * e[19] * e[10] - e[35] * e[22] * e[13] + e[14] * e[30] * e[24] + e[14] * e[21] * e[33] + e[14] * e[31] * e[25] + e[14] * e[22] * e[34] + e[14] * e[32] * e[26] + e[14] * e[23] * e[35] + e[11] * e[27] * e[24] + e[11] * e[18] * e[33] + e[11] * e[28] * e[25] + e[11] * e[19] * e[34] + e[11] * e[29] * e[26] + e[11] * e[20] * e[35] + e[23] * e[30] * e[15] + e[23] * e[12] * e[33] + e[23] * e[32] * e[17] + e[23] * e[31] * e[16] + e[23] * e[13] * e[34] + e[32] * e[21] * e[15] + e[32] * e[12] * e[24]; a[84] = e[6] * e[23] * e[17] + e[6] * e[14] * e[26] + e[6] * e[22] * e[16] + e[6] * e[13] * e[25] + e[0] * e[20] * e[14] + e[0] * e[11] * e[23] + e[0] * e[19] * e[13] + e[0] * e[10] * e[22] - e[12] * e[26] * e[8] - e[12] * e[20] * e[2] - e[12] * e[19] * e[1] + e[12] * e[22] * e[4] - e[12] * e[25] * e[7] + e[12] * e[23] * e[5] - e[21] * e[11] * e[2] - e[21] * e[10] * e[1] + e[21] * e[13] * e[4] - e[21] * e[16] * e[7] + e[21] * e[14] * e[5] - e[21] * e[17] * e[8] + e[15] * e[3] * e[24] + e[15] * e[22] * e[7] + e[15] * e[4] * e[25] + e[15] * e[23] * e[8] + e[15] * e[5] * e[26] - e[3] * e[25] * e[16] - e[3] * e[26] * e[17] - e[3] * e[20] * e[11] - e[3] * e[19] * e[10] + e[24] * e[13] * e[7] + e[24] * e[4] * e[16] + e[24] * e[14] * e[8] + e[24] * e[5] * e[17] + e[9] * e[18] * e[3] + e[9] * e[0] * e[21] + e[9] * e[19] * e[4] + e[9] * e[1] * e[22] + e[9] * e[20] * e[5] + e[9] * e[2] * e[23] + e[18] * e[0] * e[12] + e[18] * e[10] * e[4] + e[18] * e[1] * e[13] + e[18] * e[11] * e[5] + e[18] * e[2] * e[14] + 3. * e[3] * e[21] * e[12] + e[3] * e[23] * e[14] + e[3] * e[22] * e[13] + e[6] * e[21] * e[15] + e[6] * e[12] * e[24]; a[29] = 0.5 * e2[5] * e[17] + 1.5 * e[17] * e2[8] + 0.5 * e[17] * e2[7] + 0.5 * e[17] * e2[6] + 0.5 * e2[2] * e[17] - 0.5 * e[17] * e2[4] - 0.5 * e[17] * e2[0] - 0.5 * e[17] * e2[1] - 0.5 * e[17] * e2[3] + e[11] * e[1] * e[7] + e[11] * e[0] * e[6] + e[11] * e[2] * e[8] + e[5] * e[12] * e[6] + e[5] * e[3] * e[15] + e[5] * e[13] * e[7] + e[5] * e[4] * e[16] + e[5] * e[14] * e[8] + e[14] * e[4] * e[7] + e[14] * e[3] * e[6] + e[8] * e[15] * e[6] + e[8] * e[16] * e[7] - e[8] * e[10] * e[1] - e[8] * e[13] * e[4] - e[8] * e[9] * e[0] - e[8] * e[12] * e[3] + e[2] * e[9] * e[6] + e[2] * e[0] * e[15] + e[2] * e[10] * e[7] + e[2] * e[1] * e[16]; a[54] = e[6] * e[4] * e[34] + e[6] * e[32] * e[8] + e[6] * e[5] * e[35] + e[33] * e[4] * e[7] + e[33] * e[5] * e[8] + e[0] * e[27] * e[3] + e[0] * e[28] * e[4] + e[0] * e[1] * e[31] + e[0] * e[29] * e[5] + e[0] * e[2] * e[32] - e[3] * e[34] * e[7] + e[3] * e[32] * e[5] + e[3] * e[33] * e[6] - e[3] * e[35] * e[8] - e[3] * e[29] * e[2] - e[3] * e[28] * e[1] + e[3] * e[31] * e[4] + e[27] * e[1] * e[4] + e[27] * e[2] * e[5] + e[6] * e[31] * e[7] + 0.5 * e[30] * e2[4] + 0.5 * e[30] * e2[6] + 0.5 * e[30] * e2[5] - 0.5 * e[30] * e2[1] - 0.5 * e[30] * e2[7] - 0.5 * e[30] * e2[2] - 0.5 * e[30] * e2[8] + 0.5 * e2[0] * e[30] + 1.5 * e[30] * e2[3]; a[109] = 0.5 * e2[23] * e[8] + 1.5 * e2[26] * e[8] - 0.5 * e[8] * e2[18] - 0.5 * e[8] * e2[19] - 0.5 * e[8] * e2[22] + 0.5 * e[8] * e2[24] - 0.5 * e[8] * e2[21] + 0.5 * e[8] * e2[25] + 0.5 * e2[20] * e[8] + e[20] * e[18] * e[6] + e[20] * e[0] * e[24] + e[20] * e[19] * e[7] + e[20] * e[1] * e[25] + e[20] * e[2] * e[26] + e[23] * e[21] * e[6] + e[23] * e[3] * e[24] + e[23] * e[22] * e[7] + e[23] * e[4] * e[25] + e[23] * e[5] * e[26] - e[26] * e[21] * e[3] - e[26] * e[19] * e[1] - e[26] * e[22] * e[4] - e[26] * e[18] * e[0] + e[26] * e[25] * e[7] + e[26] * e[24] * e[6] + e[2] * e[19] * e[25] + e[2] * e[18] * e[24] + e[5] * e[22] * e[25] + e[5] * e[21] * e[24]; a[175] = e[19] * e[27] * e[21] + e[19] * e[18] * e[30] + e[19] * e[28] * e[22] + e[19] * e[29] * e[23] + e[19] * e[20] * e[32] + e[28] * e[18] * e[21] + e[28] * e[20] * e[23] + e[22] * e[30] * e[21] + e[22] * e[32] * e[23] + e[25] * e[30] * e[24] + e[25] * e[21] * e[33] + e[25] * e[22] * e[34] + e[25] * e[32] * e[26] + e[25] * e[23] * e[35] + e[34] * e[21] * e[24] + e[34] * e[23] * e[26] - e[22] * e[27] * e[18] - e[22] * e[33] * e[24] - e[22] * e[29] * e[20] - e[22] * e[35] * e[26] + 0.5 * e2[19] * e[31] + 1.5 * e[31] * e2[22] + 0.5 * e[31] * e2[21] + 0.5 * e[31] * e2[23] + 0.5 * e[31] * e2[25] - 0.5 * e[31] * e2[26] - 0.5 * e[31] * e2[18] - 0.5 * e[31] * e2[20] - 0.5 * e[31] * e2[24]; a[15] = -0.5 * e[13] * e2[15] + 0.5 * e[13] * e2[16] + 0.5 * e[13] * e2[12] + e[16] * e[12] * e[15] + 0.5 * e3[13] + e[10] * e[11] * e[14] + 0.5 * e[13] * e2[14] - 0.5 * e[13] * e2[17] - 0.5 * e[13] * e2[11] - 0.5 * e[13] * e2[9] + 0.5 * e2[10] * e[13] + e[10] * e[9] * e[12] + e[16] * e[14] * e[17]; a[95] = -e[13] * e[29] * e[2] - e[31] * e[11] * e[2] - e[31] * e[15] * e[6] - e[31] * e[9] * e[0] + e[31] * e[14] * e[5] + e[31] * e[12] * e[3] - e[31] * e[17] * e[8] + e[16] * e[30] * e[6] + e[16] * e[3] * e[33] + e[16] * e[4] * e[34] + e[16] * e[32] * e[8] + e[16] * e[5] * e[35] - e[4] * e[27] * e[9] + e[4] * e[28] * e[10] - e[4] * e[33] * e[15] - e[4] * e[35] * e[17] - e[4] * e[29] * e[11] + e[34] * e[12] * e[6] + e[34] * e[3] * e[15] + e[34] * e[14] * e[8] + e[34] * e[5] * e[17] + e[10] * e[27] * e[3] + e[10] * e[0] * e[30] + e[10] * e[29] * e[5] + e[10] * e[2] * e[32] + e[28] * e[9] * e[3] + e[28] * e[0] * e[12] + e[28] * e[11] * e[5] + e[28] * e[2] * e[14] + e[4] * e[30] * e[12] + e[4] * e[32] * e[14] + 3. * e[4] * e[31] * e[13] + e[7] * e[30] * e[15] + e[7] * e[12] * e[33] + e[7] * e[32] * e[17] + e[7] * e[14] * e[35] + e[7] * e[31] * e[16] + e[7] * e[13] * e[34] + e[1] * e[27] * e[12] + e[1] * e[9] * e[30] + e[1] * e[29] * e[14] + e[1] * e[11] * e[32] + e[1] * e[28] * e[13] + e[1] * e[10] * e[31] - e[13] * e[27] * e[0] + e[13] * e[32] * e[5] - e[13] * e[33] * e[6] + e[13] * e[30] * e[3] - e[13] * e[35] * e[8]; a[165] = e[25] * e[23] * e[26] + e[19] * e[20] * e[23] + e[19] * e[18] * e[21] + e[25] * e[21] * e[24] + 0.5 * e3[22] + 0.5 * e[22] * e2[23] + 0.5 * e2[19] * e[22] - 0.5 * e[22] * e2[18] - 0.5 * e[22] * e2[24] + 0.5 * e[22] * e2[21] + 0.5 * e[22] * e2[25] - 0.5 * e[22] * e2[20] - 0.5 * e[22] * e2[26]; a[55] = e[34] * e[5] * e[8] + e[1] * e[27] * e[3] + e[1] * e[0] * e[30] + e[1] * e[28] * e[4] + e[1] * e[29] * e[5] + e[1] * e[2] * e[32] - e[4] * e[27] * e[0] + e[4] * e[34] * e[7] + e[4] * e[32] * e[5] - e[4] * e[33] * e[6] + e[4] * e[30] * e[3] - e[4] * e[35] * e[8] - e[4] * e[29] * e[2] + e[28] * e[0] * e[3] + e[28] * e[2] * e[5] + e[7] * e[30] * e[6] + e[7] * e[3] * e[33] + e[7] * e[32] * e[8] + e[7] * e[5] * e[35] + e[34] * e[3] * e[6] + 0.5 * e2[1] * e[31] + 1.5 * e[31] * e2[4] - 0.5 * e[31] * e2[0] - 0.5 * e[31] * e2[6] + 0.5 * e[31] * e2[5] + 0.5 * e[31] * e2[7] + 0.5 * e[31] * e2[3] - 0.5 * e[31] * e2[2] - 0.5 * e[31] * e2[8]; a[85] = e[1] * e[20] * e[14] + e[1] * e[11] * e[23] + e[13] * e[21] * e[3] - e[13] * e[26] * e[8] - e[13] * e[20] * e[2] - e[13] * e[18] * e[0] + e[13] * e[23] * e[5] - e[13] * e[24] * e[6] - e[22] * e[11] * e[2] - e[22] * e[15] * e[6] - e[22] * e[9] * e[0] + e[22] * e[14] * e[5] + e[22] * e[12] * e[3] - e[22] * e[17] * e[8] + e[16] * e[21] * e[6] + e[16] * e[3] * e[24] + e[16] * e[4] * e[25] + e[16] * e[23] * e[8] + e[16] * e[5] * e[26] - e[4] * e[24] * e[15] - e[4] * e[26] * e[17] - e[4] * e[20] * e[11] - e[4] * e[18] * e[9] + e[25] * e[12] * e[6] + e[25] * e[3] * e[15] + e[25] * e[14] * e[8] + e[25] * e[5] * e[17] + e[10] * e[18] * e[3] + e[10] * e[0] * e[21] + e[10] * e[19] * e[4] + e[10] * e[1] * e[22] + e[10] * e[20] * e[5] + e[10] * e[2] * e[23] + e[19] * e[9] * e[3] + e[19] * e[0] * e[12] + e[19] * e[1] * e[13] + e[19] * e[11] * e[5] + e[19] * e[2] * e[14] + e[4] * e[21] * e[12] + e[4] * e[23] * e[14] + 3. * e[4] * e[22] * e[13] + e[7] * e[21] * e[15] + e[7] * e[12] * e[24] + e[7] * e[23] * e[17] + e[7] * e[14] * e[26] + e[7] * e[22] * e[16] + e[7] * e[13] * e[25] + e[1] * e[18] * e[12] + e[1] * e[9] * e[21]; a[75] = e[10] * e[27] * e[12] + e[10] * e[9] * e[30] + e[10] * e[29] * e[14] + e[10] * e[11] * e[32] + e[10] * e[28] * e[13] + e[28] * e[11] * e[14] + e[28] * e[9] * e[12] + e[13] * e[30] * e[12] + e[13] * e[32] * e[14] + e[16] * e[30] * e[15] + e[16] * e[12] * e[33] + e[16] * e[32] * e[17] + e[16] * e[14] * e[35] + e[16] * e[13] * e[34] + e[34] * e[14] * e[17] + e[34] * e[12] * e[15] - e[13] * e[27] * e[9] - e[13] * e[33] * e[15] - e[13] * e[35] * e[17] - e[13] * e[29] * e[11] + 0.5 * e2[10] * e[31] + 0.5 * e[31] * e2[16] - 0.5 * e[31] * e2[9] - 0.5 * e[31] * e2[11] + 0.5 * e[31] * e2[12] - 0.5 * e[31] * e2[15] - 0.5 * e[31] * e2[17] + 0.5 * e[31] * e2[14] + 1.5 * e[31] * e2[13]; a[5] = -0.5 * e[4] * e2[6] - 0.5 * e[4] * e2[0] + e[1] * e[2] * e[5] + 0.5 * e[4] * e2[7] + e[1] * e[0] * e[3] + e[7] * e[5] * e[8] - 0.5 * e[4] * e2[8] + 0.5 * e[4] * e2[3] + 0.5 * e[4] * e2[5] + e[7] * e[3] * e[6] - 0.5 * e[4] * e2[2] + 0.5 * e3[4] + 0.5 * e2[1] * e[4]; a[195] = e[34] * e[32] * e[35] - 0.5 * e[31] * e2[35] + 0.5 * e[31] * e2[34] + 0.5 * e2[28] * e[31] + 0.5 * e3[31] + 0.5 * e[31] * e2[32] + e[34] * e[30] * e[33] - 0.5 * e[31] * e2[27] + 0.5 * e[31] * e2[30] - 0.5 * e[31] * e2[33] - 0.5 * e[31] * e2[29] + e[28] * e[29] * e[32] + e[28] * e[27] * e[30]; a[125] = e[1] * e[27] * e[30] + e[1] * e[29] * e[32] + e[1] * e[28] * e[31] + e[31] * e[30] * e[3] + e[31] * e[32] * e[5] + e[7] * e[30] * e[33] + e[7] * e[32] * e[35] + e[7] * e[31] * e[34] + e[28] * e[27] * e[3] + e[28] * e[0] * e[30] + e[28] * e[29] * e[5] + e[28] * e[2] * e[32] + e[34] * e[30] * e[6] + e[34] * e[3] * e[33] + e[34] * e[32] * e[8] + e[34] * e[5] * e[35] - e[31] * e[27] * e[0] - e[31] * e[33] * e[6] - e[31] * e[35] * e[8] - e[31] * e[29] * e[2] + 0.5 * e[4] * e2[30] + 0.5 * e[4] * e2[32] + 1.5 * e[4] * e2[31] - 0.5 * e[4] * e2[27] + 0.5 * e[4] * e2[28] - 0.5 * e[4] * e2[29] - 0.5 * e[4] * e2[33] + 0.5 * e[4] * e2[34] - 0.5 * e[4] * e2[35]; a[185] = 0.5 * e[22] * e2[30] + 0.5 * e[22] * e2[32] + 1.5 * e[22] * e2[31] + 0.5 * e[22] * e2[34] - 0.5 * e[22] * e2[27] - 0.5 * e[22] * e2[29] - 0.5 * e[22] * e2[33] - 0.5 * e[22] * e2[35] + e[28] * e[18] * e[30] + e[28] * e[29] * e[23] + e[28] * e[20] * e[32] + e[31] * e[30] * e[21] + e[31] * e[32] * e[23] + e[25] * e[30] * e[33] + e[25] * e[32] * e[35] + e[25] * e[31] * e[34] + e[34] * e[30] * e[24] + e[34] * e[21] * e[33] + e[34] * e[32] * e[26] + e[34] * e[23] * e[35] - e[31] * e[27] * e[18] - e[31] * e[33] * e[24] - e[31] * e[29] * e[20] - e[31] * e[35] * e[26] + e[19] * e[27] * e[30] + e[19] * e[29] * e[32] + e[19] * e[28] * e[31] + e[28] * e[27] * e[21] + 0.5 * e2[28] * e[22]; a[155] = e[16] * e[30] * e[33] + e[16] * e[32] * e[35] + e[10] * e[27] * e[30] + e[10] * e[29] * e[32] + e[10] * e[28] * e[31] + e[34] * e[30] * e[15] + e[34] * e[12] * e[33] + e[34] * e[32] * e[17] + e[34] * e[14] * e[35] + e[34] * e[31] * e[16] + e[28] * e[27] * e[12] + e[28] * e[9] * e[30] + e[28] * e[29] * e[14] + e[28] * e[11] * e[32] - e[31] * e[27] * e[9] + e[31] * e[30] * e[12] + e[31] * e[32] * e[14] - e[31] * e[33] * e[15] - e[31] * e[35] * e[17] - e[31] * e[29] * e[11] - 0.5 * e[13] * e2[27] + 0.5 * e[13] * e2[32] + 0.5 * e[13] * e2[28] - 0.5 * e[13] * e2[29] + 1.5 * e[13] * e2[31] - 0.5 * e[13] * e2[33] + 0.5 * e[13] * e2[30] + 0.5 * e[13] * e2[34] - 0.5 * e[13] * e2[35]; a[134] = e[21] * e[23] * e[14] + e[21] * e[22] * e[13] + e[24] * e[21] * e[15] + e[24] * e[23] * e[17] + e[24] * e[14] * e[26] + e[24] * e[22] * e[16] + e[24] * e[13] * e[25] + e[15] * e[22] * e[25] + e[15] * e[23] * e[26] + e[9] * e[19] * e[22] + e[9] * e[18] * e[21] + e[9] * e[20] * e[23] + e[18] * e[20] * e[14] + e[18] * e[11] * e[23] + e[18] * e[19] * e[13] + e[18] * e[10] * e[22] - e[21] * e[25] * e[16] - e[21] * e[26] * e[17] - e[21] * e[20] * e[11] - e[21] * e[19] * e[10] + 1.5 * e2[21] * e[12] + 0.5 * e[12] * e2[24] - 0.5 * e[12] * e2[26] + 0.5 * e[12] * e2[18] + 0.5 * e[12] * e2[23] - 0.5 * e[12] * e2[19] - 0.5 * e[12] * e2[20] + 0.5 * e[12] * e2[22] - 0.5 * e[12] * e2[25]; a[144] = -e[12] * e[29] * e[20] - e[12] * e[35] * e[26] - e[12] * e[28] * e[19] - e[12] * e[34] * e[25] + e[18] * e[29] * e[14] + e[18] * e[11] * e[32] + e[18] * e[28] * e[13] + e[18] * e[10] * e[31] + e[27] * e[20] * e[14] + e[27] * e[11] * e[23] + e[27] * e[19] * e[13] + e[27] * e[10] * e[22] + e[15] * e[30] * e[24] + e[15] * e[21] * e[33] + e[15] * e[31] * e[25] + e[15] * e[22] * e[34] + e[15] * e[32] * e[26] + e[15] * e[23] * e[35] - e[21] * e[28] * e[10] - e[21] * e[34] * e[16] - e[21] * e[35] * e[17] - e[21] * e[29] * e[11] - e[30] * e[25] * e[16] - e[30] * e[26] * e[17] - e[30] * e[20] * e[11] - e[30] * e[19] * e[10] + e[24] * e[32] * e[17] + e[24] * e[14] * e[35] + e[24] * e[31] * e[16] + e[24] * e[13] * e[34] + e[33] * e[23] * e[17] + e[33] * e[14] * e[26] + e[33] * e[22] * e[16] + e[33] * e[13] * e[25] + 3. * e[12] * e[30] * e[21] + e[12] * e[31] * e[22] + e[12] * e[32] * e[23] + e[9] * e[27] * e[21] + e[9] * e[18] * e[30] + e[9] * e[28] * e[22] + e[9] * e[19] * e[31] + e[9] * e[29] * e[23] + e[9] * e[20] * e[32] + e[21] * e[32] * e[14] + e[21] * e[31] * e[13] + e[30] * e[23] * e[14] + e[30] * e[22] * e[13] + e[12] * e[27] * e[18] + e[12] * e[33] * e[24]; a[24] = e[0] * e[11] * e[5] + e[0] * e[2] * e[14] + e[9] * e[1] * e[4] + e[9] * e[0] * e[3] + e[9] * e[2] * e[5] + e[3] * e[13] * e[4] + e[3] * e[14] * e[5] + e[6] * e[3] * e[15] + e[6] * e[13] * e[7] + e[6] * e[4] * e[16] + e[6] * e[14] * e[8] + e[6] * e[5] * e[17] + e[15] * e[4] * e[7] + e[15] * e[5] * e[8] - e[3] * e[11] * e[2] - e[3] * e[10] * e[1] - e[3] * e[16] * e[7] - e[3] * e[17] * e[8] + e[0] * e[10] * e[4] + e[0] * e[1] * e[13] + 1.5 * e[12] * e2[3] + 0.5 * e[12] * e2[4] + 0.5 * e[12] * e2[5] + 0.5 * e[12] * e2[6] + 0.5 * e2[0] * e[12] - 0.5 * e[12] * e2[1] - 0.5 * e[12] * e2[7] - 0.5 * e[12] * e2[2] - 0.5 * e[12] * e2[8]; a[104] = e[21] * e[24] * e[6] + e[0] * e[19] * e[22] + e[0] * e[20] * e[23] + e[24] * e[22] * e[7] + e[24] * e[4] * e[25] + e[24] * e[23] * e[8] + e[24] * e[5] * e[26] + e[6] * e[22] * e[25] + e[6] * e[23] * e[26] + e[18] * e[0] * e[21] + e[18] * e[19] * e[4] + e[18] * e[1] * e[22] + e[18] * e[20] * e[5] + e[18] * e[2] * e[23] + e[21] * e[22] * e[4] + e[21] * e[23] * e[5] - e[21] * e[26] * e[8] - e[21] * e[20] * e[2] - e[21] * e[19] * e[1] - e[21] * e[25] * e[7] + 1.5 * e2[21] * e[3] + 0.5 * e[3] * e2[22] + 0.5 * e[3] * e2[23] + 0.5 * e[3] * e2[24] - 0.5 * e[3] * e2[26] - 0.5 * e[3] * e2[19] - 0.5 * e[3] * e2[20] - 0.5 * e[3] * e2[25] + 0.5 * e2[18] * e[3]; a[76] = e[11] * e[27] * e[12] + e[11] * e[9] * e[30] + e[11] * e[29] * e[14] + e[11] * e[28] * e[13] + e[11] * e[10] * e[31] + e[29] * e[9] * e[12] + e[29] * e[10] * e[13] + e[14] * e[30] * e[12] + e[14] * e[31] * e[13] + e[17] * e[30] * e[15] + e[17] * e[12] * e[33] + e[17] * e[14] * e[35] + e[17] * e[31] * e[16] + e[17] * e[13] * e[34] + e[35] * e[12] * e[15] + e[35] * e[13] * e[16] - e[14] * e[27] * e[9] - e[14] * e[28] * e[10] - e[14] * e[33] * e[15] - e[14] * e[34] * e[16] + 0.5 * e2[11] * e[32] - 0.5 * e[32] * e2[16] - 0.5 * e[32] * e2[9] + 0.5 * e[32] * e2[12] - 0.5 * e[32] * e2[15] + 0.5 * e[32] * e2[17] - 0.5 * e[32] * e2[10] + 1.5 * e[32] * e2[14] + 0.5 * e[32] * e2[13]; a[6] = e[8] * e[3] * e[6] + 0.5 * e2[2] * e[5] - 0.5 * e[5] * e2[0] + 0.5 * e[5] * e2[4] - 0.5 * e[5] * e2[6] + 0.5 * e[5] * e2[8] + e[8] * e[4] * e[7] + 0.5 * e3[5] + e[2] * e[0] * e[3] + 0.5 * e[5] * e2[3] - 0.5 * e[5] * e2[7] + e[2] * e[1] * e[4] - 0.5 * e[5] * e2[1]; a[56] = e[2] * e[27] * e[3] + e[2] * e[0] * e[30] + e[2] * e[28] * e[4] + e[2] * e[1] * e[31] + e[2] * e[29] * e[5] - e[5] * e[27] * e[0] - e[5] * e[34] * e[7] - e[5] * e[33] * e[6] + e[5] * e[30] * e[3] + e[5] * e[35] * e[8] - e[5] * e[28] * e[1] + e[5] * e[31] * e[4] + e[29] * e[1] * e[4] + e[29] * e[0] * e[3] + e[8] * e[30] * e[6] + e[8] * e[3] * e[33] + e[8] * e[31] * e[7] + e[8] * e[4] * e[34] + e[35] * e[4] * e[7] + e[35] * e[3] * e[6] + 0.5 * e2[2] * e[32] + 1.5 * e[32] * e2[5] + 0.5 * e[32] * e2[4] - 0.5 * e[32] * e2[0] - 0.5 * e[32] * e2[6] - 0.5 * e[32] * e2[1] - 0.5 * e[32] * e2[7] + 0.5 * e[32] * e2[3] + 0.5 * e[32] * e2[8]; a[86] = -e[14] * e[19] * e[1] + e[14] * e[22] * e[4] - e[14] * e[18] * e[0] - e[14] * e[25] * e[7] - e[14] * e[24] * e[6] - e[23] * e[10] * e[1] + e[23] * e[13] * e[4] - e[23] * e[16] * e[7] - e[23] * e[15] * e[6] - e[23] * e[9] * e[0] + e[23] * e[12] * e[3] + e[17] * e[21] * e[6] + e[17] * e[3] * e[24] + e[17] * e[22] * e[7] + e[17] * e[4] * e[25] + e[17] * e[5] * e[26] - e[5] * e[24] * e[15] - e[5] * e[25] * e[16] - e[5] * e[18] * e[9] - e[5] * e[19] * e[10] + e[26] * e[12] * e[6] + e[26] * e[3] * e[15] + e[26] * e[13] * e[7] + e[26] * e[4] * e[16] + e[11] * e[18] * e[3] + e[11] * e[0] * e[21] + e[11] * e[19] * e[4] + e[11] * e[1] * e[22] + e[11] * e[20] * e[5] + e[11] * e[2] * e[23] + e[20] * e[9] * e[3] + e[20] * e[0] * e[12] + e[20] * e[10] * e[4] + e[20] * e[1] * e[13] + e[20] * e[2] * e[14] + e[5] * e[21] * e[12] + 3. * e[5] * e[23] * e[14] + e[5] * e[22] * e[13] + e[8] * e[21] * e[15] + e[8] * e[12] * e[24] + e[8] * e[23] * e[17] + e[8] * e[14] * e[26] + e[8] * e[22] * e[16] + e[8] * e[13] * e[25] + e[2] * e[18] * e[12] + e[2] * e[9] * e[21] + e[2] * e[19] * e[13] + e[2] * e[10] * e[22] + e[14] * e[21] * e[3]; a[156] = -0.5 * e[14] * e2[27] + 1.5 * e[14] * e2[32] - 0.5 * e[14] * e2[28] + 0.5 * e[14] * e2[29] + 0.5 * e[14] * e2[31] - 0.5 * e[14] * e2[33] + 0.5 * e[14] * e2[30] - 0.5 * e[14] * e2[34] + 0.5 * e[14] * e2[35] + e[11] * e[27] * e[30] + e[11] * e[29] * e[32] + e[11] * e[28] * e[31] + e[35] * e[30] * e[15] + e[35] * e[12] * e[33] + e[35] * e[32] * e[17] + e[35] * e[31] * e[16] + e[35] * e[13] * e[34] + e[29] * e[27] * e[12] + e[29] * e[9] * e[30] + e[29] * e[28] * e[13] + e[29] * e[10] * e[31] - e[32] * e[27] * e[9] + e[32] * e[30] * e[12] - e[32] * e[28] * e[10] + e[32] * e[31] * e[13] - e[32] * e[33] * e[15] - e[32] * e[34] * e[16] + e[17] * e[30] * e[33] + e[17] * e[31] * e[34]; a[186] = -0.5 * e[23] * e2[33] - 0.5 * e[23] * e2[34] + 0.5 * e2[29] * e[23] + 0.5 * e[23] * e2[30] + 1.5 * e[23] * e2[32] + 0.5 * e[23] * e2[31] + 0.5 * e[23] * e2[35] - 0.5 * e[23] * e2[27] - 0.5 * e[23] * e2[28] + e[32] * e[30] * e[21] + e[32] * e[31] * e[22] + e[26] * e[30] * e[33] + e[26] * e[32] * e[35] + e[26] * e[31] * e[34] + e[35] * e[30] * e[24] + e[35] * e[21] * e[33] + e[35] * e[31] * e[25] + e[35] * e[22] * e[34] - e[32] * e[27] * e[18] - e[32] * e[33] * e[24] - e[32] * e[28] * e[19] - e[32] * e[34] * e[25] + e[20] * e[27] * e[30] + e[20] * e[29] * e[32] + e[20] * e[28] * e[31] + e[29] * e[27] * e[21] + e[29] * e[18] * e[30] + e[29] * e[28] * e[22] + e[29] * e[19] * e[31]; a[126] = e[2] * e[27] * e[30] + e[2] * e[29] * e[32] + e[2] * e[28] * e[31] + e[32] * e[30] * e[3] + e[32] * e[31] * e[4] + e[8] * e[30] * e[33] + e[8] * e[32] * e[35] + e[8] * e[31] * e[34] + e[29] * e[27] * e[3] + e[29] * e[0] * e[30] + e[29] * e[28] * e[4] + e[29] * e[1] * e[31] + e[35] * e[30] * e[6] + e[35] * e[3] * e[33] + e[35] * e[31] * e[7] + e[35] * e[4] * e[34] - e[32] * e[27] * e[0] - e[32] * e[34] * e[7] - e[32] * e[33] * e[6] - e[32] * e[28] * e[1] + 0.5 * e[5] * e2[30] + 1.5 * e[5] * e2[32] + 0.5 * e[5] * e2[31] - 0.5 * e[5] * e2[27] - 0.5 * e[5] * e2[28] + 0.5 * e[5] * e2[29] - 0.5 * e[5] * e2[33] - 0.5 * e[5] * e2[34] + 0.5 * e[5] * e2[35]; a[196] = 0.5 * e[32] * e2[31] + 0.5 * e[32] * e2[35] - 0.5 * e[32] * e2[27] + e[29] * e[27] * e[30] + e[29] * e[28] * e[31] + e[35] * e[30] * e[33] + e[35] * e[31] * e[34] + 0.5 * e2[29] * e[32] + 0.5 * e3[32] - 0.5 * e[32] * e2[33] - 0.5 * e[32] * e2[34] + 0.5 * e[32] * e2[30] - 0.5 * e[32] * e2[28]; a[25] = e[10] * e[1] * e[4] + e[10] * e[0] * e[3] + e[10] * e[2] * e[5] + e[4] * e[12] * e[3] + e[4] * e[14] * e[5] + e[7] * e[12] * e[6] + e[7] * e[3] * e[15] + e[7] * e[4] * e[16] + e[7] * e[14] * e[8] + e[7] * e[5] * e[17] + e[16] * e[3] * e[6] + e[16] * e[5] * e[8] - e[4] * e[11] * e[2] - e[4] * e[15] * e[6] - e[4] * e[9] * e[0] - e[4] * e[17] * e[8] + e[1] * e[9] * e[3] + e[1] * e[0] * e[12] + e[1] * e[11] * e[5] + e[1] * e[2] * e[14] + 1.5 * e[13] * e2[4] + 0.5 * e[13] * e2[3] + 0.5 * e[13] * e2[5] + 0.5 * e[13] * e2[7] + 0.5 * e2[1] * e[13] - 0.5 * e[13] * e2[0] - 0.5 * e[13] * e2[6] - 0.5 * e[13] * e2[2] - 0.5 * e[13] * e2[8]; a[105] = e[25] * e[21] * e[6] + e[25] * e[3] * e[24] + e[25] * e[23] * e[8] + e[25] * e[5] * e[26] + e[7] * e[21] * e[24] + e[7] * e[23] * e[26] + e[19] * e[18] * e[3] + e[19] * e[0] * e[21] + e[19] * e[1] * e[22] + e[19] * e[20] * e[5] + e[19] * e[2] * e[23] + e[22] * e[21] * e[3] + e[22] * e[23] * e[5] - e[22] * e[26] * e[8] - e[22] * e[20] * e[2] - e[22] * e[18] * e[0] + e[22] * e[25] * e[7] - e[22] * e[24] * e[6] + e[1] * e[18] * e[21] + e[1] * e[20] * e[23] + 0.5 * e[4] * e2[25] - 0.5 * e[4] * e2[26] - 0.5 * e[4] * e2[18] - 0.5 * e[4] * e2[20] - 0.5 * e[4] * e2[24] + 0.5 * e2[19] * e[4] + 1.5 * e2[22] * e[4] + 0.5 * e[4] * e2[21] + 0.5 * e[4] * e2[23]; a[135] = e[22] * e[21] * e[12] + e[22] * e[23] * e[14] + e[25] * e[21] * e[15] + e[25] * e[12] * e[24] + e[25] * e[23] * e[17] + e[25] * e[14] * e[26] + e[25] * e[22] * e[16] + e[16] * e[21] * e[24] + e[16] * e[23] * e[26] + e[10] * e[19] * e[22] + e[10] * e[18] * e[21] + e[10] * e[20] * e[23] + e[19] * e[18] * e[12] + e[19] * e[9] * e[21] + e[19] * e[20] * e[14] + e[19] * e[11] * e[23] - e[22] * e[24] * e[15] - e[22] * e[26] * e[17] - e[22] * e[20] * e[11] - e[22] * e[18] * e[9] - 0.5 * e[13] * e2[26] - 0.5 * e[13] * e2[18] + 0.5 * e[13] * e2[23] + 0.5 * e[13] * e2[19] - 0.5 * e[13] * e2[20] - 0.5 * e[13] * e2[24] + 0.5 * e[13] * e2[21] + 1.5 * e2[22] * e[13] + 0.5 * e[13] * e2[25]; a[145] = e[13] * e[30] * e[21] + 3. * e[13] * e[31] * e[22] + e[13] * e[32] * e[23] + e[10] * e[27] * e[21] + e[10] * e[18] * e[30] + e[10] * e[28] * e[22] + e[10] * e[19] * e[31] + e[10] * e[29] * e[23] + e[10] * e[20] * e[32] + e[22] * e[30] * e[12] + e[22] * e[32] * e[14] + e[31] * e[21] * e[12] + e[31] * e[23] * e[14] - e[13] * e[27] * e[18] - e[13] * e[33] * e[24] - e[13] * e[29] * e[20] - e[13] * e[35] * e[26] + e[13] * e[28] * e[19] + e[13] * e[34] * e[25] + e[19] * e[27] * e[12] + e[19] * e[9] * e[30] + e[19] * e[29] * e[14] + e[19] * e[11] * e[32] + e[28] * e[18] * e[12] + e[28] * e[9] * e[21] + e[28] * e[20] * e[14] + e[28] * e[11] * e[23] + e[16] * e[30] * e[24] + e[16] * e[21] * e[33] + e[16] * e[31] * e[25] + e[16] * e[22] * e[34] + e[16] * e[32] * e[26] + e[16] * e[23] * e[35] - e[22] * e[27] * e[9] - e[22] * e[33] * e[15] - e[22] * e[35] * e[17] - e[22] * e[29] * e[11] - e[31] * e[24] * e[15] - e[31] * e[26] * e[17] - e[31] * e[20] * e[11] - e[31] * e[18] * e[9] + e[25] * e[30] * e[15] + e[25] * e[12] * e[33] + e[25] * e[32] * e[17] + e[25] * e[14] * e[35] + e[34] * e[21] * e[15] + e[34] * e[12] * e[24] + e[34] * e[23] * e[17] + e[34] * e[14] * e[26]; a[65] = e[19] * e[11] * e[14] + e[19] * e[9] * e[12] + e[19] * e[10] * e[13] + e[13] * e[21] * e[12] + e[13] * e[23] * e[14] + e[16] * e[21] * e[15] + e[16] * e[12] * e[24] + e[16] * e[23] * e[17] + e[16] * e[14] * e[26] + e[16] * e[13] * e[25] + e[25] * e[14] * e[17] + e[25] * e[12] * e[15] - e[13] * e[24] * e[15] - e[13] * e[26] * e[17] - e[13] * e[20] * e[11] - e[13] * e[18] * e[9] + e[10] * e[18] * e[12] + e[10] * e[9] * e[21] + e[10] * e[20] * e[14] + e[10] * e[11] * e[23] + 1.5 * e[22] * e2[13] + 0.5 * e[22] * e2[14] + 0.5 * e[22] * e2[12] + 0.5 * e[22] * e2[16] + 0.5 * e2[10] * e[22] - 0.5 * e[22] * e2[9] - 0.5 * e[22] * e2[11] - 0.5 * e[22] * e2[15] - 0.5 * e[22] * e2[17]; a[35] = e[13] * e[12] * e[3] + e[13] * e[14] * e[5] + e[16] * e[12] * e[6] + e[16] * e[3] * e[15] + e[16] * e[13] * e[7] + e[16] * e[14] * e[8] + e[16] * e[5] * e[17] + e[7] * e[14] * e[17] + e[7] * e[12] * e[15] + e[1] * e[11] * e[14] + e[1] * e[9] * e[12] + e[1] * e[10] * e[13] + e[10] * e[9] * e[3] + e[10] * e[0] * e[12] + e[10] * e[11] * e[5] + e[10] * e[2] * e[14] - e[13] * e[11] * e[2] - e[13] * e[15] * e[6] - e[13] * e[9] * e[0] - e[13] * e[17] * e[8] + 1.5 * e2[13] * e[4] + 0.5 * e[4] * e2[16] - 0.5 * e[4] * e2[9] - 0.5 * e[4] * e2[11] + 0.5 * e[4] * e2[12] - 0.5 * e[4] * e2[15] - 0.5 * e[4] * e2[17] + 0.5 * e[4] * e2[10] + 0.5 * e[4] * e2[14]; a[45] = e[19] * e[1] * e[4] + e[19] * e[0] * e[3] + e[19] * e[2] * e[5] + e[4] * e[21] * e[3] + e[4] * e[23] * e[5] + e[7] * e[21] * e[6] + e[7] * e[3] * e[24] + e[7] * e[4] * e[25] + e[7] * e[23] * e[8] + e[7] * e[5] * e[26] + e[25] * e[3] * e[6] + e[25] * e[5] * e[8] + e[1] * e[18] * e[3] + e[1] * e[0] * e[21] + e[1] * e[20] * e[5] + e[1] * e[2] * e[23] - e[4] * e[26] * e[8] - e[4] * e[20] * e[2] - e[4] * e[18] * e[0] - e[4] * e[24] * e[6] + 1.5 * e[22] * e2[4] - 0.5 * e[22] * e2[0] - 0.5 * e[22] * e2[6] + 0.5 * e[22] * e2[5] + 0.5 * e[22] * e2[1] + 0.5 * e[22] * e2[7] + 0.5 * e[22] * e2[3] - 0.5 * e[22] * e2[2] - 0.5 * e[22] * e2[8]; a[115] = -e[31] * e[20] * e[2] - e[31] * e[18] * e[0] + e[31] * e[23] * e[5] - e[31] * e[24] * e[6] + e[7] * e[30] * e[24] + e[7] * e[21] * e[33] + e[7] * e[32] * e[26] + e[7] * e[23] * e[35] + e[25] * e[30] * e[6] + e[25] * e[3] * e[33] + e[25] * e[31] * e[7] + e[25] * e[4] * e[34] + e[25] * e[32] * e[8] + e[25] * e[5] * e[35] + e[34] * e[21] * e[6] + e[34] * e[3] * e[24] + e[34] * e[22] * e[7] + e[34] * e[23] * e[8] + e[34] * e[5] * e[26] + e[1] * e[27] * e[21] + e[1] * e[18] * e[30] + e[1] * e[28] * e[22] + e[1] * e[19] * e[31] + e[1] * e[29] * e[23] + e[1] * e[20] * e[32] + e[19] * e[27] * e[3] + e[19] * e[0] * e[30] + e[19] * e[28] * e[4] + e[19] * e[29] * e[5] + e[19] * e[2] * e[32] + e[28] * e[18] * e[3] + e[28] * e[0] * e[21] + e[28] * e[20] * e[5] + e[28] * e[2] * e[23] + e[4] * e[30] * e[21] + 3. * e[4] * e[31] * e[22] + e[4] * e[32] * e[23] - e[4] * e[27] * e[18] - e[4] * e[33] * e[24] - e[4] * e[29] * e[20] - e[4] * e[35] * e[26] - e[22] * e[27] * e[0] + e[22] * e[32] * e[5] - e[22] * e[33] * e[6] + e[22] * e[30] * e[3] - e[22] * e[35] * e[8] - e[22] * e[29] * e[2] + e[31] * e[21] * e[3] - e[31] * e[26] * e[8]; } colmap-3.4/src/estimators/essential_matrix_test.cc000077500000000000000000000101161323400541200225310ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/essential_matrix" #include "util/testing.h" #include #include "base/camera_models.h" #include "base/essential_matrix.h" #include "base/pose.h" #include "base/projection.h" #include "estimators/essential_matrix.h" #include "optim/ransac.h" #include "util/random.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestFivePoint) { const double points1_raw[] = { 0.4964, 1.0577, 0.3650, -0.0919, -0.5412, 0.0159, -0.5239, 0.9467, 0.3467, 0.5301, 0.2797, 0.0012, -0.1986, 0.0460, -0.1622, 0.5347, 0.0796, 0.2379, -0.3946, 0.7969, 0.2, 0.7, 0.6, 0.3}; const double points2_raw[] = { 0.7570, 2.7340, 0.3961, 0.6981, -0.6014, 0.7110, -0.7385, 2.2712, 0.4177, 1.2132, 0.3052, 0.4835, -0.2171, 0.5057, -0.2059, 1.1583, 0.0946, 0.7013, -0.6236, 3.0253, 0.5, 0.9, 0.9, 0.2}; const size_t num_points = 12; std::vector points1(num_points); std::vector points2(num_points); for (size_t i = 0; i < num_points; ++i) { points1[i] = Eigen::Vector2d(points1_raw[2 * i], points1_raw[2 * i + 1]); points2[i] = Eigen::Vector2d(points2_raw[2 * i], points2_raw[2 * i + 1]); } // Enforce repeatable tests SetPRNGSeed(0); RANSACOptions options; options.max_error = 0.02; options.confidence = 0.9999; options.min_inlier_ratio = 0.1; RANSAC ransac(options); const auto report = ransac.Estimate(points1, points2); std::vector residuals; EssentialMatrixFivePointEstimator::Residuals(points1, points2, report.model, &residuals); for (size_t i = 0; i < 10; ++i) { BOOST_CHECK_LE(residuals[i], options.max_error * options.max_error); } BOOST_CHECK(!report.inlier_mask[10]); BOOST_CHECK(!report.inlier_mask[11]); } BOOST_AUTO_TEST_CASE(TestEightPoint) { const double points1_raw[] = {1.839035, 1.924743, 0.543582, 0.375221, 0.473240, 0.142522, 0.964910, 0.598376, 0.102388, 0.140092, 15.994343, 9.622164, 0.285901, 0.430055, 0.091150, 0.254594}; const double points2_raw[] = { 1.002114, 1.129644, 1.521742, 1.846002, 1.084332, 0.275134, 0.293328, 0.588992, 0.839509, 0.087290, 1.779735, 1.116857, 0.878616, 0.602447, 0.642616, 1.028681, }; const size_t kNumPoints = 8; std::vector points1(kNumPoints); std::vector points2(kNumPoints); for (size_t i = 0; i < kNumPoints; ++i) { points1[i] = Eigen::Vector2d(points1_raw[2 * i], points1_raw[2 * i + 1]); points2[i] = Eigen::Vector2d(points2_raw[2 * i], points2_raw[2 * i + 1]); } EssentialMatrixEightPointEstimator estimator; const auto E = estimator.Estimate(points1, points2)[0]; // Reference values obtained from Matlab. BOOST_CHECK(std::abs(E(0, 0) - -0.0811666) < 1e-5); BOOST_CHECK(std::abs(E(0, 1) - 0.255449) < 1e-5); BOOST_CHECK(std::abs(E(0, 2) - -0.0478999) < 1e-5); BOOST_CHECK(std::abs(E(1, 0) - -0.192392) < 1e-5); BOOST_CHECK(std::abs(E(1, 1) - -0.0531675) < 1e-5); BOOST_CHECK(std::abs(E(1, 2) - 0.119547) < 1e-5); BOOST_CHECK(std::abs(E(2, 0) - 0.177784) < 1e-5); BOOST_CHECK(std::abs(E(2, 1) - -0.22008) < 1e-5); BOOST_CHECK(std::abs(E(2, 2) - -0.015203) < 1e-5); } colmap-3.4/src/estimators/euclidean_transform.h000077500000000000000000000031651323400541200220130ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_EUCLIDEAN_TRANSFORM_H_ #define COLMAP_SRC_ESTIMATORS_EUCLIDEAN_TRANSFORM_H_ #include "base/similarity_transform.h" #include "util/alignment.h" namespace colmap { // N-D Euclidean transform estimator from corresponding point pairs in the // source and destination coordinate systems. // // This algorithm is based on the following paper: // // S. Umeyama. Least-Squares Estimation of Transformation Parameters // Between Two Point Patterns. IEEE Transactions on Pattern Analysis and // Machine Intelligence, Volume 13 Issue 4, Page 376-380, 1991. // http://www.stanford.edu/class/cs273/refs/umeyama.pdf // // and uses the Eigen implementation. template using EuclideanTransformEstimator = SimilarityTransformEstimator; } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_EUCLIDEAN_TRANSFORM_H_ colmap-3.4/src/estimators/fundamental_matrix.cc000077500000000000000000000151141323400541200220040ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/fundamental_matrix.h" #include #include #include #include #include #include #include "base/polynomial.h" #include "estimators/utils.h" #include "util/logging.h" namespace colmap { std::vector FundamentalMatrixSevenPointEstimator::Estimate( const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), 7); CHECK_EQ(points2.size(), 7); // Note that no normalization of the points is necessary here. // Setup system of equations: [points2(i,:), 1]' * F * [points1(i,:), 1]'. Eigen::Matrix A; for (size_t i = 0; i < 7; ++i) { const double x0 = points1[i](0); const double y0 = points1[i](1); const double x1 = points2[i](0); const double y1 = points2[i](1); A(i, 0) = x1 * x0; A(i, 1) = x1 * y0; A(i, 2) = x1; A(i, 3) = y1 * x0; A(i, 4) = y1 * y0; A(i, 5) = y1; A(i, 6) = x0; A(i, 7) = y0; A(i, 8) = 1; } // 9 unknowns with 7 equations, so we have 2D null space. Eigen::JacobiSVD> svd(A, Eigen::ComputeFullV); const Eigen::Matrix f = svd.matrixV(); Eigen::Matrix f1 = f.col(7); Eigen::Matrix f2 = f.col(8); f1 -= f2; // Normalize, such that lambda + mu = 1 // and add constraint det(F) = det(lambda * f1 + (1 - lambda) * f2). const double t0 = f1(4) * f1(8) - f1(5) * f1(7); const double t1 = f1(3) * f1(8) - f1(5) * f1(6); const double t2 = f1(3) * f1(7) - f1(4) * f1(6); const double t3 = f2(4) * f2(8) - f2(5) * f2(7); const double t4 = f2(3) * f2(8) - f2(5) * f2(6); const double t5 = f2(3) * f2(7) - f2(4) * f2(6); Eigen::Vector4d coeffs; coeffs(0) = f1(0) * t0 - f1(1) * t1 + f1(2) * t2; coeffs(1) = f2(0) * t0 - f2(1) * t1 + f2(2) * t2 - f2(3) * (f1(1) * f1(8) - f1(2) * f1(7)) + f2(4) * (f1(0) * f1(8) - f1(2) * f1(6)) - f2(5) * (f1(0) * f1(7) - f1(1) * f1(6)) + f2(6) * (f1(1) * f1(5) - f1(2) * f1(4)) - f2(7) * (f1(0) * f1(5) - f1(2) * f1(3)) + f2(8) * (f1(0) * f1(4) - f1(1) * f1(3)); coeffs(2) = f1(0) * t3 - f1(1) * t4 + f1(2) * t5 - f1(3) * (f2(1) * f2(8) - f2(2) * f2(7)) + f1(4) * (f2(0) * f2(8) - f2(2) * f2(6)) - f1(5) * (f2(0) * f2(7) - f2(1) * f2(6)) + f1(6) * (f2(1) * f2(5) - f2(2) * f2(4)) - f1(7) * (f2(0) * f2(5) - f2(2) * f2(3)) + f1(8) * (f2(0) * f2(4) - f2(1) * f2(3)); coeffs(3) = f2(0) * t3 - f2(1) * t4 + f2(2) * t5; Eigen::VectorXd roots_real; Eigen::VectorXd roots_imag; if (!FindPolynomialRootsCompanionMatrix(coeffs, &roots_real, &roots_imag)) { return {}; } std::vector models; models.reserve(roots_real.size()); for (Eigen::VectorXd::Index i = 0; i < roots_real.size(); ++i) { const double kMaxRootImag = 1e-10; if (std::abs(roots_imag(i)) > kMaxRootImag) { continue; } const double lambda = roots_real(i); const double mu = 1; Eigen::MatrixXd F = lambda * f1 + mu * f2; F.resize(3, 3); const double kEps = 1e-10; if (std::abs(F(2, 2)) < kEps) { continue; } F /= F(2, 2); models.push_back(F.transpose()); } return models; } void FundamentalMatrixSevenPointEstimator::Residuals( const std::vector& points1, const std::vector& points2, const M_t& F, std::vector* residuals) { ComputeSquaredSampsonError(points1, points2, F, residuals); } std::vector FundamentalMatrixEightPointEstimator::Estimate( const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); // Center and normalize image points for better numerical stability. std::vector normed_points1; std::vector normed_points2; Eigen::Matrix3d points1_norm_matrix; Eigen::Matrix3d points2_norm_matrix; CenterAndNormalizeImagePoints(points1, &normed_points1, &points1_norm_matrix); CenterAndNormalizeImagePoints(points2, &normed_points2, &points2_norm_matrix); // Setup homogeneous linear equation as x2' * F * x1 = 0. Eigen::Matrix cmatrix(points1.size(), 9); for (size_t i = 0; i < points1.size(); ++i) { cmatrix.block<1, 3>(i, 0) = normed_points1[i].homogeneous(); cmatrix.block<1, 3>(i, 0) *= normed_points2[i].x(); cmatrix.block<1, 3>(i, 3) = normed_points1[i].homogeneous(); cmatrix.block<1, 3>(i, 3) *= normed_points2[i].y(); cmatrix.block<1, 3>(i, 6) = normed_points1[i].homogeneous(); } // Solve for the nullspace of the constraint matrix. Eigen::JacobiSVD> cmatrix_svd( cmatrix, Eigen::ComputeFullV); const Eigen::VectorXd cmatrix_nullspace = cmatrix_svd.matrixV().col(8); const Eigen::Map ematrix_t(cmatrix_nullspace.data()); // Enforcing the internal constraint that two singular values must non-zero // and one must be zero. Eigen::JacobiSVD fmatrix_svd( ematrix_t.transpose(), Eigen::ComputeFullU | Eigen::ComputeFullV); Eigen::Vector3d singular_values = fmatrix_svd.singularValues(); singular_values(2) = 0.0; const Eigen::Matrix3d F = fmatrix_svd.matrixU() * singular_values.asDiagonal() * fmatrix_svd.matrixV().transpose(); const std::vector models = {points2_norm_matrix.transpose() * F * points1_norm_matrix}; return models; } void FundamentalMatrixEightPointEstimator::Residuals( const std::vector& points1, const std::vector& points2, const M_t& E, std::vector* residuals) { ComputeSquaredSampsonError(points1, points2, E, residuals); } } // namespace colmap colmap-3.4/src/estimators/fundamental_matrix.h000077500000000000000000000104751323400541200216530ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_FUNDAMENTAL_MATRIX_H_ #define COLMAP_SRC_ESTIMATORS_FUNDAMENTAL_MATRIX_H_ #include #include #include "estimators/homography_matrix.h" #include "util/alignment.h" #include "util/types.h" namespace colmap { // Fundamental matrix estimator from corresponding point pairs. // // This algorithm solves the 7-Point problem and is based on the following // paper: // // Zhengyou Zhang and T. Kanade, Determining the Epipolar Geometry and its // Uncertainty: A Review, International Journal of Computer Vision, 1998. // http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.4540 class FundamentalMatrixSevenPointEstimator { public: typedef Eigen::Vector2d X_t; typedef Eigen::Vector2d Y_t; typedef Eigen::Matrix3d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 7; // Estimate either 1 or 3 possible fundamental matrix solutions from a set of // corresponding points. // // The number of corresponding points must be exactly 7. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points // // @return Up to 4 solutions as a vector of 3x3 fundamental matrices. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the residuals of a set of corresponding points and a given // fundamental matrix. // // Residuals are defined as the squared Sampson error. // // @param points1 First set of corresponding points as Nx2 matrix. // @param points2 Second set of corresponding points as Nx2 matrix. // @param F 3x3 fundamental matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& F, std::vector* residuals); }; // Fundamental matrix estimator from corresponding point pairs. // // This algorithm solves the 8-Point problem based on the following paper: // // Hartley and Zisserman, Multiple View Geometry, algorithm 11.1, page 282. class FundamentalMatrixEightPointEstimator { public: typedef Eigen::Vector2d X_t; typedef Eigen::Vector2d Y_t; typedef Eigen::Matrix3d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 8; // Estimate fundamental matrix solutions from a set of corresponding points. // // The number of corresponding points must be at least 8. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points // // @return Single solution as a vector of 3x3 fundamental matrices. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the residuals of a set of corresponding points and a given // fundamental matrix. // // Residuals are defined as the squared Sampson error. // // @param points1 First set of corresponding points as Nx2 matrix. // @param points2 Second set of corresponding points as Nx2 matrix. // @param F 3x3 fundamental matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& F, std::vector* residuals); }; } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_FUNDAMENTAL_MATRIX_H_ colmap-3.4/src/estimators/fundamental_matrix_test.cc000077500000000000000000000074041323400541200230460ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/fundamental_matrix" #include "util/testing.h" #include "estimators/fundamental_matrix.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestSevenPoint) { const double points1_raw[] = {0.4964, 1.0577, 0.3650, -0.0919, -0.5412, 0.0159, -0.5239, 0.9467, 0.3467, 0.5301, 0.2797, 0.0012, -0.1986, 0.0460}; const double points2_raw[] = {0.7570, 2.7340, 0.3961, 0.6981, -0.6014, 0.7110, -0.7385, 2.2712, 0.4177, 1.2132, 0.3052, 0.4835, -0.2171, 0.5057}; const size_t kNumPoints = 7; std::vector points1(kNumPoints); std::vector points2(kNumPoints); for (size_t i = 0; i < kNumPoints; ++i) { points1[i] = Eigen::Vector2d(points1_raw[2 * i], points1_raw[2 * i + 1]); points2[i] = Eigen::Vector2d(points2_raw[2 * i], points2_raw[2 * i + 1]); } FundamentalMatrixSevenPointEstimator estimator; const auto F = estimator.Estimate(points1, points2)[0]; // Reference values obtained from Matlab. BOOST_CHECK_CLOSE(F(0, 0), 4.81441976, 1e-6); BOOST_CHECK_CLOSE(F(0, 1), -8.16978909, 1e-6); BOOST_CHECK_CLOSE(F(0, 2), 6.73133404, 1e-6); BOOST_CHECK_CLOSE(F(1, 0), 5.16247992, 1e-6); BOOST_CHECK_CLOSE(F(1, 1), 0.19325606, 1e-6); BOOST_CHECK_CLOSE(F(1, 2), -2.87239381, 1e-6); BOOST_CHECK_CLOSE(F(2, 0), -9.92570126, 1e-6); BOOST_CHECK_CLOSE(F(2, 1), 3.64159554, 1e-6); BOOST_CHECK_CLOSE(F(2, 2), 1., 1e-6); } BOOST_AUTO_TEST_CASE(TestEightPoint) { const double points1_raw[] = {1.839035, 1.924743, 0.543582, 0.375221, 0.473240, 0.142522, 0.964910, 0.598376, 0.102388, 0.140092, 15.994343, 9.622164, 0.285901, 0.430055, 0.091150, 0.254594}; const double points2_raw[] = { 1.002114, 1.129644, 1.521742, 1.846002, 1.084332, 0.275134, 0.293328, 0.588992, 0.839509, 0.087290, 1.779735, 1.116857, 0.878616, 0.602447, 0.642616, 1.028681, }; const size_t kNumPoints = 8; std::vector points1(kNumPoints); std::vector points2(kNumPoints); for (size_t i = 0; i < kNumPoints; ++i) { points1[i] = Eigen::Vector2d(points1_raw[2 * i], points1_raw[2 * i + 1]); points2[i] = Eigen::Vector2d(points2_raw[2 * i], points2_raw[2 * i + 1]); } FundamentalMatrixEightPointEstimator estimator; const auto F = estimator.Estimate(points1, points2)[0]; // Reference values obtained from Matlab. BOOST_CHECK(std::abs(F(0, 0) - -0.217859) < 1e-5); BOOST_CHECK(std::abs(F(0, 1) - 0.419282) < 1e-5); BOOST_CHECK(std::abs(F(0, 2) - -0.0343075) < 1e-5); BOOST_CHECK(std::abs(F(1, 0) - -0.0717941) < 1e-5); BOOST_CHECK(std::abs(F(1, 1) - 0.0451643) < 1e-5); BOOST_CHECK(std::abs(F(1, 2) - 0.0216073) < 1e-5); BOOST_CHECK(std::abs(F(2, 0) - 0.248062) < 1e-5); BOOST_CHECK(std::abs(F(2, 1) - -0.429478) < 1e-5); BOOST_CHECK(std::abs(F(2, 2) - 0.0221019) < 1e-5); } colmap-3.4/src/estimators/generalized_absolute_pose.cc000066400000000000000000000272671323400541200233500ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/generalized_absolute_pose.h" #include #include "base/polynomial.h" #include "base/projection.h" #include "estimators/generalized_absolute_pose_coeffs.h" #include "util/logging.h" namespace colmap { namespace { // Check whether the rays are close to parallel. bool CheckParallelRays(const Eigen::Vector3d& ray1, const Eigen::Vector3d& ray2, const Eigen::Vector3d& ray3) { const double kParallelThreshold = 1e-5; return ray1.cross(ray2).isApproxToConstant(0, kParallelThreshold) && ray1.cross(ray3).isApproxToConstant(0, kParallelThreshold); } // Check whether the points are close to collinear. bool CheckCollinearPoints(const Eigen::Vector3d& X1, const Eigen::Vector3d& X2, const Eigen::Vector3d& X3) { const double kMinNonCollinearity = 1e-5; const Eigen::Vector3d X12 = X2 - X1; const double non_collinearity_measure = X12.cross(X1 - X3).squaredNorm() / X12.squaredNorm(); return non_collinearity_measure < kMinNonCollinearity; } Eigen::Vector6d ComposePlueckerLine(const Eigen::Matrix3x4d& rel_tform, const Eigen::Vector2d& point2D) { const Eigen::Matrix3x4d inv_proj_matrix = InvertProjectionMatrix(rel_tform); const Eigen::Vector3d bearing = inv_proj_matrix.leftCols<3>() * point2D.homogeneous(); const Eigen::Vector3d proj_center = inv_proj_matrix.rightCols<1>(); const Eigen::Vector3d bearing_normalized = bearing.normalized(); Eigen::Vector6d pluecker; pluecker << bearing_normalized, proj_center.cross(bearing_normalized); return pluecker; } Eigen::Vector3d PointFromPlueckerLineAndDepth(const Eigen::Vector6d& pluecker, const double depth) { return pluecker.head<3>().cross(pluecker.tail<3>()) + depth * pluecker.head<3>(); } // Compute the coefficients from the system of 3 equations, nonlinear in the // depth of the points. Inputs are three Pluecker lines and the locations of // their corresponding points in 3D. The system of equations comes from the // distance constraints between 3D points: // // || f_i - f_j ||^2 = || (q_i x q_i' + lambda_i * q_i) - // (q_j x q_j' + lambda_j * q_j) ||^2 // // where [q_i; q_i'] is the Pluecker coordinate of bearing i and f_i is the // coordinate of the corresponding 3D point in the global coordinate system. A // 3D point in the local camera coordinate system along this line is // parameterized through the depth scalar lambda_i as: // // B_fi = q_i x q_i' + lambda_i * q_i. // Eigen::Matrix ComputePolynomialCoefficients( const std::vector& plueckers, const std::vector& points3D) { CHECK_EQ(plueckers.size(), 3); CHECK_EQ(points3D.size(), 3); Eigen::Matrix K; const std::array is = {{0, 0, 1}}; const std::array js = {{1, 2, 2}}; for (int k = 0; k < 3; ++k) { const int i = is[k]; const int j = js[k]; const Eigen::Vector3d moment_difference = plueckers[i].head<3>().cross(plueckers[i].tail<3>()) - plueckers[j].head<3>().cross(plueckers[j].tail<3>()); K(k, 0) = 1; K(k, 1) = -2 * plueckers[i].head<3>().dot(plueckers[j].head<3>()); K(k, 2) = 2 * moment_difference.dot(plueckers[i].head<3>()); K(k, 3) = 1; K(k, 4) = -2 * moment_difference.dot(plueckers[j].head<3>()); K(k, 5) = moment_difference.squaredNorm() - (points3D[i] - points3D[j]).squaredNorm(); } return K; } // Solve quadratics of the form: x^2 + bx + c = 0. int SolveQuadratic(const double b, const double c, double* roots) { const double delta = b * b - 4 * c; // Do not allow complex solutions. if (delta >= 0) { const double sqrt_delta = std::sqrt(delta); roots[0] = -0.5 * (b + sqrt_delta); roots[1] = -0.5 * (b - sqrt_delta); return 2; } else { return 0; } } // Given lambda_j, return the values for lambda_i, where: // k1 lambda_i^2 + (k2 lambda_j + k3) lambda_i // + k4 lambda_j^2 + k5 lambda_j + k6 = 0. void ComputeLambdaValues(const Eigen::Matrix::ConstRowXpr& k, const double lambda_j, std::vector* lambdas_i) { // Note that we solve x^2 + bx + c = 0, since k(0) is one. double roots[2]; const int num_solutions = SolveQuadratic(k(1) * lambda_j + k(2), lambda_j * (k(3) * lambda_j + k(4)) + k(5), roots); for (int i = 0; i < num_solutions; ++i) { if (roots[i] > 0) { lambdas_i->push_back(roots[i]); } } } // Given the coefficients of the polynomial system return the depths of the // points along the Pluecker lines. Use Sylvester resultant to get and 8th // degree polynomial for lambda_3 and back-substite in the original equations. std::vector ComputeDepthsSylvester( const Eigen::Matrix& K) { const Eigen::Matrix coeffs = ComputeDepthsSylvesterCoeffs(K); Eigen::VectorXd roots_real; Eigen::VectorXd roots_imag; if (!FindPolynomialRootsCompanionMatrix(coeffs, &roots_real, &roots_imag)) { return std::vector(); } // Back-substitute every lambda_3 to the system of equations. std::vector depths; depths.reserve(roots_real.size()); for (Eigen::VectorXd::Index i = 0; i < roots_real.size(); ++i) { const double kMaxRootImagRatio = 1e-3; if (std::abs(roots_imag(i)) > kMaxRootImagRatio * std::abs(roots_real(i))) { continue; } const double lambda_3 = roots_real(i); if (lambda_3 <= 0) { continue; } std::vector lambdas_2; ComputeLambdaValues(K.row(2), lambda_3, &lambdas_2); // Now we have two depths, lambda_2 and lambda_3. From the two remaining // equations, we must get the same lambda_1, otherwise the solution is // invalid. for (const double lambda_2 : lambdas_2) { std::vector lambdas_1_1; ComputeLambdaValues(K.row(0), lambda_2, &lambdas_1_1); std::vector lambdas_1_2; ComputeLambdaValues(K.row(1), lambda_3, &lambdas_1_2); for (const double lambda_1_1 : lambdas_1_1) { for (const double lambda_1_2 : lambdas_1_2) { const double kMaxLambdaRatio = 1e-2; if (std::abs(lambda_1_1 - lambda_1_2) < kMaxLambdaRatio * std::max(lambda_1_1, lambda_1_2)) { const double lambda_1 = (lambda_1_1 + lambda_1_2) / 2; depths.emplace_back(lambda_1, lambda_2, lambda_3); } } } } } return depths; } } // namespace std::vector GP3PEstimator::Estimate( const std::vector& points2D, const std::vector& points3D) { CHECK_EQ(points2D.size(), 3); CHECK_EQ(points3D.size(), 3); if (CheckCollinearPoints(points3D[0], points3D[1], points3D[2])) { return std::vector({}); } // Transform 2D points into compact Pluecker line representation. std::vector plueckers(3); for (size_t i = 0; i < 3; ++i) { plueckers[i] = ComposePlueckerLine(points2D[i].rel_tform, points2D[i].xy); } if (CheckParallelRays(plueckers[0].head<3>(), plueckers[1].head<3>(), plueckers[2].head<3>())) { return std::vector({}); } // Compute the coefficients k1, k2, k3 using Eq. 4. const Eigen::Matrix K = ComputePolynomialCoefficients(plueckers, points3D); // Compute the depths along the Pluecker lines of the observations. const std::vector depths = ComputeDepthsSylvester(K); if (depths.empty()) { return std::vector({}); } // For all valid depth values, compute the transformation between points in // the camera and the world frame. This uses Umeyama's method rather than the // algorithm proposed in the paper, since Umeyama's method is numerically more // stable and this part is not a bottleneck. Eigen::Matrix3d points3D_world; for (size_t i = 0; i < 3; ++i) { points3D_world.col(i) = points3D[i]; } std::vector models(depths.size()); for (size_t i = 0; i < depths.size(); ++i) { Eigen::Matrix3d points3D_camera; for (size_t j = 0; j < 3; ++j) { points3D_camera.col(j) = PointFromPlueckerLineAndDepth(plueckers[j], depths[i][j]); } const Eigen::Matrix4d transform = Eigen::umeyama(points3D_world, points3D_camera, false); models[i] = transform.topLeftCorner<3, 4>(); } return models; } void GP3PEstimator::Residuals(const std::vector& points2D, const std::vector& points3D, const M_t& proj_matrix, std::vector* residuals) { CHECK_EQ(points2D.size(), points3D.size()); residuals->resize(points2D.size(), 0); // Note that this code might not be as nice as Eigen expressions, // but it is significantly faster in various tests. const double P_00 = proj_matrix(0, 0); const double P_01 = proj_matrix(0, 1); const double P_02 = proj_matrix(0, 2); const double P_03 = proj_matrix(0, 3); const double P_10 = proj_matrix(1, 0); const double P_11 = proj_matrix(1, 1); const double P_12 = proj_matrix(1, 2); const double P_13 = proj_matrix(1, 3); const double P_20 = proj_matrix(2, 0); const double P_21 = proj_matrix(2, 1); const double P_22 = proj_matrix(2, 2); const double P_23 = proj_matrix(2, 3); for (size_t i = 0; i < points2D.size(); ++i) { const Eigen::Matrix3x4d& rel_tform = points2D[i].rel_tform; const double X_0 = points3D[i](0); const double X_1 = points3D[i](1); const double X_2 = points3D[i](2); // Project 3D point from world to generalized camera. const double pgx_0 = P_00 * X_0 + P_01 * X_1 + P_02 * X_2 + P_03; const double pgx_1 = P_10 * X_0 + P_11 * X_1 + P_12 * X_2 + P_13; const double pgx_2 = P_20 * X_0 + P_21 * X_1 + P_22 * X_2 + P_23; // Projection 3D point from generalized camera to camera of the observation. const double pcx_2 = rel_tform(2, 0) * pgx_0 + rel_tform(2, 1) * pgx_1 + rel_tform(2, 2) * pgx_2 + rel_tform(2, 3); // Check if 3D point is in front of camera. if (pcx_2 > std::numeric_limits::epsilon()) { const double pcx_0 = rel_tform(0, 0) * pgx_0 + rel_tform(0, 1) * pgx_1 + rel_tform(0, 2) * pgx_2 + rel_tform(0, 3); const double pcx_1 = rel_tform(1, 0) * pgx_0 + rel_tform(1, 1) * pgx_1 + rel_tform(1, 2) * pgx_2 + rel_tform(1, 3); const double inv_pcx_norm = 1 / std::sqrt(pcx_0 * pcx_0 + pcx_1 * pcx_1 + pcx_2 * pcx_2); const double x_0 = points2D[i].xy(0); const double x_1 = points2D[i].xy(1); const double inv_x_norm = 1 / std::sqrt(x_0 * x_0 + x_1 * x_1 + 1); (*residuals)[i] = 1 - inv_pcx_norm * inv_x_norm * (pcx_0 * x_0 + pcx_1 * x_1 + pcx_2); } else { (*residuals)[i] = std::numeric_limits::max(); } } } } // namespace colmap colmap-3.4/src/estimators/generalized_absolute_pose.h000066400000000000000000000054641323400541200232050ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_GENERALIZED_ABSOLUTE_POSE_H_ #define COLMAP_SRC_ESTIMATORS_GENERALIZED_ABSOLUTE_POSE_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Solver for the Generalized P3P problem (NP3P or GP3P), based on: // // Lee, Gim Hee, et al. "Minimal solutions for pose estimation of a // multi-camera system." Robotics Research. Springer International // Publishing, 2016. 521-538. // // This class is based on an original implementation by Federico Camposeco. class GP3PEstimator { public: // The generalized image observations, which is composed of the relative pose // of the specific camera in the generalized camera and its image observation. struct X_t { EIGEN_MAKE_ALIGNED_OPERATOR_NEW // The relative transformation from the generalized camera to the camera // frame of the observation. Eigen::Matrix3x4d rel_tform; // The 2D image feature observation. Eigen::Vector2d xy; }; // The observed 3D feature points in the world frame. typedef Eigen::Vector3d Y_t; // The transformation from the world to the generalized camera frame. typedef Eigen::Matrix3x4d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 3; // Estimate the most probable solution of the GP3P problem from a set of // three 2D-3D point correspondences. static std::vector Estimate(const std::vector& points2D, const std::vector& points3D); // Calculate the cosine distance error between the rays given a set of 2D-3D // point correspondences and a projection matrix of the generalized camera. static void Residuals(const std::vector& points2D, const std::vector& points3D, const M_t& proj_matrix, std::vector* residuals); }; } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::GP3PEstimator::X_t) #endif // COLMAP_SRC_ESTIMATORS_GENERALIZED_ABSOLUTE_POSE_H_ colmap-3.4/src/estimators/generalized_absolute_pose_coeffs.cc000066400000000000000000005440511323400541200246700ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/generalized_absolute_pose_coeffs.h" namespace colmap { Eigen::Matrix ComputeDepthsSylvesterCoeffs( const Eigen::Matrix& K) { Eigen::Matrix coeffs; const double k12 = K(0, 1); const double k13 = K(0, 2); const double k15 = K(0, 4); const double k16 = K(0, 5); const double k22 = K(1, 1); const double k23 = K(1, 2); const double k25 = K(1, 4); const double k26 = K(1, 5); const double k32 = K(2, 1); const double k33 = K(2, 2); const double k35 = K(2, 4); const double k36 = K(2, 5); const double t2 = k12 * k12; const double t3 = k22 * k22; const double t4 = k32 * k32; const double t5 = t2 * t2; const double t6 = t4 * t4; const double t7 = t3 * t3; const double t8 = k13 * k13; const double t9 = k15 * k15; const double t10 = k23 * k23; const double t11 = k25 * k25; const double t12 = k33 * k33; const double t13 = k35 * k35; const double t14 = k16 * k16; const double t15 = k26 * k26; const double t16 = k36 * k36; const double t17 = t8 * t8; const double t18 = t9 * t9; const double t19 = t12 * t12; const double t20 = t10 * t10; coeffs(0) = t2 * -8.0 - t3 * 8.0 - t4 * 8.0 + t5 + t6 + t7 + t2 * t3 * 2.0 + t2 * t4 * 2.0 + t3 * t4 * 2.0 - k12 * k22 * k32 * 8.0 + t2 * t3 * t4 + k12 * k22 * k32 * t2 * 2.0 + k12 * k22 * k32 * t3 * 2.0 + k12 * k22 * k32 * t4 * 2.0 + 1.6E1; coeffs(1) = k25 * 3.2E1 + k35 * 3.2E1 - k22 * k23 * 1.6E1 - k32 * k33 * 1.6E1 - k25 * t2 * 1.6E1 - k25 * t3 * 8.0 - k25 * t4 * 1.6E1 + k25 * t5 * 2.0 + k25 * t6 * 2.0 - k35 * t2 * 1.6E1 - k35 * t3 * 1.6E1 - k35 * t4 * 8.0 + k35 * t5 * 2.0 + k35 * t7 * 2.0 + k12 * k15 * k22 * 8.0 + k12 * k13 * k32 * 8.0 - k12 * k22 * k33 * 8.0 - k12 * k23 * k32 * 8.0 + k13 * k22 * t4 * 4.0 - k13 * k22 * t6 + k22 * k23 * t2 * 4.0 + k22 * k23 * t3 * 4.0 + k22 * k23 * t4 * 4.0 + k15 * k32 * t3 * 4.0 - k15 * k32 * t7 + k32 * k33 * t2 * 4.0 + k32 * k33 * t3 * 4.0 + k32 * k33 * t4 * 4.0 + k25 * t2 * t3 * 2.0 + k25 * t2 * t4 * 4.0 + k25 * t3 * t4 * 2.0 + k35 * t2 * t3 * 4.0 + k35 * t2 * t4 * 2.0 + k35 * t3 * t4 * 2.0 - k12 * k22 * k25 * k32 * 1.2E1 - k12 * k22 * k32 * k35 * 1.2E1 - k12 * k15 * k22 * t2 * 2.0 - k12 * k15 * k22 * t3 * 2.0 - k12 * k15 * k22 * t4 * 2.0 - k12 * k13 * k32 * t2 * 2.0 - k12 * k13 * k32 * t3 * 2.0 - k12 * k13 * k32 * t4 * 2.0 + k12 * k22 * k33 * t2 * 2.0 + k12 * k23 * k32 * t2 * 2.0 + k12 * k22 * k33 * t3 * 2.0 + k12 * k23 * k32 * t3 * 6.0 + k12 * k22 * k33 * t4 * 6.0 + k12 * k23 * k32 * t4 * 2.0 - k13 * k22 * t2 * t4 * 3.0 - k13 * k22 * t3 * t4 + k22 * k23 * t2 * t4 * 2.0 - k15 * k32 * t2 * t3 * 3.0 - k15 * k32 * t3 * t4 + k32 * k33 * t2 * t3 * 2.0 + k25 * t2 * t3 * t4 + k35 * t2 * t3 * t4 + k12 * k22 * k25 * k32 * t2 * 3.0 + k12 * k22 * k25 * k32 * t3 + k12 * k22 * k25 * k32 * t4 * 3.0 + k12 * k22 * k32 * k35 * t2 * 3.0 + k12 * k22 * k32 * k35 * t3 * 3.0 + k12 * k22 * k32 * k35 * t4 - k12 * k15 * k22 * t3 * t4 - k12 * k13 * k32 * t3 * t4; coeffs(2) = k16 * -3.2E1 + k26 * 3.2E1 + k36 * 3.2E1 + t8 * 8.0 + t9 * 8.0 - t10 * 8.0 + t11 * 2.4E1 - t12 * 8.0 + t13 * 2.4E1 + k25 * k35 * 4.8E1 + k16 * t2 * 8.0 + k16 * t3 * 1.6E1 + k16 * t4 * 1.6E1 - k16 * t6 * 2.0 - k16 * t7 * 2.0 - k26 * t2 * 1.6E1 - k26 * t3 * 8.0 - k26 * t4 * 1.6E1 + k26 * t5 * 2.0 + k26 * t6 * 2.0 - k36 * t2 * 1.6E1 - k36 * t3 * 1.6E1 - k36 * t4 * 8.0 + k36 * t5 * 2.0 + k36 * t7 * 2.0 + t2 * t8 * 2.0 + t2 * t9 * 2.0 - t3 * t8 * 2.0 + t2 * t10 * 2.0 - t3 * t9 * 6.0 - t4 * t8 * 6.0 - t2 * t11 * 1.0E1 + t3 * t10 * 6.0 - t4 * t9 * 2.0 + t2 * t12 * 2.0 - t3 * t11 * 2.0 + t4 * t10 * 2.0 + t6 * t8 - t2 * t13 * 1.0E1 + t3 * t12 * 2.0 - t4 * t11 * 1.0E1 - t3 * t13 * 1.0E1 + t4 * t12 * 6.0 + t5 * t11 + t7 * t9 - t4 * t13 * 2.0 + t6 * t11 + t5 * t13 + t7 * t13 - k12 * k13 * k15 * 1.6E1 + k12 * k15 * k23 * 8.0 + k12 * k13 * k33 * 8.0 - k13 * k22 * k25 * 8.0 - k12 * k23 * k33 * 8.0 + k13 * k22 * k35 * 8.0 - k22 * k23 * k25 * 1.6E1 + k15 * k25 * k32 * 8.0 - k22 * k23 * k35 * 3.2E1 - k15 * k32 * k35 * 8.0 - k25 * k32 * k33 * 3.2E1 - k32 * k33 * k35 * 1.6E1 + k13 * k23 * t4 * 4.0 - k13 * k23 * t6 + k15 * k33 * t3 * 4.0 - k15 * k33 * t7 - k25 * k35 * t2 * 2.8E1 - k25 * k35 * t3 * 1.2E1 - k25 * k35 * t4 * 1.2E1 + k25 * k35 * t5 * 4.0 - k16 * t2 * t3 * 2.0 - k16 * t2 * t4 * 2.0 - k16 * t3 * t4 * 8.0 + k16 * t3 * t6 + k16 * t4 * t7 + k26 * t2 * t3 * 2.0 + k26 * t2 * t4 * 4.0 + k26 * t3 * t4 * 2.0 + k36 * t2 * t3 * 4.0 + k36 * t2 * t4 * 2.0 + k36 * t3 * t4 * 2.0 + t2 * t3 * t9 + t2 * t4 * t8 + t3 * t4 * t8 * 2.0 + t2 * t3 * t11 + t2 * t4 * t10 + t3 * t4 * t9 * 2.0 + t2 * t3 * t12 + t2 * t4 * t11 * 3.0 + t2 * t3 * t13 * 3.0 + t3 * t4 * t11 + t2 * t4 * t13 + t3 * t4 * t13 + k12 * k15 * k22 * k25 * 1.6E1 + k12 * k13 * k25 * k32 * 8.0 + k12 * k16 * k22 * k32 * 4.0 - k13 * k15 * k22 * k32 * 1.2E1 + k12 * k15 * k22 * k35 * 8.0 + k12 * k13 * k32 * k35 * 1.6E1 - k12 * k22 * k25 * k33 * 1.2E1 - k12 * k22 * k26 * k32 * 1.2E1 - k12 * k23 * k25 * k32 * 1.2E1 + k15 * k22 * k23 * k32 * 8.0 + k13 * k22 * k32 * k33 * 8.0 - k12 * k22 * k32 * k36 * 1.2E1 - k12 * k22 * k33 * k35 * 1.2E1 - k12 * k23 * k32 * k35 * 1.2E1 + k22 * k23 * k32 * k33 * 8.0 + k12 * k13 * k15 * t3 * 4.0 + k12 * k13 * k15 * t4 * 4.0 - k12 * k15 * k23 * t2 * 2.0 - k12 * k15 * k23 * t3 * 6.0 - k12 * k15 * k23 * t4 * 2.0 - k12 * k13 * k33 * t2 * 2.0 - k12 * k13 * k33 * t3 * 2.0 - k12 * k13 * k33 * t4 * 6.0 - k13 * k22 * k25 * t2 * 2.0 + k13 * k22 * k25 * t3 * 2.0 + k13 * k22 * k25 * t4 * 6.0 - k13 * k22 * k25 * t6 + k12 * k23 * k33 * t2 * 2.0 + k12 * k23 * k33 * t3 * 6.0 + k12 * k23 * k33 * t4 * 6.0 + k13 * k22 * k35 * t2 * 2.0 + k22 * k23 * k25 * t2 * 4.0 - k13 * k22 * k35 * t3 * 2.0 + k12 * k22 * k32 * t8 * 2.0 + k13 * k22 * k35 * t4 * 2.0 + k15 * k25 * k32 * t2 * 2.0 + k22 * k23 * k25 * t4 * 4.0 + k12 * k22 * k32 * t9 * 2.0 + k15 * k25 * k32 * t3 * 2.0 + k12 * k22 * k32 * t10 * 6.0 - k15 * k25 * k32 * t4 * 2.0 - k12 * k22 * k32 * t11 * 2.0 + k12 * k22 * k32 * t12 * 6.0 - k12 * k22 * k32 * t13 * 2.0 + k22 * k23 * k35 * t2 * 8.0 + k22 * k23 * k35 * t3 * 8.0 - k15 * k32 * k35 * t2 * 2.0 + k22 * k23 * k35 * t4 * 4.0; coeffs(2) += k15 * k32 * k35 * t3 * 6.0 + k15 * k32 * k35 * t4 * 2.0 - k15 * k32 * k35 * t7 + k25 * k32 * k33 * t2 * 8.0 + k25 * k32 * k33 * t3 * 4.0 + k25 * k32 * k33 * t4 * 8.0 + k32 * k33 * k35 * t2 * 4.0 + k32 * k33 * k35 * t3 * 4.0 - k13 * k23 * t2 * t4 * 3.0 - k13 * k23 * t3 * t4 * 3.0 - k15 * k33 * t2 * t3 * 3.0 - k15 * k33 * t3 * t4 * 3.0 + k25 * k35 * t2 * t3 * 2.0 + k25 * k35 * t2 * t4 * 2.0 + k16 * t2 * t3 * t4 * 2.0 + k26 * t2 * t3 * t4 + k36 * t2 * t3 * t4 - k12 * k13 * k22 * k23 * k32 * 4.0 - k12 * k15 * k22 * k32 * k33 * 4.0 - k12 * k22 * k25 * k32 * k35 * 2.0E1 - k12 * k15 * k22 * k25 * t2 * 2.0 - k12 * k15 * k22 * k25 * t3 * 2.0 - k12 * k15 * k22 * k25 * t4 * 2.0 - k12 * k13 * k25 * k32 * t2 * 4.0 + k12 * k16 * k22 * k32 * t2 + k13 * k15 * k22 * k32 * t2 * 3.0 - k12 * k13 * k25 * k32 * t3 * 2.0 - k12 * k16 * k22 * k32 * t3 + k13 * k15 * k22 * k32 * t3 * 3.0 - k12 * k13 * k25 * k32 * t4 * 2.0 - k12 * k15 * k22 * k35 * t2 * 4.0 - k12 * k16 * k22 * k32 * t4 + k13 * k15 * k22 * k32 * t4 * 3.0 - k12 * k15 * k22 * k35 * t3 * 2.0 - k12 * k15 * k22 * k35 * t4 * 2.0 - k12 * k13 * k32 * k35 * t2 * 2.0 + k12 * k22 * k25 * k33 * t2 * 3.0 + k12 * k22 * k26 * k32 * t2 * 3.0 + k12 * k23 * k25 * k32 * t2 * 3.0 - k15 * k22 * k23 * k32 * t2 * 6.0 - k12 * k13 * k32 * k35 * t3 * 2.0 + k12 * k22 * k25 * k33 * t3 + k12 * k22 * k26 * k32 * t3 + k12 * k23 * k25 * k32 * t3 * 3.0 - k15 * k22 * k23 * k32 * t3 * 4.0 - k12 * k13 * k32 * k35 * t4 * 2.0 + k12 * k22 * k25 * k33 * t4 * 9.0 + k12 * k22 * k26 * k32 * t4 * 3.0 + k12 * k23 * k25 * k32 * t4 * 3.0 - k15 * k22 * k23 * k32 * t4 * 2.0 - k13 * k22 * k32 * k33 * t2 * 6.0 - k13 * k22 * k32 * k33 * t3 * 2.0 + k12 * k22 * k32 * k36 * t2 * 3.0 + k12 * k22 * k33 * k35 * t2 * 3.0 + k12 * k23 * k32 * k35 * t2 * 3.0 - k13 * k22 * k32 * k33 * t4 * 4.0 + k12 * k22 * k32 * k36 * t3 * 3.0 + k12 * k22 * k33 * k35 * t3 * 3.0 + k12 * k23 * k32 * k35 * t3 * 9.0 + k12 * k22 * k32 * k36 * t4 + k12 * k22 * k33 * k35 * t4 * 3.0 + k12 * k23 * k32 * k35 * t4 + k22 * k23 * k32 * k33 * t2 * 4.0 + k12 * k13 * k15 * t3 * t4 * 2.0 - k12 * k15 * k23 * t3 * t4 * 3.0 - k12 * k13 * k33 * t3 * t4 * 3.0 - k13 * k22 * k25 * t2 * t4 * 4.0 - k13 * k22 * k25 * t3 * t4 - k13 * k22 * k35 * t2 * t4 * 2.0 + k22 * k23 * k25 * t2 * t4 * 2.0 - k15 * k25 * k32 * t2 * t3 * 2.0 + k12 * k22 * k32 * t3 * t9 + k12 * k22 * k32 * t4 * t8 + k12 * k22 * k32 * t2 * t11 + k12 * k22 * k32 * t2 * t13 + k12 * k22 * k32 * t4 * t11 + k12 * k22 * k32 * t3 * t13 + k22 * k23 * k35 * t2 * t4 * 2.0 - k15 * k32 * k35 * t2 * t3 * 4.0 - k15 * k32 * k35 * t3 * t4 + k25 * k32 * k33 * t2 * t3 * 2.0 + k32 * k33 * k35 * t2 * t3 * 2.0 + k25 * k35 * t2 * t3 * t4 - k12 * k13 * k22 * k23 * k32 * t4 * 2.0 - k12 * k15 * k22 * k32 * k33 * t3 * 2.0 + k12 * k22 * k25 * k32 * k35 * t2 * 4.0 + k12 * k22 * k25 * k32 * k35 * t3 + k12 * k22 * k25 * k32 * k35 * t4 - k12 * k13 * k25 * k32 * t3 * t4 + k12 * k16 * k22 * k32 * t3 * t4 - k12 * k15 * k22 * k35 * t3 * t4; coeffs(3) = k16 * k25 * -4.8E1 - k16 * k35 * 4.8E1 + k25 * k26 * 4.8E1 + k25 * k36 * 4.8E1 + k26 * k35 * 4.8E1 + k35 * k36 * 4.8E1 + k25 * t8 * 1.6E1 + k25 * t9 * 8.0 - k25 * t10 * 8.0 + k25 * t11 * 8.0 - k25 * t12 * 1.6E1 + k25 * t13 * 2.4E1 + k35 * t8 * 8.0 + k35 * t9 * 1.6E1 - k35 * t10 * 1.6E1 + k35 * t11 * 2.4E1 - k35 * t12 * 8.0 + k35 * t13 * 8.0 - k13 * k16 * k22 * 8.0 - k13 * k22 * k26 * 8.0 - k13 * k23 * k25 * 8.0 + k16 * k22 * k23 * 3.2E1 - k15 * k16 * k32 * 8.0 + k13 * k22 * k36 * 8.0 + k13 * k23 * k35 * 8.0 - k22 * k23 * k26 * 1.6E1 + k15 * k25 * k33 * 8.0 + k15 * k26 * k32 * 8.0 + k16 * k32 * k33 * 3.2E1 - k22 * k23 * k36 * 3.2E1 - k15 * k32 * k36 * 8.0 - k15 * k33 * k35 * 8.0 - k26 * k32 * k33 * 3.2E1 - k32 * k33 * k36 * 1.6E1 + k16 * k25 * t2 * 1.2E1 + k13 * k22 * t9 * 8.0 + k16 * k25 * t3 * 1.2E1 + k16 * k25 * t4 * 2.0E1 - k13 * k22 * t11 * 8.0 + k13 * k22 * t12 * 4.0 - k16 * k25 * t6 * 2.0 + k13 * k22 * t13 * 8.0 + k16 * k35 * t2 * 1.2E1 - k22 * k23 * t8 * 4.0 - k25 * k26 * t2 * 2.0E1 + k16 * k35 * t3 * 2.0E1 - k22 * k23 * t9 * 1.2E1 - k25 * k26 * t3 * 4.0 + k15 * k32 * t8 * 8.0 + k16 * k35 * t4 * 1.2E1 + k22 * k23 * t10 * 4.0 - k25 * k26 * t4 * 2.0E1 - k22 * k23 * t11 * 4.0 + k25 * k26 * t5 * 2.0 + k15 * k32 * t10 * 4.0 + k22 * k23 * t12 * 4.0 + k25 * k26 * t6 * 2.0 + k15 * k32 * t11 * 8.0 - k16 * k35 * t7 * 2.0 - k22 * k23 * t13 * 2.0E1 - k15 * k32 * t13 * 8.0 - k25 * k36 * t2 * 2.8E1 - k26 * k35 * t2 * 2.8E1 - k25 * k36 * t3 * 1.2E1 - k26 * k35 * t3 * 1.2E1 - k25 * k36 * t4 * 1.2E1 - k26 * k35 * t4 * 1.2E1 + k25 * k36 * t5 * 4.0 + k26 * k35 * t5 * 4.0 - k32 * k33 * t8 * 1.2E1 - k35 * k36 * t2 * 2.0E1 - k32 * k33 * t9 * 4.0 - k35 * k36 * t3 * 2.0E1 + k32 * k33 * t10 * 4.0 - k35 * k36 * t4 * 4.0 - k32 * k33 * t11 * 2.0E1 + k35 * k36 * t5 * 2.0 + k32 * k33 * t12 * 4.0 - k32 * k33 * t13 * 4.0 + k35 * k36 * t7 * 2.0 + k25 * t2 * t8 * 4.0 + k25 * t2 * t9 * 2.0 - k25 * t3 * t8 * 2.0 + k25 * t2 * t10 * 2.0 - k25 * t3 * t9 * 4.0 - k25 * t4 * t8 * 8.0 - k25 * t2 * t11 * 2.0 - k25 * t4 * t9 * 2.0 + k25 * t2 * t12 * 4.0 + k25 * t4 * t10 * 2.0 + k25 * t6 * t8 - k25 * t2 * t13 * 1.4E1 + k25 * t3 * t12 * 2.0 - k25 * t4 * t11 * 2.0 - k25 * t3 * t13 * 4.0 + k25 * t4 * t12 * 1.2E1 - k25 * t4 * t13 * 2.0 + k25 * t5 * t13 * 2.0 + k35 * t2 * t8 * 2.0 + k35 * t2 * t9 * 4.0 - k35 * t3 * t8 * 2.0 + k35 * t2 * t10 * 4.0 - k35 * t3 * t9 * 8.0 - k35 * t4 * t8 * 4.0 - k35 * t2 * t11 * 1.4E1 + k35 * t3 * t10 * 1.2E1 - k35 * t4 * t9 * 2.0 + k35 * t2 * t12 * 2.0 - k35 * t3 * t11 * 2.0 + k35 * t4 * t10 * 2.0 - k35 * t2 * t13 * 2.0 + k35 * t3 * t12 * 2.0 - k35 * t4 * t11 * 4.0 - k35 * t3 * t13 * 2.0 + k35 * t5 * t11 * 2.0 + k35 * t7 * t9 - k12 * k13 * k15 * k25 * 2.4E1 - k12 * k13 * k15 * k35 * 2.4E1 + k12 * k15 * k22 * k26 * 1.6E1 + k12 * k15 * k23 * k25 * 1.6E1 + k12 * k13 * k25 * k33 * 8.0 + k12 * k13 * k26 * k32 * 8.0 + k12 * k16 * k22 * k33 * 4.0 + k12 * k16 * k23 * k32 * 4.0 - k13 * k15 * k22 * k33 * 1.2E1 - k13 * k15 * k23 * k32 * 1.2E1 + k12 * k15 * k22 * k36 * 8.0 + k12 * k15 * k23 * k35 * 8.0 + k12 * k13 * k32 * k36 * 1.6E1 + k12 * k13 * k33 * k35 * 1.6E1 - k12 * k22 * k26 * k33 * 1.2E1 - k12 * k23 * k25 * k33 * 1.2E1 - k12 * k23 * k26 * k32 * 1.2E1 + k15 * k22 * k23 * k33 * 8.0 + k13 * k23 * k32 * k33 * 8.0 - k12 * k22 * k33 * k36 * 1.2E1 - k12 * k23 * k32 * k36 * 1.2E1 - k12 * k23 * k33 * k35 * 1.2E1 - k22 * k23 * k25 * k35 * 2.4E1 - k25 * k32 * k33 * k35 * 2.4E1 - k13 * k16 * k22 * t2 * 2.0 + k13 * k16 * k22 * t3 * 2.0 + k13 * k16 * k22 * t4 * 6.0 - k12 * k15 * k22 * t8 * 2.0 - k13 * k16 * k22 * t6 - k12 * k15 * k22 * t9 * 2.0 - k12 * k15 * k22 * t10 * 6.0 + k12 * k15 * k22 * t11 * 6.0 - k12 * k15 * k22 * t12 * 2.0 - k12 * k15 * k22 * t13 * 2.0 - k13 * k22 * k26 * t2 * 2.0 - k13 * k23 * k25 * t2 * 2.0 - k16 * k22 * k23 * t2 * 4.0 + k13 * k22 * k26 * t3 * 2.0 + k13 * k23 * k25 * t3 * 6.0 - k16 * k22 * k23 * t3 * 8.0 - k12 * k13 * k32 * t8 * 2.0 + k13 * k22 * k26 * t4 * 6.0 + k13 * k23 * k25 * t4 * 6.0 - k15 * k16 * k32 * t2 * 2.0 - k16 * k22 * k23 * t4 * 1.6E1 - k12 * k13 * k32 * t9 * 2.0 + k15 * k16 * k32 * t3 * 6.0 - k12 * k13 * k32 * t10 * 2.0 - k13 * k22 * k26 * t6 - k13 * k23 * k25 * t6 + k15 * k16 * k32 * t4 * 2.0 + k16 * k22 * k23 * t6 * 2.0 - k12 * k13 * k32 * t11 * 2.0 - k12 * k13 * k32 * t12 * 6.0 + k12 * k13 * k32 * t13 * 6.0 - k15 * k16 * k32 * t7 + k13 * k22 * k36 * t2 * 2.0 + k13 * k23 * k35 * t2 * 2.0 + k22 * k23 * k26 * t2 * 4.0 - k13 * k22 * k36 * t3 * 2.0 - k13 * k23 * k35 * t3 * 6.0 + k12 * k22 * k33 * t8 * 2.0 + k12 * k23 * k32 * t8 * 2.0 + k13 * k22 * k36 * t4 * 2.0 + k13 * k23 * k35 * t4 * 2.0 + k15 * k25 * k33 * t2 * 2.0 + k15 * k26 * k32 * t2 * 2.0 + k22 * k23 * k26 * t4 * 4.0 + k12 * k22 * k33 * t9 * 2.0 + k12 * k23 * k32 * t9 * 2.0 + k15 * k25 * k33 * t3 * 2.0 + k15 * k26 * k32 * t3 * 2.0 + k12 * k22 * k33 * t10 * 6.0 + k12 * k23 * k32 * t10 * 2.0 - k15 * k25 * k33 * t4 * 6.0 - k15 * k26 * k32 * t4 * 2.0 - k12 * k22 * k33 * t11 * 2.0 - k12 * k23 * k32 * t11 * 2.0 + k12 * k22 * k33 * t12 * 2.0 + k12 * k23 * k32 * t12 * 6.0 - k12 * k22 * k33 * t13 * 2.0 - k12 * k23 * k32 * t13 * 2.0 - k16 * k32 * k33 * t2 * 4.0 + k22 * k23 * k36 * t2 * 8.0 - k16 * k32 * k33 * t3 * 1.6E1 + k22 * k23 * k36 * t3 * 8.0 - k15 * k32 * k36 * t2 * 2.0 - k15 * k33 * k35 * t2 * 2.0 - k16 * k32 * k33 * t4 * 8.0 + k22 * k23 * k36 * t4 * 4.0 + k15 * k32 * k36 * t3 * 6.0 + k15 * k33 * k35 * t3 * 6.0 + k15 * k32 * k36 * t4 * 2.0 + k15 * k33 * k35 * t4 * 6.0 + k16 * k32 * k33 * t7 * 2.0 - k15 * k32 * k36 * t7 - k15 * k33 * k35 * t7 + k26 * k32 * k33 * t2 * 8.0 + k26 * k32 * k33 * t3 * 4.0 + k26 * k32 * k33 * t4 * 8.0 + k32 * k33 * k36 * t2 * 4.0 + k32 * k33 * k36 * t3 * 4.0 - k13 * k22 * t3 * t9 * 2.0 - k13 * k22 * t4 * t8 - k16 * k25 * t2 * t4 * 4.0 - k13 * k22 * t2 * t11 * 2.0 - k13 * k22 * t4 * t9 * 3.0 - k16 * k25 * t3 * t4 * 4.0 - k13 * k22 * t2 * t12 * 3.0 - k13 * k22 * t4 * t10 * 3.0 + k13 * k22 * t2 * t13 * 2.0 - k13 * k22 * t3 * t12 + k13 * k22 * t4 * t11 - k13 * k22 * t3 * t13 * 2.0 - k13 * k22 * t4 * t12 * 6.0 - k13 * k22 * t4 * t13 - k16 * k35 * t2 * t3 * 4.0 + k22 * k23 * t2 * t9 * 2.0 + k25 * k26 * t2 * t3 * 2.0 + k22 * k23 * t3 * t9 * 4.0 + k22 * k23 * t4 * t8 * 4.0 + k25 * k26 * t2 * t4 * 6.0 - k15 * k32 * t3 * t8 * 3.0 - k16 * k35 * t3 * t4 * 4.0 + k22 * k23 * t2 * t11 * 2.0 + k22 * k23 * t4 * t9 * 4.0 + k25 * k26 * t3 * t4 * 2.0 - k15 * k32 * t2 * t10 * 3.0 - k15 * k32 * t3 * t9 - k15 * k32 * t4 * t8 * 2.0 + k22 * k23 * t2 * t12 * 2.0 + k15 * k32 * t2 * t11 * 2.0 - k15 * k32 * t3 * t10 * 6.0 + k22 * k23 * t2 * t13 * 6.0 + k22 * k23 * t4 * t11 * 2.0 - k15 * k32 * t3 * t11 - k15 * k32 * t4 * t10 + k22 * k23 * t3 * t13 * 4.0 - k15 * k32 * t2 * t13 * 2.0 - k15 * k32 * t3 * t12 * 3.0 - k15 * k32 * t4 * t11 * 2.0 + k22 * k23 * t4 * t13 * 2.0 + k15 * k32 * t3 * t13 + k25 * k36 * t2 * t3 * 2.0 + k26 * k35 * t2 * t3 * 2.0 + k25 * k36 * t2 * t4 * 2.0 + k26 * k35 * t2 * t4 * 2.0 + k32 * k33 * t2 * t8 * 2.0 + k32 * k33 * t3 * t8 * 4.0 + k35 * k36 * t2 * t3 * 6.0 + k32 * k33 * t2 * t10 * 2.0 + k32 * k33 * t3 * t9 * 4.0 + k32 * k33 * t4 * t8 * 4.0 + k35 * k36 * t2 * t4 * 2.0 + k32 * k33 * t2 * t11 * 6.0 + k35 * k36 * t3 * t4 * 2.0 + k32 * k33 * t3 * t11 * 2.0 + k32 * k33 * t2 * t13 * 2.0 + k32 * k33 * t4 * t11 * 4.0 + k32 * k33 * t3 * t13 * 2.0 + k25 * t2 * t4 * t8 * 2.0 + k25 * t3 * t4 * t8 * 2.0 + k25 * t2 * t4 * t10 + k25 * t2 * t3 * t12 + k25 * t2 * t4 * t11 + k25 * t2 * t4 * t13 + k35 * t2 * t3 * t9 * 2.0 + k35 * t2 * t3 * t11 + k35 * t2 * t4 * t10 + k35 * t3 * t4 * t9 * 2.0 + k35 * t2 * t3 * t12; coeffs(3) += k35 * t2 * t3 * t13 + k12 * k13 * k15 * k22 * k23 * 8.0 - k12 * k13 * k22 * k23 * k33 * 4.0 + k12 * k13 * k15 * k32 * k33 * 8.0 + k12 * k16 * k22 * k25 * k32 * 4.0 - k13 * k15 * k22 * k25 * k32 * 1.2E1 + k12 * k15 * k22 * k25 * k35 * 2.0E1 - k12 * k15 * k23 * k32 * k33 * 4.0 + k12 * k13 * k25 * k32 * k35 * 2.0E1 + k12 * k16 * k22 * k32 * k35 * 4.0 - k12 * k22 * k25 * k26 * k32 * 4.0 - k13 * k15 * k22 * k32 * k35 * 1.2E1 + k15 * k22 * k23 * k25 * k32 * 4.0 + k13 * k22 * k25 * k32 * k33 * 1.2E1 - k12 * k22 * k25 * k32 * k36 * 2.0E1 - k12 * k22 * k25 * k33 * k35 * 2.0E1 - k12 * k22 * k26 * k32 * k35 * 2.0E1 - k12 * k23 * k25 * k32 * k35 * 2.0E1 + k15 * k22 * k23 * k32 * k35 * 1.2E1 + k13 * k22 * k32 * k33 * k35 * 4.0 + k22 * k23 * k25 * k32 * k33 * 8.0 - k12 * k22 * k32 * k35 * k36 * 4.0 + k22 * k23 * k32 * k33 * k35 * 8.0 + k12 * k13 * k15 * k25 * t3 * 4.0 + k12 * k13 * k15 * k25 * t4 * 4.0 - k12 * k15 * k16 * k22 * t4 * 2.0 - k12 * k13 * k16 * k32 * t3 * 2.0 - k12 * k15 * k22 * k26 * t2 * 2.0 - k12 * k15 * k23 * k25 * t2 * 2.0 + k12 * k13 * k15 * k35 * t3 * 4.0 - k12 * k15 * k22 * k26 * t3 * 2.0 - k12 * k15 * k23 * k25 * t3 * 6.0 + k12 * k13 * k15 * k35 * t4 * 4.0 - k12 * k15 * k22 * k26 * t4 * 2.0 - k12 * k15 * k23 * k25 * t4 * 2.0 - k12 * k13 * k25 * k33 * t2 * 4.0 - k12 * k13 * k26 * k32 * t2 * 4.0 + k12 * k16 * k22 * k33 * t2 + k12 * k16 * k23 * k32 * t2 + k13 * k15 * k22 * k33 * t2 * 3.0 + k13 * k15 * k23 * k32 * t2 * 3.0 - k12 * k13 * k25 * k33 * t3 * 2.0 - k12 * k13 * k26 * k32 * t3 * 2.0 - k12 * k16 * k22 * k33 * t3 - k12 * k16 * k23 * k32 * t3 * 3.0 + k13 * k15 * k22 * k33 * t3 * 3.0 + k13 * k15 * k23 * k32 * t3 * 9.0 - k12 * k13 * k25 * k33 * t4 * 6.0 - k12 * k13 * k26 * k32 * t4 * 2.0 - k12 * k15 * k22 * k36 * t2 * 4.0 - k12 * k15 * k23 * k35 * t2 * 4.0 - k12 * k16 * k22 * k33 * t4 * 3.0 - k12 * k16 * k23 * k32 * t4 + k13 * k15 * k22 * k33 * t4 * 9.0 + k13 * k15 * k23 * k32 * t4 * 3.0 - k12 * k15 * k22 * k36 * t3 * 2.0 - k12 * k15 * k23 * k35 * t3 * 6.0 - k12 * k15 * k22 * k36 * t4 * 2.0 - k12 * k15 * k23 * k35 * t4 * 2.0 - k12 * k13 * k32 * k36 * t2 * 2.0 - k12 * k13 * k33 * k35 * t2 * 2.0 + k12 * k22 * k26 * k33 * t2 * 3.0 + k12 * k23 * k25 * k33 * t2 * 3.0 + k12 * k23 * k26 * k32 * t2 * 3.0 - k15 * k22 * k23 * k33 * t2 * 6.0 - k12 * k13 * k32 * k36 * t3 * 2.0 - k12 * k13 * k33 * k35 * t3 * 2.0 + k12 * k22 * k26 * k33 * t3 + k12 * k23 * k25 * k33 * t3 * 3.0 + k12 * k23 * k26 * k32 * t3 * 3.0 - k15 * k22 * k23 * k33 * t3 * 4.0 - k12 * k13 * k32 * k36 * t4 * 2.0 - k12 * k13 * k33 * k35 * t4 * 6.0 + k12 * k22 * k26 * k33 * t4 * 9.0 + k12 * k23 * k25 * k33 * t4 * 9.0 + k12 * k23 * k26 * k32 * t4 * 3.0 - k15 * k22 * k23 * k33 * t4 * 6.0 + k13 * k22 * k25 * k35 * t3 * 2.0 + k12 * k22 * k25 * k32 * t8 * 5.0 + k13 * k22 * k25 * k35 * t4 * 4.0 - k12 * k22 * k25 * k32 * t9 + k12 * k22 * k25 * k32 * t10 * 3.0 + k12 * k22 * k25 * k32 * t11 + k12 * k22 * k25 * k32 * t12 * 9.0 - k13 * k23 * k32 * k33 * t2 * 6.0 - k12 * k22 * k25 * k32 * t13 * 5.0 - k13 * k23 * k32 * k33 * t3 * 6.0 + k12 * k22 * k33 * k36 * t2 * 3.0 + k12 * k23 * k32 * k36 * t2 * 3.0 + k12 * k23 * k33 * k35 * t2 * 3.0 - k13 * k23 * k32 * k33 * t4 * 4.0 + k12 * k22 * k33 * k36 * t3 * 3.0 + k12 * k23 * k32 * k36 * t3 * 9.0 + k12 * k23 * k33 * k35 * t3 * 9.0 + k12 * k22 * k33 * k36 * t4 * 3.0 + k12 * k23 * k32 * k36 * t4 + k12 * k23 * k33 * k35 * t4 * 3.0 + k22 * k23 * k25 * k35 * t2 * 4.0 - k12 * k22 * k32 * k35 * t8 + k12 * k22 * k32 * k35 * t9 * 5.0 + k15 * k25 * k32 * k35 * t3 * 4.0 + k12 * k22 * k32 * k35 * t10 * 9.0 + k15 * k25 * k32 * k35 * t4 * 2.0 - k12 * k22 * k32 * k35 * t11 * 5.0 + k12 * k22 * k32 * k35 * t12 * 3.0 + k12 * k22 * k32 * k35 * t13 + k25 * k32 * k33 * k35 * t2 * 4.0 - k13 * k16 * k22 * t2 * t4 - k13 * k16 * k22 * t3 * t4 * 2.0 - k12 * k15 * k22 * t4 * t8 - k12 * k15 * k22 * t4 * t10 * 3.0 - k12 * k15 * k22 * t2 * t13 * 2.0 - k12 * k15 * k22 * t3 * t12 - k12 * k15 * k22 * t4 * t11 - k12 * k15 * k22 * t4 * t13 - k13 * k22 * k26 * t2 * t4 * 4.0 - k13 * k23 * k25 * t2 * t4 * 4.0 + k16 * k22 * k23 * t2 * t4 * 4.0 - k13 * k22 * k26 * t3 * t4 - k13 * k23 * k25 * t3 * t4 * 3.0 - k15 * k16 * k32 * t2 * t3 + k16 * k22 * k23 * t3 * t4 * 4.0 - k12 * k13 * k32 * t3 * t9 - k12 * k13 * k32 * t2 * t11 * 2.0 - k15 * k16 * k32 * t3 * t4 * 2.0 - k12 * k13 * k32 * t3 * t11 - k12 * k13 * k32 * t4 * t10 - k12 * k13 * k32 * t3 * t12 * 3.0 - k12 * k13 * k32 * t3 * t13 - k13 * k22 * k36 * t2 * t4 * 2.0 - k13 * k23 * k35 * t2 * t4 * 2.0 + k22 * k23 * k26 * t2 * t4 * 2.0 - k15 * k25 * k33 * t2 * t3 * 2.0 - k15 * k26 * k32 * t2 * t3 * 2.0 + k12 * k22 * k33 * t3 * t9 + k12 * k22 * k33 * t4 * t8 * 3.0 + k12 * k23 * k32 * t3 * t9 * 3.0 + k12 * k23 * k32 * t4 * t8 + k12 * k22 * k33 * t2 * t11 + k12 * k23 * k32 * t2 * t11 + k12 * k22 * k33 * t2 * t13 + k12 * k22 * k33 * t4 * t11 * 3.0 + k12 * k23 * k32 * t2 * t13 + k12 * k23 * k32 * t4 * t11 + k12 * k22 * k33 * t3 * t13 + k12 * k23 * k32 * t3 * t13 * 3.0 + k16 * k32 * k33 * t2 * t3 * 4.0 + k22 * k23 * k36 * t2 * t4 * 2.0 - k15 * k32 * k36 * t2 * t3 * 4.0 - k15 * k33 * k35 * t2 * t3 * 4.0 + k16 * k32 * k33 * t3 * t4 * 4.0 - k15 * k32 * k36 * t3 * t4 - k15 * k33 * k35 * t3 * t4 * 3.0 + k26 * k32 * k33 * t2 * t3 * 2.0 + k32 * k33 * k36 * t2 * t3 * 2.0 + k16 * k25 * t2 * t3 * t4 - k13 * k22 * t2 * t4 * t11 + k16 * k35 * t2 * t3 * t4 - k15 * k32 * t2 * t3 * t13 + k25 * k36 * t2 * t3 * t4 + k26 * k35 * t2 * t3 * t4 - k12 * k13 * k22 * k23 * k25 * k32 * 4.0 - k12 * k13 * k22 * k23 * k32 * k35 * 4.0 - k12 * k15 * k22 * k25 * k32 * k33 * 4.0 - k12 * k15 * k22 * k32 * k33 * k35 * 4.0 + k12 * k13 * k15 * k22 * k23 * t4 * 4.0 - k12 * k13 * k22 * k23 * k33 * t4 * 6.0 + k12 * k13 * k15 * k32 * k33 * t3 * 4.0 + k12 * k16 * k22 * k25 * k32 * t2 + k13 * k15 * k22 * k25 * k32 * t2 * 3.0 + k12 * k16 * k22 * k25 * k32 * t3 + k13 * k15 * k22 * k25 * k32 * t3 - k12 * k15 * k22 * k25 * k35 * t2 * 4.0 - k12 * k16 * k22 * k25 * k32 * t4 * 2.0 + k13 * k15 * k22 * k25 * k32 * t4 * 2.0 - k12 * k15 * k22 * k25 * k35 * t3 * 2.0 - k12 * k15 * k23 * k32 * k33 * t3 * 6.0 - k12 * k13 * k25 * k32 * k35 * t2 * 4.0 + k12 * k16 * k22 * k32 * k35 * t2 + k12 * k22 * k25 * k26 * k32 * t2 * 2.0 + k13 * k15 * k22 * k32 * k35 * t2 * 3.0 - k15 * k22 * k23 * k25 * k32 * t2 * 4.0 - k12 * k16 * k22 * k32 * k35 * t3 * 2.0 + k13 * k15 * k22 * k32 * k35 * t3 * 2.0 - k12 * k13 * k25 * k32 * k35 * t4 * 2.0 + k12 * k16 * k22 * k32 * k35 * t4 + k12 * k22 * k25 * k26 * k32 * t4 * 2.0 + k13 * k15 * k22 * k32 * k35 * t4 - k13 * k22 * k25 * k32 * k33 * t2 * 8.0 - k13 * k22 * k25 * k32 * k33 * t3 * 2.0 + k12 * k22 * k25 * k32 * k36 * t2 * 4.0 + k12 * k22 * k25 * k33 * k35 * t2 * 4.0 + k12 * k22 * k26 * k32 * k35 * t2 * 4.0 + k12 * k23 * k25 * k32 * k35 * t2 * 4.0 - k13 * k22 * k25 * k32 * k33 * t4 * 4.0 - k15 * k22 * k23 * k32 * k35 * t2 * 8.0 + k12 * k22 * k25 * k32 * k36 * t3 + k12 * k22 * k25 * k33 * k35 * t3 + k12 * k22 * k26 * k32 * k35 * t3 + k12 * k23 * k25 * k32 * k35 * t3 * 3.0 - k15 * k22 * k23 * k32 * k35 * t3 * 4.0 + k12 * k22 * k25 * k32 * k36 * t4 + k12 * k22 * k25 * k33 * k35 * t4 * 3.0 + k12 * k22 * k26 * k32 * k35 * t4 + k12 * k23 * k25 * k32 * k35 * t4 - k15 * k22 * k23 * k32 * k35 * t4 * 2.0 - k13 * k22 * k32 * k33 * k35 * t2 * 4.0 + k22 * k23 * k25 * k32 * k33 * t2 * 4.0 + k12 * k22 * k32 * k35 * k36 * t2 * 2.0 + k12 * k22 * k32 * k35 * k36 * t3 * 2.0 + k22 * k23 * k32 * k33 * k35 * t2 * 4.0 + k12 * k13 * k15 * k25 * t3 * t4 - k12 * k15 * k16 * k22 * t3 * t4 - k12 * k13 * k16 * k32 * t3 * t4 + k12 * k13 * k15 * k35 * t3 * t4 - k12 * k13 * k25 * k33 * t3 * t4 * 3.0 - k12 * k13 * k26 * k32 * t3 * t4 + k12 * k16 * k22 * k33 * t3 * t4 * 3.0 + k12 * k16 * k23 * k32 * t3 * t4 * 3.0 - k12 * k15 * k22 * k36 * t3 * t4 - k12 * k15 * k23 * k35 * t3 * t4 * 3.0 - k13 * k22 * k25 * k35 * t2 * t4 * 2.0 + k12 * k22 * k25 * k32 * t4 * t8 + k12 * k22 * k25 * k32 * t2 * t13 + k22 * k23 * k25 * k35 * t2 * t4 * 2.0 - k15 * k25 * k32 * k35 * t2 * t3 * 2.0 + k12 * k22 * k32 * k35 * t3 * t9 + k12 * k22 * k32 * k35 * t2 * t11 + k25 * k32 * k33 * k35 * t2 * t3 * 2.0 - k12 * k13 * k22 * k23 * k25 * k32 * t4 * 2.0 - k12 * k15 * k22 * k32 * k33 * k35 * t3 * 2.0; coeffs(4) = t14 * 2.4E1 + t15 * 2.4E1 + t16 * 2.4E1 + t17 + t18 + t19 + t20 - k16 * k26 * 4.8E1 - k16 * k36 * 4.8E1 + k26 * k36 * 4.8E1 - k16 * t8 * 8.0 - k16 * t9 * 8.0 + k16 * t10 * 1.6E1 - k16 * t11 * 2.4E1 + k16 * t12 * 1.6E1 - k16 * t13 * 2.4E1 + k26 * t8 * 1.6E1 + k26 * t9 * 8.0 - k26 * t10 * 8.0 + k26 * t11 * 2.4E1 - k26 * t12 * 1.6E1 + k26 * t13 * 2.4E1 + k36 * t8 * 8.0 + k36 * t9 * 1.6E1 - k36 * t10 * 1.6E1 + k36 * t11 * 2.4E1 - k36 * t12 * 8.0 + k36 * t13 * 2.4E1 - t2 * t14 * 2.0 - t2 * t15 * 1.0E1 - t3 * t14 * 1.0E1 - t8 * t9 * 2.0 - t2 * t16 * 1.0E1 - t3 * t15 * 2.0 - t4 * t14 * 1.0E1 - t8 * t10 * 2.0 - t3 * t16 * 1.0E1 - t4 * t15 * 1.0E1 + t8 * t11 * 1.0E1 - t9 * t10 * 6.0 - t4 * t16 * 2.0 + t5 * t15 + t6 * t14 - t8 * t12 * 6.0 + t9 * t11 * 2.0 + t5 * t16 + t6 * t15 + t7 * t14 + t8 * t13 * 2.0 - t9 * t12 * 2.0 - t10 * t11 * 2.0 + t9 * t13 * 1.0E1 + t10 * t12 * 2.0 + t7 * t16 - t10 * t13 * 1.0E1 - t11 * t12 * 1.0E1 + t11 * t13 * 6.0 - t12 * t13 * 2.0 + t11 * t11 + t13 * t13 - k13 * k16 * k23 * 8.0 - k13 * k23 * k26 * 8.0 - k15 * k16 * k33 * 8.0 + k13 * k23 * k36 * 8.0 + k15 * k26 * k33 * 8.0 - k16 * k25 * k35 * 4.8E1 - k15 * k33 * k36 * 8.0 + k25 * k26 * k35 * 4.8E1 + k25 * k35 * k36 * 4.8E1 + k16 * k26 * t2 * 1.2E1 + k13 * k23 * t9 * 8.0 + k16 * k26 * t3 * 1.2E1 + k16 * k26 * t4 * 2.0E1 - k13 * k23 * t11 * 8.0 + k13 * k23 * t12 * 4.0 - k16 * k26 * t6 * 2.0 + k13 * k23 * t13 * 8.0 + k16 * k36 * t2 * 1.2E1 + k16 * k36 * t3 * 2.0E1 + k15 * k33 * t8 * 8.0 + k16 * k36 * t4 * 1.2E1 + k15 * k33 * t10 * 4.0 + k15 * k33 * t11 * 8.0 - k16 * k36 * t7 * 2.0 - k15 * k33 * t13 * 8.0 - k26 * k36 * t2 * 2.8E1 - k26 * k36 * t3 * 1.2E1 - k26 * k36 * t4 * 1.2E1 + k26 * k36 * t5 * 4.0 + k25 * k35 * t8 * 1.2E1 + k25 * k35 * t9 * 1.2E1 - k25 * k35 * t10 * 1.2E1 + k25 * k35 * t11 * 4.0 - k25 * k35 * t12 * 1.2E1 + k25 * k35 * t13 * 4.0 + k16 * t3 * t8 * 2.0 - k16 * t2 * t10 * 2.0 + k16 * t3 * t9 * 2.0 + k16 * t4 * t8 * 2.0 + k16 * t2 * t11 * 4.0 - k16 * t3 * t10 * 1.2E1 + k16 * t4 * t9 * 2.0 - k16 * t2 * t12 * 2.0 + k16 * t3 * t11 * 2.0 - k16 * t4 * t10 * 8.0 + k16 * t2 * t13 * 4.0 - k16 * t3 * t12 * 8.0 + k16 * t4 * t11 * 6.0 + k16 * t3 * t13 * 6.0 - k16 * t4 * t12 * 1.2E1 + k16 * t6 * t10 + k16 * t4 * t13 * 2.0 + k16 * t7 * t12 + k26 * t2 * t8 * 4.0 + k26 * t2 * t9 * 2.0 - k26 * t3 * t8 * 2.0 + k26 * t2 * t10 * 2.0 - k26 * t3 * t9 * 4.0 - k26 * t4 * t8 * 8.0 - k26 * t2 * t11 * 6.0 - k26 * t4 * t9 * 2.0 + k26 * t2 * t12 * 4.0 + k26 * t4 * t10 * 2.0 + k26 * t6 * t8 - k26 * t2 * t13 * 1.4E1 + k26 * t3 * t12 * 2.0 - k26 * t4 * t11 * 6.0 - k26 * t3 * t13 * 4.0 + k26 * t4 * t12 * 1.2E1 - k26 * t4 * t13 * 2.0 + k26 * t5 * t13 * 2.0 + k36 * t2 * t8 * 2.0 + k36 * t2 * t9 * 4.0 - k36 * t3 * t8 * 2.0 + k36 * t2 * t10 * 4.0 - k36 * t3 * t9 * 8.0 - k36 * t4 * t8 * 4.0 - k36 * t2 * t11 * 1.4E1 + k36 * t3 * t10 * 1.2E1 - k36 * t4 * t9 * 2.0 + k36 * t2 * t12 * 2.0 - k36 * t3 * t11 * 2.0 + k36 * t4 * t10 * 2.0 - k36 * t2 * t13 * 6.0 + k36 * t3 * t12 * 2.0 - k36 * t4 * t11 * 4.0 - k36 * t3 * t13 * 6.0 + k36 * t5 * t11 * 2.0 + k36 * t7 * t9 + t2 * t3 * t14 + t2 * t3 * t15 + t2 * t4 * t14 + t3 * t8 * t9 + t2 * t3 * t16 * 3.0 + t2 * t4 * t15 * 3.0 + t2 * t8 * t11 * 2.0 + t2 * t9 * t10 + t3 * t4 * t14 * 3.0 + t4 * t8 * t9 + t2 * t4 * t16 + t2 * t8 * t12 + t3 * t4 * t15 + t3 * t8 * t11 + t3 * t9 * t10 * 6.0 + t4 * t8 * t10 * 2.0 + t2 * t10 * t11 + t3 * t4 * t16 + t3 * t8 * t12 * 2.0 - t4 * t8 * t11 * 2.0 + t4 * t9 * t10 * 2.0 + t2 * t9 * t13 * 2.0 + t2 * t10 * t12 + t3 * t8 * t13 + t3 * t9 * t12 * 2.0 + t4 * t8 * t12 * 6.0 + t4 * t9 * t11 + t2 * t10 * t13 * 3.0 + t2 * t11 * t12 * 3.0 - t3 * t9 * t13 * 2.0 + t4 * t10 * t11 - t2 * t11 * t13 * 4.0 + t3 * t10 * t13 * 6.0 + t3 * t11 * t12 + t4 * t9 * t13 + t2 * t12 * t13 + t4 * t10 * t13 + t4 * t11 * t12 * 6.0 + t3 * t12 * t13 + t5 * t11 * t13 + k12 * k13 * k15 * k16 * 8.0 - k12 * k13 * k15 * k26 * 2.4E1 - k12 * k13 * k15 * k36 * 2.4E1 + k12 * k15 * k23 * k26 * 1.6E1 + k12 * k13 * k26 * k33 * 8.0 + k12 * k16 * k23 * k33 * 4.0 - k13 * k15 * k23 * k33 * 1.2E1 + k12 * k15 * k23 * k36 * 8.0 - k13 * k16 * k22 * k35 * 1.6E1 - k13 * k22 * k25 * k26 * 1.6E1 + k16 * k22 * k23 * k25 * 2.4E1 - k15 * k16 * k25 * k32 * 1.6E1 + k12 * k13 * k33 * k36 * 1.6E1 - k12 * k23 * k26 * k33 * 1.2E1 + k16 * k22 * k23 * k35 * 4.0E1 - k22 * k23 * k25 * k26 * 8.0 + k15 * k25 * k26 * k32 * 1.6E1 - k12 * k23 * k33 * k36 * 1.2E1 + k13 * k22 * k35 * k36 * 1.6E1 + k16 * k25 * k32 * k33 * 4.0E1 - k22 * k23 * k25 * k36 * 2.4E1 - k22 * k23 * k26 * k35 * 2.4E1 + k16 * k32 * k33 * k35 * 2.4E1 - k22 * k23 * k35 * k36 * 4.0E1 - k25 * k26 * k32 * k33 * 4.0E1 - k15 * k32 * k35 * k36 * 1.6E1 - k25 * k32 * k33 * k36 * 2.4E1 - k26 * k32 * k33 * k35 * 2.4E1 - k32 * k33 * k35 * k36 * 8.0 + k12 * k13 * k15 * t10 * 4.0 - k12 * k13 * k15 * t11 * 8.0 + k12 * k13 * k15 * t12 * 4.0 - k12 * k13 * k15 * t13 * 8.0 - k13 * k16 * k23 * t2 * 2.0 + k13 * k16 * k23 * t3 * 6.0 + k13 * k16 * k23 * t4 * 6.0 - k12 * k15 * k23 * t8 * 2.0 - k13 * k16 * k23 * t6 - k12 * k15 * k23 * t9 * 2.0 - k12 * k15 * k23 * t10 * 2.0 + k12 * k15 * k23 * t11 * 6.0 - k12 * k15 * k23 * t12 * 2.0 - k12 * k15 * k23 * t13 * 2.0 - k13 * k23 * k26 * t2 * 2.0 + k13 * k23 * k26 * t3 * 6.0 - k12 * k13 * k33 * t8 * 2.0 + k13 * k23 * k26 * t4 * 6.0 - k15 * k16 * k33 * t2 * 2.0 - k12 * k13 * k33 * t9 * 2.0 + k15 * k16 * k33 * t3 * 6.0 - k12 * k13 * k33 * t10 * 2.0 - k13 * k22 * k25 * t8 * 2.0 - k13 * k23 * k26 * t6 + k15 * k16 * k33 * t4 * 6.0 - k12 * k13 * k33 * t11 * 2.0 + k13 * k22 * k25 * t9 * 6.0 - k12 * k13 * k33 * t12 * 2.0 + k13 * k22 * k25 * t10 * 6.0 + k12 * k13 * k33 * t13 * 6.0 - k13 * k22 * k25 * t11 * 2.0 - k15 * k16 * k33 * t7 + k13 * k22 * k25 * t12 * 6.0 + k13 * k22 * k25 * t13 * 2.0 + k13 * k23 * k36 * t2 * 2.0 - k13 * k23 * k36 * t3 * 6.0 + k12 * k23 * k33 * t8 * 2.0 + k13 * k23 * k36 * t4 * 2.0 + k15 * k26 * k33 * t2 * 2.0 + k12 * k23 * k33 * t9 * 2.0 + k15 * k26 * k33 * t3 * 2.0 + k12 * k23 * k33 * t10 * 2.0 + k13 * k22 * k35 * t8 * 2.0 - k15 * k26 * k33 * t4 * 6.0 + k16 * k25 * k35 * t2 * 1.6E1 - k22 * k23 * k25 * t8 * 4.0 - k12 * k23 * k33 * t11 * 2.0 + k13 * k22 * k35 * t9 * 1.0E1 + k16 * k25 * k35 * t3 * 8.0 - k22 * k23 * k25 * t9 * 8.0 - k12 * k22 * k32 * t14 * 2.0 + k12 * k23 * k33 * t12 * 2.0 - k13 * k22 * k35 * t10 * 6.0 + k15 * k25 * k32 * t8 * 1.0E1 + k16 * k25 * k35 * t4 * 8.0 - k12 * k22 * k32 * t15 * 2.0 - k12 * k23 * k33 * t13 * 2.0 - k13 * k22 * k35 * t11 * 2.0 + k15 * k25 * k32 * t9 * 2.0 - k12 * k22 * k32 * t16 * 2.0 + k13 * k22 * k35 * t12 * 2.0 + k15 * k25 * k32 * t10 * 2.0 + k22 * k23 * k25 * t12 * 4.0 + k13 * k22 * k35 * t13 * 2.0 + k15 * k25 * k32 * t11 * 2.0 - k22 * k23 * k25 * t13 * 8.0 - k15 * k25 * k32 * t12 * 6.0 - k15 * k25 * k32 * t13 * 2.0 - k15 * k33 * k36 * t2 * 2.0 + k15 * k33 * k36 * t3 * 6.0 + k15 * k33 * k36 * t4 * 6.0 - k22 * k23 * k35 * t8 * 4.0 - k25 * k26 * k35 * t2 * 2.8E1 - k22 * k23 * k35 * t9 * 1.6E1 - k25 * k26 * k35 * t3 * 4.0 + k15 * k32 * k35 * t8 * 6.0 + k22 * k23 * k35 * t10 * 8.0 - k25 * k26 * k35 * t4 * 8.0 - k15 * k32 * k35 * t9 * 2.0 - k15 * k33 * k36 * t7 - k22 * k23 * k35 * t11 * 4.0 + k25 * k26 * k35 * t5 * 4.0 + k15 * k32 * k35 * t10 * 6.0 + k22 * k23 * k35 * t12 * 4.0 + k15 * k32 * k35 * t11 * 2.0 - k22 * k23 * k35 * t13 * 4.0 + k15 * k32 * k35 * t12 * 6.0 - k15 * k32 * k35 * t13 * 2.0 - k25 * k32 * k33 * t8 * 1.6E1 - k25 * k35 * k36 * t2 * 2.8E1 - k25 * k32 * k33 * t9 * 4.0 - k25 * k35 * k36 * t3 * 8.0 + k25 * k32 * k33 * t10 * 4.0 - k25 * k35 * k36 * t4 * 4.0 - k25 * k32 * k33 * t11 * 4.0 + k25 * k35 * k36 * t5 * 4.0 + k25 * k32 * k33 * t12 * 8.0 - k25 * k32 * k33 * t13 * 4.0 - k32 * k33 * k35 * t8 * 8.0 - k32 * k33 * k35 * t9 * 4.0 + k32 * k33 * k35 * t10 * 4.0 - k32 * k33 * k35 * t11 * 8.0 - k13 * k23 * t3 * t9 * 6.0 - k13 * k23 * t4 * t8 - k16 * k26 * t2 * t4 * 4.0 - k13 * k23 * t2 * t11 * 2.0 - k13 * k23 * t4 * t9 * 3.0 - k16 * k26 * t3 * t4 * 4.0 - k13 * k23 * t2 * t12 * 3.0 - k13 * k23 * t4 * t10 + k13 * k23 * t2 * t13 * 2.0 - k13 * k23 * t3 * t12 * 3.0 + k13 * k23 * t4 * t11 - k13 * k23 * t3 * t13 * 6.0 - k13 * k23 * t4 * t12 * 6.0 - k13 * k23 * t4 * t13 - k16 * k36 * t2 * t3 * 4.0 - k15 * k33 * t3 * t8 * 3.0 - k16 * k36 * t3 * t4 * 4.0 - k15 * k33 * t2 * t10 * 3.0 - k15 * k33 * t3 * t9 - k15 * k33 * t4 * t8 * 6.0 + k15 * k33 * t2 * t11 * 2.0 - k15 * k33 * t3 * t10 * 6.0 - k15 * k33 * t3 * t11 - k15 * k33 * t4 * t10 * 3.0 - k15 * k33 * t2 * t13 * 2.0 - k15 * k33 * t3 * t12 - k15 * k33 * t4 * t11 * 6.0 + k15 * k33 * t3 * t13 + k26 * k36 * t2 * t3 * 2.0 + k26 * k36 * t2 * t4 * 2.0 + k25 * k35 * t2 * t8 * 4.0 + k25 * k35 * t2 * t9 * 4.0 - k25 * k35 * t3 * t8 * 4.0 + k25 * k35 * t2 * t10 * 2.0 - k25 * k35 * t3 * t9 * 4.0 - k25 * k35 * t4 * t8 * 4.0 - k25 * k35 * t2 * t11 * 2.0 - k25 * k35 * t4 * t9 * 4.0 + k25 * k35 * t2 * t12 * 2.0 - k25 * k35 * t2 * t13 * 2.0 + k16 * t3 * t4 * t8 + k16 * t2 * t4 * t10 * 2.0 + k16 * t3 * t4 * t9 + k16 * t2 * t3 * t12 * 2.0 - k16 * t2 * t4 * t11 * 2.0 + k16 * t3 * t4 * t10 * 6.0 - k16 * t2 * t3 * t13 * 2.0 + k16 * t3 * t4 * t12 * 6.0 + k26 * t2 * t4 * t8 * 2.0 + k26 * t3 * t4 * t8 * 2.0 + k26 * t2 * t4 * t10 + k26 * t2 * t3 * t12 + k26 * t2 * t4 * t11 * 3.0 + k26 * t2 * t4 * t13 + k36 * t2 * t3 * t9 * 2.0 + k36 * t2 * t3 * t11 + k36 * t2 * t4 * t10 + k36 * t3 * t4 * t9 * 2.0 + k36 * t2 * t3 * t12 + k36 * t2 * t3 * t13 * 3.0 + t2 * t4 * t8 * t11 + t2 * t3 * t9 * t13 - k12 * k15 * k16 * k22 * k25 * 4.0 + k12 * k13 * k16 * k25 * k32 * 4.0 - k13 * k15 * k16 * k22 * k32 * 4.0 - k12 * k13 * k15 * k25 * k35 * 3.2E1 + k12 * k15 * k16 * k22 * k35 * 4.0 + k12 * k15 * k22 * k25 * k26 * 1.2E1 - k12 * k13 * k16 * k32 * k35 * 4.0 - k12 * k13 * k25 * k26 * k32 * 4.0 + k12 * k16 * k22 * k25 * k33 * 4.0 + k12 * k16 * k22 * k26 * k32 * 4.0 + k12 * k16 * k23 * k25 * k32 * 4.0 - k13 * k15 * k22 * k25 * k33 * 1.2E1 - k13 * k15 * k22 * k26 * k32 * 1.2E1 - k13 * k15 * k23 * k25 * k32 * 1.2E1 + k15 * k16 * k22 * k23 * k32 * 1.2E1 + k12 * k15 * k22 * k25 * k36 * 2.0E1 + k12 * k15 * k22 * k26 * k35 * 2.0E1 + k12 * k15 * k23 * k25 * k35 * 2.0E1 + k13 * k16 * k22 * k32 * k33 * 1.2E1 + k12 * k13 * k25 * k32 * k36 * 2.0E1 + k12 * k13 * k25 * k33 * k35 * 2.0E1 + k12 * k13 * k26 * k32 * k35 * 2.0E1 + k12 * k16 * k22 * k32 * k36 * 4.0 + k12 * k16 * k22 * k33 * k35 * 4.0 + k12 * k16 * k23 * k32 * k35 * 4.0 - k12 * k22 * k25 * k26 * k33 * 4.0 - k12 * k23 * k25 * k26 * k32 * 4.0 - k13 * k15 * k22 * k32 * k36 * 1.2E1 - k13 * k15 * k22 * k33 * k35 * 1.2E1 - k13 * k15 * k23 * k32 * k35 * 1.2E1 + k15 * k22 * k23 * k25 * k33 * 4.0 + k15 * k22 * k23 * k26 * k32 * 4.0 - k12 * k15 * k22 * k35 * k36 * 4.0 + k13 * k22 * k26 * k32 * k33 * 1.2E1 + k13 * k23 * k25 * k32 * k33 * 1.2E1 - k16 * k22 * k23 * k32 * k33 * 3.2E1 + k12 * k13 * k32 * k35 * k36 * 1.2E1 - k12 * k22 * k25 * k33 * k36 * 2.0E1 - k12 * k22 * k26 * k32 * k36 * 2.0E1 - k12 * k22 * k26 * k33 * k35 * 2.0E1 - k12 * k23 * k25 * k32 * k36 * 2.0E1 - k12 * k23 * k25 * k33 * k35 * 2.0E1 - k12 * k23 * k26 * k32 * k35 * 2.0E1 + k15 * k22 * k23 * k32 * k36 * 1.2E1 + k15 * k22 * k23 * k33 * k35 * 1.2E1 + k13 * k22 * k32 * k33 * k36 * 4.0 + k13 * k23 * k32 * k33 * k35 * 4.0 + k22 * k23 * k26 * k32 * k33 * 8.0 - k12 * k22 * k33 * k35 * k36 * 4.0 - k12 * k23 * k32 * k35 * k36 * 4.0 + k22 * k23 * k32 * k33 * k36 * 8.0 + k12 * k13 * k15 * k26 * t3 * 4.0 + k12 * k13 * k15 * k26 * t4 * 4.0 - k12 * k15 * k16 * k23 * t4 * 2.0 - k12 * k13 * k16 * k33 * t3 * 2.0 - k12 * k15 * k23 * k26 * t2 * 2.0 - k13 * k16 * k22 * k25 * t2 * 2.0 + k12 * k13 * k15 * k36 * t3 * 4.0 - k12 * k15 * k23 * k26 * t3 * 6.0 - k13 * k16 * k22 * k25 * t3 * 2.0 + k12 * k13 * k15 * k36 * t4 * 4.0 - k12 * k15 * k23 * k26 * t4 * 2.0 + k13 * k16 * k22 * k25 * t4 * 2.0 - k12 * k15 * k22 * k25 * t8 * 2.0 - k12 * k15 * k22 * k25 * t10 * 6.0 - k12 * k13 * k26 * k33 * t2 * 4.0 - k12 * k15 * k22 * k25 * t12 * 2.0 + k12 * k16 * k23 * k33 * t2 + k13 * k15 * k23 * k33 * t2 * 3.0 - k12 * k13 * k26 * k33 * t3 * 2.0 + k12 * k15 * k22 * k25 * t13 * 4.0 - k12 * k16 * k23 * k33 * t3 * 3.0 + k13 * k15 * k23 * k33 * t3 * 9.0 - k12 * k13 * k26 * k33 * t4 * 6.0 - k12 * k15 * k23 * k36 * t2 * 4.0 - k12 * k16 * k23 * k33 * t4 * 3.0 + k13 * k15 * k23 * k33 * t4 * 9.0 - k13 * k16 * k22 * k35 * t2 * 2.0 - k13 * k22 * k25 * k26 * t2 * 4.0 - k12 * k15 * k23 * k36 * t3 * 6.0 + k13 * k16 * k22 * k35 * t3 * 4.0 - k12 * k13 * k25 * k32 * t8 * 4.0 - k12 * k15 * k23 * k36 * t4 * 2.0 + k12 * k16 * k22 * k32 * t8 * 3.0 + k13 * k15 * k22 * k32 * t8 + k13 * k16 * k22 * k35 * t4 * 4.0 + k13 * k22 * k25 * k26 * t4 * 2.0 - k15 * k16 * k25 * k32 * t2 * 2.0 - k16 * k22 * k23 * k25 * t4 * 8.0 - k12 * k13 * k25 * k32 * t9 * 2.0 + k12 * k16 * k22 * k32 * t9 * 3.0 + k13 * k15 * k22 * k32 * t9 + k15 * k16 * k25 * k32 * t3 * 4.0 - k12 * k13 * k25 * k32 * t10 * 2.0 - k12 * k15 * k22 * k35 * t8 * 2.0 - k12 * k16 * k22 * k32 * t10 * 3.0 + k13 * k15 * k22 * k32 * t10 * 9.0 + k15 * k16 * k25 * k32 * t4 * 4.0 - k12 * k13 * k25 * k32 * t11 * 2.0 - k12 * k15 * k22 * k35 * t9 * 4.0 - k12 * k16 * k22 * k32 * t11 - k13 * k15 * k22 * k32 * t11 - k12 * k13 * k25 * k32 * t12 * 6.0 - k12 * k15 * k22 * k35 * t10 * 6.0 - k12 * k16 * k22 * k32 * t12 * 3.0 + k13 * k15 * k22 * k32 * t12 * 9.0; coeffs(4) += k12 * k13 * k25 * k32 * t13 * 6.0 + k12 * k15 * k22 * k35 * t11 * 6.0 - k12 * k16 * k22 * k32 * t13 - k13 * k15 * k22 * k32 * t13 - k12 * k13 * k33 * k36 * t2 * 2.0 - k12 * k15 * k22 * k35 * t12 * 2.0 + k12 * k23 * k26 * k33 * t2 * 3.0 - k12 * k13 * k33 * k36 * t3 * 2.0 - k12 * k15 * k22 * k35 * t13 * 2.0 + k12 * k23 * k26 * k33 * t3 * 3.0 - k12 * k13 * k33 * k36 * t4 * 6.0 + k12 * k23 * k26 * k33 * t4 * 9.0 - k16 * k22 * k23 * k35 * t2 * 8.0 + k22 * k23 * k25 * k26 * t2 * 4.0 + k13 * k22 * k25 * k36 * t3 * 2.0 + k13 * k22 * k26 * k35 * t3 * 2.0 + k13 * k23 * k25 * k35 * t3 * 6.0 - k16 * k22 * k23 * k35 * t3 * 8.0 + k12 * k22 * k25 * k33 * t8 * 5.0 + k12 * k22 * k26 * k32 * t8 * 5.0 + k12 * k23 * k25 * k32 * t8 * 5.0 + k13 * k22 * k25 * k36 * t4 * 4.0 + k13 * k22 * k26 * k35 * t4 * 4.0 + k13 * k23 * k25 * k35 * t4 * 4.0 - k15 * k16 * k32 * k35 * t2 * 2.0 - k15 * k22 * k23 * k32 * t8 * 6.0 + k15 * k25 * k26 * k32 * t2 * 4.0 - k16 * k22 * k23 * k35 * t4 * 8.0 + k22 * k23 * k25 * k26 * t4 * 4.0 - k12 * k13 * k32 * k35 * t9 * 2.0 - k12 * k22 * k25 * k33 * t9 - k12 * k22 * k26 * k32 * t9 - k12 * k23 * k25 * k32 * t9 + k15 * k16 * k32 * k35 * t3 * 2.0 - k15 * k22 * k23 * k32 * t9 * 2.0 - k15 * k25 * k26 * k32 * t3 * 2.0 - k12 * k13 * k32 * k35 * t10 * 2.0 + k12 * k22 * k25 * k33 * t10 * 3.0 + k12 * k22 * k26 * k32 * t10 * 3.0 + k12 * k23 * k25 * k32 * t10 - k15 * k16 * k32 * k35 * t4 * 2.0 - k15 * k22 * k23 * k32 * t10 * 4.0 - k15 * k25 * k26 * k32 * t4 * 4.0 + k12 * k13 * k32 * k35 * t11 * 4.0 + k12 * k22 * k25 * k33 * t11 + k12 * k22 * k26 * k32 * t11 * 3.0 + k12 * k23 * k25 * k32 * t11 - k15 * k22 * k23 * k32 * t11 * 2.0 - k12 * k13 * k32 * k35 * t12 * 6.0 + k12 * k22 * k25 * k33 * t12 * 3.0 + k12 * k22 * k26 * k32 * t12 * 9.0 + k12 * k23 * k25 * k32 * t12 * 9.0 - k15 * k22 * k23 * k32 * t12 * 6.0 - k12 * k22 * k25 * k33 * t13 * 5.0 - k12 * k22 * k26 * k32 * t13 * 5.0 - k12 * k23 * k25 * k32 * t13 * 5.0 + k15 * k22 * k23 * k32 * t13 * 2.0 + k12 * k23 * k33 * k36 * t2 * 3.0 + k12 * k23 * k33 * k36 * t3 * 9.0 + k12 * k23 * k33 * k36 * t4 * 3.0 - k13 * k22 * k32 * k33 * t8 * 2.0 + k13 * k22 * k35 * k36 * t2 * 4.0 - k16 * k25 * k32 * k33 * t2 * 8.0 + k22 * k23 * k25 * k36 * t2 * 4.0 + k22 * k23 * k26 * k35 * t2 * 4.0 - k13 * k22 * k32 * k33 * t9 * 6.0 - k13 * k22 * k35 * k36 * t3 * 4.0 - k16 * k25 * k32 * k33 * t3 * 8.0 - k12 * k22 * k32 * k36 * t8 - k12 * k22 * k33 * k35 * t8 - k12 * k23 * k32 * k35 * t8 - k13 * k22 * k32 * k33 * t10 * 6.0 - k13 * k22 * k35 * k36 * t4 * 2.0 - k16 * k25 * k32 * k33 * t4 * 8.0 + k12 * k22 * k32 * k36 * t9 * 5.0 + k12 * k22 * k33 * k35 * t9 * 5.0 + k12 * k23 * k32 * k35 * t9 * 5.0 + k13 * k22 * k32 * k33 * t11 * 2.0 + k15 * k25 * k32 * k36 * t3 * 4.0 + k15 * k25 * k33 * k35 * t3 * 4.0 + k15 * k26 * k32 * k35 * t3 * 4.0 + k12 * k22 * k32 * k36 * t10 * 9.0 + k12 * k22 * k33 * k35 * t10 * 9.0 + k12 * k23 * k32 * k35 * t10 * 3.0 - k13 * k22 * k32 * k33 * t12 * 4.0 + k15 * k25 * k32 * k36 * t4 * 2.0 + k15 * k25 * k33 * k35 * t4 * 6.0 + k15 * k26 * k32 * k35 * t4 * 2.0 - k12 * k22 * k32 * k36 * t11 * 5.0 - k12 * k22 * k33 * k35 * t11 * 5.0 - k12 * k23 * k32 * k35 * t11 * 5.0 - k13 * k22 * k32 * k33 * t13 * 2.0 + k12 * k22 * k32 * k36 * t12 * 3.0 + k12 * k22 * k33 * k35 * t12 + k12 * k23 * k32 * k35 * t12 * 3.0 + k12 * k22 * k32 * k36 * t13 * 3.0 + k12 * k22 * k33 * k35 * t13 + k12 * k23 * k32 * k35 * t13 + k22 * k23 * k32 * k33 * t8 * 8.0 + k22 * k23 * k35 * k36 * t2 * 1.2E1 + k25 * k26 * k32 * k33 * t2 * 1.2E1 - k16 * k32 * k33 * k35 * t3 * 8.0 + k22 * k23 * k32 * k33 * t9 * 8.0 + k22 * k23 * k35 * k36 * t3 * 8.0 + k25 * k26 * k32 * k33 * t3 * 4.0 - k15 * k32 * k35 * k36 * t2 * 4.0 + k22 * k23 * k35 * k36 * t4 * 4.0 + k25 * k26 * k32 * k33 * t4 * 8.0 + k15 * k32 * k35 * k36 * t3 * 2.0 + k22 * k23 * k32 * k33 * t11 * 4.0 + k22 * k23 * k32 * k33 * t13 * 4.0 + k25 * k32 * k33 * k36 * t2 * 4.0 + k26 * k32 * k33 * k35 * t2 * 4.0 + k32 * k33 * k35 * k36 * t2 * 4.0 + k32 * k33 * k35 * k36 * t3 * 4.0 + k12 * k13 * k15 * t4 * t10 * 2.0 + k12 * k13 * k15 * t3 * t12 * 2.0 - k13 * k16 * k23 * t2 * t4 - k13 * k16 * k23 * t3 * t4 * 6.0 - k12 * k15 * k23 * t4 * t8 - k12 * k15 * k23 * t4 * t10 - k12 * k15 * k23 * t2 * t13 * 2.0 - k12 * k15 * k23 * t3 * t12 * 3.0 - k12 * k15 * k23 * t4 * t11 - k12 * k15 * k23 * t4 * t13 - k13 * k23 * k26 * t2 * t4 * 4.0 - k13 * k23 * k26 * t3 * t4 * 3.0 - k15 * k16 * k33 * t2 * t3 - k12 * k13 * k33 * t3 * t9 - k12 * k13 * k33 * t2 * t11 * 2.0 - k15 * k16 * k33 * t3 * t4 * 6.0 - k12 * k13 * k33 * t3 * t11 - k12 * k13 * k33 * t4 * t10 * 3.0 - k13 * k22 * k25 * t4 * t8 - k12 * k13 * k33 * t3 * t12 - k13 * k22 * k25 * t4 * t9 - k12 * k13 * k33 * t3 * t13 - k13 * k22 * k25 * t2 * t12 * 4.0 - k13 * k22 * k25 * t4 * t10 * 3.0 + k13 * k22 * k25 * t2 * t13 * 2.0 - k13 * k22 * k25 * t3 * t12 - k13 * k22 * k25 * t4 * t12 * 6.0 - k13 * k23 * k36 * t2 * t4 * 2.0 - k15 * k26 * k33 * t2 * t3 * 2.0 + k12 * k23 * k33 * t3 * t9 * 3.0 + k12 * k23 * k33 * t4 * t8 * 3.0 + k12 * k23 * k33 * t2 * t11 - k13 * k22 * k35 * t3 * t9 * 2.0 + k22 * k23 * k25 * t4 * t8 * 4.0 + k12 * k22 * k32 * t2 * t15 + k12 * k22 * k32 * t3 * t14 + k12 * k23 * k33 * t2 * t13 + k12 * k23 * k33 * t4 * t11 * 3.0 - k13 * k22 * k35 * t2 * t11 * 2.0 - k13 * k22 * k35 * t4 * t9 * 2.0 - k15 * k25 * k32 * t3 * t8 * 2.0 + k12 * k22 * k32 * t2 * t16 + k12 * k22 * k32 * t4 * t14 + k12 * k23 * k33 * t3 * t13 * 3.0 - k13 * k22 * k35 * t2 * t12 * 2.0 - k15 * k25 * k32 * t2 * t10 * 2.0 - k15 * k25 * k32 * t4 * t8 * 2.0 + k22 * k23 * k25 * t2 * t12 * 2.0 + k12 * k22 * k32 * t3 * t16 + k12 * k22 * k32 * t4 * t15 + k12 * k22 * k32 * t8 * t11 * 3.0 + k12 * k22 * k32 * t9 * t10 * 3.0 + k12 * k22 * k32 * t8 * t12 * 3.0 - k15 * k25 * k32 * t2 * t13 * 2.0 + k12 * k22 * k32 * t9 * t13 * 3.0 + k12 * k22 * k32 * t10 * t13 * 3.0 + k12 * k22 * k32 * t11 * t12 * 3.0 - k15 * k33 * k36 * t2 * t3 * 4.0 - k15 * k33 * k36 * t3 * t4 * 3.0 + k22 * k23 * k35 * t2 * t9 * 4.0 + k25 * k26 * k35 * t2 * t3 * 2.0 + k22 * k23 * k35 * t3 * t9 * 4.0 - k15 * k32 * k35 * t3 * t8 + k22 * k23 * k35 * t2 * t11 * 2.0 + k22 * k23 * k35 * t4 * t9 * 4.0 - k15 * k32 * k35 * t2 * t10 * 4.0 - k15 * k32 * k35 * t3 * t9 + k22 * k23 * k35 * t2 * t12 * 2.0 + k15 * k32 * k35 * t2 * t11 * 2.0 - k15 * k32 * k35 * t3 * t10 * 6.0 + k22 * k23 * k35 * t2 * t13 * 2.0 - k15 * k32 * k35 * t4 * t10 - k15 * k32 * k35 * t3 * t12 * 3.0 + k25 * k32 * k33 * t2 * t8 * 4.0 + k25 * k32 * k33 * t3 * t8 * 4.0 + k25 * k32 * k33 * t2 * t10 * 2.0 + k25 * k32 * k33 * t4 * t8 * 4.0 + k25 * k35 * k36 * t2 * t4 * 2.0 + k25 * k32 * k33 * t2 * t11 * 2.0 + k25 * k32 * k33 * t2 * t13 * 2.0 + k32 * k33 * k35 * t2 * t10 * 2.0 + k32 * k33 * k35 * t3 * t9 * 4.0 + k16 * k26 * t2 * t3 * t4 - k13 * k23 * t2 * t4 * t11 + k16 * k36 * t2 * t3 * t4 - k15 * k33 * t2 * t3 * t13 + k26 * k36 * t2 * t3 * t4 + k25 * k35 * t2 * t4 * t10 + k25 * k35 * t2 * t3 * t12; coeffs(4) += k12 * k13 * k15 * k22 * k23 * k25 * 8.0 - k12 * k13 * k16 * k22 * k23 * k32 * 4.0 + k12 * k13 * k15 * k22 * k23 * k35 * 8.0 - k12 * k13 * k22 * k23 * k25 * k33 * 4.0 - k12 * k13 * k22 * k23 * k26 * k32 * 4.0 + k12 * k13 * k15 * k25 * k32 * k33 * 8.0 - k12 * k15 * k16 * k22 * k32 * k33 * 4.0 - k12 * k13 * k22 * k23 * k32 * k36 * 4.0 - k12 * k13 * k22 * k23 * k33 * k35 * 4.0 + k12 * k13 * k15 * k32 * k33 * k35 * 8.0 - k12 * k15 * k22 * k26 * k32 * k33 * 4.0 - k12 * k15 * k23 * k25 * k32 * k33 * 4.0 + k12 * k16 * k22 * k25 * k32 * k35 * 6.0 - k13 * k15 * k22 * k25 * k32 * k35 * 1.0E1 - k12 * k15 * k22 * k32 * k33 * k36 * 4.0 - k12 * k15 * k23 * k32 * k33 * k35 * 4.0 - k12 * k22 * k25 * k26 * k32 * k35 * 1.0E1 + k15 * k22 * k23 * k25 * k32 * k35 * 8.0 + k13 * k22 * k25 * k32 * k33 * k35 * 8.0 - k12 * k22 * k25 * k32 * k35 * k36 * 1.0E1 + k12 * k15 * k16 * k22 * k25 * t4 * 2.0 - k12 * k13 * k16 * k25 * k32 * t3 * 4.0 + k13 * k15 * k16 * k22 * k32 * t3 * 2.0 + k13 * k15 * k16 * k22 * k32 * t4 * 2.0 + k12 * k13 * k15 * k25 * k35 * t3 * 4.0 + k12 * k13 * k15 * k25 * k35 * t4 * 4.0 - k12 * k15 * k16 * k22 * k35 * t4 * 4.0 - k12 * k15 * k22 * k25 * k26 * t4 * 2.0 - k12 * k13 * k25 * k26 * k32 * t2 * 4.0 + k12 * k16 * k22 * k25 * k33 * t2 + k12 * k16 * k22 * k26 * k32 * t2 + k12 * k16 * k23 * k25 * k32 * t2 + k13 * k15 * k22 * k25 * k33 * t2 * 3.0 + k13 * k15 * k22 * k26 * k32 * t2 * 3.0 + k13 * k15 * k23 * k25 * k32 * t2 * 3.0 - k15 * k16 * k22 * k23 * k32 * t2 * 2.0 + k12 * k13 * k16 * k32 * k35 * t3 * 2.0 - k12 * k13 * k22 * k23 * k32 * t9 * 2.0 - k12 * k13 * k25 * k26 * k32 * t3 * 2.0 + k12 * k16 * k22 * k25 * k33 * t3 + k12 * k16 * k22 * k26 * k32 * t3 + k12 * k16 * k23 * k25 * k32 * t3 * 3.0 + k13 * k15 * k22 * k25 * k33 * t3 + k13 * k15 * k22 * k26 * k32 * t3 + k13 * k15 * k23 * k25 * k32 * t3 * 3.0 - k15 * k16 * k22 * k23 * k32 * t3 * 4.0 - k12 * k15 * k22 * k25 * k36 * t2 * 4.0 - k12 * k15 * k22 * k26 * k35 * t2 * 4.0 - k12 * k15 * k23 * k25 * k35 * t2 * 4.0 - k12 * k16 * k22 * k25 * k33 * t4 * 6.0 - k12 * k16 * k22 * k26 * k32 * t4 * 2.0 - k12 * k16 * k23 * k25 * k32 * t4 * 2.0 + k13 * k15 * k22 * k25 * k33 * t4 * 6.0 + k13 * k15 * k22 * k26 * k32 * t4 * 2.0 + k13 * k15 * k23 * k25 * k32 * t4 * 2.0 - k15 * k16 * k22 * k23 * k32 * t4 * 4.0 - k12 * k13 * k22 * k23 * k32 * t11 * 2.0 - k12 * k15 * k22 * k25 * k36 * t3 * 2.0 - k12 * k15 * k22 * k26 * k35 * t3 * 2.0 - k12 * k15 * k23 * k25 * k35 * t3 * 6.0 - k12 * k13 * k22 * k23 * k32 * t12 * 6.0 - k12 * k13 * k22 * k23 * k32 * t13 * 2.0 - k13 * k16 * k22 * k32 * k33 * t2 * 2.0 - k13 * k16 * k22 * k32 * k33 * t3 * 4.0 - k12 * k13 * k25 * k32 * k36 * t2 * 4.0 - k12 * k13 * k25 * k33 * k35 * t2 * 4.0 - k12 * k13 * k26 * k32 * k35 * t2 * 4.0 + k12 * k16 * k22 * k32 * k36 * t2 + k12 * k16 * k22 * k33 * k35 * t2 + k12 * k16 * k23 * k32 * k35 * t2 + k12 * k22 * k25 * k26 * k33 * t2 * 2.0 + k12 * k23 * k25 * k26 * k32 * t2 * 2.0 + k13 * k15 * k22 * k32 * k36 * t2 * 3.0 + k13 * k15 * k22 * k33 * k35 * t2 * 3.0 + k13 * k15 * k23 * k32 * k35 * t2 * 3.0 - k13 * k16 * k22 * k32 * k33 * t4 * 4.0 - k15 * k22 * k23 * k25 * k33 * t2 * 4.0 - k15 * k22 * k23 * k26 * k32 * t2 * 4.0 - k12 * k16 * k22 * k32 * k36 * t3 * 2.0 - k12 * k16 * k22 * k33 * k35 * t3 * 2.0 - k12 * k16 * k23 * k32 * k35 * t3 * 6.0 + k13 * k15 * k22 * k32 * k36 * t3 * 2.0 + k13 * k15 * k22 * k33 * k35 * t3 * 2.0 + k13 * k15 * k23 * k32 * k35 * t3 * 6.0 - k12 * k13 * k25 * k32 * k36 * t4 * 2.0 - k12 * k13 * k25 * k33 * k35 * t4 * 6.0 - k12 * k13 * k26 * k32 * k35 * t4 * 2.0 - k12 * k15 * k22 * k32 * k33 * t8 * 2.0 - k12 * k15 * k22 * k35 * k36 * t2 * 4.0 + k12 * k16 * k22 * k32 * k36 * t4 + k12 * k16 * k22 * k33 * k35 * t4 * 3.0 + k12 * k16 * k23 * k32 * k35 * t4 + k12 * k22 * k25 * k26 * k33 * t4 * 6.0 + k12 * k23 * k25 * k26 * k32 * t4 * 2.0 + k13 * k15 * k22 * k32 * k36 * t4 + k13 * k15 * k22 * k33 * k35 * t4 * 3.0 + k13 * k15 * k23 * k32 * k35 * t4 - k12 * k15 * k22 * k32 * k33 * t10 * 6.0 - k12 * k15 * k22 * k35 * k36 * t4 * 2.0 - k12 * k15 * k22 * k32 * k33 * t11 * 2.0 - k12 * k15 * k22 * k32 * k33 * t13 * 2.0 - k13 * k22 * k26 * k32 * k33 * t2 * 8.0 - k13 * k23 * k25 * k32 * k33 * t2 * 8.0; coeffs(4) += k16 * k22 * k23 * k32 * k33 * t2 * 8.0 - k13 * k22 * k26 * k32 * k33 * t3 * 2.0 - k13 * k23 * k25 * k32 * k33 * t3 * 6.0 + k16 * k22 * k23 * k32 * k33 * t3 * 8.0 + k12 * k22 * k25 * k33 * k36 * t2 * 4.0 + k12 * k22 * k26 * k32 * k36 * t2 * 4.0 + k12 * k22 * k26 * k33 * k35 * t2 * 4.0 + k12 * k23 * k25 * k32 * k36 * t2 * 4.0 + k12 * k23 * k25 * k33 * k35 * t2 * 4.0 + k12 * k23 * k26 * k32 * k35 * t2 * 4.0 - k13 * k22 * k26 * k32 * k33 * t4 * 4.0 - k13 * k23 * k25 * k32 * k33 * t4 * 4.0 - k15 * k22 * k23 * k32 * k36 * t2 * 8.0 - k15 * k22 * k23 * k33 * k35 * t2 * 8.0 + k16 * k22 * k23 * k32 * k33 * t4 * 8.0 - k12 * k13 * k32 * k35 * k36 * t3 * 2.0 + k12 * k22 * k25 * k33 * k36 * t3 + k12 * k22 * k26 * k32 * k36 * t3 + k12 * k22 * k26 * k33 * k35 * t3 + k12 * k23 * k25 * k32 * k36 * t3 * 3.0 + k12 * k23 * k25 * k33 * k35 * t3 * 3.0 + k12 * k23 * k26 * k32 * k35 * t3 * 3.0 - k15 * k22 * k23 * k32 * k36 * t3 * 4.0 - k15 * k22 * k23 * k33 * k35 * t3 * 4.0 + k12 * k22 * k25 * k33 * k36 * t4 * 3.0 + k12 * k22 * k26 * k32 * k36 * t4 + k12 * k22 * k26 * k33 * k35 * t4 * 3.0 + k12 * k23 * k25 * k32 * k36 * t4 + k12 * k23 * k25 * k33 * k35 * t4 * 3.0 + k12 * k23 * k26 * k32 * k35 * t4 - k15 * k22 * k23 * k32 * k36 * t4 * 2.0 - k15 * k22 * k23 * k33 * k35 * t4 * 6.0 - k12 * k22 * k25 * k32 * k35 * t8 - k12 * k22 * k25 * k32 * k35 * t9 + k12 * k22 * k25 * k32 * k35 * t10 * 3.0 + k12 * k22 * k25 * k32 * k35 * t12 * 3.0 - k13 * k22 * k32 * k33 * k36 * t2 * 4.0 - k13 * k23 * k32 * k33 * k35 * t2 * 4.0 + k22 * k23 * k26 * k32 * k33 * t2 * 4.0 + k12 * k22 * k33 * k35 * k36 * t2 * 2.0 + k12 * k23 * k32 * k35 * k36 * t2 * 2.0 + k12 * k22 * k33 * k35 * k36 * t3 * 2.0 + k12 * k23 * k32 * k35 * k36 * t3 * 6.0 + k22 * k23 * k32 * k33 * k36 * t2 * 4.0 + k12 * k13 * k15 * k16 * t3 * t4 + k12 * k13 * k15 * k26 * t3 * t4 - k12 * k15 * k16 * k23 * t3 * t4 * 3.0 - k12 * k13 * k16 * k33 * t3 * t4 * 3.0 - k13 * k16 * k22 * k25 * t2 * t4 + k12 * k13 * k15 * k36 * t3 * t4 - k12 * k15 * k22 * k25 * t4 * t8 - k12 * k15 * k22 * k25 * t2 * t13 * 2.0 - k12 * k13 * k26 * k33 * t3 * t4 * 3.0 + k12 * k16 * k23 * k33 * t3 * t4 * 9.0 - k13 * k22 * k25 * k26 * t2 * t4 * 2.0 + k16 * k22 * k23 * k25 * t2 * t4 * 2.0 - k12 * k15 * k23 * k36 * t3 * t4 * 3.0 - k12 * k13 * k25 * k32 * t4 * t10 + k12 * k16 * k22 * k32 * t4 * t10 * 3.0 - k12 * k13 * k25 * k32 * t3 * t12 * 3.0 + k12 * k16 * k22 * k32 * t3 * t12 * 3.0 - k12 * k15 * k22 * k35 * t4 * t10 * 3.0 - k12 * k15 * k22 * k35 * t3 * t12 - k13 * k22 * k25 * k36 * t2 * t4 * 2.0 - k13 * k22 * k26 * k35 * t2 * t4 * 2.0 - k13 * k23 * k25 * k35 * t2 * t4 * 2.0 + k16 * k22 * k23 * k35 * t2 * t4 * 2.0 - k15 * k16 * k32 * k35 * t2 * t3 - k12 * k13 * k32 * k35 * t3 * t9 + k12 * k22 * k25 * k33 * t4 * t8 * 3.0 + k12 * k22 * k26 * k32 * t4 * t8 + k12 * k23 * k25 * k32 * t4 * t8 - k12 * k13 * k32 * k35 * t2 * t11 * 2.0 + k12 * k22 * k25 * k33 * t2 * t13 + k12 * k22 * k26 * k32 * t2 * t13 + k12 * k23 * k25 * k32 * t2 * t13 - k15 * k22 * k23 * k32 * t2 * t13 * 2.0 + k16 * k25 * k32 * k33 * t2 * t3 * 2.0 + k22 * k23 * k25 * k36 * t2 * t4 * 2.0 + k22 * k23 * k26 * k35 * t2 * t4 * 2.0 - k13 * k22 * k32 * k33 * t2 * t11 * 2.0 - k15 * k25 * k32 * k36 * t2 * t3 * 2.0 - k15 * k25 * k33 * k35 * t2 * t3 * 2.0 - k15 * k26 * k32 * k35 * t2 * t3 * 2.0 + k12 * k22 * k32 * k36 * t3 * t9 + k12 * k22 * k33 * k35 * t3 * t9 + k12 * k23 * k32 * k35 * t3 * t9 * 3.0 + k12 * k22 * k32 * k36 * t2 * t11 + k12 * k22 * k33 * k35 * t2 * t11 + k12 * k23 * k32 * k35 * t2 * t11 + k16 * k32 * k33 * k35 * t2 * t3 * 2.0 - k15 * k32 * k35 * k36 * t2 * t3 * 2.0 + k25 * k32 * k33 * k36 * t2 * t3 * 2.0 + k26 * k32 * k33 * k35 * t2 * t3 * 2.0 + k12 * k13 * k15 * k22 * k23 * k32 * k33 * 8.0 + k12 * k13 * k15 * k22 * k23 * k25 * t4 * 2.0 - k12 * k13 * k16 * k22 * k23 * k32 * t4 * 2.0 + k12 * k13 * k15 * k22 * k23 * k35 * t4 * 2.0 - k12 * k13 * k22 * k23 * k25 * k33 * t4 * 6.0 - k12 * k13 * k22 * k23 * k26 * k32 * t4 * 2.0 + k12 * k13 * k15 * k25 * k32 * k33 * t3 * 2.0 - k12 * k15 * k16 * k22 * k32 * k33 * t3 * 2.0 + k12 * k13 * k15 * k32 * k33 * k35 * t3 * 2.0 + k12 * k16 * k22 * k25 * k32 * k35 * t2 + k13 * k15 * k22 * k25 * k32 * k35 * t2 * 3.0 - k12 * k15 * k22 * k32 * k33 * k36 * t3 * 2.0 - k12 * k15 * k23 * k32 * k33 * k35 * t3 * 6.0 + k12 * k22 * k25 * k26 * k32 * k35 * t2 * 2.0 - k15 * k22 * k23 * k25 * k32 * k35 * t2 * 4.0 - k13 * k22 * k25 * k32 * k33 * k35 * t2 * 4.0 + k12 * k22 * k25 * k32 * k35 * k36 * t2 * 2.0 + k22 * k23 * k25 * k32 * k33 * k35 * t2 * 4.0; coeffs(5) = k25 * t14 * 2.4E1 + k25 * t15 * 2.4E1 + k25 * t16 * 2.4E1 + k25 * t17 * 2.0 + k25 * t19 * 2.0 + k35 * t14 * 2.4E1 + k35 * t15 * 2.4E1 + k35 * t16 * 2.4E1 + k35 * t18 * 2.0 + k35 * t20 * 2.0 - k16 * k25 * k26 * 4.8E1 - k16 * k25 * k36 * 4.8E1 - k16 * k26 * k35 * 4.8E1 - k16 * k35 * k36 * 4.8E1 + k25 * k26 * k36 * 4.8E1 + k26 * k35 * k36 * 4.8E1 + k13 * k22 * t14 * 8.0 - k16 * k25 * t8 * 1.2E1 - k13 * k22 * t15 * 8.0 - k16 * k25 * t9 * 4.0 + k13 * k22 * t16 * 8.0 + k16 * k25 * t10 * 1.2E1 - k16 * k25 * t11 * 4.0 + k16 * k25 * t12 * 2.0E1 - k13 * k22 * t19 - k16 * k25 * t13 * 1.2E1 - k16 * k35 * t8 * 4.0 - k22 * k23 * t14 * 2.0E1 + k25 * k26 * t8 * 2.0E1 - k16 * k35 * t9 * 1.2E1 - k22 * k23 * t15 * 4.0 + k25 * k26 * t9 * 4.0 + k15 * k32 * t14 * 8.0 + k16 * k35 * t10 * 2.0E1 - k22 * k23 * t16 * 2.0E1 - k25 * k26 * t10 * 4.0 + k15 * k32 * t15 * 8.0 - k16 * k35 * t11 * 1.2E1 + k25 * k26 * t11 * 4.0 - k15 * k32 * t16 * 8.0 + k16 * k35 * t12 * 1.2E1 - k25 * k26 * t12 * 2.0E1 - k16 * k35 * t13 * 4.0 + k25 * k26 * t13 * 1.2E1 - k15 * k32 * t20 + k25 * k36 * t8 * 1.2E1 + k26 * k35 * t8 * 1.2E1 + k25 * k36 * t9 * 1.2E1 + k26 * k35 * t9 * 1.2E1 - k25 * k36 * t10 * 1.2E1 - k26 * k35 * t10 * 1.2E1 + k25 * k36 * t11 * 4.0 + k26 * k35 * t11 * 1.2E1 - k25 * k36 * t12 * 1.2E1 - k26 * k35 * t12 * 1.2E1 + k25 * k36 * t13 * 1.2E1 + k26 * k35 * t13 * 4.0 - k32 * k33 * t14 * 2.0E1 + k35 * k36 * t8 * 4.0 - k32 * k33 * t15 * 2.0E1 + k35 * k36 * t9 * 2.0E1 - k32 * k33 * t16 * 4.0 - k35 * k36 * t10 * 2.0E1 + k35 * k36 * t11 * 1.2E1 - k35 * k36 * t12 * 4.0 + k35 * k36 * t13 * 4.0 - k25 * t2 * t14 * 2.0 - k25 * t2 * t15 * 6.0 - k25 * t3 * t14 * 4.0 - k25 * t8 * t9 * 2.0 - k25 * t2 * t16 * 1.4E1 - k25 * t4 * t14 * 6.0 - k25 * t8 * t10 * 2.0 - k25 * t3 * t16 * 4.0 - k25 * t4 * t15 * 6.0 + k25 * t8 * t11 * 2.0 - k25 * t9 * t10 * 4.0 - k25 * t4 * t16 * 2.0 - k25 * t8 * t12 * 8.0 + k25 * t5 * t16 * 2.0 + k25 * t8 * t13 * 2.0 - k25 * t9 * t12 * 2.0 + k25 * t9 * t13 * 4.0 + k25 * t10 * t12 * 2.0 - k25 * t10 * t13 * 4.0 - k25 * t11 * t12 * 2.0 - k25 * t12 * t13 * 2.0 - k35 * t2 * t14 * 2.0 - k35 * t2 * t15 * 1.4E1 - k35 * t3 * t14 * 6.0 - k35 * t8 * t9 * 2.0 - k35 * t2 * t16 * 6.0 - k35 * t3 * t15 * 2.0 - k35 * t4 * t14 * 4.0 - k35 * t8 * t10 * 2.0 - k35 * t3 * t16 * 6.0 - k35 * t4 * t15 * 4.0 + k35 * t8 * t11 * 4.0 - k35 * t9 * t10 * 8.0 + k35 * t5 * t15 * 2.0 - k35 * t8 * t12 * 4.0 + k35 * t9 * t11 * 2.0 - k35 * t9 * t12 * 2.0 - k35 * t10 * t11 * 2.0 + k35 * t9 * t13 * 2.0 + k35 * t10 * t12 * 2.0 - k35 * t10 * t13 * 2.0 - k35 * t11 * t12 * 4.0 - k13 * k16 * k22 * k36 * 1.6E1 - k13 * k16 * k23 * k35 * 1.6E1 - k13 * k23 * k25 * k26 * 1.6E1 + k16 * k22 * k23 * k26 * 2.4E1 - k15 * k16 * k25 * k33 * 1.6E1 - k15 * k16 * k26 * k32 * 1.6E1 + k16 * k22 * k23 * k36 * 4.0E1 + k15 * k25 * k26 * k33 * 1.6E1 + k13 * k23 * k35 * k36 * 1.6E1 + k16 * k26 * k32 * k33 * 4.0E1 - k22 * k23 * k26 * k36 * 2.4E1 + k16 * k32 * k33 * k36 * 2.4E1 - k15 * k33 * k35 * k36 * 1.6E1 - k26 * k32 * k33 * k36 * 2.4E1 - k13 * k16 * k22 * t8 * 2.0 - k13 * k16 * k22 * t9 * 2.0 + k13 * k16 * k22 * t10 * 6.0 + k13 * k16 * k22 * t11 * 2.0 - k12 * k15 * k22 * t14 * 2.0 + k13 * k16 * k22 * t12 * 6.0 + k12 * k15 * k22 * t15 * 6.0 - k13 * k16 * k22 * t13 * 6.0 - k12 * k15 * k22 * t16 * 2.0 - k13 * k22 * k26 * t8 * 2.0 - k13 * k23 * k25 * t8 * 2.0 + k16 * k22 * k23 * t8 * 4.0 + k16 * k25 * k26 * t2 * 8.0 + k13 * k22 * k26 * t9 * 6.0 + k13 * k23 * k25 * t9 * 6.0 + k16 * k22 * k23 * t9 * 4.0 + k16 * k25 * k26 * t3 * 4.0 - k12 * k13 * k32 * t14 * 2.0 + k13 * k22 * k26 * t10 * 6.0 + k13 * k23 * k25 * t10 * 2.0 - k15 * k16 * k32 * t8 * 2.0 - k16 * k22 * k23 * t10 * 8.0 + k16 * k25 * k26 * t4 * 1.2E1 - k12 * k13 * k32 * t15 * 2.0 - k13 * k22 * k26 * t11 * 6.0 - k13 * k23 * k25 * t11 * 2.0 - k15 * k16 * k32 * t9 * 2.0 + k16 * k22 * k23 * t11 * 4.0 + k12 * k13 * k32 * t16 * 6.0 + k13 * k22 * k26 * t12 * 6.0 + k13 * k23 * k25 * t12 * 6.0 + k15 * k16 * k32 * t10 * 6.0 - k16 * k22 * k23 * t12 * 1.6E1 + k13 * k22 * k26 * t13 * 2.0 + k13 * k23 * k25 * t13 * 2.0 - k15 * k16 * k32 * t11 * 6.0 + k16 * k22 * k23 * t13 * 1.2E1 + k15 * k16 * k32 * t12 * 6.0 + k15 * k16 * k32 * t13 * 2.0 + k13 * k22 * k36 * t8 * 2.0 + k13 * k23 * k35 * t8 * 2.0 + k16 * k25 * k36 * t2 * 1.6E1 + k16 * k26 * k35 * t2 * 1.6E1 - k22 * k23 * k26 * t8 * 4.0 + k13 * k22 * k36 * t9 * 1.0E1 + k13 * k23 * k35 * t9 * 1.0E1 + k16 * k25 * k36 * t3 * 8.0 + k16 * k26 * k35 * t3 * 8.0 - k22 * k23 * k26 * t9 * 8.0 - k12 * k22 * k33 * t14 * 2.0 - k12 * k23 * k32 * t14 * 2.0 - k13 * k22 * k36 * t10 * 6.0 - k13 * k23 * k35 * t10 * 2.0 + k15 * k25 * k33 * t8 * 1.0E1 + k15 * k26 * k32 * t8 * 1.0E1 + k16 * k25 * k36 * t4 * 8.0 + k16 * k26 * k35 * t4 * 8.0 - k12 * k22 * k33 * t15 * 2.0 - k12 * k23 * k32 * t15 * 2.0 - k13 * k22 * k36 * t11 * 2.0 - k13 * k23 * k35 * t11 * 2.0 + k15 * k25 * k33 * t9 * 2.0 + k15 * k26 * k32 * t9 * 2.0 - k12 * k22 * k33 * t16 * 2.0 - k12 * k23 * k32 * t16 * 2.0 + k13 * k22 * k36 * t12 * 2.0 + k13 * k23 * k35 * t12 * 2.0 + k15 * k25 * k33 * t10 * 2.0 + k15 * k26 * k32 * t10 * 2.0 + k22 * k23 * k26 * t12 * 4.0 + k13 * k22 * k36 * t13 * 6.0 + k13 * k23 * k35 * t13 * 2.0 + k15 * k25 * k33 * t11 * 2.0 + k15 * k26 * k32 * t11 * 6.0 - k22 * k23 * k26 * t13 * 8.0 - k15 * k25 * k33 * t12 * 2.0 - k15 * k26 * k32 * t12 * 6.0 - k15 * k25 * k33 * t13 * 2.0 - k15 * k26 * k32 * t13 * 2.0 + k16 * k32 * k33 * t8 * 4.0 + k16 * k35 * k36 * t2 * 8.0 - k22 * k23 * k36 * t8 * 4.0 - k25 * k26 * k36 * t2 * 2.8E1 + k16 * k32 * k33 * t9 * 4.0 + k16 * k35 * k36 * t3 * 1.2E1 - k22 * k23 * k36 * t9 * 1.6E1 - k25 * k26 * k36 * t3 * 4.0 + k15 * k32 * k36 * t8 * 6.0 + k15 * k33 * k35 * t8 * 6.0 - k16 * k32 * k33 * t10 * 1.6E1 + k16 * k35 * k36 * t4 * 4.0 + k22 * k23 * k36 * t10 * 8.0 - k25 * k26 * k36 * t4 * 8.0 - k15 * k32 * k36 * t9 * 2.0 - k15 * k33 * k35 * t9 * 2.0 + k16 * k32 * k33 * t11 * 1.2E1 - k22 * k23 * k36 * t11 * 4.0 + k25 * k26 * k36 * t5 * 4.0 + k15 * k32 * k36 * t10 * 6.0 + k15 * k33 * k35 * t10 * 6.0 - k16 * k32 * k33 * t12 * 8.0 + k22 * k23 * k36 * t12 * 4.0 + k15 * k32 * k36 * t11 * 2.0 + k15 * k33 * k35 * t11 * 2.0 + k16 * k32 * k33 * t13 * 4.0 - k22 * k23 * k36 * t13 * 1.2E1 + k15 * k32 * k36 * t12 * 6.0 + k15 * k33 * k35 * t12 * 2.0 - k15 * k32 * k36 * t13 * 6.0 - k15 * k33 * k35 * t13 * 2.0 - k26 * k32 * k33 * t8 * 1.6E1 - k26 * k35 * k36 * t2 * 2.8E1 - k26 * k32 * k33 * t9 * 4.0 - k26 * k35 * k36 * t3 * 8.0 + k26 * k32 * k33 * t10 * 4.0 - k26 * k35 * k36 * t4 * 4.0 - k26 * k32 * k33 * t11 * 1.2E1 + k26 * k35 * k36 * t5 * 4.0 + k26 * k32 * k33 * t12 * 8.0 - k26 * k32 * k33 * t13 * 4.0 - k32 * k33 * k36 * t8 * 8.0 - k32 * k33 * k36 * t9 * 4.0 + k32 * k33 * k36 * t10 * 4.0 - k32 * k33 * k36 * t11 * 8.0 - k13 * k22 * t2 * t15 * 2.0 - k13 * k22 * t3 * t14 * 2.0 + k16 * k25 * t3 * t8 * 4.0 + k13 * k22 * t2 * t16 * 2.0 - k13 * k22 * t4 * t14 * 3.0 + k16 * k25 * t4 * t8 * 2.0 - k13 * k22 * t3 * t16 * 2.0 + k13 * k22 * t4 * t15 - k13 * k22 * t8 * t11 * 2.0 - k13 * k22 * t9 * t10 * 6.0 - k16 * k25 * t4 * t9 * 2.0 - k13 * k22 * t4 * t16 - k13 * k22 * t8 * t12 - k16 * k25 * t2 * t12 * 4.0 - k16 * k25 * t4 * t10 * 4.0 - k13 * k22 * t9 * t12 * 3.0 + k16 * k25 * t2 * t13 * 4.0 - k16 * k25 * t3 * t12 * 4.0 + k13 * k22 * t9 * t13 * 2.0 - k13 * k22 * t10 * t12 * 3.0 - k16 * k25 * t4 * t12 * 1.2E1 - k13 * k22 * t10 * t13 * 6.0 + k13 * k22 * t11 * t12 - k13 * k22 * t12 * t13 + k22 * k23 * t2 * t14 * 2.0 + k25 * k26 * t2 * t8 * 4.0 - k16 * k35 * t3 * t8 * 2.0 + k22 * k23 * t2 * t15 * 2.0 + k22 * k23 * t3 * t14 * 4.0 + k22 * k23 * t8 * t9 * 2.0 + k25 * k26 * t3 * t8 * 2.0 - k16 * k35 * t2 * t10 * 4.0 + k16 * k35 * t3 * t9 * 2.0 + k22 * k23 * t2 * t16 * 6.0 + k22 * k23 * t4 * t14 * 6.0 + k25 * k26 * t2 * t10 * 2.0 - k25 * k26 * t4 * t8 * 4.0 + k15 * k32 * t2 * t15 * 2.0 - k15 * k32 * t3 * t14 * 3.0 + k16 * k35 * t2 * t11 * 4.0 - k16 * k35 * t3 * t10 * 1.2E1 + k16 * k35 * t4 * t9 * 4.0 + k22 * k23 * t3 * t16 * 4.0 + k22 * k23 * t4 * t15 * 2.0 + k22 * k23 * t8 * t11 * 2.0 + k22 * k23 * t9 * t10 * 4.0 + k25 * k26 * t4 * t9 * 2.0 - k15 * k32 * t2 * t16 * 2.0 - k15 * k32 * t3 * t15 - k15 * k32 * t4 * t14 * 2.0 - k15 * k32 * t8 * t10 * 3.0 - k16 * k35 * t4 * t10 * 4.0 + k22 * k23 * t4 * t16 * 2.0 + k22 * k23 * t8 * t12 * 4.0 + k25 * k26 * t2 * t12 * 6.0 + k25 * k26 * t4 * t10 * 2.0 + k15 * k32 * t3 * t16 - k15 * k32 * t4 * t15 * 2.0 + k15 * k32 * t8 * t11 * 2.0 - k15 * k32 * t9 * t10 - k16 * k35 * t3 * t12 * 4.0 + k22 * k23 * t8 * t13 * 2.0 + k22 * k23 * t9 * t12 * 4.0 - k25 * k26 * t2 * t13 * 8.0 + k25 * k26 * t3 * t12 * 2.0 - k15 * k32 * t8 * t12 * 6.0 - k22 * k23 * t9 * t13 * 4.0 + k25 * k26 * t4 * t12 * 1.2E1 - k15 * k32 * t10 * t11 + k22 * k23 * t10 * t13 * 4.0 + k22 * k23 * t11 * t12 * 2.0 - k15 * k32 * t9 * t13 * 2.0 - k15 * k32 * t10 * t12 * 3.0 + k25 * k26 * t5 * t13 * 2.0 + k15 * k32 * t10 * t13 - k15 * k32 * t11 * t12 * 6.0 + k22 * k23 * t12 * t13 * 2.0 + k25 * k36 * t2 * t8 * 4.0 + k26 * k35 * t2 * t8 * 4.0 + k25 * k36 * t2 * t9 * 4.0 - k25 * k36 * t3 * t8 * 4.0 + k26 * k35 * t2 * t9 * 4.0 - k26 * k35 * t3 * t8 * 4.0 + k25 * k36 * t2 * t10 * 2.0 - k25 * k36 * t3 * t9 * 4.0 - k25 * k36 * t4 * t8 * 4.0 + k26 * k35 * t2 * t10 * 2.0 - k26 * k35 * t3 * t9 * 4.0 - k26 * k35 * t4 * t8 * 4.0 - k25 * k36 * t2 * t11 * 2.0 - k25 * k36 * t4 * t9 * 4.0 - k26 * k35 * t2 * t11 * 6.0 - k26 * k35 * t4 * t9 * 4.0; coeffs(5) += k25 * k36 * t2 * t12 * 2.0 + k26 * k35 * t2 * t12 * 2.0 - k25 * k36 * t2 * t13 * 6.0 - k26 * k35 * t2 * t13 * 2.0 + k32 * k33 * t2 * t14 * 2.0 + k32 * k33 * t2 * t15 * 6.0 + k32 * k33 * t3 * t14 * 6.0 + k32 * k33 * t8 * t9 * 2.0 + k35 * k36 * t2 * t9 * 4.0 + k35 * k36 * t3 * t8 * 2.0 + k32 * k33 * t2 * t16 * 2.0 + k32 * k33 * t3 * t15 * 2.0 + k32 * k33 * t4 * t14 * 4.0 + k32 * k33 * t8 * t10 * 4.0 + k35 * k36 * t2 * t10 * 6.0 - k35 * k36 * t3 * t9 * 4.0 + k32 * k33 * t3 * t16 * 2.0 + k32 * k33 * t4 * t15 * 4.0 - k32 * k33 * t8 * t11 * 4.0 + k32 * k33 * t9 * t10 * 4.0 - k35 * k36 * t2 * t11 * 8.0 + k35 * k36 * t3 * t10 * 1.2E1 + k35 * k36 * t4 * t9 * 2.0 + k32 * k33 * t8 * t12 * 4.0 + k32 * k33 * t9 * t11 * 2.0 + k35 * k36 * t2 * t12 * 2.0 + k35 * k36 * t4 * t10 * 2.0 + k32 * k33 * t10 * t11 * 2.0 + k35 * k36 * t3 * t12 * 2.0 + k32 * k33 * t9 * t13 * 2.0 + k35 * k36 * t5 * t11 * 2.0 + k32 * k33 * t10 * t13 * 2.0 + k32 * k33 * t11 * t12 * 4.0 + k25 * t2 * t4 * t14 + k25 * t2 * t4 * t15 * 3.0 + k25 * t4 * t8 * t9 + k25 * t2 * t4 * t16 + k25 * t2 * t8 * t12 * 2.0 + k25 * t4 * t8 * t10 * 2.0 + k25 * t3 * t8 * t12 * 2.0 + k25 * t2 * t9 * t13 * 2.0 + k25 * t2 * t10 * t12 + k25 * t4 * t8 * t12 * 6.0 + k25 * t2 * t11 * t12 + k25 * t2 * t12 * t13 + k35 * t2 * t3 * t14 + k35 * t2 * t3 * t15 + k35 * t3 * t8 * t9 + k35 * t2 * t3 * t16 * 3.0 + k35 * t2 * t8 * t11 * 2.0 + k35 * t2 * t9 * t10 * 2.0 + k35 * t3 * t9 * t10 * 6.0 + k35 * t2 * t10 * t11 + k35 * t4 * t9 * t10 * 2.0 + k35 * t2 * t10 * t12 + k35 * t3 * t9 * t12 * 2.0 + k35 * t2 * t10 * t13 + k12 * k13 * k15 * k16 * k25 * 8.0 + k12 * k13 * k15 * k16 * k35 * 8.0 - k12 * k13 * k15 * k25 * k26 * 1.6E1 - k12 * k15 * k16 * k22 * k26 * 4.0 - k12 * k15 * k16 * k23 * k25 * 4.0 + k12 * k13 * k16 * k25 * k33 * 4.0 + k12 * k13 * k16 * k26 * k32 * 4.0 - k13 * k15 * k16 * k22 * k33 * 4.0 - k13 * k15 * k16 * k23 * k32 * 4.0 - k12 * k13 * k15 * k25 * k36 * 3.2E1 - k12 * k13 * k15 * k26 * k35 * 3.2E1 + k12 * k15 * k16 * k22 * k36 * 4.0 + k12 * k15 * k16 * k23 * k35 * 4.0 + k12 * k15 * k23 * k25 * k26 * 1.2E1 - k12 * k13 * k16 * k32 * k36 * 4.0 - k12 * k13 * k16 * k33 * k35 * 4.0 - k12 * k13 * k25 * k26 * k33 * 4.0 + k12 * k16 * k22 * k26 * k33 * 4.0 + k12 * k16 * k23 * k25 * k33 * 4.0 + k12 * k16 * k23 * k26 * k32 * 4.0 - k13 * k15 * k22 * k26 * k33 * 1.2E1 - k13 * k15 * k23 * k25 * k33 * 1.2E1 - k13 * k15 * k23 * k26 * k32 * 1.2E1 + k15 * k16 * k22 * k23 * k33 * 1.2E1 - k12 * k13 * k15 * k35 * k36 * 1.6E1 + k12 * k15 * k22 * k26 * k36 * 2.0E1 + k12 * k15 * k23 * k25 * k36 * 2.0E1 + k12 * k15 * k23 * k26 * k35 * 2.0E1 - k13 * k16 * k22 * k25 * k35 * 4.0 + k13 * k16 * k23 * k32 * k33 * 1.2E1 + k12 * k13 * k25 * k33 * k36 * 2.0E1 + k12 * k13 * k26 * k32 * k36 * 2.0E1 + k12 * k13 * k26 * k33 * k35 * 2.0E1 + k12 * k16 * k22 * k33 * k36 * 4.0 + k12 * k16 * k23 * k32 * k36 * 4.0 + k12 * k16 * k23 * k33 * k35 * 4.0 - k12 * k23 * k25 * k26 * k33 * 4.0 - k13 * k15 * k22 * k33 * k36 * 1.2E1 - k13 * k15 * k23 * k32 * k36 * 1.2E1 - k13 * k15 * k23 * k33 * k35 * 1.2E1 + k15 * k22 * k23 * k26 * k33 * 4.0 - k12 * k15 * k23 * k35 * k36 * 4.0 - k13 * k22 * k25 * k26 * k35 * 4.0 + k16 * k22 * k23 * k25 * k35 * 1.6E1 - k15 * k16 * k25 * k32 * k35 * 4.0 + k13 * k23 * k26 * k32 * k33 * 1.2E1 + k12 * k13 * k33 * k35 * k36 * 1.2E1 - k12 * k22 * k26 * k33 * k36 * 2.0E1 - k12 * k23 * k25 * k33 * k36 * 2.0E1 - k12 * k23 * k26 * k32 * k36 * 2.0E1 - k12 * k23 * k26 * k33 * k35 * 2.0E1 + k15 * k22 * k23 * k33 * k36 * 1.2E1 + k13 * k22 * k25 * k35 * k36 * 4.0 - k22 * k23 * k25 * k26 * k35 * 8.0 + k15 * k25 * k26 * k32 * k35 * 4.0 + k13 * k23 * k32 * k33 * k36 * 4.0 - k12 * k23 * k33 * k35 * k36 * 4.0 + k16 * k25 * k32 * k33 * k35 * 1.6E1 - k22 * k23 * k25 * k35 * k36 * 1.6E1 - k15 * k25 * k32 * k35 * k36 * 4.0 - k25 * k26 * k32 * k33 * k35 * 1.6E1 - k25 * k32 * k33 * k35 * k36 * 8.0 + k12 * k13 * k15 * k25 * t10 * 4.0 + k12 * k13 * k15 * k25 * t12 * 4.0 - k12 * k15 * k16 * k22 * t12 * 2.0 - k12 * k13 * k15 * k25 * t13 * 8.0 + k12 * k15 * k16 * k22 * t13 * 4.0 - k13 * k16 * k22 * k26 * t2 * 2.0 - k13 * k16 * k23 * k25 * t2 * 2.0 - k13 * k16 * k22 * k26 * t3 * 2.0 - k13 * k16 * k23 * k25 * t3 * 6.0 + k13 * k16 * k22 * k26 * t4 * 2.0 + k13 * k16 * k23 * k25 * t4 * 2.0 - k12 * k13 * k16 * k32 * t10 * 2.0 - k12 * k15 * k22 * k26 * t8 * 2.0 - k12 * k15 * k23 * k25 * t8 * 2.0 + k12 * k13 * k16 * k32 * t11 * 4.0 + k12 * k13 * k15 * k35 * t10 * 4.0 - k12 * k15 * k22 * k26 * t10 * 6.0 - k12 * k15 * k23 * k25 * t10 * 2.0 - k12 * k13 * k15 * k35 * t11 * 8.0 + k12 * k13 * k15 * k35 * t12 * 4.0 - k12 * k15 * k22 * k26 * t12 * 2.0 - k12 * k15 * k23 * k25 * t12 * 2.0 + k12 * k15 * k22 * k26 * t13 * 4.0 + k12 * k15 * k23 * k25 * t13 * 4.0 - k13 * k16 * k22 * k36 * t2 * 2.0 - k13 * k16 * k23 * k35 * t2 * 2.0 - k13 * k23 * k25 * k26 * t2 * 4.0 + k13 * k16 * k22 * k36 * t3 * 4.0 + k13 * k16 * k23 * k35 * t3 * 1.2E1 - k12 * k13 * k25 * k33 * t8 * 4.0 - k12 * k13 * k26 * k32 * t8 * 4.0 + k12 * k16 * k22 * k33 * t8 * 3.0 + k12 * k16 * k23 * k32 * t8 * 3.0 + k13 * k15 * k22 * k33 * t8 + k13 * k15 * k23 * k32 * t8 + k13 * k16 * k22 * k36 * t4 * 4.0 + k13 * k16 * k23 * k35 * t4 * 4.0 + k13 * k23 * k25 * k26 * t4 * 2.0 - k15 * k16 * k25 * k33 * t2 * 2.0 - k15 * k16 * k26 * k32 * t2 * 2.0 - k16 * k22 * k23 * k26 * t4 * 8.0 - k12 * k13 * k25 * k33 * t9 * 2.0 - k12 * k13 * k26 * k32 * t9 * 2.0 + k12 * k16 * k22 * k33 * t9 * 3.0 + k12 * k16 * k23 * k32 * t9 * 3.0 + k13 * k15 * k22 * k33 * t9 + k13 * k15 * k23 * k32 * t9 + k15 * k16 * k25 * k33 * t3 * 4.0 + k15 * k16 * k26 * k32 * t3 * 4.0 - k12 * k13 * k25 * k33 * t10 * 2.0 - k12 * k13 * k26 * k32 * t10 * 2.0 - k12 * k15 * k22 * k36 * t8 * 2.0 - k12 * k15 * k23 * k35 * t8 * 2.0 - k12 * k16 * k22 * k33 * t10 * 3.0 - k12 * k16 * k23 * k32 * t10 + k13 * k15 * k22 * k33 * t10 * 9.0 + k13 * k15 * k23 * k32 * t10 * 3.0 + k15 * k16 * k25 * k33 * t4 * 1.2E1 + k15 * k16 * k26 * k32 * t4 * 4.0 - k12 * k13 * k25 * k33 * t11 * 2.0 - k12 * k13 * k26 * k32 * t11 * 6.0 - k12 * k15 * k22 * k36 * t9 * 4.0 - k12 * k15 * k23 * k35 * t9 * 4.0 - k12 * k16 * k22 * k33 * t11 - k12 * k16 * k23 * k32 * t11 - k13 * k15 * k22 * k33 * t11 - k13 * k15 * k23 * k32 * t11 - k12 * k13 * k25 * k33 * t12 * 2.0 - k12 * k13 * k26 * k32 * t12 * 6.0 - k12 * k15 * k22 * k36 * t10 * 6.0 - k12 * k15 * k23 * k35 * t10 * 2.0 - k12 * k16 * k22 * k33 * t12 - k12 * k16 * k23 * k32 * t12 * 3.0 + k13 * k15 * k22 * k33 * t12 * 3.0 + k13 * k15 * k23 * k32 * t12 * 9.0 + k12 * k13 * k25 * k33 * t13 * 6.0 + k12 * k13 * k26 * k32 * t13 * 6.0 + k12 * k15 * k22 * k36 * t11 * 6.0 + k12 * k15 * k23 * k35 * t11 * 6.0 - k12 * k16 * k22 * k33 * t13 - k12 * k16 * k23 * k32 * t13 - k13 * k15 * k22 * k33 * t13 - k13 * k15 * k23 * k32 * t13 - k12 * k15 * k22 * k36 * t12 * 2.0 - k12 * k15 * k23 * k35 * t12 * 2.0 - k12 * k15 * k22 * k36 * t13 * 6.0 - k12 * k15 * k23 * k35 * t13 * 2.0 - k16 * k22 * k23 * k36 * t2 * 8.0 + k13 * k22 * k26 * k36 * t3 * 2.0 + k13 * k23 * k25 * k36 * t3 * 6.0 + k13 * k23 * k26 * k35 * t3 * 6.0 - k16 * k22 * k23 * k36 * t3 * 8.0 + k12 * k22 * k26 * k33 * t8 * 5.0 + k12 * k23 * k25 * k33 * t8 * 5.0 + k12 * k23 * k26 * k32 * t8 * 5.0 + k13 * k22 * k26 * k36 * t4 * 4.0 + k13 * k23 * k25 * k36 * t4 * 4.0 + k13 * k23 * k26 * k35 * t4 * 4.0 - k15 * k16 * k32 * k36 * t2 * 2.0 - k15 * k16 * k33 * k35 * t2 * 2.0 - k15 * k22 * k23 * k33 * t8 * 6.0 + k15 * k25 * k26 * k33 * t2 * 4.0 - k16 * k22 * k23 * k36 * t4 * 8.0 - k12 * k13 * k32 * k36 * t9 * 2.0 - k12 * k13 * k33 * k35 * t9 * 2.0 - k12 * k22 * k26 * k33 * t9 - k12 * k23 * k25 * k33 * t9 - k12 * k23 * k26 * k32 * t9 + k15 * k16 * k32 * k36 * t3 * 2.0 + k15 * k16 * k33 * k35 * t3 * 2.0 - k15 * k22 * k23 * k33 * t9 * 2.0 - k15 * k25 * k26 * k33 * t3 * 2.0 - k12 * k13 * k32 * k36 * t10 * 2.0 - k12 * k13 * k33 * k35 * t10 * 2.0 + k12 * k22 * k26 * k33 * t10 * 3.0 + k12 * k23 * k25 * k33 * t10 + k12 * k23 * k26 * k32 * t10 + k13 * k22 * k25 * k35 * t8 * 2.0 - k15 * k16 * k32 * k36 * t4 * 2.0 - k15 * k16 * k33 * k35 * t4 * 6.0 - k15 * k22 * k23 * k33 * t10 * 4.0 - k15 * k25 * k26 * k33 * t4 * 1.2E1 + k12 * k13 * k32 * k36 * t11 * 4.0 + k12 * k13 * k33 * k35 * t11 * 4.0 + k12 * k22 * k26 * k33 * t11 * 3.0 + k12 * k23 * k25 * k33 * t11 + k12 * k23 * k26 * k32 * t11 * 3.0 + k13 * k22 * k25 * k35 * t9 * 6.0 - k15 * k22 * k23 * k33 * t11 * 2.0 - k12 * k13 * k32 * k36 * t12 * 6.0 - k12 * k13 * k33 * k35 * t12 * 2.0 - k12 * k22 * k25 * k32 * t14; coeffs(5) += k12 * k22 * k26 * k33 * t12 * 3.0 + k12 * k23 * k25 * k33 * t12 * 3.0 + k12 * k23 * k26 * k32 * t12 * 9.0 + k13 * k22 * k25 * k35 * t10 * 6.0 - k15 * k22 * k23 * k33 * t12 * 2.0 + k12 * k22 * k25 * k32 * t15 * 3.0 - k12 * k22 * k26 * k33 * t13 * 5.0 - k12 * k23 * k25 * k33 * t13 * 5.0 - k12 * k23 * k26 * k32 * t13 * 5.0 + k15 * k22 * k23 * k33 * t13 * 2.0 - k12 * k22 * k25 * k32 * t16 * 5.0 + k13 * k22 * k25 * k35 * t12 * 4.0 - k13 * k23 * k32 * k33 * t8 * 2.0 + k13 * k23 * k35 * k36 * t2 * 4.0 - k16 * k26 * k32 * k33 * t2 * 8.0 + k22 * k23 * k26 * k36 * t2 * 4.0 - k13 * k23 * k32 * k33 * t9 * 6.0 - k13 * k23 * k35 * k36 * t3 * 1.2E1 - k16 * k26 * k32 * k33 * t3 * 8.0 - k12 * k22 * k33 * k36 * t8 - k12 * k23 * k32 * k36 * t8 - k12 * k23 * k33 * k35 * t8 - k13 * k23 * k32 * k33 * t10 * 2.0 - k13 * k23 * k35 * k36 * t4 * 2.0 - k16 * k26 * k32 * k33 * t4 * 8.0 + k12 * k22 * k33 * k36 * t9 * 5.0 + k12 * k23 * k32 * k36 * t9 * 5.0 + k12 * k23 * k33 * k35 * t9 * 5.0 + k13 * k23 * k32 * k33 * t11 * 2.0 + k15 * k25 * k33 * k36 * t3 * 4.0 + k15 * k26 * k32 * k36 * t3 * 4.0 + k15 * k26 * k33 * k35 * t3 * 4.0 + k12 * k22 * k33 * k36 * t10 * 9.0 + k12 * k23 * k32 * k36 * t10 * 3.0 + k12 * k23 * k33 * k35 * t10 * 3.0 - k13 * k23 * k32 * k33 * t12 * 4.0 + k15 * k25 * k33 * k36 * t4 * 6.0 + k15 * k26 * k32 * k36 * t4 * 2.0 + k15 * k26 * k33 * k35 * t4 * 6.0 - k22 * k23 * k25 * k35 * t8 * 8.0 - k12 * k22 * k33 * k36 * t11 * 5.0 - k12 * k23 * k32 * k36 * t11 * 5.0 - k12 * k23 * k33 * k35 * t11 * 5.0 - k13 * k23 * k32 * k33 * t13 * 2.0 - k22 * k23 * k25 * k35 * t9 * 8.0 - k12 * k22 * k32 * k35 * t14 + k12 * k22 * k33 * k36 * t12 + k12 * k23 * k32 * k36 * t12 * 3.0 + k12 * k23 * k33 * k35 * t12 + k15 * k25 * k32 * k35 * t8 * 6.0 - k12 * k22 * k32 * k35 * t15 * 5.0 + k12 * k22 * k33 * k36 * t13 * 3.0 + k12 * k23 * k32 * k36 * t13 * 3.0 + k12 * k23 * k33 * k35 * t13 + k15 * k25 * k32 * k35 * t9 * 2.0 + k12 * k22 * k32 * k35 * t16 * 3.0 + k15 * k25 * k32 * k35 * t10 * 4.0 + k15 * k25 * k32 * k35 * t12 * 6.0 - k16 * k32 * k33 * k36 * t3 * 8.0 - k15 * k33 * k35 * k36 * t2 * 4.0 + k15 * k33 * k35 * k36 * t3 * 2.0 + k26 * k32 * k33 * k36 * t2 * 4.0 - k25 * k32 * k33 * k35 * t8 * 8.0 - k25 * k32 * k33 * k35 * t9 * 8.0 - k13 * k16 * k22 * t4 * t9 - k13 * k16 * k22 * t2 * t12 - k13 * k16 * k22 * t4 * t10 * 6.0 - k13 * k16 * k22 * t3 * t12 * 2.0 - k12 * k15 * k22 * t2 * t16 * 2.0 - k12 * k15 * k22 * t4 * t14 - k13 * k16 * k22 * t4 * t12 * 6.0 - k12 * k15 * k22 * t4 * t15 - k12 * k15 * k22 * t4 * t16 - k12 * k15 * k22 * t8 * t12 - k12 * k15 * k22 * t9 * t13 * 2.0 - k12 * k15 * k22 * t10 * t12 * 3.0 - k12 * k15 * k22 * t11 * t12 - k13 * k22 * k26 * t4 * t8 - k13 * k23 * k25 * t4 * t8 + k16 * k22 * k23 * t4 * t8 * 2.0 - k16 * k25 * k26 * t2 * t4 * 4.0 - k12 * k13 * k32 * t2 * t15 * 2.0 - k12 * k13 * k32 * t3 * t14 - k12 * k15 * k22 * t12 * t13 - k13 * k22 * k26 * t4 * t9 - k13 * k23 * k25 * t4 * t9 - k15 * k16 * k32 * t3 * t8 + k16 * k22 * k23 * t4 * t9 * 2.0 - k12 * k13 * k32 * t3 * t15 - k13 * k22 * k26 * t2 * t12 * 4.0 - k13 * k22 * k26 * t4 * t10 * 3.0 - k13 * k23 * k25 * t2 * t12 * 4.0 - k13 * k23 * k25 * t4 * t10 - k15 * k16 * k32 * t2 * t10 + k16 * k22 * k23 * t2 * t12 * 4.0 + k16 * k22 * k23 * t4 * t10 * 4.0 - k12 * k13 * k32 * t3 * t16 - k12 * k13 * k32 * t8 * t11 * 2.0 - k12 * k13 * k32 * t9 * t10 + k13 * k22 * k26 * t2 * t13 * 2.0 - k13 * k22 * k26 * t3 * t12 + k13 * k23 * k25 * t2 * t13 * 2.0 - k13 * k23 * k25 * t3 * t12 * 3.0 - k15 * k16 * k32 * t3 * t10 * 6.0 - k16 * k22 * k23 * t2 * t13 * 4.0 + k16 * k22 * k23 * t3 * t12 * 4.0 - k13 * k22 * k26 * t4 * t12 * 6.0 - k13 * k23 * k25 * t4 * t12 * 6.0 - k15 * k16 * k32 * t4 * t10 * 2.0 + k16 * k22 * k23 * t4 * t12 * 1.2E1 - k12 * k13 * k32 * t10 * t11 - k15 * k16 * k32 * t3 * t12 * 6.0 - k12 * k13 * k32 * t10 * t12 * 3.0 - k12 * k13 * k32 * t10 * t13 - k13 * k22 * k36 * t3 * t9 * 2.0 - k13 * k23 * k35 * t3 * t9 * 6.0 + k22 * k23 * k26 * t4 * t8 * 4.0 + k12 * k22 * k33 * t2 * t15 + k12 * k22 * k33 * t3 * t14 + k12 * k23 * k32 * t2 * t15 + k12 * k23 * k32 * t3 * t14 * 3.0 - k13 * k22 * k36 * t2 * t11 * 2.0 - k13 * k22 * k36 * t4 * t9 * 2.0 - k13 * k23 * k35 * t2 * t11 * 2.0 - k13 * k23 * k35 * t4 * t9 * 2.0 - k15 * k25 * k33 * t3 * t8 * 2.0 - k15 * k26 * k32 * t3 * t8 * 2.0 + k12 * k22 * k33 * t2 * t16 + k12 * k22 * k33 * t4 * t14 * 3.0 + k12 * k23 * k32 * t2 * t16 + k12 * k23 * k32 * t4 * t14 - k13 * k22 * k36 * t2 * t12 * 2.0 - k13 * k23 * k35 * t2 * t12 * 2.0 - k15 * k25 * k33 * t2 * t10 * 2.0 - k15 * k25 * k33 * t4 * t8 * 6.0 - k15 * k26 * k32 * t2 * t10 * 2.0 - k15 * k26 * k32 * t4 * t8 * 2.0 + k22 * k23 * k26 * t2 * t12 * 2.0 + k12 * k22 * k33 * t3 * t16 + k12 * k22 * k33 * t4 * t15 * 3.0 + k12 * k22 * k33 * t8 * t11 * 3.0 + k12 * k22 * k33 * t9 * t10 * 3.0 + k12 * k23 * k32 * t3 * t16 * 3.0 + k12 * k23 * k32 * t4 * t15 + k12 * k23 * k32 * t8 * t11 * 3.0 + k12 * k23 * k32 * t9 * t10 + k12 * k22 * k33 * t8 * t12 + k12 * k23 * k32 * t8 * t12 * 3.0 - k15 * k25 * k33 * t2 * t13 * 2.0 - k15 * k26 * k32 * t2 * t13 * 2.0 + k12 * k22 * k33 * t9 * t13 * 3.0 + k12 * k23 * k32 * t9 * t13 * 3.0 + k12 * k22 * k33 * t10 * t13 * 3.0 + k12 * k22 * k33 * t11 * t12 + k12 * k23 * k32 * t10 * t13 + k12 * k23 * k32 * t11 * t12 * 3.0 + k16 * k32 * k33 * t3 * t8 * 2.0 - k16 * k35 * k36 * t2 * t3 * 4.0 + k22 * k23 * k36 * t2 * t9 * 4.0 + k25 * k26 * k36 * t2 * t3 * 2.0 + k16 * k32 * k33 * t2 * t10 * 4.0 + k16 * k32 * k33 * t3 * t9 * 2.0 + k22 * k23 * k36 * t3 * t9 * 4.0 - k15 * k32 * k36 * t3 * t8 - k15 * k33 * k35 * t3 * t8 - k16 * k32 * k33 * t2 * t11 * 4.0 + k16 * k32 * k33 * t3 * t10 * 1.2E1 + k22 * k23 * k36 * t2 * t11 * 2.0 + k22 * k23 * k36 * t4 * t9 * 4.0 - k15 * k32 * k36 * t2 * t10 * 4.0 - k15 * k32 * k36 * t3 * t9 - k15 * k33 * k35 * t2 * t10 * 4.0 - k15 * k33 * k35 * t3 * t9 + k16 * k32 * k33 * t4 * t10 * 4.0 + k22 * k23 * k36 * t2 * t12 * 2.0 + k15 * k32 * k36 * t2 * t11 * 2.0 - k15 * k32 * k36 * t3 * t10 * 6.0 + k15 * k33 * k35 * t2 * t11 * 2.0 - k15 * k33 * k35 * t3 * t10 * 6.0 + k16 * k32 * k33 * t3 * t12 * 4.0 + k22 * k23 * k36 * t2 * t13 * 6.0 - k15 * k32 * k36 * t4 * t10 - k15 * k33 * k35 * t4 * t10 * 3.0 - k15 * k32 * k36 * t3 * t12 * 3.0 - k15 * k33 * k35 * t3 * t12 + k26 * k32 * k33 * t2 * t8 * 4.0 + k26 * k32 * k33 * t3 * t8 * 4.0 + k26 * k32 * k33 * t2 * t10 * 2.0 + k26 * k32 * k33 * t4 * t8 * 4.0 + k26 * k35 * k36 * t2 * t4 * 2.0 + k26 * k32 * k33 * t2 * t11 * 6.0 + k26 * k32 * k33 * t2 * t13 * 2.0 + k32 * k33 * k36 * t2 * t10 * 2.0 + k32 * k33 * k36 * t3 * t9 * 4.0 - k13 * k22 * t2 * t4 * t15 + k16 * k25 * t2 * t4 * t10 + k16 * k25 * t2 * t3 * t12 - k13 * k22 * t2 * t11 * t12 + k25 * k26 * t2 * t4 * t8 * 2.0 + k16 * k35 * t2 * t4 * t10 - k15 * k32 * t2 * t3 * t16 + k16 * k35 * t2 * t3 * t12 + k22 * k23 * t2 * t9 * t13 * 2.0 - k15 * k32 * t2 * t10 * t13 + k25 * k36 * t2 * t4 * t10 + k26 * k35 * t2 * t4 * t10 + k25 * k36 * t2 * t3 * t12 + k26 * k35 * t2 * t3 * t12 + k35 * k36 * t2 * t3 * t9 * 2.0 + k32 * k33 * t2 * t8 * t11 * 2.0 + k12 * k13 * k15 * k22 * k23 * k26 * 8.0 - k12 * k13 * k16 * k22 * k23 * k33 * 4.0 + k12 * k13 * k15 * k22 * k23 * k36 * 8.0 - k13 * k15 * k16 * k22 * k25 * k32 * 2.0 - k12 * k15 * k16 * k22 * k25 * k35 * 4.0 - k12 * k13 * k22 * k23 * k26 * k33 * 4.0 + k12 * k13 * k15 * k26 * k32 * k33 * 8.0 - k12 * k15 * k16 * k23 * k32 * k33 * 4.0 - k12 * k13 * k16 * k25 * k32 * k35 * 4.0 - k12 * k16 * k22 * k25 * k26 * k32 * 2.0 - k13 * k15 * k16 * k22 * k32 * k35 * 2.0 - k13 * k15 * k22 * k25 * k26 * k32 * 2.0 + k15 * k16 * k22 * k23 * k25 * k32 * 8.0 + k12 * k15 * k22 * k25 * k26 * k35 * 1.2E1 - k12 * k13 * k22 * k23 * k33 * k36 * 4.0 + k12 * k13 * k15 * k32 * k33 * k36 * 8.0 - k12 * k15 * k23 * k26 * k32 * k33 * 4.0 + k13 * k16 * k22 * k25 * k32 * k33 * 4.0 + k12 * k13 * k25 * k26 * k32 * k35 * 8.0 + k12 * k16 * k22 * k25 * k32 * k36 * 6.0 + k12 * k16 * k22 * k25 * k33 * k35 * 6.0 + k12 * k16 * k22 * k26 * k32 * k35 * 6.0 + k12 * k16 * k23 * k25 * k32 * k35 * 6.0 - k13 * k15 * k22 * k25 * k32 * k36 * 1.0E1 - k13 * k15 * k22 * k25 * k33 * k35 * 1.0E1 - k13 * k15 * k22 * k26 * k32 * k35 * 1.0E1 - k13 * k15 * k23 * k25 * k32 * k35 * 1.0E1 + k15 * k16 * k22 * k23 * k32 * k35 * 4.0 - k15 * k22 * k23 * k25 * k26 * k32 * 4.0 + k12 * k15 * k22 * k25 * k35 * k36 * 8.0 - k12 * k15 * k23 * k32 * k33 * k36 * 4.0 + k13 * k16 * k22 * k32 * k33 * k35 * 8.0 + k13 * k22 * k25 * k26 * k32 * k33 * 4.0 - k16 * k22 * k23 * k25 * k32 * k33 * 1.6E1 + k12 * k13 * k25 * k32 * k35 * k36 * 1.2E1 - k12 * k16 * k22 * k32 * k35 * k36 * 2.0 - k12 * k22 * k25 * k26 * k32 * k36 * 1.0E1 - k12 * k22 * k25 * k26 * k33 * k35 * 1.0E1 - k12 * k23 * k25 * k26 * k32 * k35 * 1.0E1 - k13 * k15 * k22 * k32 * k35 * k36 * 2.0 + k15 * k22 * k23 * k25 * k32 * k36 * 8.0 + k15 * k22 * k23 * k25 * k33 * k35 * 8.0 + k15 * k22 * k23 * k26 * k32 * k35 * 8.0 + k13 * k22 * k25 * k32 * k33 * k36 * 8.0 + k13 * k22 * k26 * k32 * k33 * k35 * 8.0 + k13 * k23 * k25 * k32 * k33 * k35 * 8.0 - k16 * k22 * k23 * k32 * k33 * k35 * 1.6E1 + k22 * k23 * k25 * k26 * k32 * k33 * 8.0 - k12 * k22 * k25 * k33 * k35 * k36 * 1.0E1 - k12 * k22 * k26 * k32 * k35 * k36 * 1.0E1 - k12 * k23 * k25 * k32 * k35 * k36 * 1.0E1 + k15 * k22 * k23 * k32 * k35 * k36 * 4.0 - k13 * k22 * k32 * k33 * k35 * k36 * 4.0 + k22 * k23 * k32 * k33 * k35 * k36 * 8.0 + k12 * k15 * k16 * k22 * k26 * t4 * 2.0 + k12 * k15 * k16 * k23 * k25 * t4 * 2.0 + k12 * k13 * k15 * k22 * k23 * t12 * 4.0 - k12 * k13 * k16 * k25 * k33 * t3 * 4.0 - k12 * k13 * k16 * k26 * k32 * t3 * 4.0 + k13 * k15 * k16 * k22 * k33 * t3 * 2.0 + k13 * k15 * k16 * k23 * k32 * t3 * 6.0 + k13 * k15 * k16 * k22 * k33 * t4 * 6.0 + k13 * k15 * k16 * k23 * k32 * t4 * 2.0 + k12 * k13 * k15 * k25 * k36 * t3 * 4.0 + k12 * k13 * k15 * k26 * k35 * t3 * 4.0 + k12 * k13 * k15 * k25 * k36 * t4 * 4.0 + k12 * k13 * k15 * k26 * k35 * t4 * 4.0 - k12 * k15 * k16 * k22 * k36 * t4 * 4.0 - k12 * k15 * k16 * k23 * k35 * t4 * 4.0 - k12 * k15 * k23 * k25 * k26 * t4 * 2.0 - k12 * k13 * k25 * k26 * k33 * t2 * 4.0 + k12 * k16 * k22 * k26 * k33 * t2 + k12 * k16 * k23 * k25 * k33 * t2 + k12 * k16 * k23 * k26 * k32 * t2 + k13 * k15 * k22 * k26 * k33 * t2 * 3.0 + k13 * k15 * k23 * k25 * k33 * t2 * 3.0 + k13 * k15 * k23 * k26 * k32 * t2 * 3.0 - k15 * k16 * k22 * k23 * k33 * t2 * 2.0 + k12 * k13 * k16 * k32 * k36 * t3 * 2.0 + k12 * k13 * k16 * k33 * k35 * t3 * 2.0 - k12 * k13 * k22 * k23 * k33 * t9 * 2.0 - k12 * k13 * k25 * k26 * k33 * t3 * 2.0 + k12 * k16 * k22 * k26 * k33 * t3 + k12 * k16 * k23 * k25 * k33 * t3 * 3.0 + k12 * k16 * k23 * k26 * k32 * t3 * 3.0 + k13 * k15 * k22 * k26 * k33 * t3 + k13 * k15 * k23 * k25 * k33 * t3 * 3.0 + k13 * k15 * k23 * k26 * k32 * t3 * 3.0 - k15 * k16 * k22 * k23 * k33 * t3 * 4.0 - k12 * k15 * k22 * k26 * k36 * t2 * 4.0 - k12 * k15 * k23 * k25 * k36 * t2 * 4.0 - k12 * k15 * k23 * k26 * k35 * t2 * 4.0 - k12 * k16 * k22 * k26 * k33 * t4 * 6.0 - k12 * k16 * k23 * k25 * k33 * t4 * 6.0 - k12 * k16 * k23 * k26 * k32 * t4 * 2.0 + k13 * k15 * k22 * k26 * k33 * t4 * 6.0 + k13 * k15 * k23 * k25 * k33 * t4 * 6.0 + k13 * k15 * k23 * k26 * k32 * t4 * 2.0 - k13 * k16 * k22 * k25 * k35 * t2 * 2.0 - k15 * k16 * k22 * k23 * k33 * t4 * 1.2E1 - k12 * k13 * k22 * k23 * k33 * t11 * 2.0 - k12 * k15 * k22 * k26 * k36 * t3 * 2.0 - k12 * k15 * k23 * k25 * k36 * t3 * 6.0 - k12 * k15 * k23 * k26 * k35 * t3 * 6.0 + k12 * k13 * k15 * k32 * k33 * t10 * 4.0 - k12 * k13 * k22 * k23 * k33 * t12 * 2.0 + k12 * k16 * k22 * k25 * k32 * t8 * 3.0 + k13 * k15 * k22 * k25 * k32 * t8 - k12 * k13 * k22 * k23 * k33 * t13 * 2.0 - k12 * k15 * k22 * k25 * k35 * t8 * 2.0 + k12 * k16 * k22 * k25 * k32 * t10 * 3.0 + k13 * k15 * k22 * k25 * k32 * t10 * 3.0 - k12 * k15 * k22 * k25 * k35 * t10 * 6.0 - k12 * k16 * k22 * k25 * k32 * t12 * 6.0 + k13 * k15 * k22 * k25 * k32 * t12 * 6.0 - k13 * k16 * k23 * k32 * k33 * t2 * 2.0 - k13 * k16 * k23 * k32 * k33 * t3 * 1.2E1 - k12 * k13 * k25 * k33 * k36 * t2 * 4.0 - k12 * k13 * k26 * k32 * k36 * t2 * 4.0 - k12 * k13 * k26 * k33 * k35 * t2 * 4.0 + k12 * k16 * k22 * k33 * k36 * t2 + k12 * k16 * k23 * k32 * k36 * t2 + k12 * k16 * k23 * k33 * k35 * t2 + k12 * k23 * k25 * k26 * k33 * t2 * 2.0 + k13 * k15 * k22 * k33 * k36 * t2 * 3.0 + k13 * k15 * k23 * k32 * k36 * t2 * 3.0 + k13 * k15 * k23 * k33 * k35 * t2 * 3.0 - k13 * k16 * k23 * k32 * k33 * t4 * 4.0 - k15 * k22 * k23 * k26 * k33 * t2 * 4.0 - k12 * k16 * k22 * k33 * k36 * t3 * 2.0 - k12 * k16 * k23 * k32 * k36 * t3 * 6.0 - k12 * k16 * k23 * k33 * k35 * t3 * 6.0 + k13 * k15 * k22 * k33 * k36 * t3 * 2.0 + k13 * k15 * k23 * k32 * k36 * t3 * 6.0 + k13 * k15 * k23 * k33 * k35 * t3 * 6.0 - k12 * k13 * k25 * k33 * k36 * t4 * 6.0 - k12 * k13 * k26 * k32 * k36 * t4 * 2.0 - k12 * k13 * k26 * k33 * k35 * t4 * 6.0 - k12 * k15 * k23 * k32 * k33 * t8 * 2.0 - k12 * k15 * k23 * k35 * k36 * t2 * 4.0 + k12 * k16 * k22 * k33 * k36 * t4 * 3.0 + k12 * k16 * k23 * k32 * k36 * t4 + k12 * k16 * k23 * k33 * k35 * t4 * 3.0 + k12 * k23 * k25 * k26 * k33 * t4 * 6.0 + k13 * k15 * k22 * k33 * k36 * t4 * 3.0; coeffs(5) += k13 * k15 * k23 * k32 * k36 * t4 + k13 * k15 * k23 * k33 * k35 * t4 * 3.0 - k13 * k22 * k25 * k26 * k35 * t2 * 4.0 - k12 * k15 * k23 * k32 * k33 * t10 * 2.0 - k12 * k15 * k23 * k35 * k36 * t4 * 2.0 + k12 * k22 * k25 * k26 * k32 * t8 * 6.0 - k15 * k16 * k25 * k32 * k35 * t2 * 2.0 - k15 * k22 * k23 * k25 * k32 * t8 * 4.0 - k12 * k13 * k25 * k32 * k35 * t9 * 2.0 - k12 * k15 * k23 * k32 * k33 * t11 * 2.0 + k12 * k16 * k22 * k32 * k35 * t9 * 3.0 + k13 * k15 * k22 * k32 * k35 * t9 - k12 * k16 * k22 * k32 * k35 * t10 * 6.0 + k13 * k15 * k22 * k32 * k35 * t10 * 6.0 - k12 * k15 * k23 * k32 * k33 * t13 * 2.0 - k12 * k13 * k25 * k32 * k35 * t12 * 6.0 + k12 * k16 * k22 * k32 * k35 * t12 * 3.0 + k12 * k22 * k25 * k26 * k32 * t12 * 6.0 + k13 * k15 * k22 * k32 * k35 * t12 * 3.0 - k13 * k23 * k26 * k32 * k33 * t2 * 8.0 - k13 * k23 * k26 * k32 * k33 * t3 * 6.0 + k12 * k22 * k26 * k33 * k36 * t2 * 4.0 + k12 * k23 * k25 * k33 * k36 * t2 * 4.0 + k12 * k23 * k26 * k32 * k36 * t2 * 4.0 + k12 * k23 * k26 * k33 * k35 * t2 * 4.0 - k13 * k23 * k26 * k32 * k33 * t4 * 4.0 - k15 * k22 * k23 * k33 * k36 * t2 * 8.0 - k12 * k13 * k33 * k35 * k36 * t3 * 2.0 + k12 * k22 * k26 * k33 * k36 * t3 + k12 * k23 * k25 * k33 * k36 * t3 * 3.0 + k12 * k23 * k26 * k32 * k36 * t3 * 3.0 + k12 * k23 * k26 * k33 * k35 * t3 * 3.0 - k15 * k22 * k23 * k33 * k36 * t3 * 4.0 + k12 * k22 * k26 * k33 * k36 * t4 * 3.0 + k12 * k23 * k25 * k33 * k36 * t4 * 3.0 + k12 * k23 * k26 * k32 * k36 * t4 + k12 * k23 * k26 * k33 * k35 * t4 * 3.0 - k13 * k22 * k25 * k32 * k33 * t8 * 2.0 + k13 * k22 * k25 * k35 * k36 * t2 * 4.0 - k15 * k22 * k23 * k33 * k36 * t4 * 6.0 + k22 * k23 * k25 * k26 * k35 * t2 * 4.0 - k13 * k22 * k25 * k32 * k33 * t9 * 2.0 - k12 * k22 * k25 * k32 * k36 * t8 - k12 * k22 * k25 * k33 * k35 * t8 - k12 * k22 * k26 * k32 * k35 * t8 - k12 * k23 * k25 * k32 * k35 * t8 - k13 * k22 * k25 * k32 * k33 * t10 * 6.0 - k15 * k22 * k23 * k32 * k35 * t8 * 2.0 + k15 * k25 * k26 * k32 * k35 * t2 * 4.0 - k12 * k22 * k25 * k32 * k36 * t9 - k12 * k22 * k25 * k33 * k35 * t9 - k12 * k22 * k26 * k32 * k35 * t9 - k12 * k23 * k25 * k32 * k35 * t9 - k15 * k22 * k23 * k32 * k35 * t9 * 2.0 + k12 * k22 * k25 * k32 * k36 * t10 * 3.0 + k12 * k22 * k25 * k33 * k35 * t10 * 3.0 + k12 * k22 * k26 * k32 * k35 * t10 * 3.0 + k12 * k23 * k25 * k32 * k35 * t10 - k13 * k22 * k25 * k32 * k33 * t12 * 4.0 - k15 * k22 * k23 * k32 * k35 * t10 * 4.0 + k12 * k22 * k25 * k32 * k36 * t12 * 3.0 + k12 * k22 * k25 * k33 * k35 * t12 + k12 * k22 * k26 * k32 * k35 * t12 * 3.0 + k12 * k23 * k25 * k32 * k35 * t12 * 3.0 - k13 * k23 * k32 * k33 * k36 * t2 * 4.0 - k15 * k22 * k23 * k32 * k35 * t12 * 6.0 + k12 * k23 * k33 * k35 * k36 * t2 * 2.0 + k12 * k23 * k33 * k35 * k36 * t3 * 6.0 + k22 * k23 * k25 * k32 * k33 * t8 * 8.0 - k13 * k22 * k32 * k33 * k35 * t9 * 4.0 - k15 * k25 * k32 * k35 * k36 * t2 * 4.0 + k12 * k22 * k32 * k35 * k36 * t9 * 6.0 + k12 * k22 * k32 * k35 * k36 * t10 * 6.0 + k22 * k23 * k32 * k33 * k35 * t9 * 8.0 + k25 * k32 * k33 * k35 * k36 * t2 * 4.0 + k12 * k13 * k15 * k25 * t4 * t10 - k12 * k15 * k16 * k22 * t4 * t10 * 3.0 + k12 * k13 * k15 * k25 * t3 * t12 - k12 * k15 * k16 * k22 * t3 * t12 - k13 * k16 * k22 * k26 * t2 * t4 - k13 * k16 * k23 * k25 * t2 * t4 - k12 * k13 * k16 * k32 * t4 * t10 - k12 * k15 * k22 * k26 * t4 * t8 - k12 * k15 * k23 * k25 * t4 * t8 - k12 * k13 * k16 * k32 * t3 * t12 * 3.0 + k12 * k13 * k15 * k35 * t4 * t10 + k12 * k13 * k15 * k35 * t3 * t12 - k12 * k15 * k22 * k26 * t2 * t13 * 2.0 - k12 * k15 * k23 * k25 * t2 * t13 * 2.0 - k13 * k23 * k25 * k26 * t2 * t4 * 2.0 + k16 * k22 * k23 * k26 * t2 * t4 * 2.0 - k12 * k13 * k25 * k33 * t4 * t10 * 3.0 - k12 * k13 * k26 * k32 * t4 * t10 + k12 * k16 * k22 * k33 * t4 * t10 * 9.0 + k12 * k16 * k23 * k32 * t4 * t10 - k12 * k13 * k25 * k33 * t3 * t12 - k12 * k13 * k26 * k32 * t3 * t12 * 3.0 + k12 * k16 * k22 * k33 * t3 * t12 + k12 * k16 * k23 * k32 * t3 * t12 * 9.0 - k12 * k15 * k22 * k36 * t4 * t10 * 3.0 - k12 * k15 * k23 * k35 * t4 * t10 - k12 * k15 * k22 * k36 * t3 * t12 - k12 * k15 * k23 * k35 * t3 * t12 * 3.0 - k13 * k22 * k26 * k36 * t2 * t4 * 2.0 - k13 * k23 * k25 * k36 * t2 * t4 * 2.0 - k13 * k23 * k26 * k35 * t2 * t4 * 2.0 + k16 * k22 * k23 * k36 * t2 * t4 * 2.0 - k15 * k16 * k32 * k36 * t2 * t3 - k15 * k16 * k33 * k35 * t2 * t3 - k12 * k13 * k32 * k36 * t3 * t9 - k12 * k13 * k33 * k35 * t3 * t9 + k12 * k22 * k26 * k33 * t4 * t8 * 3.0 + k12 * k23 * k25 * k33 * t4 * t8 * 3.0 + k12 * k23 * k26 * k32 * t4 * t8 - k12 * k13 * k32 * k36 * t2 * t11 * 2.0 - k12 * k13 * k33 * k35 * t2 * t11 * 2.0 + k12 * k22 * k26 * k33 * t2 * t13 + k12 * k23 * k25 * k33 * t2 * t13 + k12 * k23 * k26 * k32 * t2 * t13 - k15 * k22 * k23 * k33 * t2 * t13 * 2.0 + k12 * k22 * k25 * k32 * t2 * t16 - k13 * k22 * k25 * k35 * t2 * t12 * 2.0 + k12 * k22 * k25 * k32 * t8 * t12 * 3.0 + k16 * k26 * k32 * k33 * t2 * t3 * 2.0 + k22 * k23 * k26 * k36 * t2 * t4 * 2.0 - k13 * k23 * k32 * k33 * t2 * t11 * 2.0 - k15 * k25 * k33 * k36 * t2 * t3 * 2.0 - k15 * k26 * k32 * k36 * t2 * t3 * 2.0 - k15 * k26 * k33 * k35 * t2 * t3 * 2.0 + k12 * k22 * k33 * k36 * t3 * t9 + k12 * k23 * k32 * k36 * t3 * t9 * 3.0 + k12 * k23 * k33 * k35 * t3 * t9 * 3.0 + k12 * k22 * k33 * k36 * t2 * t11 + k12 * k23 * k32 * k36 * t2 * t11 + k12 * k23 * k33 * k35 * t2 * t11 + k12 * k22 * k32 * k35 * t2 * t15 - k15 * k25 * k32 * k35 * t2 * t10 * 2.0 + k22 * k23 * k25 * k35 * t2 * t12 * 2.0 + k12 * k22 * k32 * k35 * t9 * t10 * 3.0 + k16 * k32 * k33 * k36 * t2 * t3 * 2.0 - k15 * k33 * k35 * k36 * t2 * t3 * 2.0 + k26 * k32 * k33 * k36 * t2 * t3 * 2.0 + k25 * k32 * k33 * k35 * t2 * t10 * 2.0 - k12 * k13 * k16 * k22 * k23 * k25 * k32 * 8.0 + k12 * k13 * k15 * k22 * k23 * k25 * k35 * 8.0 + k12 * k13 * k16 * k22 * k23 * k32 * k35 * 4.0 - k12 * k13 * k22 * k23 * k25 * k26 * k32 * 4.0 + k12 * k15 * k16 * k22 * k25 * k32 * k33 * 4.0 + k12 * k13 * k15 * k25 * k32 * k33 * k35 * 8.0 - k12 * k15 * k16 * k22 * k32 * k33 * k35 * 8.0 - k12 * k15 * k22 * k25 * k26 * k32 * k33 * 4.0 - k12 * k13 * k22 * k23 * k32 * k35 * k36 * 4.0 - k12 * k15 * k22 * k32 * k33 * k35 * k36 * 4.0 + k12 * k13 * k15 * k16 * k22 * k23 * t4 * 2.0 + k12 * k13 * k15 * k22 * k23 * k26 * t4 * 2.0 - k12 * k13 * k16 * k22 * k23 * k33 * t4 * 6.0 + k12 * k13 * k15 * k16 * k32 * k33 * t3 * 2.0 + k12 * k13 * k15 * k22 * k23 * k36 * t4 * 2.0 - k12 * k13 * k22 * k23 * k26 * k33 * t4 * 6.0 + k12 * k13 * k15 * k26 * k32 * k33 * t3 * 2.0 - k12 * k15 * k16 * k23 * k32 * k33 * t3 * 6.0 - k12 * k13 * k22 * k23 * k25 * k32 * t12 * 6.0 - k13 * k16 * k22 * k25 * k32 * k33 * t2 * 2.0 + k12 * k13 * k15 * k32 * k33 * k36 * t3 * 2.0 - k12 * k13 * k25 * k26 * k32 * k35 * t2 * 4.0 + k12 * k16 * k22 * k25 * k32 * k36 * t2 + k12 * k16 * k22 * k25 * k33 * k35 * t2 + k12 * k16 * k22 * k26 * k32 * k35 * t2 + k12 * k16 * k23 * k25 * k32 * k35 * t2 + k13 * k15 * k22 * k25 * k32 * k36 * t2 * 3.0 + k13 * k15 * k22 * k25 * k33 * k35 * t2 * 3.0 + k13 * k15 * k22 * k26 * k32 * k35 * t2 * 3.0 + k13 * k15 * k23 * k25 * k32 * k35 * t2 * 3.0 - k15 * k16 * k22 * k23 * k32 * k35 * t2 * 2.0 - k12 * k13 * k22 * k23 * k32 * k35 * t9 * 2.0 - k12 * k15 * k22 * k25 * k32 * k33 * t8 * 2.0 - k12 * k15 * k22 * k25 * k35 * k36 * t2 * 4.0 - k13 * k22 * k25 * k26 * k32 * k33 * t2 * 4.0 + k16 * k22 * k23 * k25 * k32 * k33 * t2 * 4.0 - k12 * k15 * k23 * k32 * k33 * k36 * t3 * 6.0 + k12 * k22 * k25 * k26 * k32 * k36 * t2 * 2.0 + k12 * k22 * k25 * k26 * k33 * k35 * t2 * 2.0 + k12 * k23 * k25 * k26 * k32 * k35 * t2 * 2.0 - k15 * k22 * k23 * k25 * k32 * k36 * t2 * 4.0 - k15 * k22 * k23 * k25 * k33 * k35 * t2 * 4.0 - k15 * k22 * k23 * k26 * k32 * k35 * t2 * 4.0 - k12 * k15 * k22 * k32 * k33 * k35 * t10 * 6.0 - k13 * k22 * k25 * k32 * k33 * k36 * t2 * 4.0 - k13 * k22 * k26 * k32 * k33 * k35 * t2 * 4.0 - k13 * k23 * k25 * k32 * k33 * k35 * t2 * 4.0 + k16 * k22 * k23 * k32 * k33 * k35 * t2 * 4.0 + k12 * k22 * k25 * k33 * k35 * k36 * t2 * 2.0 + k12 * k22 * k26 * k32 * k35 * k36 * t2 * 2.0 + k12 * k23 * k25 * k32 * k35 * k36 * t2 * 2.0 - k15 * k22 * k23 * k32 * k35 * k36 * t2 * 4.0 + k22 * k23 * k25 * k32 * k33 * k36 * t2 * 4.0 + k22 * k23 * k26 * k32 * k33 * k35 * t2 * 4.0 + k12 * k13 * k15 * k22 * k23 * k25 * k32 * k33 * 4.0 + k12 * k13 * k15 * k22 * k23 * k32 * k33 * k35 * 4.0; coeffs(6) = k16 * t14 * -8.0 - k16 * t15 * 2.4E1 - k16 * t16 * 2.4E1 - k16 * t19 * 2.0 - k16 * t20 * 2.0 + k26 * t14 * 2.4E1 + k26 * t15 * 8.0 + k26 * t16 * 2.4E1 + k26 * t17 * 2.0 + k26 * t19 * 2.0 + k36 * t14 * 2.4E1 + k36 * t15 * 2.4E1 + k36 * t16 * 8.0 + k36 * t18 * 2.0 + k36 * t20 * 2.0 + t8 * t14 * 2.0 + t8 * t15 * 1.0E1 + t9 * t14 * 2.0 + t8 * t16 * 2.0 + t9 * t15 * 2.0 - t10 * t14 * 1.0E1 + t9 * t16 * 1.0E1 - t10 * t15 * 2.0 + t11 * t14 * 6.0 - t10 * t16 * 1.0E1 + t11 * t15 * 6.0 - t12 * t14 * 1.0E1 + t8 * t19 + t11 * t16 * 6.0 - t12 * t15 * 1.0E1 + t13 * t14 * 6.0 + t11 * t17 - t12 * t16 * 2.0 + t13 * t15 * 6.0 + t9 * t20 + t13 * t16 * 6.0 + t11 * t19 + t13 * t18 + t13 * t20 - k16 * k26 * k36 * 4.8E1 + k13 * k23 * t14 * 8.0 - k16 * k26 * t8 * 1.2E1 - k13 * k23 * t15 * 8.0 - k16 * k26 * t9 * 4.0 + k13 * k23 * t16 * 8.0 + k16 * k26 * t10 * 1.2E1 - k16 * k26 * t11 * 1.2E1 + k16 * k26 * t12 * 2.0E1 - k13 * k23 * t19 - k16 * k26 * t13 * 1.2E1 - k16 * k36 * t8 * 4.0 - k16 * k36 * t9 * 1.2E1 + k15 * k33 * t14 * 8.0 + k16 * k36 * t10 * 2.0E1 + k15 * k33 * t15 * 8.0 - k16 * k36 * t11 * 1.2E1 - k15 * k33 * t16 * 8.0 + k16 * k36 * t12 * 1.2E1 - k16 * k36 * t13 * 1.2E1 - k15 * k33 * t20 + k26 * k36 * t8 * 1.2E1 + k26 * k36 * t9 * 1.2E1 - k26 * k36 * t10 * 1.2E1 + k26 * k36 * t11 * 1.2E1 + k25 * k35 * t14 * 1.2E1 - k26 * k36 * t12 * 1.2E1 + k25 * k35 * t15 * 1.2E1 + k26 * k36 * t13 * 1.2E1 + k25 * k35 * t16 * 1.2E1 + k16 * t2 * t15 * 4.0 + k16 * t3 * t14 * 2.0 + k16 * t2 * t16 * 4.0 + k16 * t3 * t15 * 2.0 + k16 * t4 * t14 * 2.0 + k16 * t8 * t10 * 2.0 + k16 * t3 * t16 * 6.0 + k16 * t4 * t15 * 6.0 - k16 * t8 * t11 * 4.0 + k16 * t9 * t10 * 2.0 + k16 * t4 * t16 * 2.0 + k16 * t8 * t12 * 2.0 + k16 * t9 * t12 * 2.0 + k16 * t10 * t11 * 2.0 + k16 * t3 * t19 - k16 * t9 * t13 * 4.0 - k16 * t10 * t12 * 8.0 + k16 * t10 * t13 * 6.0 + k16 * t11 * t12 * 6.0 + k16 * t4 * t20 + k16 * t12 * t13 * 2.0 - k26 * t2 * t14 * 2.0 - k26 * t2 * t15 * 2.0 - k26 * t3 * t14 * 4.0 - k26 * t8 * t9 * 2.0 - k26 * t2 * t16 * 1.4E1 - k26 * t4 * t14 * 6.0 - k26 * t8 * t10 * 2.0 - k26 * t3 * t16 * 4.0 - k26 * t4 * t15 * 2.0 + k26 * t8 * t11 * 6.0 - k26 * t9 * t10 * 4.0 - k26 * t4 * t16 * 2.0 - k26 * t8 * t12 * 8.0 + k26 * t5 * t16 * 2.0 + k26 * t8 * t13 * 2.0 - k26 * t9 * t12 * 2.0 + k26 * t9 * t13 * 4.0 + k26 * t10 * t12 * 2.0 - k26 * t10 * t13 * 4.0 - k26 * t11 * t12 * 6.0 - k26 * t12 * t13 * 2.0 - k36 * t2 * t14 * 2.0 - k36 * t2 * t15 * 1.4E1 - k36 * t3 * t14 * 6.0 - k36 * t8 * t9 * 2.0 - k36 * t2 * t16 * 2.0 - k36 * t3 * t15 * 2.0 - k36 * t4 * t14 * 4.0 - k36 * t8 * t10 * 2.0 - k36 * t3 * t16 * 2.0 - k36 * t4 * t15 * 4.0 + k36 * t8 * t11 * 4.0 - k36 * t9 * t10 * 8.0 + k36 * t5 * t15 * 2.0 - k36 * t8 * t12 * 4.0 + k36 * t9 * t11 * 2.0 - k36 * t9 * t12 * 2.0 - k36 * t10 * t11 * 2.0 + k36 * t9 * t13 * 6.0 + k36 * t10 * t12 * 2.0 - k36 * t10 * t13 * 6.0 - k36 * t11 * t12 * 4.0 + t2 * t8 * t15 * 2.0 + t3 * t8 * t14 + t2 * t10 * t14 + t3 * t8 * t15 + t2 * t9 * t16 * 2.0 + t2 * t10 * t15 + t3 * t8 * t16 + t3 * t10 * t14 * 6.0 - t4 * t8 * t15 * 2.0 + t4 * t9 * t14 + t8 * t9 * t10 + t2 * t10 * t16 * 3.0 + t2 * t12 * t14 - t3 * t9 * t16 * 2.0 + t4 * t9 * t15 + t4 * t10 * t14 * 3.0 - t2 * t11 * t16 * 4.0 + t2 * t12 * t15 * 3.0 + t3 * t10 * t16 * 6.0 + t3 * t12 * t14 * 3.0 + t4 * t9 * t16 + t4 * t10 * t15 + t8 * t9 * t12 + t8 * t10 * t11 + t2 * t12 * t16 - t2 * t13 * t15 * 4.0 + t3 * t12 * t15 + t4 * t10 * t16 + t4 * t12 * t14 * 6.0 + t8 * t10 * t12 * 2.0 + t3 * t12 * t16 + t4 * t12 * t15 * 6.0 + t8 * t10 * t13 - t8 * t11 * t12 * 2.0 + t9 * t10 * t12 * 2.0 + t5 * t11 * t16 - t9 * t10 * t13 * 2.0 + t9 * t11 * t12 + t5 * t13 * t15 + t10 * t11 * t12 + t9 * t12 * t13 + t10 * t12 * t13 - k13 * k16 * k23 * k36 * 1.6E1 - k15 * k16 * k26 * k33 * 1.6E1 - k16 * k25 * k26 * k35 * 2.4E1 - k16 * k25 * k35 * k36 * 2.4E1 + k25 * k26 * k35 * k36 * 2.4E1 - k12 * k13 * k15 * t15 * 8.0 - k12 * k13 * k15 * t16 * 8.0 - k13 * k16 * k23 * t8 * 2.0 - k13 * k16 * k23 * t9 * 2.0 + k13 * k16 * k23 * t10 * 2.0 + k13 * k16 * k23 * t11 * 2.0 - k12 * k15 * k23 * t14 * 2.0 + k13 * k16 * k23 * t12 * 6.0 + k12 * k15 * k23 * t15 * 6.0 - k13 * k16 * k23 * t13 * 6.0 - k12 * k15 * k23 * t16 * 2.0 - k13 * k23 * k26 * t8 * 2.0 + k13 * k23 * k26 * t9 * 6.0 - k12 * k13 * k33 * t14 * 2.0 + k13 * k23 * k26 * t10 * 2.0 - k15 * k16 * k33 * t8 * 2.0 - k12 * k13 * k33 * t15 * 2.0 - k13 * k23 * k26 * t11 * 6.0 - k15 * k16 * k33 * t9 * 2.0 + k12 * k13 * k33 * t16 * 6.0 + k13 * k22 * k25 * t14 * 2.0 + k13 * k23 * k26 * t12 * 6.0 + k15 * k16 * k33 * t10 * 6.0 - k13 * k22 * k25 * t15 * 6.0 + k13 * k23 * k26 * t13 * 2.0 - k15 * k16 * k33 * t11 * 6.0 + k13 * k22 * k25 * t16 * 2.0 + k15 * k16 * k33 * t12 * 2.0 + k15 * k16 * k33 * t13 * 2.0 - k13 * k22 * k25 * t19 + k13 * k23 * k36 * t8 * 2.0 + k16 * k26 * k36 * t2 * 1.6E1 + k13 * k23 * k36 * t9 * 1.0E1 + k16 * k26 * k36 * t3 * 8.0 - k12 * k23 * k33 * t14 * 2.0 - k13 * k23 * k36 * t10 * 2.0 + k15 * k26 * k33 * t8 * 1.0E1 + k16 * k26 * k36 * t4 * 8.0 - k12 * k23 * k33 * t15 * 2.0 - k13 * k23 * k36 * t11 * 2.0 + k15 * k26 * k33 * t9 * 2.0 - k12 * k23 * k33 * t16 * 2.0 + k13 * k22 * k35 * t14 * 6.0 + k13 * k23 * k36 * t12 * 2.0 + k15 * k26 * k33 * t10 * 2.0 - k16 * k25 * k35 * t8 * 4.0 - k22 * k23 * k25 * t14 * 8.0 - k13 * k22 * k35 * t15 * 2.0 + k13 * k23 * k36 * t13 * 6.0 + k15 * k26 * k33 * t11 * 6.0 - k16 * k25 * k35 * t9 * 4.0 + k13 * k22 * k35 * t16 * 6.0 + k15 * k25 * k32 * t14 * 6.0 - k15 * k26 * k33 * t12 * 2.0 + k16 * k25 * k35 * t10 * 8.0 - k22 * k23 * k25 * t16 * 8.0 + k15 * k25 * k32 * t15 * 6.0 - k15 * k26 * k33 * t13 * 2.0 - k15 * k25 * k32 * t16 * 2.0 + k16 * k25 * k35 * t12 * 8.0 + k15 * k33 * k36 * t8 * 6.0 - k15 * k33 * k36 * t9 * 2.0 + k15 * k33 * k36 * t10 * 6.0 - k22 * k23 * k35 * t14 * 1.2E1 + k25 * k26 * k35 * t8 * 8.0 + k15 * k33 * k36 * t11 * 2.0 - k22 * k23 * k35 * t15 * 4.0 + k25 * k26 * k35 * t9 * 4.0 + k15 * k32 * k35 * t14 * 2.0 + k15 * k33 * k36 * t12 * 2.0 - k22 * k23 * k35 * t16 * 1.2E1 - k25 * k26 * k35 * t10 * 4.0 + k15 * k32 * k35 * t15 * 2.0 - k15 * k33 * k36 * t13 * 6.0 - k15 * k32 * k35 * t16 * 6.0 - k25 * k26 * k35 * t12 * 8.0 - k15 * k32 * k35 * t20 - k25 * k32 * k33 * t14 * 1.2E1 + k25 * k35 * k36 * t8 * 4.0 - k25 * k32 * k33 * t15 * 1.2E1 + k25 * k35 * k36 * t9 * 8.0 - k25 * k32 * k33 * t16 * 4.0 - k25 * k35 * k36 * t10 * 8.0 - k25 * k35 * k36 * t12 * 4.0 - k32 * k33 * k35 * t14 * 8.0 - k32 * k33 * k35 * t15 * 8.0 - k13 * k23 * t2 * t15 * 2.0 - k13 * k23 * t3 * t14 * 6.0 + k16 * k26 * t3 * t8 * 4.0 + k13 * k23 * t2 * t16 * 2.0 - k13 * k23 * t4 * t14 * 3.0 + k16 * k26 * t4 * t8 * 2.0 - k13 * k23 * t3 * t16 * 6.0 + k13 * k23 * t4 * t15 - k13 * k23 * t8 * t11 * 2.0 - k13 * k23 * t9 * t10 * 2.0 - k16 * k26 * t4 * t9 * 2.0 - k13 * k23 * t4 * t16 - k13 * k23 * t8 * t12 - k16 * k26 * t2 * t12 * 4.0 - k16 * k26 * t4 * t10 * 4.0 - k13 * k23 * t9 * t12 * 3.0 + k16 * k26 * t2 * t13 * 4.0 - k16 * k26 * t3 * t12 * 4.0 + k13 * k23 * t9 * t13 * 2.0 - k13 * k23 * t10 * t12 - k16 * k26 * t4 * t12 * 1.2E1 - k13 * k23 * t10 * t13 * 2.0 + k13 * k23 * t11 * t12 - k13 * k23 * t12 * t13 - k16 * k36 * t3 * t8 * 2.0 - k16 * k36 * t2 * t10 * 4.0 + k16 * k36 * t3 * t9 * 2.0 + k15 * k33 * t2 * t15 * 2.0 - k15 * k33 * t3 * t14 * 3.0 + k16 * k36 * t2 * t11 * 4.0 - k16 * k36 * t3 * t10 * 1.2E1 + k16 * k36 * t4 * t9 * 4.0 - k15 * k33 * t2 * t16 * 2.0 - k15 * k33 * t3 * t15 - k15 * k33 * t4 * t14 * 6.0 - k15 * k33 * t8 * t10 * 3.0 - k16 * k36 * t4 * t10 * 4.0 + k15 * k33 * t3 * t16 - k15 * k33 * t4 * t15 * 6.0 + k15 * k33 * t8 * t11 * 2.0 - k15 * k33 * t9 * t10 - k16 * k36 * t3 * t12 * 4.0 - k15 * k33 * t8 * t12 * 2.0 - k15 * k33 * t10 * t11 - k15 * k33 * t9 * t13 * 2.0 - k15 * k33 * t10 * t12 + k15 * k33 * t10 * t13 - k15 * k33 * t11 * t12 * 2.0 + k26 * k36 * t2 * t8 * 4.0 + k26 * k36 * t2 * t9 * 4.0 - k26 * k36 * t3 * t8 * 4.0 + k26 * k36 * t2 * t10 * 2.0 - k26 * k36 * t3 * t9 * 4.0 - k26 * k36 * t4 * t8 * 4.0 - k26 * k36 * t2 * t11 * 6.0 - k26 * k36 * t4 * t9 * 4.0 - k25 * k35 * t2 * t14 * 2.0 + k26 * k36 * t2 * t12 * 2.0 - k25 * k35 * t2 * t15 * 6.0 - k25 * k35 * t8 * t9 * 2.0 - k26 * k36 * t2 * t13 * 6.0 - k25 * k35 * t2 * t16 * 6.0 - k25 * k35 * t8 * t10 * 4.0 - k25 * k35 * t9 * t10 * 4.0 - k25 * k35 * t8 * t12 * 4.0 - k25 * k35 * t9 * t12 * 4.0 - k16 * t2 * t3 * t16 * 2.0 - k16 * t2 * t4 * t15 * 2.0 + k16 * t4 * t8 * t10 + k16 * t3 * t8 * t12 + k16 * t4 * t9 * t10 + k16 * t2 * t10 * t12 * 2.0 + k16 * t3 * t9 * t12 - k16 * t2 * t10 * t13 * 2.0 - k16 * t2 * t11 * t12 * 2.0 + k16 * t3 * t10 * t12 * 6.0 + k16 * t4 * t10 * t12 * 6.0 + k26 * t2 * t4 * t14 + k26 * t2 * t4 * t15 + k26 * t4 * t8 * t9 + k26 * t2 * t4 * t16 + k26 * t2 * t8 * t12 * 2.0 + k26 * t4 * t8 * t10 * 2.0 + k26 * t3 * t8 * t12 * 2.0 + k26 * t2 * t9 * t13 * 2.0 + k26 * t2 * t10 * t12 + k26 * t4 * t8 * t12 * 6.0 + k26 * t2 * t11 * t12 * 3.0 + k26 * t2 * t12 * t13 + k36 * t2 * t3 * t14 + k36 * t2 * t3 * t15 + k36 * t3 * t8 * t9 + k36 * t2 * t3 * t16 + k36 * t2 * t8 * t11 * 2.0 + k36 * t2 * t9 * t10 * 2.0 + k36 * t3 * t9 * t10 * 6.0 + k36 * t2 * t10 * t11 + k36 * t4 * t9 * t10 * 2.0 + k36 * t2 * t10 * t12 + k36 * t3 * t9 * t12 * 2.0 + k36 * t2 * t10 * t13 * 3.0 + t2 * t4 * t8 * t15 + t2 * t3 * t9 * t16 + t2 * t8 * t11 * t12 + t2 * t9 * t10 * t13 + k12 * k13 * k15 * k16 * k26 * 8.0; coeffs(6) += k12 * k13 * k15 * k16 * k36 * 8.0 - k12 * k15 * k16 * k23 * k26 * 4.0 + k12 * k13 * k16 * k26 * k33 * 4.0 - k13 * k15 * k16 * k23 * k33 * 4.0 - k12 * k13 * k15 * k26 * k36 * 3.2E1 + k12 * k15 * k16 * k23 * k36 * 4.0 + k13 * k16 * k22 * k25 * k26 * 4.0 - k12 * k13 * k16 * k33 * k36 * 4.0 + k12 * k16 * k23 * k26 * k33 * 4.0 - k13 * k15 * k23 * k26 * k33 * 1.2E1 + k12 * k15 * k23 * k26 * k36 * 2.0E1 - k13 * k16 * k22 * k25 * k36 * 4.0 - k13 * k16 * k22 * k26 * k35 * 4.0 - k13 * k16 * k23 * k25 * k35 * 4.0 + k16 * k22 * k23 * k25 * k26 * 8.0 - k15 * k16 * k25 * k26 * k32 * 1.2E1 + k12 * k13 * k26 * k33 * k36 * 2.0E1 + k12 * k16 * k23 * k33 * k36 * 4.0 - k13 * k15 * k23 * k33 * k36 * 1.2E1 - k13 * k16 * k22 * k35 * k36 * 1.2E1 - k13 * k22 * k25 * k26 * k36 * 4.0 - k13 * k23 * k25 * k26 * k35 * 4.0 + k16 * k22 * k23 * k25 * k36 * 1.6E1 + k16 * k22 * k23 * k26 * k35 * 1.6E1 - k15 * k16 * k25 * k32 * k36 * 4.0 - k15 * k16 * k25 * k33 * k35 * 4.0 - k15 * k16 * k26 * k32 * k35 * 4.0 - k12 * k23 * k26 * k33 * k36 * 2.0E1 + k13 * k22 * k26 * k35 * k36 * 4.0 + k13 * k23 * k25 * k35 * k36 * 4.0 + k16 * k22 * k23 * k35 * k36 * 2.4E1 + k16 * k25 * k26 * k32 * k33 * 2.4E1 - k22 * k23 * k25 * k26 * k36 * 8.0 + k15 * k16 * k32 * k35 * k36 * 4.0 + k15 * k25 * k26 * k32 * k36 * 4.0 + k15 * k25 * k26 * k33 * k35 * 4.0 + k16 * k25 * k32 * k33 * k36 * 1.6E1 + k16 * k26 * k32 * k33 * k35 * 1.6E1 - k22 * k23 * k26 * k35 * k36 * 1.6E1 - k15 * k25 * k33 * k35 * k36 * 4.0 - k15 * k26 * k32 * k35 * k36 * 4.0 + k16 * k32 * k33 * k35 * k36 * 8.0 - k25 * k26 * k32 * k33 * k36 * 1.6E1 - k26 * k32 * k33 * k35 * k36 * 8.0 + k12 * k13 * k15 * k26 * t10 * 4.0 + k12 * k13 * k15 * k26 * t12 * 4.0 - k12 * k15 * k16 * k23 * t12 * 2.0 - k12 * k13 * k15 * k26 * t13 * 8.0 + k12 * k15 * k16 * k23 * t13 * 4.0 - k13 * k16 * k23 * k26 * t2 * 2.0 - k13 * k16 * k23 * k26 * t3 * 6.0 + k13 * k16 * k23 * k26 * t4 * 2.0 - k12 * k13 * k16 * k33 * t10 * 2.0 - k12 * k15 * k23 * k26 * t8 * 2.0 - k13 * k16 * k22 * k25 * t8 * 2.0 + k12 * k13 * k16 * k33 * t11 * 4.0 + k12 * k13 * k15 * k36 * t10 * 4.0 - k12 * k15 * k23 * k26 * t10 * 2.0 - k13 * k16 * k22 * k25 * t10 * 6.0 - k12 * k13 * k15 * k36 * t11 * 8.0 + k12 * k13 * k15 * k36 * t12 * 4.0 - k12 * k15 * k23 * k26 * t12 * 2.0 + k13 * k16 * k22 * k25 * t12 * 2.0 + k12 * k15 * k23 * k26 * t13 * 4.0 + k12 * k15 * k22 * k25 * t16 * 4.0 - k13 * k16 * k23 * k36 * t2 * 2.0 + k13 * k16 * k23 * k36 * t3 * 1.2E1 - k12 * k13 * k26 * k33 * t8 * 4.0 + k12 * k16 * k23 * k33 * t8 * 3.0 + k13 * k15 * k23 * k33 * t8 + k13 * k16 * k23 * k36 * t4 * 4.0 - k15 * k16 * k26 * k33 * t2 * 2.0 - k12 * k13 * k26 * k33 * t9 * 2.0 + k12 * k16 * k23 * k33 * t9 * 3.0 + k13 * k15 * k23 * k33 * t9 + k15 * k16 * k26 * k33 * t3 * 4.0 - k12 * k13 * k26 * k33 * t10 * 2.0 - k12 * k15 * k23 * k36 * t8 * 2.0 - k12 * k16 * k23 * k33 * t10 + k13 * k15 * k23 * k33 * t10 * 3.0 - k13 * k22 * k25 * k26 * t8 * 4.0 + k15 * k16 * k26 * k33 * t4 * 1.2E1 + k16 * k22 * k23 * k25 * t8 * 8.0 - k12 * k13 * k26 * k33 * t11 * 6.0 - k12 * k15 * k23 * k36 * t9 * 4.0 - k12 * k16 * k23 * k33 * t11 - k13 * k15 * k23 * k33 * t11 - k13 * k16 * k22 * k35 * t9 * 2.0 - k12 * k13 * k25 * k32 * t14 * 2.0 - k12 * k13 * k26 * k33 * t12 * 2.0 - k12 * k15 * k23 * k36 * t10 * 2.0 + k12 * k16 * k22 * k32 * t14 - k12 * k16 * k23 * k33 * t12 + k13 * k15 * k22 * k32 * t14 * 3.0 + k13 * k15 * k23 * k33 * t12 * 3.0 + k13 * k16 * k22 * k35 * t10 * 1.2E1 - k15 * k16 * k25 * k32 * t8 * 2.0 - k12 * k13 * k25 * k32 * t15 * 6.0 + k12 * k13 * k26 * k33 * t13 * 6.0 + k12 * k15 * k23 * k36 * t11 * 6.0 - k12 * k16 * k22 * k32 * t15 - k12 * k16 * k23 * k33 * t13 - k13 * k15 * k22 * k32 * t15 - k13 * k15 * k23 * k33 * t13 + k12 * k13 * k25 * k32 * t16 * 6.0 - k12 * k15 * k22 * k35 * t14 * 2.0 - k12 * k15 * k23 * k36 * t12 * 2.0 - k12 * k16 * k22 * k32 * t16 - k13 * k15 * k22 * k32 * t16 + k13 * k16 * k22 * k35 * t12 * 4.0 + k13 * k22 * k25 * k26 * t12 * 2.0 + k15 * k16 * k25 * k32 * t10 * 4.0 - k16 * k22 * k23 * k25 * t12 * 8.0 + k12 * k15 * k22 * k35 * t15 * 6.0 - k12 * k15 * k23 * k36 * t13 * 6.0 - k12 * k15 * k22 * k35 * t16 * 6.0 + k15 * k16 * k25 * k32 * t12 * 1.2E1 + k13 * k23 * k26 * k36 * t3 * 6.0 + k12 * k23 * k26 * k33 * t8 * 5.0 + k13 * k23 * k26 * k36 * t4 * 4.0 - k15 * k16 * k33 * k36 * t2 * 2.0 - k12 * k13 * k33 * k36 * t9 * 2.0 - k12 * k23 * k26 * k33 * t9 + k15 * k16 * k33 * k36 * t3 * 2.0 - k12 * k13 * k33 * k36 * t10 * 2.0 + k12 * k23 * k26 * k33 * t10 + k13 * k22 * k25 * k36 * t8 * 2.0 + k13 * k22 * k26 * k35 * t8 * 2.0 + k13 * k23 * k25 * k35 * t8 * 2.0 - k15 * k16 * k33 * k36 * t4 * 6.0 - k16 * k22 * k23 * k35 * t8 * 4.0 + k16 * k25 * k26 * k35 * t2 * 8.0 + k22 * k23 * k25 * k26 * t8 * 4.0 + k12 * k13 * k33 * k36 * t11 * 4.0 + k12 * k23 * k26 * k33 * t11 * 3.0 + k13 * k22 * k25 * k36 * t9 * 6.0 + k13 * k22 * k26 * k35 * t9 * 6.0 + k13 * k23 * k25 * k35 * t9 * 6.0 + k16 * k22 * k23 * k35 * t9 * 4.0 - k12 * k13 * k33 * k36 * t12 * 2.0 - k12 * k22 * k25 * k33 * t14 - k12 * k22 * k26 * k32 * t14 - k12 * k23 * k25 * k32 * t14 + k12 * k23 * k26 * k33 * t12 * 3.0 + k13 * k22 * k25 * k36 * t10 * 6.0 + k13 * k22 * k26 * k35 * t10 * 6.0 + k13 * k23 * k25 * k35 * t10 * 2.0 - k15 * k22 * k23 * k32 * t14 * 6.0 + k15 * k25 * k26 * k32 * t8 * 4.0 - k16 * k22 * k23 * k35 * t10 * 8.0 + k12 * k13 * k32 * k35 * t15 * 4.0 + k12 * k22 * k25 * k33 * t15 * 3.0 + k12 * k22 * k26 * k32 * t15 + k12 * k23 * k25 * k32 * t15 * 3.0 - k12 * k23 * k26 * k33 * t13 * 5.0 - k15 * k16 * k32 * k35 * t9 * 2.0 - k15 * k22 * k23 * k32 * t15 * 2.0 - k12 * k22 * k25 * k33 * t16 * 5.0 - k12 * k22 * k26 * k32 * t16 * 5.0 - k12 * k23 * k25 * k32 * t16 * 5.0 + k13 * k22 * k25 * k36 * t12 * 4.0 + k13 * k22 * k26 * k35 * t12 * 4.0 + k13 * k23 * k25 * k35 * t12 * 4.0 + k15 * k16 * k32 * k35 * t10 * 2.0 + k15 * k22 * k23 * k32 * t16 * 2.0 - k15 * k25 * k26 * k32 * t10 * 2.0 - k16 * k22 * k23 * k35 * t12 * 8.0 + k22 * k23 * k25 * k26 * t12 * 4.0 - k15 * k16 * k32 * k35 * t12 * 6.0 - k15 * k25 * k26 * k32 * t12 * 1.2E1 - k12 * k23 * k33 * k36 * t8 + k12 * k23 * k33 * k36 * t9 * 5.0 + k15 * k26 * k33 * k36 * t3 * 4.0 + k12 * k23 * k33 * k36 * t10 * 3.0 - k13 * k22 * k32 * k33 * t14 * 6.0 + k15 * k26 * k33 * k36 * t4 * 6.0 + k16 * k25 * k32 * k33 * t8 * 4.0 + k16 * k25 * k35 * k36 * t2 * 8.0 - k22 * k23 * k25 * k36 * t8 * 8.0 - k22 * k23 * k26 * k35 * t8 * 8.0 - k12 * k23 * k33 * k36 * t11 * 5.0 + k13 * k22 * k32 * k33 * t15 * 2.0 + k13 * k22 * k35 * k36 * t9 * 4.0 - k16 * k25 * k32 * k33 * t9 * 4.0 - k22 * k23 * k25 * k36 * t9 * 8.0 - k22 * k23 * k26 * k35 * t9 * 8.0 - k12 * k22 * k32 * k36 * t14 - k12 * k22 * k33 * k35 * t14 - k12 * k23 * k32 * k35 * t14 + k12 * k23 * k33 * k36 * t12 - k13 * k22 * k32 * k33 * t16 * 2.0 - k13 * k22 * k35 * k36 * t10 * 1.2E1 + k15 * k25 * k32 * k36 * t8 * 6.0 + k15 * k25 * k33 * k35 * t8 * 6.0 + k15 * k26 * k32 * k35 * t8 * 6.0 - k16 * k25 * k32 * k33 * t10 * 8.0 - k12 * k22 * k32 * k36 * t15 * 5.0 - k12 * k22 * k33 * k35 * t15 * 5.0 - k12 * k23 * k32 * k35 * t15 * 5.0 + k12 * k23 * k33 * k36 * t13 * 3.0 + k15 * k25 * k32 * k36 * t9 * 2.0 + k15 * k25 * k33 * k35 * t9 * 2.0 + k15 * k26 * k32 * k35 * t9 * 2.0 + k12 * k22 * k32 * k36 * t16 + k12 * k22 * k33 * k35 * t16 * 3.0 + k12 * k23 * k32 * k35 * t16 * 3.0 - k13 * k22 * k35 * k36 * t12 * 2.0 + k15 * k25 * k32 * k36 * t10 * 4.0 + k15 * k25 * k33 * k35 * t10 * 4.0 + k15 * k26 * k32 * k35 * t10 * 4.0 - k16 * k25 * k32 * k33 * t12 * 8.0 + k15 * k25 * k32 * k36 * t12 * 6.0 + k15 * k25 * k33 * k35 * t12 * 2.0 + k15 * k26 * k32 * k35 * t12 * 6.0 + k22 * k23 * k32 * k33 * t14 * 1.2E1 + k22 * k23 * k35 * k36 * t8 * 4.0 - k25 * k26 * k32 * k33 * t8 * 8.0 - k25 * k26 * k35 * k36 * t2 * 1.6E1 + k16 * k32 * k33 * k35 * t9 * 8.0 + k22 * k23 * k32 * k33 * t15 * 4.0 - k22 * k23 * k35 * k36 * t9 * 8.0 + k25 * k26 * k32 * k33 * t9 * 4.0 - k16 * k32 * k33 * k35 * t10 * 8.0 + k22 * k23 * k32 * k33 * t16 * 4.0 + k22 * k23 * k35 * k36 * t10 * 8.0 + k25 * k26 * k32 * k33 * t10 * 4.0 - k15 * k32 * k35 * k36 * t9 * 4.0 + k25 * k26 * k35 * k36 * t5 * 4.0 + k15 * k32 * k35 * k36 * t10 * 2.0 + k22 * k23 * k35 * k36 * t12 * 4.0 + k25 * k26 * k32 * k33 * t12 * 8.0 - k25 * k32 * k33 * k36 * t8 * 8.0 - k26 * k32 * k33 * k35 * t8 * 8.0 - k25 * k32 * k33 * k36 * t9 * 8.0 - k26 * k32 * k33 * k35 * t9 * 8.0 + k32 * k33 * k35 * k36 * t9 * 4.0 + k32 * k33 * k35 * k36 * t10 * 4.0 + k12 * k13 * k15 * t10 * t12 * 2.0 - k13 * k16 * k23 * t4 * t9 - k13 * k16 * k23 * t2 * t12 - k13 * k16 * k23 * t4 * t10 * 2.0 - k13 * k16 * k23 * t3 * t12 * 6.0 - k12 * k15 * k23 * t2 * t16 * 2.0 - k12 * k15 * k23 * t4 * t14 - k13 * k16 * k23 * t4 * t12 * 6.0 - k12 * k15 * k23 * t4 * t15 - k12 * k15 * k23 * t4 * t16 - k12 * k15 * k23 * t8 * t12 - k12 * k15 * k23 * t9 * t13 * 2.0 - k12 * k15 * k23 * t10 * t12 - k12 * k15 * k23 * t11 * t12 - k13 * k23 * k26 * t4 * t8 - k12 * k13 * k33 * t2 * t15 * 2.0 - k12 * k13 * k33 * t3 * t14 - k12 * k15 * k23 * t12 * t13 - k13 * k23 * k26 * t4 * t9 - k15 * k16 * k33 * t3 * t8 - k12 * k13 * k33 * t3 * t15 - k13 * k23 * k26 * t2 * t12 * 4.0 - k13 * k23 * k26 * t4 * t10 - k15 * k16 * k33 * t2 * t10 - k12 * k13 * k33 * t3 * t16 - k12 * k13 * k33 * t8 * t11 * 2.0 - k12 * k13 * k33 * t9 * t10 + k13 * k23 * k26 * t2 * t13 * 2.0 - k13 * k23 * k26 * t3 * t12 * 3.0 - k15 * k16 * k33 * t3 * t10 * 6.0 + k13 * k22 * k25 * t2 * t16 * 2.0 - k13 * k23 * k26 * t4 * t12 * 6.0 - k15 * k16 * k33 * t4 * t10 * 6.0 - k12 * k13 * k33 * t10 * t11 - k15 * k16 * k33 * t3 * t12 * 2.0 - k12 * k13 * k33 * t10 * t12 - k13 * k22 * k25 * t8 * t12 - k12 * k13 * k33 * t10 * t13 - k13 * k22 * k25 * t9 * t12 - k13 * k22 * k25 * t10 * t12 * 3.0 - k13 * k23 * k36 * t3 * t9 * 6.0 + k12 * k23 * k33 * t2 * t15 + k12 * k23 * k33 * t3 * t14 * 3.0 - k13 * k23 * k36 * t2 * t11 * 2.0 - k13 * k23 * k36 * t4 * t9 * 2.0 - k15 * k26 * k33 * t3 * t8 * 2.0 + k12 * k23 * k33 * t2 * t16 + k12 * k23 * k33 * t4 * t14 * 3.0 - k13 * k23 * k36 * t2 * t12 * 2.0 - k15 * k26 * k33 * t2 * t10 * 2.0 - k15 * k26 * k33 * t4 * t8 * 6.0 + k12 * k23 * k33 * t3 * t16 * 3.0 + k12 * k23 * k33 * t4 * t15 * 3.0 + k12 * k23 * k33 * t8 * t11 * 3.0 + k12 * k23 * k33 * t9 * t10 - k13 * k22 * k35 * t2 * t15 * 2.0 + k12 * k23 * k33 * t8 * t12 + k12 * k22 * k32 * t8 * t15 * 3.0 - k13 * k22 * k35 * t9 * t10 * 6.0 - k15 * k26 * k33 * t2 * t13 * 2.0 + k12 * k22 * k32 * t10 * t14 * 3.0 + k12 * k23 * k33 * t9 * t13 * 3.0 - k15 * k25 * k32 * t2 * t16 * 2.0 - k15 * k25 * k32 * t8 * t10 * 2.0 + k22 * k23 * k25 * t8 * t12 * 4.0 + k12 * k22 * k32 * t9 * t16 * 3.0 + k12 * k23 * k33 * t10 * t13 + k12 * k23 * k33 * t11 * t12 - k13 * k22 * k35 * t9 * t12 * 2.0 + k12 * k22 * k32 * t10 * t16 * 3.0 + k12 * k22 * k32 * t12 * t14 * 3.0 - k15 * k25 * k32 * t8 * t12 * 6.0 + k12 * k22 * k32 * t12 * t15 * 3.0 - k15 * k33 * k36 * t3 * t8 - k15 * k33 * k36 * t2 * t10 * 4.0 - k15 * k33 * k36 * t3 * t9 + k22 * k23 * k35 * t2 * t14 * 2.0 + k25 * k26 * k35 * t2 * t8 * 4.0 + k15 * k33 * k36 * t2 * t11 * 2.0 - k15 * k33 * k36 * t3 * t10 * 6.0 + k22 * k23 * k35 * t2 * t15 * 2.0 + k22 * k23 * k35 * t8 * t9 * 2.0 - k15 * k33 * k36 * t4 * t10 * 3.0 + k22 * k23 * k35 * t2 * t16 * 6.0 + k25 * k26 * k35 * t2 * t10 * 2.0 + k15 * k32 * k35 * t2 * t15 * 2.0 - k15 * k33 * k36 * t3 * t12 + k22 * k23 * k35 * t9 * t10 * 4.0 - k15 * k32 * k35 * t8 * t10 - k15 * k32 * k35 * t9 * t10 + k22 * k23 * k35 * t9 * t12 * 4.0 - k15 * k32 * k35 * t10 * t12 * 3.0 + k25 * k32 * k33 * t2 * t14 * 2.0 + k25 * k32 * k33 * t2 * t15 * 6.0 + k25 * k32 * k33 * t8 * t9 * 2.0 + k25 * k35 * k36 * t2 * t9 * 4.0 + k25 * k32 * k33 * t2 * t16 * 2.0 + k25 * k32 * k33 * t8 * t10 * 4.0 + k25 * k32 * k33 * t8 * t12 * 4.0 + k25 * k35 * k36 * t2 * t12 * 2.0 + k32 * k33 * k35 * t9 * t10 * 4.0 - k13 * k23 * t2 * t4 * t15 + k16 * k26 * t2 * t4 * t10 + k16 * k26 * t2 * t3 * t12 - k13 * k23 * t2 * t11 * t12 + k16 * k36 * t2 * t4 * t10 - k15 * k33 * t2 * t3 * t16 + k16 * k36 * t2 * t3 * t12 - k15 * k33 * t2 * t10 * t13 + k26 * k36 * t2 * t4 * t10 + k26 * k36 * t2 * t3 * t12 + k25 * k35 * t2 * t10 * t12 + k12 * k13 * k15 * k16 * k25 * k35 * 8.0; coeffs(6) += k12 * k13 * k16 * k25 * k26 * k32 * 8.0 - k13 * k15 * k16 * k22 * k25 * k33 * 2.0 - k13 * k15 * k16 * k22 * k26 * k32 * 2.0 - k13 * k15 * k16 * k23 * k25 * k32 * 2.0 - k12 * k13 * k15 * k25 * k26 * k35 * 1.6E1 - k12 * k15 * k16 * k22 * k25 * k36 * 4.0 - k12 * k15 * k16 * k22 * k26 * k35 * 4.0 - k12 * k15 * k16 * k23 * k25 * k35 * 4.0 - k12 * k13 * k16 * k25 * k32 * k36 * 4.0 - k12 * k13 * k16 * k25 * k33 * k35 * 4.0 - k12 * k13 * k16 * k26 * k32 * k35 * 4.0 - k12 * k16 * k22 * k25 * k26 * k33 * 2.0 - k12 * k16 * k23 * k25 * k26 * k32 * 2.0 - k13 * k15 * k16 * k22 * k32 * k36 * 2.0 - k13 * k15 * k16 * k22 * k33 * k35 * 2.0 - k13 * k15 * k16 * k23 * k32 * k35 * 2.0 - k13 * k15 * k22 * k25 * k26 * k33 * 2.0 - k13 * k15 * k23 * k25 * k26 * k32 * 2.0 + k15 * k16 * k22 * k23 * k25 * k33 * 8.0 + k15 * k16 * k22 * k23 * k26 * k32 * 8.0 - k12 * k13 * k15 * k25 * k35 * k36 * 1.6E1 + k12 * k15 * k16 * k22 * k35 * k36 * 8.0 + k12 * k15 * k22 * k25 * k26 * k36 * 1.2E1 + k12 * k15 * k23 * k25 * k26 * k35 * 1.2E1 + k13 * k16 * k22 * k26 * k32 * k33 * 4.0 + k13 * k16 * k23 * k25 * k32 * k33 * 4.0 + k12 * k13 * k25 * k26 * k32 * k36 * 8.0 + k12 * k13 * k25 * k26 * k33 * k35 * 8.0 + k12 * k16 * k22 * k25 * k33 * k36 * 6.0 + k12 * k16 * k22 * k26 * k32 * k36 * 6.0 + k12 * k16 * k22 * k26 * k33 * k35 * 6.0 + k12 * k16 * k23 * k25 * k32 * k36 * 6.0 + k12 * k16 * k23 * k25 * k33 * k35 * 6.0 + k12 * k16 * k23 * k26 * k32 * k35 * 6.0 - k13 * k15 * k22 * k25 * k33 * k36 * 1.0E1 - k13 * k15 * k22 * k26 * k32 * k36 * 1.0E1 - k13 * k15 * k22 * k26 * k33 * k35 * 1.0E1 - k13 * k15 * k23 * k25 * k32 * k36 * 1.0E1 - k13 * k15 * k23 * k25 * k33 * k35 * 1.0E1 - k13 * k15 * k23 * k26 * k32 * k35 * 1.0E1 + k15 * k16 * k22 * k23 * k32 * k36 * 4.0 + k15 * k16 * k22 * k23 * k33 * k35 * 4.0 - k15 * k22 * k23 * k25 * k26 * k33 * 4.0 + k12 * k15 * k22 * k26 * k35 * k36 * 8.0 + k12 * k15 * k23 * k25 * k35 * k36 * 8.0 + k13 * k16 * k22 * k32 * k33 * k36 * 8.0 + k13 * k16 * k23 * k32 * k33 * k35 * 8.0 + k13 * k23 * k25 * k26 * k32 * k33 * 4.0 - k16 * k22 * k23 * k26 * k32 * k33 * 1.6E1 + k12 * k13 * k25 * k33 * k35 * k36 * 1.2E1 + k12 * k13 * k26 * k32 * k35 * k36 * 1.2E1 - k12 * k16 * k22 * k33 * k35 * k36 * 2.0 - k12 * k16 * k23 * k32 * k35 * k36 * 2.0 - k12 * k22 * k25 * k26 * k33 * k36 * 1.0E1 - k12 * k23 * k25 * k26 * k32 * k36 * 1.0E1 - k12 * k23 * k25 * k26 * k33 * k35 * 1.0E1 - k13 * k15 * k22 * k33 * k35 * k36 * 2.0 - k13 * k15 * k23 * k32 * k35 * k36 * 2.0 + k15 * k22 * k23 * k25 * k33 * k36 * 8.0 + k15 * k22 * k23 * k26 * k32 * k36 * 8.0 + k15 * k22 * k23 * k26 * k33 * k35 * 8.0 + k13 * k22 * k26 * k32 * k33 * k36 * 8.0 + k13 * k23 * k25 * k32 * k33 * k36 * 8.0 + k13 * k23 * k26 * k32 * k33 * k35 * 8.0 - k16 * k22 * k23 * k32 * k33 * k36 * 1.6E1 - k12 * k22 * k26 * k33 * k35 * k36 * 1.0E1 - k12 * k23 * k25 * k33 * k35 * k36 * 1.0E1 - k12 * k23 * k26 * k32 * k35 * k36 * 1.0E1 + k15 * k22 * k23 * k33 * k35 * k36 * 4.0 - k13 * k23 * k32 * k33 * k35 * k36 * 4.0 + k12 * k15 * k16 * k23 * k26 * t4 * 2.0 + k12 * k15 * k16 * k22 * k25 * t12 * 2.0 - k12 * k13 * k16 * k26 * k33 * t3 * 4.0 + k13 * k15 * k16 * k23 * k33 * t3 * 6.0 + k13 * k15 * k16 * k23 * k33 * t4 * 6.0 + k12 * k13 * k15 * k26 * k36 * t3 * 4.0 + k12 * k13 * k15 * k26 * k36 * t4 * 4.0 - k12 * k15 * k16 * k23 * k36 * t4 * 4.0 - k12 * k13 * k16 * k25 * k32 * t10 * 4.0 + k13 * k15 * k16 * k22 * k32 * t10 * 6.0 + k12 * k13 * k15 * k25 * k35 * t10 * 4.0 + k13 * k15 * k16 * k22 * k32 * t12 * 6.0 + k12 * k13 * k15 * k25 * k35 * t12 * 4.0 - k12 * k15 * k16 * k22 * k35 * t12 * 4.0 - k12 * k15 * k22 * k25 * k26 * t12 * 2.0 + k12 * k16 * k23 * k26 * k33 * t2 + k13 * k15 * k23 * k26 * k33 * t2 * 3.0 + k12 * k13 * k16 * k33 * k36 * t3 * 2.0 + k12 * k16 * k23 * k26 * k33 * t3 * 3.0 + k13 * k15 * k23 * k26 * k33 * t3 * 3.0 - k12 * k15 * k23 * k26 * k36 * t2 * 4.0 - k12 * k16 * k23 * k26 * k33 * t4 * 6.0 + k13 * k15 * k23 * k26 * k33 * t4 * 6.0 - k13 * k16 * k22 * k25 * k36 * t2 * 2.0 - k13 * k16 * k22 * k26 * k35 * t2 * 2.0 - k13 * k16 * k23 * k25 * k35 * t2 * 2.0 - k12 * k15 * k23 * k26 * k36 * t3 * 6.0 - k12 * k13 * k22 * k23 * k32 * t14 * 2.0 - k12 * k13 * k25 * k26 * k32 * t8 * 4.0 + k12 * k16 * k22 * k25 * k33 * t8 * 3.0 + k12 * k16 * k22 * k26 * k32 * t8 * 3.0 + k12 * k16 * k23 * k25 * k32 * t8 * 3.0 + k13 * k15 * k22 * k25 * k33 * t8 + k13 * k15 * k22 * k26 * k32 * t8 + k13 * k15 * k23 * k25 * k32 * t8 - k15 * k16 * k22 * k23 * k32 * t8 * 2.0 - k12 * k13 * k22 * k23 * k32 * t15 * 2.0 + k12 * k13 * k16 * k32 * k35 * t10 * 2.0 - k12 * k13 * k22 * k23 * k32 * t16 * 2.0 - k12 * k13 * k25 * k26 * k32 * t10 * 2.0 - k12 * k15 * k22 * k25 * k36 * t8 * 2.0 - k12 * k15 * k22 * k26 * k35 * t8 * 2.0 - k12 * k15 * k23 * k25 * k35 * t8 * 2.0 + k12 * k16 * k22 * k25 * k33 * t10 * 3.0 + k12 * k16 * k22 * k26 * k32 * t10 * 3.0 + k12 * k16 * k23 * k25 * k32 * t10 + k13 * k15 * k22 * k25 * k33 * t10 * 3.0 + k13 * k15 * k22 * k26 * k32 * t10 * 3.0 + k13 * k15 * k23 * k25 * k32 * t10 - k15 * k16 * k22 * k23 * k32 * t10 * 4.0 - k12 * k15 * k22 * k25 * k36 * t10 * 6.0 - k12 * k15 * k22 * k26 * k35 * t10 * 6.0 - k12 * k15 * k23 * k25 * k35 * t10 * 2.0 - k12 * k16 * k22 * k25 * k33 * t12 * 2.0 - k12 * k16 * k22 * k26 * k32 * t12 * 6.0 - k12 * k16 * k23 * k25 * k32 * t12 * 6.0 + k13 * k15 * k22 * k25 * k33 * t12 * 2.0 + k13 * k15 * k22 * k26 * k32 * t12 * 6.0 + k13 * k15 * k23 * k25 * k32 * t12 * 6.0 - k15 * k16 * k22 * k23 * k32 * t12 * 1.2E1 - k12 * k13 * k26 * k33 * k36 * t2 * 4.0 + k12 * k16 * k23 * k33 * k36 * t2 + k13 * k15 * k23 * k33 * k36 * t2 * 3.0 - k12 * k16 * k23 * k33 * k36 * t3 * 6.0 + k13 * k15 * k23 * k33 * k36 * t3 * 6.0 - k12 * k13 * k26 * k33 * k36 * t4 * 6.0 + k12 * k16 * k23 * k33 * k36 * t4 * 3.0 + k13 * k15 * k23 * k33 * k36 * t4 * 3.0 - k13 * k22 * k25 * k26 * k36 * t2 * 4.0 - k13 * k23 * k25 * k26 * k35 * t2 * 4.0 - k13 * k16 * k22 * k32 * k33 * t9 * 2.0 + k12 * k22 * k25 * k26 * k33 * t8 * 6.0 + k12 * k23 * k25 * k26 * k32 * t8 * 6.0 - k13 * k16 * k22 * k32 * k33 * t10 * 1.2E1 - k15 * k16 * k25 * k32 * k36 * t2 * 2.0 - k15 * k16 * k25 * k33 * k35 * t2 * 2.0 - k15 * k16 * k26 * k32 * k35 * t2 * 2.0 - k15 * k22 * k23 * k25 * k33 * t8 * 4.0 - k15 * k22 * k23 * k26 * k32 * t8 * 4.0 - k12 * k13 * k25 * k32 * k36 * t9 * 2.0 - k12 * k13 * k25 * k33 * k35 * t9 * 2.0 - k12 * k13 * k26 * k32 * k35 * t9 * 2.0; coeffs(6) += k12 * k16 * k22 * k32 * k36 * t9 * 3.0 + k12 * k16 * k22 * k33 * k35 * t9 * 3.0 + k12 * k16 * k23 * k32 * k35 * t9 * 3.0 + k13 * k15 * k22 * k32 * k36 * t9 + k13 * k15 * k22 * k33 * k35 * t9 + k13 * k15 * k23 * k32 * k35 * t9 - k12 * k15 * k22 * k32 * k33 * t14 * 2.0 - k12 * k16 * k22 * k32 * k36 * t10 * 6.0 - k12 * k16 * k22 * k33 * k35 * t10 * 6.0 - k12 * k16 * k23 * k32 * k35 * t10 * 2.0 + k13 * k15 * k22 * k32 * k36 * t10 * 6.0 + k13 * k15 * k22 * k33 * k35 * t10 * 6.0 + k13 * k15 * k23 * k32 * k35 * t10 * 2.0 - k13 * k16 * k22 * k32 * k33 * t12 * 4.0 - k12 * k15 * k22 * k32 * k33 * t15 * 2.0 - k12 * k15 * k22 * k35 * k36 * t9 * 4.0 - k12 * k13 * k25 * k32 * k36 * t12 * 6.0 - k12 * k13 * k25 * k33 * k35 * t12 * 2.0 - k12 * k13 * k26 * k32 * k35 * t12 * 6.0 - k12 * k15 * k22 * k32 * k33 * t16 * 2.0 + k12 * k16 * k22 * k32 * k36 * t12 * 3.0 + k12 * k16 * k22 * k33 * k35 * t12 + k12 * k16 * k23 * k32 * k35 * t12 * 3.0 + k12 * k22 * k25 * k26 * k33 * t12 * 2.0 + k12 * k23 * k25 * k26 * k32 * t12 * 6.0 + k13 * k15 * k22 * k32 * k36 * t12 * 3.0 + k13 * k15 * k22 * k33 * k35 * t12 + k13 * k15 * k23 * k32 * k35 * t12 * 3.0 - k12 * k15 * k22 * k35 * k36 * t12 * 2.0 + k12 * k23 * k26 * k33 * k36 * t2 * 4.0 + k12 * k23 * k26 * k33 * k36 * t3 * 3.0 + k12 * k23 * k26 * k33 * k36 * t4 * 3.0 - k13 * k22 * k26 * k32 * k33 * t8 * 2.0 + k13 * k22 * k26 * k35 * k36 * t2 * 4.0 - k13 * k23 * k25 * k32 * k33 * t8 * 2.0 + k13 * k23 * k25 * k35 * k36 * t2 * 4.0 + k16 * k22 * k23 * k32 * k33 * t8 * 4.0 - k16 * k22 * k23 * k35 * k36 * t2 * 8.0 - k16 * k25 * k26 * k32 * k33 * t2 * 8.0 + k22 * k23 * k25 * k26 * k36 * t2 * 4.0 - k13 * k22 * k26 * k32 * k33 * t9 * 2.0 - k13 * k23 * k25 * k32 * k33 * t9 * 2.0 + k16 * k22 * k23 * k32 * k33 * t9 * 4.0 - k12 * k22 * k25 * k33 * k36 * t8 - k12 * k22 * k26 * k32 * k36 * t8 - k12 * k22 * k26 * k33 * k35 * t8 - k12 * k23 * k25 * k32 * k36 * t8 - k12 * k23 * k25 * k33 * k35 * t8 - k12 * k23 * k26 * k32 * k35 * t8 - k13 * k22 * k26 * k32 * k33 * t10 * 6.0 - k13 * k23 * k25 * k32 * k33 * t10 * 2.0 - k15 * k22 * k23 * k32 * k36 * t8 * 2.0 - k15 * k22 * k23 * k33 * k35 * t8 * 2.0 + k15 * k25 * k26 * k32 * k36 * t2 * 4.0 + k15 * k25 * k26 * k33 * k35 * t2 * 4.0 + k16 * k22 * k23 * k32 * k33 * t10 * 8.0 - k12 * k22 * k25 * k33 * k36 * t9 - k12 * k22 * k26 * k32 * k36 * t9 - k12 * k22 * k26 * k33 * k35 * t9 - k12 * k23 * k25 * k32 * k36 * t9 - k12 * k23 * k25 * k33 * k35 * t9 - k12 * k23 * k26 * k32 * k35 * t9 - k15 * k22 * k23 * k32 * k36 * t9 * 2.0 - k15 * k22 * k23 * k33 * k35 * t9 * 2.0 - k12 * k13 * k32 * k35 * k36 * t10 * 2.0 + k12 * k22 * k25 * k33 * k36 * t10 * 3.0 + k12 * k22 * k26 * k32 * k36 * t10 * 3.0 + k12 * k22 * k26 * k33 * k35 * t10 * 3.0 + k12 * k23 * k25 * k32 * k36 * t10 + k12 * k23 * k25 * k33 * k35 * t10 + k12 * k23 * k26 * k32 * k35 * t10 - k13 * k22 * k26 * k32 * k33 * t12 * 4.0 - k13 * k23 * k25 * k32 * k33 * t12 * 4.0 - k15 * k22 * k23 * k32 * k36 * t10 * 4.0 - k15 * k22 * k23 * k33 * k35 * t10 * 4.0 + k16 * k22 * k23 * k32 * k33 * t12 * 8.0 + k12 * k22 * k25 * k33 * k36 * t12 + k12 * k22 * k26 * k32 * k36 * t12 * 3.0 + k12 * k22 * k26 * k33 * k35 * t12 + k12 * k23 * k25 * k32 * k36 * t12 * 3.0 + k12 * k23 * k25 * k33 * k35 * t12 + k12 * k23 * k26 * k32 * k35 * t12 * 3.0 - k15 * k22 * k23 * k32 * k36 * t12 * 6.0 - k15 * k22 * k23 * k33 * k35 * t12 * 2.0 + k22 * k23 * k26 * k32 * k33 * t8 * 8.0 - k13 * k22 * k32 * k33 * k36 * t9 * 4.0 - k13 * k23 * k32 * k33 * k35 * t9 * 4.0 - k15 * k25 * k33 * k35 * k36 * t2 * 4.0 - k15 * k26 * k32 * k35 * k36 * t2 * 4.0 + k12 * k22 * k33 * k35 * k36 * t9 * 6.0 + k12 * k23 * k32 * k35 * k36 * t9 * 6.0 + k12 * k22 * k33 * k35 * k36 * t10 * 6.0 + k12 * k23 * k32 * k35 * k36 * t10 * 2.0 + k22 * k23 * k32 * k33 * k36 * t9 * 8.0 + k26 * k32 * k33 * k35 * k36 * t2 * 4.0 + k12 * k13 * k15 * k16 * t4 * t10 + k12 * k13 * k15 * k16 * t3 * t12 + k12 * k13 * k15 * k26 * t4 * t10 - k12 * k15 * k16 * k23 * t4 * t10 + k12 * k13 * k15 * k26 * t3 * t12 - k12 * k15 * k16 * k23 * t3 * t12 * 3.0 - k13 * k16 * k23 * k26 * t2 * t4 - k12 * k13 * k16 * k33 * t4 * t10 * 3.0 - k12 * k15 * k23 * k26 * t4 * t8 - k12 * k13 * k16 * k33 * t3 * t12 + k12 * k13 * k15 * k36 * t4 * t10 - k13 * k16 * k22 * k25 * t2 * t12 + k12 * k13 * k15 * k36 * t3 * t12 - k12 * k15 * k23 * k26 * t2 * t13 * 2.0 - k12 * k15 * k22 * k25 * t2 * t16 * 2.0 - k12 * k15 * k22 * k25 * t8 * t12 - k12 * k13 * k26 * k33 * t4 * t10 * 3.0 + k12 * k16 * k23 * k33 * t4 * t10 * 3.0 - k12 * k13 * k26 * k33 * t3 * t12 + k12 * k16 * k23 * k33 * t3 * t12 * 3.0 - k12 * k15 * k23 * k36 * t4 * t10 - k13 * k22 * k25 * k26 * t2 * t12 * 2.0 + k16 * k22 * k23 * k25 * t2 * t12 * 2.0 - k12 * k15 * k23 * k36 * t3 * t12 * 3.0 - k12 * k13 * k25 * k32 * t10 * t12 * 3.0 + k12 * k16 * k22 * k32 * t10 * t12 * 9.0 - k13 * k23 * k26 * k36 * t2 * t4 * 2.0 - k15 * k16 * k33 * k36 * t2 * t3 - k12 * k13 * k33 * k36 * t3 * t9 - k12 * k15 * k22 * k35 * t10 * t12 * 3.0 + k12 * k23 * k26 * k33 * t4 * t8 * 3.0 - k12 * k13 * k33 * k36 * t2 * t11 * 2.0 - k12 * k13 * k32 * k35 * t2 * t15 * 2.0 + k12 * k23 * k26 * k33 * t2 * t13 + k12 * k22 * k25 * k33 * t2 * t16 + k12 * k22 * k26 * k32 * t2 * t16 + k12 * k23 * k25 * k32 * t2 * t16 - k13 * k22 * k25 * k36 * t2 * t12 * 2.0 - k13 * k22 * k26 * k35 * t2 * t12 * 2.0 - k13 * k23 * k25 * k35 * t2 * t12 * 2.0 - k15 * k16 * k32 * k35 * t2 * t10 - k15 * k22 * k23 * k32 * t2 * t16 * 2.0 + k16 * k22 * k23 * k35 * t2 * t12 * 2.0 - k12 * k13 * k32 * k35 * t9 * t10 + k12 * k22 * k25 * k33 * t8 * t12 + k12 * k22 * k26 * k32 * t8 * t12 * 3.0 + k12 * k23 * k25 * k32 * t8 * t12 * 3.0 - k15 * k26 * k33 * k36 * t2 * t3 * 2.0 + k12 * k23 * k33 * k36 * t3 * t9 * 3.0 + k12 * k23 * k33 * k36 * t2 * t11 - k13 * k22 * k32 * k33 * t2 * t15 * 2.0 + k16 * k25 * k32 * k33 * t2 * t10 * 2.0 + k12 * k22 * k32 * k36 * t2 * t15 + k12 * k22 * k33 * k35 * t2 * t15 + k12 * k23 * k32 * k35 * t2 * t15 - k15 * k25 * k32 * k36 * t2 * t10 * 2.0 - k15 * k25 * k33 * k35 * t2 * t10 * 2.0 - k15 * k26 * k32 * k35 * t2 * t10 * 2.0 + k22 * k23 * k25 * k36 * t2 * t12 * 2.0 + k22 * k23 * k26 * k35 * t2 * t12 * 2.0 + k12 * k22 * k32 * k36 * t9 * t10 * 3.0 + k12 * k22 * k33 * k35 * t9 * t10 * 3.0 + k12 * k23 * k32 * k35 * t9 * t10 + k25 * k26 * k32 * k33 * t2 * t8 * 4.0 + k22 * k23 * k35 * k36 * t2 * t9 * 4.0 + k16 * k32 * k33 * k35 * t2 * t10 * 2.0 - k15 * k32 * k35 * k36 * t2 * t10 * 2.0 + k25 * k32 * k33 * k36 * t2 * t10 * 2.0 + k26 * k32 * k33 * k35 * t2 * t10 * 2.0 - k12 * k13 * k16 * k22 * k23 * k25 * k33 * 8.0 - k12 * k13 * k16 * k22 * k23 * k26 * k32 * 8.0 + k12 * k13 * k15 * k22 * k23 * k25 * k36 * 8.0 + k12 * k13 * k15 * k22 * k23 * k26 * k35 * 8.0 + k12 * k13 * k16 * k22 * k23 * k32 * k36 * 4.0 + k12 * k13 * k16 * k22 * k23 * k33 * k35 * 4.0 - k12 * k13 * k22 * k23 * k25 * k26 * k33 * 4.0 + k12 * k15 * k16 * k22 * k26 * k32 * k33 * 4.0 + k12 * k15 * k16 * k23 * k25 * k32 * k33 * 4.0 + k12 * k13 * k15 * k25 * k32 * k33 * k36 * 8.0 + k12 * k13 * k15 * k26 * k32 * k33 * k35 * 8.0 - k12 * k15 * k16 * k22 * k32 * k33 * k36 * 8.0 - k12 * k15 * k16 * k23 * k32 * k33 * k35 * 8.0 - k12 * k15 * k23 * k25 * k26 * k32 * k33 * 4.0 - k12 * k13 * k22 * k23 * k33 * k35 * k36 * 4.0 - k12 * k15 * k23 * k32 * k33 * k35 * k36 * 4.0 + k12 * k13 * k15 * k22 * k23 * k25 * t12 * 2.0 - k12 * k13 * k16 * k22 * k23 * k32 * t12 * 6.0 + k12 * k13 * k15 * k22 * k23 * k35 * t12 * 2.0 + k12 * k13 * k15 * k25 * k32 * k33 * t10 * 2.0 - k12 * k13 * k22 * k23 * k25 * k33 * t12 * 2.0 - k12 * k13 * k22 * k23 * k26 * k32 * t12 * 6.0 - k12 * k15 * k16 * k22 * k32 * k33 * t10 * 6.0 - k13 * k16 * k22 * k26 * k32 * k33 * t2 * 2.0 - k13 * k16 * k23 * k25 * k32 * k33 * t2 * 2.0 - k12 * k13 * k25 * k26 * k32 * k36 * t2 * 4.0 - k12 * k13 * k25 * k26 * k33 * k35 * t2 * 4.0 + k12 * k16 * k22 * k25 * k33 * k36 * t2 + k12 * k16 * k22 * k26 * k32 * k36 * t2 + k12 * k16 * k22 * k26 * k33 * k35 * t2 + k12 * k16 * k23 * k25 * k32 * k36 * t2 + k12 * k16 * k23 * k25 * k33 * k35 * t2 + k12 * k16 * k23 * k26 * k32 * k35 * t2 + k13 * k15 * k22 * k25 * k33 * k36 * t2 * 3.0 + k13 * k15 * k22 * k26 * k32 * k36 * t2 * 3.0 + k13 * k15 * k22 * k26 * k33 * k35 * t2 * 3.0 + k13 * k15 * k23 * k25 * k32 * k36 * t2 * 3.0 + k13 * k15 * k23 * k25 * k33 * k35 * t2 * 3.0 + k13 * k15 * k23 * k26 * k32 * k35 * t2 * 3.0 - k15 * k16 * k22 * k23 * k32 * k36 * t2 * 2.0 - k15 * k16 * k22 * k23 * k33 * k35 * t2 * 2.0 - k12 * k13 * k22 * k23 * k32 * k36 * t9 * 2.0 - k12 * k13 * k22 * k23 * k33 * k35 * t9 * 2.0 - k12 * k15 * k22 * k26 * k32 * k33 * t8 * 2.0 - k12 * k15 * k22 * k26 * k35 * k36 * t2 * 4.0 - k12 * k15 * k23 * k25 * k32 * k33 * t8 * 2.0 - k12 * k15 * k23 * k25 * k35 * k36 * t2 * 4.0 + k12 * k13 * k15 * k32 * k33 * k35 * t10 * 2.0 - k13 * k23 * k25 * k26 * k32 * k33 * t2 * 4.0 + k16 * k22 * k23 * k26 * k32 * k33 * t2 * 4.0 + k12 * k22 * k25 * k26 * k33 * k36 * t2 * 2.0 + k12 * k23 * k25 * k26 * k32 * k36 * t2 * 2.0 + k12 * k23 * k25 * k26 * k33 * k35 * t2 * 2.0 - k15 * k22 * k23 * k25 * k33 * k36 * t2 * 4.0 - k15 * k22 * k23 * k26 * k32 * k36 * t2 * 4.0 - k15 * k22 * k23 * k26 * k33 * k35 * t2 * 4.0 - k12 * k15 * k22 * k32 * k33 * k36 * t10 * 6.0 - k12 * k15 * k23 * k32 * k33 * k35 * t10 * 2.0 - k13 * k22 * k26 * k32 * k33 * k36 * t2 * 4.0 - k13 * k23 * k25 * k32 * k33 * k36 * t2 * 4.0 - k13 * k23 * k26 * k32 * k33 * k35 * t2 * 4.0 + k16 * k22 * k23 * k32 * k33 * k36 * t2 * 4.0 + k12 * k22 * k26 * k33 * k35 * k36 * t2 * 2.0 + k12 * k23 * k25 * k33 * k35 * k36 * t2 * 2.0 + k12 * k23 * k26 * k32 * k35 * k36 * t2 * 2.0 - k15 * k22 * k23 * k33 * k35 * k36 * t2 * 4.0 + k22 * k23 * k26 * k32 * k33 * k36 * t2 * 4.0 + k12 * k13 * k15 * k16 * k22 * k23 * k32 * k33 * 4.0 + k12 * k13 * k15 * k22 * k23 * k26 * k32 * k33 * 4.0 + k12 * k13 * k15 * k22 * k23 * k32 * k33 * k36 * 4.0; coeffs(7) = k16 * k25 * t14 * -4.0 - k16 * k25 * t15 * 1.2E1 - k16 * k25 * t16 * 1.2E1 - k16 * k25 * t19 * 2.0 - k16 * k35 * t14 * 4.0 + k25 * k26 * t14 * 1.2E1 - k16 * k35 * t15 * 1.2E1 + k25 * k26 * t15 * 4.0 - k16 * k35 * t16 * 1.2E1 + k25 * k26 * t16 * 1.2E1 + k25 * k26 * t17 * 2.0 + k25 * k26 * t19 * 2.0 - k16 * k35 * t20 * 2.0 + k25 * k36 * t14 * 1.2E1 + k26 * k35 * t14 * 1.2E1 + k25 * k36 * t15 * 1.2E1 + k26 * k35 * t15 * 4.0 + k25 * k36 * t16 * 4.0 + k26 * k35 * t16 * 1.2E1 + k35 * k36 * t14 * 1.2E1 + k35 * k36 * t15 * 1.2E1 + k35 * k36 * t16 * 4.0 + k35 * k36 * t18 * 2.0 + k35 * k36 * t20 * 2.0 + k25 * t8 * t14 * 2.0 + k25 * t8 * t15 * 6.0 + k25 * t8 * t16 * 2.0 - k25 * t10 * t14 * 4.0 + k25 * t9 * t16 * 4.0 - k25 * t10 * t16 * 4.0 - k25 * t12 * t14 * 6.0 + k25 * t8 * t19 - k25 * t12 * t15 * 6.0 - k25 * t12 * t16 * 2.0 + k35 * t8 * t15 * 4.0 + k35 * t9 * t14 * 2.0 + k35 * t9 * t15 * 2.0 - k35 * t10 * t14 * 6.0 + k35 * t9 * t16 * 6.0 - k35 * t10 * t15 * 2.0 - k35 * t10 * t16 * 6.0 - k35 * t12 * t14 * 4.0 - k35 * t12 * t15 * 4.0 + k35 * t9 * t20 - k16 * k25 * k26 * k36 * 2.4E1 - k16 * k26 * k35 * k36 * 2.4E1 - k13 * k16 * k22 * t14 * 2.0 + k13 * k16 * k22 * t15 * 2.0 - k13 * k16 * k22 * t16 * 6.0 - k13 * k16 * k22 * t19 + k13 * k22 * k26 * t14 * 2.0 + k13 * k23 * k25 * t14 * 2.0 + k16 * k22 * k23 * t14 * 4.0 - k16 * k25 * k26 * t8 * 8.0 - k13 * k22 * k26 * t15 * 2.0 - k13 * k23 * k25 * t15 * 6.0 + k16 * k22 * k23 * t15 * 4.0 + k13 * k22 * k26 * t16 * 2.0 + k13 * k23 * k25 * t16 * 2.0 - k15 * k16 * k32 * t14 * 2.0 + k16 * k22 * k23 * t16 * 1.2E1 + k16 * k25 * k26 * t10 * 4.0 - k15 * k16 * k32 * t15 * 6.0 + k15 * k16 * k32 * t16 * 2.0 + k16 * k25 * k26 * t12 * 1.2E1 - k13 * k22 * k26 * t19 - k13 * k23 * k25 * t19 + k16 * k22 * k23 * t19 * 2.0 - k15 * k16 * k32 * t20 + k13 * k22 * k36 * t14 * 6.0 + k13 * k23 * k35 * t14 * 6.0 - k16 * k25 * k36 * t8 * 4.0 - k16 * k26 * k35 * t8 * 4.0 - k22 * k23 * k26 * t14 * 8.0 - k13 * k22 * k36 * t15 * 2.0 - k13 * k23 * k35 * t15 * 2.0 - k16 * k25 * k36 * t9 * 4.0 - k16 * k26 * k35 * t9 * 4.0 + k13 * k22 * k36 * t16 * 2.0 + k13 * k23 * k35 * t16 * 6.0 + k15 * k25 * k33 * t14 * 6.0 + k15 * k26 * k32 * t14 * 6.0 + k16 * k25 * k36 * t10 * 8.0 + k16 * k26 * k35 * t10 * 8.0 - k22 * k23 * k26 * t16 * 8.0 + k15 * k25 * k33 * t15 * 6.0 + k15 * k26 * k32 * t15 * 2.0 - k15 * k25 * k33 * t16 * 2.0 - k15 * k26 * k32 * t16 * 2.0 + k16 * k25 * k36 * t12 * 8.0 + k16 * k26 * k35 * t12 * 8.0 + k16 * k32 * k33 * t14 * 4.0 - k22 * k23 * k36 * t14 * 1.2E1 + k25 * k26 * k36 * t8 * 8.0 + k16 * k32 * k33 * t15 * 1.2E1 - k16 * k35 * k36 * t9 * 8.0 - k22 * k23 * k36 * t15 * 4.0 + k25 * k26 * k36 * t9 * 4.0 + k15 * k32 * k36 * t14 * 2.0 + k15 * k33 * k35 * t14 * 2.0 + k16 * k32 * k33 * t16 * 4.0 + k16 * k35 * k36 * t10 * 1.2E1 - k22 * k23 * k36 * t16 * 4.0 - k25 * k26 * k36 * t10 * 4.0 + k15 * k32 * k36 * t15 * 2.0 + k15 * k33 * k35 * t15 * 2.0 - k15 * k32 * k36 * t16 * 2.0 - k15 * k33 * k35 * t16 * 6.0 + k16 * k35 * k36 * t12 * 4.0 - k25 * k26 * k36 * t12 * 8.0 + k16 * k32 * k33 * t20 * 2.0 - k15 * k32 * k36 * t20 - k15 * k33 * k35 * t20 - k26 * k32 * k33 * t14 * 1.2E1 + k26 * k35 * k36 * t8 * 4.0 - k26 * k32 * k33 * t15 * 4.0 + k26 * k35 * k36 * t9 * 8.0 - k26 * k32 * k33 * t16 * 4.0 - k26 * k35 * k36 * t10 * 8.0 - k26 * k35 * k36 * t12 * 4.0 - k32 * k33 * k36 * t14 * 8.0 - k32 * k33 * k36 * t15 * 8.0 - k13 * k22 * t8 * t15 * 2.0 - k13 * k22 * t10 * t14 * 6.0 + k16 * k25 * t2 * t16 * 4.0 + k16 * k25 * t8 * t10 * 4.0 + k13 * k22 * t9 * t16 * 2.0 - k13 * k22 * t10 * t16 * 6.0 - k13 * k22 * t12 * t14 * 3.0 + k16 * k25 * t8 * t12 * 2.0 + k13 * k22 * t12 * t15 - k16 * k25 * t9 * t12 * 2.0 - k13 * k22 * t12 * t16 - k16 * k25 * t10 * t12 * 4.0 + k22 * k23 * t8 * t14 * 2.0 + k16 * k35 * t2 * t15 * 4.0 + k22 * k23 * t8 * t15 * 2.0 - k16 * k35 * t8 * t10 * 2.0 + k22 * k23 * t8 * t16 * 2.0 + k22 * k23 * t10 * t14 * 4.0 - k25 * k26 * t2 * t16 * 8.0 + k25 * k26 * t8 * t10 * 2.0 + k15 * k32 * t8 * t15 * 2.0 + k16 * k35 * t9 * t10 * 2.0 - k22 * k23 * t9 * t16 * 4.0 - k15 * k32 * t10 * t14 * 3.0 + k22 * k23 * t10 * t16 * 4.0 + k22 * k23 * t12 * t14 * 6.0 - k25 * k26 * t8 * t12 * 4.0 - k15 * k32 * t9 * t16 * 2.0 - k15 * k32 * t10 * t15 + k16 * k35 * t9 * t12 * 4.0 + k22 * k23 * t12 * t15 * 2.0 + k25 * k26 * t5 * t16 * 2.0 + k25 * k26 * t9 * t12 * 2.0; coeffs(7) += k15 * k32 * t10 * t16 - k15 * k32 * t12 * t14 * 6.0 - k16 * k35 * t10 * t12 * 4.0 + k22 * k23 * t12 * t16 * 2.0 + k25 * k26 * t10 * t12 * 2.0 - k15 * k32 * t12 * t15 * 6.0 - k25 * k36 * t2 * t14 * 2.0 - k26 * k35 * t2 * t14 * 2.0 - k25 * k36 * t2 * t15 * 6.0 - k25 * k36 * t8 * t9 * 2.0 - k26 * k35 * t2 * t15 * 2.0 - k26 * k35 * t8 * t9 * 2.0 - k25 * k36 * t2 * t16 * 2.0 - k25 * k36 * t8 * t10 * 4.0 - k26 * k35 * t2 * t16 * 6.0 - k26 * k35 * t8 * t10 * 4.0 - k25 * k36 * t9 * t10 * 4.0 - k26 * k35 * t9 * t10 * 4.0 - k25 * k36 * t8 * t12 * 4.0 - k26 * k35 * t8 * t12 * 4.0 - k25 * k36 * t9 * t12 * 4.0 - k26 * k35 * t9 * t12 * 4.0 - k32 * k33 * t8 * t15 * 4.0 + k32 * k33 * t9 * t14 * 2.0 - k35 * k36 * t2 * t15 * 8.0 + k32 * k33 * t9 * t15 * 2.0 + k32 * k33 * t10 * t14 * 6.0 + k35 * k36 * t8 * t10 * 2.0 + k32 * k33 * t9 * t16 * 2.0 + k32 * k33 * t10 * t15 * 2.0 - k35 * k36 * t9 * t10 * 4.0 + k32 * k33 * t10 * t16 * 2.0 + k32 * k33 * t12 * t14 * 4.0 + k35 * k36 * t5 * t15 * 2.0 + k32 * k33 * t12 * t15 * 4.0 + k35 * k36 * t9 * t12 * 2.0 + k35 * k36 * t10 * t12 * 2.0 + k25 * t2 * t9 * t16 * 2.0 + k25 * t2 * t12 * t14 + k25 * t2 * t12 * t15 * 3.0 + k25 * t8 * t9 * t12 + k25 * t2 * t12 * t16 + k25 * t8 * t10 * t12 * 2.0 + k35 * t2 * t8 * t15 * 2.0 + k35 * t2 * t10 * t14 + k35 * t2 * t10 * t15 + k35 * t8 * t9 * t10 + k35 * t2 * t10 * t16 * 3.0 + k35 * t9 * t10 * t12 * 2.0 + k13 * k16 * k23 * k25 * k26 * 4.0 - k13 * k16 * k22 * k26 * k36 * 4.0 - k13 * k16 * k23 * k25 * k36 * 4.0 - k13 * k16 * k23 * k26 * k35 * 4.0 - k15 * k16 * k25 * k26 * k33 * 1.2E1 - k13 * k16 * k23 * k35 * k36 * 1.2E1 - k13 * k23 * k25 * k26 * k36 * 4.0 + k16 * k22 * k23 * k26 * k36 * 1.6E1 - k15 * k16 * k25 * k33 * k36 * 4.0 - k15 * k16 * k26 * k32 * k36 * 4.0 - k15 * k16 * k26 * k33 * k35 * 4.0 + k13 * k23 * k26 * k35 * k36 * 4.0 + k15 * k16 * k33 * k35 * k36 * 4.0 + k15 * k25 * k26 * k33 * k36 * 4.0 + k16 * k26 * k32 * k33 * k36 * 1.6E1 - k15 * k26 * k33 * k35 * k36 * 4.0 - k12 * k13 * k15 * k25 * t16 * 8.0 + k12 * k15 * k16 * k22 * t16 * 4.0 - k13 * k16 * k22 * k26 * t8 * 2.0 - k13 * k16 * k23 * k25 * t8 * 2.0 - k13 * k16 * k22 * k26 * t10 * 6.0 - k13 * k16 * k23 * k25 * t10 * 2.0 + k12 * k13 * k16 * k32 * t15 * 4.0 + k13 * k16 * k22 * k26 * t12 * 2.0 + k13 * k16 * k23 * k25 * t12 * 2.0 - k12 * k13 * k15 * k35 * t15 * 8.0 + k12 * k15 * k22 * k26 * t16 * 4.0 + k12 * k15 * k23 * k25 * t16 * 4.0 - k13 * k23 * k25 * k26 * t8 * 4.0 + k16 * k22 * k23 * k26 * t8 * 8.0 - k13 * k16 * k22 * k36 * t9 * 2.0 - k13 * k16 * k23 * k35 * t9 * 2.0 - k12 * k13 * k25 * k33 * t14 * 2.0 - k12 * k13 * k26 * k32 * t14 * 2.0 + k12 * k16 * k22 * k33 * t14 + k12 * k16 * k23 * k32 * t14 + k13 * k15 * k22 * k33 * t14 * 3.0 + k13 * k15 * k23 * k32 * t14 * 3.0 + k13 * k16 * k22 * k36 * t10 * 1.2E1 + k13 * k16 * k23 * k35 * t10 * 4.0 - k15 * k16 * k25 * k33 * t8 * 2.0 - k15 * k16 * k26 * k32 * t8 * 2.0 - k12 * k13 * k25 * k33 * t15 * 6.0 - k12 * k13 * k26 * k32 * t15 * 2.0 - k12 * k16 * k22 * k33 * t15 - k12 * k16 * k23 * k32 * t15 - k13 * k15 * k22 * k33 * t15 - k13 * k15 * k23 * k32 * t15 + k12 * k13 * k25 * k33 * t16 * 6.0 + k12 * k13 * k26 * k32 * t16 * 6.0 - k12 * k15 * k22 * k36 * t14 * 2.0 - k12 * k15 * k23 * k35 * t14 * 2.0 - k12 * k16 * k22 * k33 * t16 - k12 * k16 * k23 * k32 * t16 - k13 * k15 * k22 * k33 * t16 - k13 * k15 * k23 * k32 * t16 + k13 * k16 * k22 * k36 * t12 * 4.0 + k13 * k16 * k23 * k35 * t12 * 4.0 + k13 * k23 * k25 * k26 * t12 * 2.0 + k15 * k16 * k25 * k33 * t10 * 4.0 + k15 * k16 * k26 * k32 * t10 * 4.0 - k16 * k22 * k23 * k26 * t12 * 8.0 + k12 * k15 * k22 * k36 * t15 * 6.0 + k12 * k15 * k23 * k35 * t15 * 6.0 - k12 * k15 * k22 * k36 * t16 * 2.0 - k12 * k15 * k23 * k35 * t16 * 6.0 + k15 * k16 * k25 * k33 * t12 * 4.0 + k15 * k16 * k26 * k32 * t12 * 1.2E1 + k13 * k22 * k26 * k36 * t8 * 2.0 + k13 * k23 * k25 * k36 * t8 * 2.0 + k13 * k23 * k26 * k35 * t8 * 2.0 - k16 * k22 * k23 * k36 * t8 * 4.0 + k16 * k25 * k26 * k36 * t2 * 8.0 + k13 * k22 * k26 * k36 * t9 * 6.0 + k13 * k23 * k25 * k36 * t9 * 6.0 + k13 * k23 * k26 * k35 * t9 * 6.0 + k16 * k22 * k23 * k36 * t9 * 4.0 - k12 * k22 * k26 * k33 * t14 - k12 * k23 * k25 * k33 * t14 - k12 * k23 * k26 * k32 * t14 + k13 * k22 * k26 * k36 * t10 * 6.0 + k13 * k23 * k25 * k36 * t10 * 2.0 + k13 * k23 * k26 * k35 * t10 * 2.0 - k15 * k22 * k23 * k33 * t14 * 6.0 + k15 * k25 * k26 * k33 * t8 * 4.0 - k16 * k22 * k23 * k36 * t10 * 8.0 + k12 * k13 * k32 * k36 * t15 * 4.0 + k12 * k13 * k33 * k35 * t15 * 4.0 + k12 * k22 * k26 * k33 * t15 + k12 * k23 * k25 * k33 * t15 * 3.0 + k12 * k23 * k26 * k32 * t15 - k15 * k16 * k32 * k36 * t9 * 2.0 - k15 * k16 * k33 * k35 * t9 * 2.0 - k15 * k22 * k23 * k33 * t15 * 2.0 - k12 * k22 * k26 * k33 * t16 * 5.0 - k12 * k23 * k25 * k33 * t16 * 5.0 - k12 * k23 * k26 * k32 * t16 * 5.0 + k13 * k22 * k26 * k36 * t12 * 4.0 + k13 * k23 * k25 * k36 * t12 * 4.0 + k13 * k23 * k26 * k35 * t12 * 4.0 + k15 * k16 * k32 * k36 * t10 * 2.0 + k15 * k16 * k33 * k35 * t10 * 2.0 + k15 * k22 * k23 * k33 * t16 * 2.0 - k15 * k25 * k26 * k33 * t10 * 2.0 - k16 * k22 * k23 * k36 * t12 * 8.0 - k15 * k16 * k32 * k36 * t12 * 6.0 - k15 * k16 * k33 * k35 * t12 * 2.0 - k15 * k25 * k26 * k33 * t12 * 4.0 - k13 * k23 * k32 * k33 * t14 * 6.0 + k16 * k26 * k32 * k33 * t8 * 4.0 + k16 * k26 * k35 * k36 * t2 * 8.0 - k22 * k23 * k26 * k36 * t8 * 8.0 + k13 * k23 * k32 * k33 * t15 * 2.0 + k13 * k23 * k35 * k36 * t9 * 4.0 - k16 * k26 * k32 * k33 * t9 * 4.0 - k22 * k23 * k26 * k36 * t9 * 8.0 - k12 * k22 * k33 * k36 * t14 - k12 * k23 * k32 * k36 * t14 - k12 * k23 * k33 * k35 * t14 - k13 * k23 * k32 * k33 * t16 * 2.0 - k13 * k23 * k35 * k36 * t10 * 4.0 + k15 * k25 * k33 * k36 * t8 * 6.0 + k15 * k26 * k32 * k36 * t8 * 6.0 + k15 * k26 * k33 * k35 * t8 * 6.0 - k16 * k26 * k32 * k33 * t10 * 8.0 - k12 * k22 * k33 * k36 * t15 * 5.0 - k12 * k23 * k32 * k36 * t15 * 5.0 - k12 * k23 * k33 * k35 * t15 * 5.0 + k15 * k25 * k33 * k36 * t9 * 2.0 + k15 * k26 * k32 * k36 * t9 * 2.0 + k15 * k26 * k33 * k35 * t9 * 2.0 + k12 * k22 * k33 * k36 * t16 + k12 * k23 * k32 * k36 * t16 + k12 * k23 * k33 * k35 * t16 * 3.0 - k13 * k23 * k35 * k36 * t12 * 2.0 + k15 * k25 * k33 * k36 * t10 * 4.0 + k15 * k26 * k32 * k36 * t10 * 4.0 + k15 * k26 * k33 * k35 * t10 * 4.0 - k16 * k26 * k32 * k33 * t12 * 8.0 + k15 * k25 * k33 * k36 * t12 * 2.0 + k15 * k26 * k32 * k36 * t12 * 6.0 + k15 * k26 * k33 * k35 * t12 * 2.0 + k16 * k32 * k33 * k36 * t9 * 8.0 - k16 * k32 * k33 * k36 * t10 * 8.0 - k15 * k33 * k35 * k36 * t9 * 4.0 + k15 * k33 * k35 * k36 * t10 * 2.0 - k26 * k32 * k33 * k36 * t8 * 8.0 - k26 * k32 * k33 * k36 * t9 * 8.0 - k13 * k16 * k22 * t9 * t12 - k13 * k16 * k22 * t10 * t12 * 6.0 - k12 * k15 * k22 * t9 * t16 * 2.0 - k12 * k15 * k22 * t12 * t14 - k12 * k15 * k22 * t12 * t15 - k12 * k15 * k22 * t12 * t16 + k13 * k22 * k26 * t2 * t16 * 2.0 + k13 * k23 * k25 * t2 * t16 * 2.0 - k16 * k22 * k23 * t2 * t16 * 4.0 - k12 * k13 * k32 * t8 * t15 * 2.0 - k12 * k13 * k32 * t10 * t14 - k13 * k22 * k26 * t8 * t12 - k13 * k23 * k25 * t8 * t12 - k15 * k16 * k32 * t8 * t10 + k16 * k22 * k23 * t8 * t12 * 2.0 - k16 * k25 * k26 * t2 * t12 * 4.0 - k12 * k13 * k32 * t10 * t15 - k13 * k22 * k26 * t9 * t12 - k13 * k23 * k25 * t9 * t12 + k16 * k22 * k23 * t9 * t12 * 2.0 - k12 * k13 * k32 * t10 * t16 - k13 * k22 * k26 * t10 * t12 * 3.0 - k13 * k23 * k25 * t10 * t12 + k16 * k22 * k23 * t10 * t12 * 4.0 - k15 * k16 * k32 * t10 * t12 * 6.0 - k13 * k22 * k36 * t2 * t15 * 2.0 - k13 * k23 * k35 * t2 * t15 * 2.0 + k12 * k22 * k33 * t8 * t15 * 3.0 + k12 * k23 * k32 * t8 * t15 * 3.0 - k13 * k22 * k36 * t9 * t10 * 6.0 - k13 * k23 * k35 * t9 * t10 * 2.0 + k12 * k22 * k33 * t10 * t14 * 3.0 + k12 * k23 * k32 * t10 * t14 - k15 * k25 * k33 * t2 * t16 * 2.0 - k15 * k25 * k33 * t8 * t10 * 2.0 - k15 * k26 * k32 * t2 * t16 * 2.0 - k15 * k26 * k32 * t8 * t10 * 2.0 + k22 * k23 * k26 * t8 * t12 * 4.0 + k12 * k22 * k33 * t9 * t16 * 3.0 + k12 * k23 * k32 * t9 * t16 * 3.0 - k13 * k22 * k36 * t9 * t12 * 2.0 - k13 * k23 * k35 * t9 * t12 * 2.0 + k12 * k22 * k33 * t10 * t16 * 3.0 + k12 * k22 * k33 * t12 * t14 + k12 * k23 * k32 * t10 * t16 + k12 * k23 * k32 * t12 * t14 * 3.0 - k15 * k25 * k33 * t8 * t12 * 2.0 - k15 * k26 * k32 * t8 * t12 * 6.0 + k12 * k22 * k33 * t12 * t15 + k12 * k23 * k32 * t12 * t15 * 3.0 + k22 * k23 * k36 * t2 * t14 * 2.0 + k25 * k26 * k36 * t2 * t8 * 4.0 - k16 * k32 * k33 * t2 * t15 * 4.0 + k22 * k23 * k36 * t2 * t15 * 2.0 + k22 * k23 * k36 * t8 * t9 * 2.0 + k16 * k32 * k33 * t8 * t10 * 2.0 - k16 * k35 * k36 * t2 * t10 * 4.0 + k22 * k23 * k36 * t2 * t16 * 2.0 + k25 * k26 * k36 * t2 * t10 * 2.0 + k15 * k32 * k36 * t2 * t15 * 2.0 + k15 * k33 * k35 * t2 * t15 * 2.0 + k16 * k32 * k33 * t9 * t10 * 2.0 + k22 * k23 * k36 * t9 * t10 * 4.0 - k15 * k32 * k36 * t8 * t10 - k15 * k33 * k35 * t8 * t10 - k15 * k32 * k36 * t9 * t10 - k15 * k33 * k35 * t9 * t10 + k22 * k23 * k36 * t9 * t12 * 4.0 + k16 * k32 * k33 * t10 * t12 * 4.0 - k15 * k32 * k36 * t10 * t12 * 3.0 - k15 * k33 * k35 * t10 * t12 + k26 * k32 * k33 * t2 * t14 * 2.0 + k26 * k32 * k33 * t2 * t15 * 2.0 + k26 * k32 * k33 * t8 * t9 * 2.0 + k26 * k35 * k36 * t2 * t9 * 4.0 + k26 * k32 * k33 * t2 * t16 * 2.0 + k26 * k32 * k33 * t8 * t10 * 4.0 + k26 * k32 * k33 * t8 * t12 * 4.0 + k26 * k35 * k36 * t2 * t12 * 2.0 + k32 * k33 * k36 * t9 * t10 * 4.0 - k13 * k22 * t2 * t12 * t15 + k16 * k25 * t2 * t10 * t12 + k22 * k23 * t2 * t9 * t16 * 2.0 + k25 * k26 * t2 * t8 * t12 * 2.0 - k15 * k32 * t2 * t10 * t16 + k16 * k35 * t2 * t10 * t12 + k25 * k36 * t2 * t10 * t12 + k26 * k35 * t2 * t10 * t12 + k32 * k33 * t2 * t8 * t15 * 2.0; coeffs(7) += k35 * k36 * t2 * t9 * t10 * 2.0 + k12 * k13 * k15 * k16 * k25 * k36 * 8.0 + k12 * k13 * k15 * k16 * k26 * k35 * 8.0 + k12 * k13 * k16 * k25 * k26 * k33 * 8.0 - k13 * k15 * k16 * k22 * k26 * k33 * 2.0 - k13 * k15 * k16 * k23 * k25 * k33 * 2.0 - k13 * k15 * k16 * k23 * k26 * k32 * 2.0 - k12 * k13 * k15 * k25 * k26 * k36 * 1.6E1 - k12 * k15 * k16 * k22 * k26 * k36 * 4.0 - k12 * k15 * k16 * k23 * k25 * k36 * 4.0 - k12 * k15 * k16 * k23 * k26 * k35 * 4.0 - k12 * k13 * k16 * k25 * k33 * k36 * 4.0 - k12 * k13 * k16 * k26 * k32 * k36 * 4.0 - k12 * k13 * k16 * k26 * k33 * k35 * 4.0 - k12 * k16 * k23 * k25 * k26 * k33 * 2.0 - k13 * k15 * k16 * k22 * k33 * k36 * 2.0 - k13 * k15 * k16 * k23 * k32 * k36 * 2.0 - k13 * k15 * k16 * k23 * k33 * k35 * 2.0 - k13 * k15 * k23 * k25 * k26 * k33 * 2.0 + k15 * k16 * k22 * k23 * k26 * k33 * 8.0 - k12 * k13 * k15 * k26 * k35 * k36 * 1.6E1 + k12 * k15 * k16 * k23 * k35 * k36 * 8.0 + k12 * k15 * k23 * k25 * k26 * k36 * 1.2E1 + k13 * k16 * k23 * k26 * k32 * k33 * 4.0 + k12 * k13 * k25 * k26 * k33 * k36 * 8.0 + k12 * k16 * k22 * k26 * k33 * k36 * 6.0 + k12 * k16 * k23 * k25 * k33 * k36 * 6.0 + k12 * k16 * k23 * k26 * k32 * k36 * 6.0 + k12 * k16 * k23 * k26 * k33 * k35 * 6.0 - k13 * k15 * k22 * k26 * k33 * k36 * 1.0E1 - k13 * k15 * k23 * k25 * k33 * k36 * 1.0E1 - k13 * k15 * k23 * k26 * k32 * k36 * 1.0E1 - k13 * k15 * k23 * k26 * k33 * k35 * 1.0E1 + k15 * k16 * k22 * k23 * k33 * k36 * 4.0 + k12 * k15 * k23 * k26 * k35 * k36 * 8.0 + k13 * k16 * k23 * k32 * k33 * k36 * 8.0 + k12 * k13 * k26 * k33 * k35 * k36 * 1.2E1 - k12 * k16 * k23 * k33 * k35 * k36 * 2.0 - k12 * k23 * k25 * k26 * k33 * k36 * 1.0E1 - k13 * k15 * k23 * k33 * k35 * k36 * 2.0 + k15 * k22 * k23 * k26 * k33 * k36 * 8.0 + k13 * k23 * k26 * k32 * k33 * k36 * 8.0 - k12 * k23 * k26 * k33 * k35 * k36 * 1.0E1 + k12 * k15 * k16 * k22 * k26 * t12 * 2.0 + k12 * k15 * k16 * k23 * k25 * t12 * 2.0 - k12 * k13 * k16 * k25 * k33 * t10 * 4.0 - k12 * k13 * k16 * k26 * k32 * t10 * 4.0 + k13 * k15 * k16 * k22 * k33 * t10 * 6.0 + k13 * k15 * k16 * k23 * k32 * t10 * 2.0 + k12 * k13 * k15 * k25 * k36 * t10 * 4.0 + k12 * k13 * k15 * k26 * k35 * t10 * 4.0 + k13 * k15 * k16 * k22 * k33 * t12 * 2.0 + k13 * k15 * k16 * k23 * k32 * t12 * 6.0 + k12 * k13 * k15 * k25 * k36 * t12 * 4.0 + k12 * k13 * k15 * k26 * k35 * t12 * 4.0 - k12 * k15 * k16 * k22 * k36 * t12 * 4.0 - k12 * k15 * k16 * k23 * k35 * t12 * 4.0 - k12 * k15 * k23 * k25 * k26 * t12 * 2.0 - k13 * k16 * k22 * k26 * k36 * t2 * 2.0 - k13 * k16 * k23 * k25 * k36 * t2 * 2.0 - k13 * k16 * k23 * k26 * k35 * t2 * 2.0 - k12 * k13 * k22 * k23 * k33 * t14 * 2.0 - k12 * k13 * k25 * k26 * k33 * t8 * 4.0 + k12 * k16 * k22 * k26 * k33 * t8 * 3.0 + k12 * k16 * k23 * k25 * k33 * t8 * 3.0 + k12 * k16 * k23 * k26 * k32 * t8 * 3.0 + k13 * k15 * k22 * k26 * k33 * t8 + k13 * k15 * k23 * k25 * k33 * t8 + k13 * k15 * k23 * k26 * k32 * t8 - k15 * k16 * k22 * k23 * k33 * t8 * 2.0 - k12 * k13 * k22 * k23 * k33 * t15 * 2.0 + k12 * k13 * k16 * k32 * k36 * t10 * 2.0 + k12 * k13 * k16 * k33 * k35 * t10 * 2.0 - k12 * k13 * k22 * k23 * k33 * t16 * 2.0 - k12 * k13 * k25 * k26 * k33 * t10 * 2.0 - k12 * k15 * k22 * k26 * k36 * t8 * 2.0 - k12 * k15 * k23 * k25 * k36 * t8 * 2.0 - k12 * k15 * k23 * k26 * k35 * t8 * 2.0 + k12 * k16 * k22 * k26 * k33 * t10 * 3.0 + k12 * k16 * k23 * k25 * k33 * t10 + k12 * k16 * k23 * k26 * k32 * t10 + k13 * k15 * k22 * k26 * k33 * t10 * 3.0 + k13 * k15 * k23 * k25 * k33 * t10 + k13 * k15 * k23 * k26 * k32 * t10 - k15 * k16 * k22 * k23 * k33 * t10 * 4.0 - k12 * k15 * k22 * k26 * k36 * t10 * 6.0 - k12 * k15 * k23 * k25 * k36 * t10 * 2.0 - k12 * k15 * k23 * k26 * k35 * t10 * 2.0 - k12 * k16 * k22 * k26 * k33 * t12 * 2.0 - k12 * k16 * k23 * k25 * k33 * t12 * 2.0 - k12 * k16 * k23 * k26 * k32 * t12 * 6.0 + k13 * k15 * k22 * k26 * k33 * t12 * 2.0 + k13 * k15 * k23 * k25 * k33 * t12 * 2.0 + k13 * k15 * k23 * k26 * k32 * t12 * 6.0 - k15 * k16 * k22 * k23 * k33 * t12 * 4.0 - k13 * k23 * k25 * k26 * k36 * t2 * 4.0 - k13 * k16 * k23 * k32 * k33 * t9 * 2.0 + k12 * k23 * k25 * k26 * k33 * t8 * 6.0 - k13 * k16 * k23 * k32 * k33 * t10 * 4.0 - k15 * k16 * k25 * k33 * k36 * t2 * 2.0 - k15 * k16 * k26 * k32 * k36 * t2 * 2.0 - k15 * k16 * k26 * k33 * k35 * t2 * 2.0 - k15 * k22 * k23 * k26 * k33 * t8 * 4.0 - k12 * k13 * k25 * k33 * k36 * t9 * 2.0 - k12 * k13 * k26 * k32 * k36 * t9 * 2.0 - k12 * k13 * k26 * k33 * k35 * t9 * 2.0 + k12 * k16 * k22 * k33 * k36 * t9 * 3.0 + k12 * k16 * k23 * k32 * k36 * t9 * 3.0; coeffs(7) += k12 * k16 * k23 * k33 * k35 * t9 * 3.0 + k13 * k15 * k22 * k33 * k36 * t9 + k13 * k15 * k23 * k32 * k36 * t9 + k13 * k15 * k23 * k33 * k35 * t9 - k12 * k15 * k23 * k32 * k33 * t14 * 2.0 - k12 * k16 * k22 * k33 * k36 * t10 * 6.0 - k12 * k16 * k23 * k32 * k36 * t10 * 2.0 - k12 * k16 * k23 * k33 * k35 * t10 * 2.0 + k13 * k15 * k22 * k33 * k36 * t10 * 6.0 + k13 * k15 * k23 * k32 * k36 * t10 * 2.0 + k13 * k15 * k23 * k33 * k35 * t10 * 2.0 - k13 * k16 * k23 * k32 * k33 * t12 * 4.0 - k12 * k15 * k23 * k32 * k33 * t15 * 2.0 - k12 * k15 * k23 * k35 * k36 * t9 * 4.0 - k12 * k13 * k25 * k33 * k36 * t12 * 2.0 - k12 * k13 * k26 * k32 * k36 * t12 * 6.0 - k12 * k13 * k26 * k33 * k35 * t12 * 2.0 - k12 * k15 * k23 * k32 * k33 * t16 * 2.0 + k12 * k16 * k22 * k33 * k36 * t12 + k12 * k16 * k23 * k32 * k36 * t12 * 3.0 + k12 * k16 * k23 * k33 * k35 * t12 + k12 * k23 * k25 * k26 * k33 * t12 * 2.0 + k13 * k15 * k22 * k33 * k36 * t12 + k13 * k15 * k23 * k32 * k36 * t12 * 3.0 + k13 * k15 * k23 * k33 * k35 * t12 - k12 * k15 * k23 * k35 * k36 * t12 * 2.0 - k13 * k23 * k26 * k32 * k33 * t8 * 2.0 + k13 * k23 * k26 * k35 * k36 * t2 * 4.0 - k13 * k23 * k26 * k32 * k33 * t9 * 2.0 - k12 * k22 * k26 * k33 * k36 * t8 - k12 * k23 * k25 * k33 * k36 * t8 - k12 * k23 * k26 * k32 * k36 * t8 - k12 * k23 * k26 * k33 * k35 * t8 - k13 * k23 * k26 * k32 * k33 * t10 * 2.0 - k15 * k22 * k23 * k33 * k36 * t8 * 2.0 + k15 * k25 * k26 * k33 * k36 * t2 * 4.0 - k12 * k22 * k26 * k33 * k36 * t9 - k12 * k23 * k25 * k33 * k36 * t9 - k12 * k23 * k26 * k32 * k36 * t9 - k12 * k23 * k26 * k33 * k35 * t9 - k15 * k22 * k23 * k33 * k36 * t9 * 2.0 - k12 * k13 * k33 * k35 * k36 * t10 * 2.0 + k12 * k22 * k26 * k33 * k36 * t10 * 3.0 + k12 * k23 * k25 * k33 * k36 * t10 + k12 * k23 * k26 * k32 * k36 * t10 + k12 * k23 * k26 * k33 * k35 * t10 - k13 * k23 * k26 * k32 * k33 * t12 * 4.0 - k15 * k22 * k23 * k33 * k36 * t10 * 4.0 + k12 * k22 * k26 * k33 * k36 * t12 + k12 * k23 * k25 * k33 * k36 * t12 + k12 * k23 * k26 * k32 * k36 * t12 * 3.0 + k12 * k23 * k26 * k33 * k35 * t12 - k15 * k22 * k23 * k33 * k36 * t12 * 2.0 - k13 * k23 * k32 * k33 * k36 * t9 * 4.0 - k15 * k26 * k33 * k35 * k36 * t2 * 4.0 + k12 * k23 * k33 * k35 * k36 * t9 * 6.0 + k12 * k23 * k33 * k35 * k36 * t10 * 2.0 + k12 * k13 * k15 * k25 * t10 * t12 - k12 * k15 * k16 * k22 * t10 * t12 * 3.0 - k13 * k16 * k22 * k26 * t2 * t12 - k13 * k16 * k23 * k25 * t2 * t12 - k12 * k15 * k22 * k26 * t2 * t16 * 2.0 - k12 * k15 * k23 * k25 * t2 * t16 * 2.0 - k12 * k13 * k16 * k32 * t10 * t12 * 3.0 - k12 * k15 * k22 * k26 * t8 * t12 - k12 * k15 * k23 * k25 * t8 * t12 + k12 * k13 * k15 * k35 * t10 * t12 - k13 * k23 * k25 * k26 * t2 * t12 * 2.0 + k16 * k22 * k23 * k26 * t2 * t12 * 2.0 - k12 * k13 * k25 * k33 * t10 * t12 - k12 * k13 * k26 * k32 * t10 * t12 * 3.0 + k12 * k16 * k22 * k33 * t10 * t12 * 3.0 + k12 * k16 * k23 * k32 * t10 * t12 * 3.0 - k12 * k15 * k22 * k36 * t10 * t12 * 3.0 - k12 * k15 * k23 * k35 * t10 * t12 - k12 * k13 * k32 * k36 * t2 * t15 * 2.0 - k12 * k13 * k33 * k35 * t2 * t15 * 2.0 + k12 * k22 * k26 * k33 * t2 * t16 + k12 * k23 * k25 * k33 * t2 * t16 + k12 * k23 * k26 * k32 * t2 * t16 - k13 * k22 * k26 * k36 * t2 * t12 * 2.0 - k13 * k23 * k25 * k36 * t2 * t12 * 2.0 - k13 * k23 * k26 * k35 * t2 * t12 * 2.0 - k15 * k16 * k32 * k36 * t2 * t10 - k15 * k16 * k33 * k35 * t2 * t10 - k15 * k22 * k23 * k33 * t2 * t16 * 2.0 + k16 * k22 * k23 * k36 * t2 * t12 * 2.0 - k12 * k13 * k32 * k36 * t9 * t10 - k12 * k13 * k33 * k35 * t9 * t10 + k12 * k22 * k26 * k33 * t8 * t12 + k12 * k23 * k25 * k33 * t8 * t12 + k12 * k23 * k26 * k32 * t8 * t12 * 3.0 - k13 * k23 * k32 * k33 * t2 * t15 * 2.0 + k16 * k26 * k32 * k33 * t2 * t10 * 2.0 + k12 * k22 * k33 * k36 * t2 * t15 + k12 * k23 * k32 * k36 * t2 * t15 + k12 * k23 * k33 * k35 * t2 * t15 - k15 * k25 * k33 * k36 * t2 * t10 * 2.0 - k15 * k26 * k32 * k36 * t2 * t10 * 2.0 - k15 * k26 * k33 * k35 * t2 * t10 * 2.0 + k22 * k23 * k26 * k36 * t2 * t12 * 2.0 + k12 * k22 * k33 * k36 * t9 * t10 * 3.0 + k12 * k23 * k32 * k36 * t9 * t10 + k12 * k23 * k33 * k35 * t9 * t10 + k16 * k32 * k33 * k36 * t2 * t10 * 2.0 - k15 * k33 * k35 * k36 * t2 * t10 * 2.0 + k26 * k32 * k33 * k36 * t2 * t10 * 2.0 - k12 * k13 * k16 * k22 * k23 * k26 * k33 * 8.0 + k12 * k13 * k15 * k22 * k23 * k26 * k36 * 8.0 + k12 * k13 * k16 * k22 * k23 * k33 * k36 * 4.0 + k12 * k15 * k16 * k23 * k26 * k32 * k33 * 4.0 + k12 * k13 * k15 * k26 * k32 * k33 * k36 * 8.0 - k12 * k15 * k16 * k23 * k32 * k33 * k36 * 8.0 + k12 * k13 * k15 * k16 * k22 * k23 * t12 * 2.0 + k12 * k13 * k15 * k22 * k23 * k26 * t12 * 2.0 + k12 * k13 * k15 * k16 * k32 * k33 * t10 * 2.0 - k12 * k13 * k16 * k22 * k23 * k33 * t12 * 2.0 + k12 * k13 * k15 * k22 * k23 * k36 * t12 * 2.0 + k12 * k13 * k15 * k26 * k32 * k33 * t10 * 2.0 - k12 * k13 * k22 * k23 * k26 * k33 * t12 * 2.0 - k12 * k15 * k16 * k23 * k32 * k33 * t10 * 2.0 - k13 * k16 * k23 * k26 * k32 * k33 * t2 * 2.0 - k12 * k13 * k25 * k26 * k33 * k36 * t2 * 4.0 + k12 * k16 * k22 * k26 * k33 * k36 * t2 + k12 * k16 * k23 * k25 * k33 * k36 * t2 + k12 * k16 * k23 * k26 * k32 * k36 * t2 + k12 * k16 * k23 * k26 * k33 * k35 * t2 + k13 * k15 * k22 * k26 * k33 * k36 * t2 * 3.0 + k13 * k15 * k23 * k25 * k33 * k36 * t2 * 3.0 + k13 * k15 * k23 * k26 * k32 * k36 * t2 * 3.0 + k13 * k15 * k23 * k26 * k33 * k35 * t2 * 3.0 - k15 * k16 * k22 * k23 * k33 * k36 * t2 * 2.0 - k12 * k13 * k22 * k23 * k33 * k36 * t9 * 2.0 - k12 * k15 * k23 * k26 * k32 * k33 * t8 * 2.0 - k12 * k15 * k23 * k26 * k35 * k36 * t2 * 4.0 + k12 * k13 * k15 * k32 * k33 * k36 * t10 * 2.0 + k12 * k23 * k25 * k26 * k33 * k36 * t2 * 2.0 - k15 * k22 * k23 * k26 * k33 * k36 * t2 * 4.0 - k12 * k15 * k23 * k32 * k33 * k36 * t10 * 2.0 - k13 * k23 * k26 * k32 * k33 * k36 * t2 * 4.0 + k12 * k23 * k26 * k33 * k35 * k36 * t2 * 2.0; coeffs(8) = t14 * t15 * 6.0 + t14 * t16 * 6.0 + t15 * t16 * 6.0 + t15 * t17 + t14 * t19 + t14 * t20 + t15 * t19 + t16 * t18 + t16 * t20 + t14 * t14 + t15 * t15 + t16 * t16 - k16 * k26 * t14 * 4.0 - k16 * k26 * t15 * 4.0 - k16 * k26 * t16 * 1.2E1 - k16 * k26 * t19 * 2.0 - k16 * k36 * t14 * 4.0 - k16 * k36 * t15 * 1.2E1 - k16 * k36 * t16 * 4.0 - k16 * k36 * t20 * 2.0 + k26 * k36 * t14 * 1.2E1 + k26 * k36 * t15 * 4.0 + k26 * k36 * t16 * 4.0 - k16 * t8 * t15 * 4.0 + k16 * t10 * t14 * 2.0 - k16 * t9 * t16 * 4.0 + k16 * t10 * t15 * 2.0 + k16 * t10 * t16 * 6.0 + k16 * t12 * t14 * 2.0 + k16 * t12 * t15 * 6.0 + k16 * t12 * t16 * 2.0 + k16 * t10 * t19 + k16 * t12 * t20 + k26 * t8 * t14 * 2.0 + k26 * t8 * t15 * 2.0 + k26 * t8 * t16 * 2.0 - k26 * t10 * t14 * 4.0 + k26 * t9 * t16 * 4.0 - k26 * t10 * t16 * 4.0 - k26 * t12 * t14 * 6.0 + k26 * t8 * t19 - k26 * t12 * t15 * 2.0 - k26 * t12 * t16 * 2.0 + k36 * t8 * t15 * 4.0 + k36 * t9 * t14 * 2.0 + k36 * t9 * t15 * 2.0 - k36 * t10 * t14 * 6.0 + k36 * t9 * t16 * 2.0 - k36 * t10 * t15 * 2.0 - k36 * t10 * t16 * 2.0 - k36 * t12 * t14 * 4.0 - k36 * t12 * t15 * 4.0 + k36 * t9 * t20 + t8 * t10 * t14 - t2 * t15 * t16 * 4.0 + t8 * t10 * t15 + t8 * t10 * t16 - t8 * t12 * t15 * 2.0 - t9 * t10 * t16 * 2.0 + t9 * t12 * t14 + t5 * t15 * t16 + t9 * t12 * t15 + t10 * t12 * t14 * 3.0 + t9 * t12 * t16 + t10 * t12 * t15 + t10 * t12 * t16 - k13 * k16 * k23 * t14 * 2.0 + k13 * k16 * k23 * t15 * 2.0 - k13 * k16 * k23 * t16 * 6.0 - k13 * k16 * k23 * t19 + k13 * k23 * k26 * t14 * 2.0 - k13 * k23 * k26 * t15 * 2.0 + k13 * k23 * k26 * t16 * 2.0 - k15 * k16 * k33 * t14 * 2.0 - k15 * k16 * k33 * t15 * 6.0 + k15 * k16 * k33 * t16 * 2.0 - k13 * k23 * k26 * t19 - k15 * k16 * k33 * t20 + k13 * k23 * k36 * t14 * 6.0 - k16 * k26 * k36 * t8 * 4.0 - k13 * k23 * k36 * t15 * 2.0 - k16 * k26 * k36 * t9 * 4.0 + k13 * k23 * k36 * t16 * 2.0 + k15 * k26 * k33 * t14 * 6.0 + k16 * k26 * k36 * t10 * 8.0 + k15 * k26 * k33 * t15 * 2.0 - k15 * k26 * k33 * t16 * 2.0 + k16 * k26 * k36 * t12 * 8.0 + k15 * k33 * k36 * t14 * 2.0 + k15 * k33 * k36 * t15 * 2.0 - k15 * k33 * k36 * t16 * 2.0 - k15 * k33 * k36 * t20 - k13 * k23 * t8 * t15 * 2.0 - k13 * k23 * t10 * t14 * 2.0 + k16 * k26 * t2 * t16 * 4.0 + k16 * k26 * t8 * t10 * 4.0 + k13 * k23 * t9 * t16 * 2.0 - k13 * k23 * t10 * t16 * 2.0 - k13 * k23 * t12 * t14 * 3.0 + k16 * k26 * t8 * t12 * 2.0 + k13 * k23 * t12 * t15 - k16 * k26 * t9 * t12 * 2.0 - k13 * k23 * t12 * t16 - k16 * k26 * t10 * t12 * 4.0 + k16 * k36 * t2 * t15 * 4.0 - k16 * k36 * t8 * t10 * 2.0 + k15 * k33 * t8 * t15 * 2.0 + k16 * k36 * t9 * t10 * 2.0 - k15 * k33 * t10 * t14 * 3.0 - k15 * k33 * t9 * t16 * 2.0 - k15 * k33 * t10 * t15 + k16 * k36 * t9 * t12 * 4.0 + k15 * k33 * t10 * t16 - k15 * k33 * t12 * t14 * 2.0 - k16 * k36 * t10 * t12 * 4.0 - k15 * k33 * t12 * t15 * 2.0 - k26 * k36 * t2 * t14 * 2.0 - k26 * k36 * t2 * t15 * 2.0 - k26 * k36 * t8 * t9 * 2.0 - k26 * k36 * t2 * t16 * 2.0 - k26 * k36 * t8 * t10 * 4.0 - k26 * k36 * t9 * t10 * 4.0 - k26 * k36 * t8 * t12 * 4.0 - k26 * k36 * t9 * t12 * 4.0 - k16 * t2 * t10 * t16 * 2.0 - k16 * t2 * t12 * t15 * 2.0 + k16 * t8 * t10 * t12 + k16 * t9 * t10 * t12 + k26 * t2 * t9 * t16 * 2.0 + k26 * t2 * t12 * t14 + k26 * t2 * t12 * t15 + k26 * t8 * t9 * t12 + k26 * t2 * t12 * t16 + k26 * t8 * t10 * t12 * 2.0 + k36 * t2 * t8 * t15 * 2.0 + k36 * t2 * t10 * t14 + k36 * t2 * t10 * t15 + k36 * t8 * t9 * t10 + k36 * t2 * t10 * t16 + k36 * t9 * t10 * t12 * 2.0 + t2 * t8 * t12 * t15 + t2 * t9 * t10 * t16 - k13 * k16 * k23 * k26 * k36 * 4.0 - k15 * k16 * k26 * k33 * k36 * 4.0 - k12 * k13 * k15 * k26 * t16 * 8.0 + k12 * k15 * k16 * k23 * t16 * 4.0 - k13 * k16 * k23 * k26 * t8 * 2.0 - k13 * k16 * k23 * k26 * t10 * 2.0 + k12 * k13 * k16 * k33 * t15 * 4.0 + k13 * k16 * k23 * k26 * t12 * 2.0 - k12 * k13 * k15 * k36 * t15 * 8.0 + k12 * k15 * k23 * k26 * t16 * 4.0 - k13 * k16 * k23 * k36 * t9 * 2.0 - k12 * k13 * k26 * k33 * t14 * 2.0 + k12 * k16 * k23 * k33 * t14 + k13 * k15 * k23 * k33 * t14 * 3.0 + k13 * k16 * k23 * k36 * t10 * 4.0 - k15 * k16 * k26 * k33 * t8 * 2.0 - k12 * k13 * k26 * k33 * t15 * 2.0 - k12 * k16 * k23 * k33 * t15 - k13 * k15 * k23 * k33 * t15 + k12 * k13 * k26 * k33 * t16 * 6.0 - k12 * k15 * k23 * k36 * t14 * 2.0 - k12 * k16 * k23 * k33 * t16 - k13 * k15 * k23 * k33 * t16 + k13 * k16 * k23 * k36 * t12 * 4.0 + k15 * k16 * k26 * k33 * t10 * 4.0 + k12 * k15 * k23 * k36 * t15 * 6.0 - k12 * k15 * k23 * k36 * t16 * 2.0 + k15 * k16 * k26 * k33 * t12 * 4.0 + k13 * k23 * k26 * k36 * t8 * 2.0 + k13 * k23 * k26 * k36 * t9 * 6.0 - k12 * k23 * k26 * k33 * t14 + k13 * k23 * k26 * k36 * t10 * 2.0 + k12 * k13 * k33 * k36 * t15 * 4.0 + k12 * k23 * k26 * k33 * t15 - k15 * k16 * k33 * k36 * t9 * 2.0 - k12 * k23 * k26 * k33 * t16 * 5.0 + k13 * k23 * k26 * k36 * t12 * 4.0 + k15 * k16 * k33 * k36 * t10 * 2.0 - k15 * k16 * k33 * k36 * t12 * 2.0 - k12 * k23 * k33 * k36 * t14 + k15 * k26 * k33 * k36 * t8 * 6.0 - k12 * k23 * k33 * k36 * t15 * 5.0 + k15 * k26 * k33 * k36 * t9 * 2.0 + k12 * k23 * k33 * k36 * t16 + k15 * k26 * k33 * k36 * t10 * 4.0 + k15 * k26 * k33 * k36 * t12 * 2.0 - k13 * k16 * k23 * t9 * t12 - k13 * k16 * k23 * t10 * t12 * 2.0 - k12 * k15 * k23 * t9 * t16 * 2.0 - k12 * k15 * k23 * t12 * t14 - k12 * k15 * k23 * t12 * t15 - k12 * k15 * k23 * t12 * t16 + k13 * k23 * k26 * t2 * t16 * 2.0 - k12 * k13 * k33 * t8 * t15 * 2.0 - k12 * k13 * k33 * t10 * t14 - k13 * k23 * k26 * t8 * t12 - k15 * k16 * k33 * t8 * t10 - k12 * k13 * k33 * t10 * t15 - k13 * k23 * k26 * t9 * t12 - k12 * k13 * k33 * t10 * t16 - k13 * k23 * k26 * t10 * t12 - k15 * k16 * k33 * t10 * t12 * 2.0 - k13 * k23 * k36 * t2 * t15 * 2.0 + k12 * k23 * k33 * t8 * t15 * 3.0 - k13 * k23 * k36 * t9 * t10 * 2.0 + k12 * k23 * k33 * t10 * t14 - k15 * k26 * k33 * t2 * t16 * 2.0 - k15 * k26 * k33 * t8 * t10 * 2.0 + k12 * k23 * k33 * t9 * t16 * 3.0 - k13 * k23 * k36 * t9 * t12 * 2.0; coeffs(8) += k12 * k23 * k33 * t10 * t16 + k12 * k23 * k33 * t12 * t14 - k15 * k26 * k33 * t8 * t12 * 2.0 + k12 * k23 * k33 * t12 * t15 + k15 * k33 * k36 * t2 * t15 * 2.0 - k15 * k33 * k36 * t8 * t10 - k15 * k33 * k36 * t9 * t10 - k15 * k33 * k36 * t10 * t12 - k13 * k23 * t2 * t12 * t15 + k16 * k26 * t2 * t10 * t12 - k15 * k33 * t2 * t10 * t16 + k16 * k36 * t2 * t10 * t12 + k26 * k36 * t2 * t10 * t12 + k12 * k13 * k15 * k16 * k26 * k36 * 8.0 - k13 * k15 * k16 * k23 * k26 * k33 * 2.0 - k12 * k15 * k16 * k23 * k26 * k36 * 4.0 - k12 * k13 * k16 * k26 * k33 * k36 * 4.0 - k13 * k15 * k16 * k23 * k33 * k36 * 2.0 + k12 * k16 * k23 * k26 * k33 * k36 * 6.0 - k13 * k15 * k23 * k26 * k33 * k36 * 1.0E1 + k12 * k15 * k16 * k23 * k26 * t12 * 2.0 - k12 * k13 * k16 * k26 * k33 * t10 * 4.0 + k13 * k15 * k16 * k23 * k33 * t10 * 2.0 + k12 * k13 * k15 * k26 * k36 * t10 * 4.0 + k13 * k15 * k16 * k23 * k33 * t12 * 2.0 + k12 * k13 * k15 * k26 * k36 * t12 * 4.0 - k12 * k15 * k16 * k23 * k36 * t12 * 4.0 - k13 * k16 * k23 * k26 * k36 * t2 * 2.0 + k12 * k16 * k23 * k26 * k33 * t8 * 3.0 + k13 * k15 * k23 * k26 * k33 * t8 + k12 * k13 * k16 * k33 * k36 * t10 * 2.0 - k12 * k15 * k23 * k26 * k36 * t8 * 2.0 + k12 * k16 * k23 * k26 * k33 * t10 + k13 * k15 * k23 * k26 * k33 * t10 - k12 * k15 * k23 * k26 * k36 * t10 * 2.0 - k12 * k16 * k23 * k26 * k33 * t12 * 2.0 + k13 * k15 * k23 * k26 * k33 * t12 * 2.0 - k15 * k16 * k26 * k33 * k36 * t2 * 2.0 - k12 * k13 * k26 * k33 * k36 * t9 * 2.0 + k12 * k16 * k23 * k33 * k36 * t9 * 3.0 + k13 * k15 * k23 * k33 * k36 * t9 - k12 * k16 * k23 * k33 * k36 * t10 * 2.0 + k13 * k15 * k23 * k33 * k36 * t10 * 2.0 - k12 * k13 * k26 * k33 * k36 * t12 * 2.0 + k12 * k16 * k23 * k33 * k36 * t12 + k13 * k15 * k23 * k33 * k36 * t12 - k12 * k23 * k26 * k33 * k36 * t8 - k12 * k23 * k26 * k33 * k36 * t9 + k12 * k23 * k26 * k33 * k36 * t10 + k12 * k23 * k26 * k33 * k36 * t12 + k12 * k13 * k15 * k16 * t10 * t12 + k12 * k13 * k15 * k26 * t10 * t12 - k12 * k15 * k16 * k23 * t10 * t12 - k13 * k16 * k23 * k26 * t2 * t12 - k12 * k15 * k23 * k26 * t2 * t16 * 2.0 - k12 * k13 * k16 * k33 * t10 * t12 - k12 * k15 * k23 * k26 * t8 * t12 + k12 * k13 * k15 * k36 * t10 * t12 - k12 * k13 * k26 * k33 * t10 * t12 + k12 * k16 * k23 * k33 * t10 * t12 - k12 * k15 * k23 * k36 * t10 * t12 - k12 * k13 * k33 * k36 * t2 * t15 * 2.0 + k12 * k23 * k26 * k33 * t2 * t16 - k13 * k23 * k26 * k36 * t2 * t12 * 2.0 - k15 * k16 * k33 * k36 * t2 * t10 - k12 * k13 * k33 * k36 * t9 * t10 + k12 * k23 * k26 * k33 * t8 * t12 + k12 * k23 * k33 * k36 * t2 * t15 - k15 * k26 * k33 * k36 * t2 * t10 * 2.0 + k12 * k23 * k33 * k36 * t9 * t10 + k12 * k16 * k23 * k26 * k33 * k36 * t2 + k13 * k15 * k23 * k26 * k33 * k36 * t2 * 3.0; return coeffs; } } // namespace colmap colmap-3.4/src/estimators/generalized_absolute_pose_coeffs.h000066400000000000000000000021741323400541200245250ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_GENERALIZED_ABSOLUTE_POSE_COEFFS_H_ #define COLMAP_SRC_ESTIMATORS_GENERALIZED_ABSOLUTE_POSE_COEFFS_H_ #include namespace colmap { Eigen::Matrix ComputeDepthsSylvesterCoeffs( const Eigen::Matrix& K); } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_GENERALIZED_ABSOLUTE_POSE_COEFFS_H_ colmap-3.4/src/estimators/generalized_absolute_pose_test.cc000066400000000000000000000101151323400541200243670ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/generalized_absolute_pose" #include "util/testing.h" #include #include #include "base/pose.h" #include "base/projection.h" #include "base/similarity_transform.h" #include "estimators/generalized_absolute_pose.h" #include "optim/ransac.h" #include "util/random.h" using namespace colmap; BOOST_AUTO_TEST_CASE(Estimate) { SetPRNGSeed(0); std::vector points3D; points3D.emplace_back(1, 1, 1); points3D.emplace_back(0, 1, 1); points3D.emplace_back(3, 1.0, 4); points3D.emplace_back(3, 1.1, 4); points3D.emplace_back(3, 1.2, 4); points3D.emplace_back(3, 1.3, 4); points3D.emplace_back(3, 1.4, 4); points3D.emplace_back(2, 1, 7); auto points3D_faulty = points3D; for (size_t i = 0; i < points3D.size(); ++i) { points3D_faulty[i](0) = 20; } for (double qx = 0; qx < 1; qx += 0.2) { for (double tx = 0; tx < 1; tx += 0.1) { const int kRefTform = 1; const int kNumTforms = 3; const std::array orig_tforms = {{ SimilarityTransform3(1, Eigen::Vector4d(1, qx, 0, 0), Eigen::Vector3d(tx, -0.1, 0)), SimilarityTransform3(1, Eigen::Vector4d(1, qx, 0, 0), Eigen::Vector3d(tx, 0, 0)), SimilarityTransform3(1, Eigen::Vector4d(1, qx, 0, 0), Eigen::Vector3d(tx, 0.1, 0)), }}; std::array rel_tforms; for (size_t i = 0; i < kNumTforms; ++i) { Eigen::Vector4d rel_qvec; Eigen::Vector3d rel_tvec; ComputeRelativePose(orig_tforms[kRefTform].Rotation(), orig_tforms[kRefTform].Translation(), orig_tforms[i].Rotation(), orig_tforms[i].Translation(), &rel_qvec, &rel_tvec); rel_tforms[i] = ComposeProjectionMatrix(rel_qvec, rel_tvec); } // Project points to camera coordinate system. std::vector points2D; for (size_t i = 0; i < points3D.size(); ++i) { Eigen::Vector3d point3D_camera = points3D[i]; orig_tforms[i % kNumTforms].TransformPoint(&point3D_camera); points2D.emplace_back(); points2D.back().rel_tform = rel_tforms[i % kNumTforms]; points2D.back().xy = point3D_camera.hnormalized(); } RANSACOptions options; options.max_error = 1e-5; RANSAC ransac(options); const auto report = ransac.Estimate(points2D, points3D); BOOST_CHECK_EQUAL(report.success, true); // Test if correct transformation has been determined. const double matrix_diff = (orig_tforms[kRefTform].Matrix().topLeftCorner<3, 4>() - report.model) .norm(); BOOST_CHECK(matrix_diff < 1e-2); // Test residuals of exact points. std::vector residuals; GP3PEstimator::Residuals(points2D, points3D, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] < 1e-3); } // Test residuals of faulty points. GP3PEstimator::Residuals(points2D, points3D_faulty, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] > 0.1); } } } } colmap-3.4/src/estimators/generalized_relative_pose.cc000066400000000000000000000577731323400541200233520ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . // Note that part of this code is licensed under the following conditions. // Author: Laurent Kneip // Contact: kneip.laurent@gmail.com // License: Copyright (c) 2013 Laurent Kneip, ANU. All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are met: // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above copyright // notice, this list of conditions and the following disclaimer in the // documentation and/or other materials provided with the distribution. // * Neither the name of ANU nor the names of its contributors may be // used to endorse or promote products derived from this software without // specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE // ARE DISCLAIMED. IN NO EVENT SHALL ANU OR THE CONTRIBUTORS BE LIABLE FOR ANY // DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES // (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; // LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND // ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #include "estimators/generalized_relative_pose.h" #include "base/essential_matrix.h" #include "base/pose.h" #include "base/projection.h" #include "base/triangulation.h" #include "util/logging.h" #include "util/random.h" namespace colmap { namespace { void ComposePlueckerData(const Eigen::Matrix3x4d& rel_tform, const Eigen::Vector2d& point2D, Eigen::Vector3d* proj_center, Eigen::Vector6d* pluecker) { const Eigen::Matrix3x4d inv_proj_matrix = InvertProjectionMatrix(rel_tform); const Eigen::Vector3d bearing = inv_proj_matrix.leftCols<3>() * point2D.homogeneous(); const Eigen::Vector3d bearing_normalized = bearing.normalized(); *proj_center = inv_proj_matrix.rightCols<1>(); *pluecker << bearing_normalized, proj_center->cross(bearing_normalized); } Eigen::Matrix3d CayleyToRotationMatrix(const Eigen::Vector3d& cayley) { const double cayley0_sqr = cayley[0] * cayley[0]; const double cayley1_sqr = cayley[1] * cayley[1]; const double cayley2_sqr = cayley[2] * cayley[2]; const double cayley01 = cayley[0] * cayley[1]; const double cayley12 = cayley[1] * cayley[2]; const double cayley02 = cayley[0] * cayley[2]; const double scale = 1 + cayley0_sqr + cayley1_sqr + cayley2_sqr; const double inv_scale = 1.0 / scale; Eigen::Matrix3d R; R(0, 0) = inv_scale * (1 + cayley0_sqr - cayley1_sqr - cayley2_sqr); R(0, 1) = inv_scale * (2 * (cayley01 - cayley[2])); R(0, 2) = inv_scale * (2 * (cayley02 + cayley[1])); R(1, 0) = inv_scale * (2 * (cayley01 + cayley[2])); R(1, 1) = inv_scale * (1 - cayley0_sqr + cayley1_sqr - cayley2_sqr); R(1, 2) = inv_scale * (2 * (cayley12 - cayley[0])); R(2, 0) = inv_scale * (2 * (cayley02 - cayley[1])); R(2, 1) = inv_scale * (2 * (cayley12 + cayley[0])); R(2, 2) = inv_scale * (1 - cayley0_sqr - cayley1_sqr + cayley2_sqr); return R; } Eigen::Vector3d RotationMatrixToCaley(const Eigen::Matrix3d& R) { const Eigen::Matrix3d C1 = R - Eigen::Matrix3d::Identity(); const Eigen::Matrix3d C2 = R + Eigen::Matrix3d::Identity(); const Eigen::Matrix3d C = C1 * C2.inverse(); return Eigen::Vector3d(-C(1, 2), C(0, 2), -C(0, 1)); } Eigen::Vector3d ComputeRotationBetweenPoints( const std::vector& plueckers1, const std::vector& plueckers2) { CHECK_EQ(plueckers1.size(), plueckers2.size()); // Compute the center of all observed points. Eigen::Vector3d points_center1 = Eigen::Vector3d::Zero(); Eigen::Vector3d points_center2 = Eigen::Vector3d::Zero(); for (size_t i = 0; i < plueckers1.size(); i++) { points_center1 += plueckers1[i].head<3>(); points_center2 += plueckers2[i].head<3>(); } points_center1 = points_center1 / plueckers1.size(); points_center2 = points_center2 / plueckers1.size(); Eigen::Matrix3d Hcross = Eigen::Matrix3d::Zero(); for (size_t i = 0; i < plueckers1.size(); i++) { const Eigen::Vector3d f1 = plueckers1[i].head<3>() - points_center1; const Eigen::Vector3d f2 = plueckers2[i].head<3>() - points_center2; Hcross += f2 * f1.transpose(); } const Eigen::JacobiSVD svd( Hcross, Eigen::ComputeFullU | Eigen::ComputeFullV); const Eigen::Matrix3d V = svd.matrixV(); const Eigen::Matrix3d U = svd.matrixU(); Eigen::Matrix3d R = V * U.transpose(); if (R.determinant() < 0) { Eigen::Matrix3d V_prime; V_prime.col(0) = V.col(0); V_prime.col(1) = V.col(1); V_prime.col(2) = -V.col(2); R = V_prime * U.transpose(); } return RotationMatrixToCaley(R); } Eigen::Matrix4d ComposeG(const Eigen::Matrix3d& xxF, const Eigen::Matrix3d& yyF, const Eigen::Matrix3d& zzF, const Eigen::Matrix3d& xyF, const Eigen::Matrix3d& yzF, const Eigen::Matrix3d& zxF, const Eigen::Matrix& x1P, const Eigen::Matrix& y1P, const Eigen::Matrix& z1P, const Eigen::Matrix& x2P, const Eigen::Matrix& y2P, const Eigen::Matrix& z2P, const Eigen::Matrix& m11P, const Eigen::Matrix& m12P, const Eigen::Matrix& m22P, const Eigen::Vector3d& rotation) { const Eigen::Matrix3d R = CayleyToRotationMatrix(rotation); Eigen::Matrix R_rows; R_rows << R.row(0), R.row(1), R.row(2); Eigen::Matrix R_cols; R_cols << R.col(0), R.col(1), R.col(2); const Eigen::Vector3d xxFr1t = xxF * R.row(1).transpose(); const Eigen::Vector3d yyFr0t = yyF * R.row(0).transpose(); const Eigen::Vector3d zzFr0t = zzF * R.row(0).transpose(); const Eigen::Vector3d yzFr0t = yzF * R.row(0).transpose(); const Eigen::Vector3d xyFr1t = xyF * R.row(1).transpose(); const Eigen::Vector3d xyFr2t = xyF * R.row(2).transpose(); const Eigen::Vector3d zxFr1t = zxF * R.row(1).transpose(); const Eigen::Vector3d zxFr2t = zxF * R.row(2).transpose(); const Eigen::Vector3d x1PC = x1P * R_cols; const Eigen::Vector3d y1PC = y1P * R_cols; const Eigen::Vector3d z1PC = z1P * R_cols; const Eigen::Vector3d x2PR = x2P * R_rows.transpose(); const Eigen::Vector3d y2PR = y2P * R_rows.transpose(); const Eigen::Vector3d z2PR = z2P * R_rows.transpose(); Eigen::Matrix4d G; G(0, 0) = R.row(2) * yyF * R.row(2).transpose(); G(0, 0) += -2.0 * R.row(2) * yzF * R.row(1).transpose(); G(0, 0) += R.row(1) * zzF * R.row(1).transpose(); G(0, 1) = R.row(2) * yzFr0t; G(0, 1) += -1.0 * R.row(2) * xyFr2t; G(0, 1) += -1.0 * R.row(1) * zzFr0t; G(0, 1) += R.row(1) * zxFr2t; G(0, 2) = R.row(2) * xyFr1t; G(0, 2) += -1.0 * R.row(2) * yyFr0t; G(0, 2) += -1.0 * R.row(1) * zxFr1t; G(0, 2) += R.row(1) * yzFr0t; G(1, 1) = R.row(0) * zzFr0t; G(1, 1) += -2.0 * R.row(0) * zxFr2t; G(1, 1) += R.row(2) * xxF * R.row(2).transpose(); G(1, 2) = R.row(0) * zxFr1t; G(1, 2) += -1.0 * R.row(0) * yzFr0t; G(1, 2) += -1.0 * R.row(2) * xxFr1t; G(1, 2) += R.row(0) * xyFr2t; G(2, 2) = R.row(1) * xxFr1t; G(2, 2) += -2.0 * R.row(0) * xyFr1t; G(2, 2) += R.row(0) * yyFr0t; G(1, 0) = G(0, 1); G(2, 0) = G(0, 2); G(2, 1) = G(1, 2); G(0, 3) = R.row(2) * y1PC; G(0, 3) += R.row(2) * y2PR; G(0, 3) += -1.0 * R.row(1) * z1PC; G(0, 3) += -1.0 * R.row(1) * z2PR; G(1, 3) = R.row(0) * z1PC; G(1, 3) += R.row(0) * z2PR; G(1, 3) += -1.0 * R.row(2) * x1PC; G(1, 3) += -1.0 * R.row(2) * x2PR; G(2, 3) = R.row(1) * x1PC; G(2, 3) += R.row(1) * x2PR; G(2, 3) += -1.0 * R.row(0) * y1PC; G(2, 3) += -1.0 * R.row(0) * y2PR; G(3, 3) = -1.0 * R_cols.transpose() * m11P * R_cols; G(3, 3) += -1.0 * R_rows * m22P * R_rows.transpose(); G(3, 3) += -2.0 * R_rows * m12P * R_cols; G(3, 0) = G(0, 3); G(3, 1) = G(1, 3); G(3, 2) = G(2, 3); return G; } Eigen::Vector4d ComputeEigenValue( const Eigen::Matrix3d& xxF, const Eigen::Matrix3d& yyF, const Eigen::Matrix3d& zzF, const Eigen::Matrix3d& xyF, const Eigen::Matrix3d& yzF, const Eigen::Matrix3d& zxF, const Eigen::Matrix& x1P, const Eigen::Matrix& y1P, const Eigen::Matrix& z1P, const Eigen::Matrix& x2P, const Eigen::Matrix& y2P, const Eigen::Matrix& z2P, const Eigen::Matrix& m11P, const Eigen::Matrix& m12P, const Eigen::Matrix& m22P, const Eigen::Vector3d& rotation) { const Eigen::Matrix4d G = ComposeG(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, rotation); // Compute the roots in closed-form. // const double G00_2 = G(0,0) * G(0,0); const double G01_2 = G(0, 1) * G(0, 1); const double G02_2 = G(0, 2) * G(0, 2); const double G03_2 = G(0, 3) * G(0, 3); // const double G11_2 = G(1,1) * G(1,1); const double G12_2 = G(1, 2) * G(1, 2); const double G13_2 = G(1, 3) * G(1, 3); // const double G22_2 = G(2,2) * G(2,2); const double G23_2 = G(2, 3) * G(2, 3); // const double G33_2 = G(3,3) * G(3,3); const double B = -G(3, 3) - G(2, 2) - G(1, 1) - G(0, 0); const double C = -G23_2 + G(2, 2) * G(3, 3) - G13_2 - G12_2 + G(1, 1) * G(3, 3) + G(1, 1) * G(2, 2) - G03_2 - G02_2 - G01_2 + G(0, 0) * G(3, 3) + G(0, 0) * G(2, 2) + G(0, 0) * G(1, 1); const double D = G13_2 * G(2, 2) - 2.0 * G(1, 2) * G(1, 3) * G(2, 3) + G12_2 * G(3, 3) + G(1, 1) * G23_2 - G(1, 1) * G(2, 2) * G(3, 3) + G03_2 * G(2, 2) + G03_2 * G(1, 1) - 2.0 * G(0, 2) * G(0, 3) * G(2, 3) + G02_2 * G(3, 3) + G02_2 * G(1, 1) - 2.0 * G(0, 1) * G(0, 3) * G(1, 3) - 2.0 * G(0, 1) * G(0, 2) * G(1, 2) + G01_2 * G(3, 3) + G01_2 * G(2, 2) + G(0, 0) * G23_2 - G(0, 0) * G(2, 2) * G(3, 3) + G(0, 0) * G13_2 + G(0, 0) * G12_2 - G(0, 0) * G(1, 1) * G(3, 3) - G(0, 0) * G(1, 1) * G(2, 2); const double E = G03_2 * G12_2 - G03_2 * G(1, 1) * G(2, 2) - 2.0 * G(0, 2) * G(0, 3) * G(1, 2) * G(1, 3) + 2.0 * G(0, 2) * G(0, 3) * G(1, 1) * G(2, 3) + G02_2 * G13_2 - G02_2 * G(1, 1) * G(3, 3) + 2.0 * G(0, 1) * G(0, 3) * G(1, 3) * G(2, 2) - 2.0 * G(0, 1) * G(0, 3) * G(1, 2) * G(2, 3) - 2.0 * G(0, 1) * G(0, 2) * G(1, 3) * G(2, 3) + 2.0 * G(0, 1) * G(0, 2) * G(1, 2) * G(3, 3) + G01_2 * G23_2 - G01_2 * G(2, 2) * G(3, 3) - G(0, 0) * G13_2 * G(2, 2) + 2.0 * G(0, 0) * G(1, 2) * G(1, 3) * G(2, 3) - G(0, 0) * G12_2 * G(3, 3) - G(0, 0) * G(1, 1) * G23_2 + G(0, 0) * G(1, 1) * G(2, 2) * G(3, 3); const double B_pw2 = B * B; const double B_pw3 = B_pw2 * B; const double B_pw4 = B_pw3 * B; const double alpha = -0.375 * B_pw2 + C; const double beta = B_pw3 / 8.0 - B * C / 2.0 + D; const double gamma = -0.01171875 * B_pw4 + B_pw2 * C / 16.0 - B * D / 4.0 + E; const double alpha_pw2 = alpha * alpha; const double alpha_pw3 = alpha_pw2 * alpha; const double p = -alpha_pw2 / 12.0 - gamma; const double q = -alpha_pw3 / 108.0 + alpha * gamma / 3.0 - beta * beta / 8.0; const double helper1 = -p * p * p / 27.0; const double theta2 = pow(helper1, (1.0 / 3.0)); const double theta1 = std::sqrt(theta2) * std::cos((1.0 / 3.0) * std::acos((-q / 2.0) / std::sqrt(helper1))); const double y = -(5.0 / 6.0) * alpha - ((1.0 / 3.0) * p * theta1 - theta1 * theta2) / theta2; const double w = std::sqrt(alpha + 2.0 * y); Eigen::Vector4d roots; roots(0) = -B / 4.0 + 0.5 * w + 0.5 * std::sqrt(-3.0 * alpha - 2.0 * y - 2.0 * beta / w); roots(1) = -B / 4.0 + 0.5 * w - 0.5 * std::sqrt(-3.0 * alpha - 2.0 * y - 2.0 * beta / w); roots(2) = -B / 4.0 - 0.5 * w + 0.5 * std::sqrt(-3.0 * alpha - 2.0 * y + 2.0 * beta / w); roots(3) = -B / 4.0 - 0.5 * w - 0.5 * std::sqrt(-3.0 * alpha - 2.0 * y + 2.0 * beta / w); return roots; } double ComputeCost(const Eigen::Matrix3d& xxF, const Eigen::Matrix3d& yyF, const Eigen::Matrix3d& zzF, const Eigen::Matrix3d& xyF, const Eigen::Matrix3d& yzF, const Eigen::Matrix3d& zxF, const Eigen::Matrix& x1P, const Eigen::Matrix& y1P, const Eigen::Matrix& z1P, const Eigen::Matrix& x2P, const Eigen::Matrix& y2P, const Eigen::Matrix& z2P, const Eigen::Matrix& m11P, const Eigen::Matrix& m12P, const Eigen::Matrix& m22P, const Eigen::Vector3d& rotation, const int step) { CHECK_GE(step, 0); CHECK_LE(step, 1); const Eigen::Vector4d roots = ComputeEigenValue(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, rotation); if (step == 0) { return roots[2]; } else if (step == 1) { return roots[3]; } return 0; } Eigen::Vector3d ComputeJacobian( const Eigen::Matrix3d& xxF, const Eigen::Matrix3d& yyF, const Eigen::Matrix3d& zzF, const Eigen::Matrix3d& xyF, const Eigen::Matrix3d& yzF, const Eigen::Matrix3d& zxF, const Eigen::Matrix& x1P, const Eigen::Matrix& y1P, const Eigen::Matrix& z1P, const Eigen::Matrix& x2P, const Eigen::Matrix& y2P, const Eigen::Matrix& z2P, const Eigen::Matrix& m11P, const Eigen::Matrix& m12P, const Eigen::Matrix& m22P, const Eigen::Vector3d& rotation, const double current_cost, const int step) { Eigen::Vector3d jacobian; const double kEpsilon = 0.00000001; for (int j = 0; j < 3; j++) { Eigen::Vector3d cayley_j = rotation; cayley_j[j] += kEpsilon; const double cost_j = ComputeCost(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, cayley_j, step); jacobian(j) = cost_j - current_cost; } return jacobian; } } // namespace std::vector GR6PEstimator::Estimate( const std::vector& points1, const std::vector& points2) { CHECK_GE(points1.size(), 6); CHECK_EQ(points1.size(), points2.size()); std::vector proj_centers1(points1.size()); std::vector proj_centers2(points1.size()); std::vector plueckers1(points1.size()); std::vector plueckers2(points1.size()); for (size_t i = 0; i < points1.size(); ++i) { ComposePlueckerData(points1[i].rel_tform, points1[i].xy, &proj_centers1[i], &plueckers1[i]); ComposePlueckerData(points2[i].rel_tform, points2[i].xy, &proj_centers2[i], &plueckers2[i]); } Eigen::Matrix3d xxF = Eigen::Matrix3d::Zero(); Eigen::Matrix3d yyF = Eigen::Matrix3d::Zero(); Eigen::Matrix3d zzF = Eigen::Matrix3d::Zero(); Eigen::Matrix3d xyF = Eigen::Matrix3d::Zero(); Eigen::Matrix3d yzF = Eigen::Matrix3d::Zero(); Eigen::Matrix3d zxF = Eigen::Matrix3d::Zero(); Eigen::Matrix x1P = Eigen::Matrix::Zero(); Eigen::Matrix y1P = Eigen::Matrix::Zero(); Eigen::Matrix z1P = Eigen::Matrix::Zero(); Eigen::Matrix x2P = Eigen::Matrix::Zero(); Eigen::Matrix y2P = Eigen::Matrix::Zero(); Eigen::Matrix z2P = Eigen::Matrix::Zero(); Eigen::Matrix m11P = Eigen::Matrix::Zero(); Eigen::Matrix m12P = Eigen::Matrix::Zero(); Eigen::Matrix m22P = Eigen::Matrix::Zero(); for (size_t i = 0; i < points1.size(); ++i) { const Eigen::Vector3d f1 = plueckers1[i].head<3>(); const Eigen::Vector3d f2 = plueckers2[i].head<3>(); const Eigen::Vector3d t1 = proj_centers1[i]; const Eigen::Vector3d t2 = proj_centers2[i]; const Eigen::Matrix3d F = f2 * f2.transpose(); xxF += f1[0] * f1[0] * F; yyF += f1[1] * f1[1] * F; zzF += f1[2] * f1[2] * F; xyF += f1[0] * f1[1] * F; yzF += f1[1] * f1[2] * F; zxF += f1[2] * f1[0] * F; Eigen::Matrix ff1; ff1(0) = f1[0] * (f2[1] * t2[2] - f2[2] * t2[1]); ff1(1) = f1[1] * (f2[1] * t2[2] - f2[2] * t2[1]); ff1(2) = f1[2] * (f2[1] * t2[2] - f2[2] * t2[1]); ff1(3) = f1[0] * (f2[2] * t2[0] - f2[0] * t2[2]); ff1(4) = f1[1] * (f2[2] * t2[0] - f2[0] * t2[2]); ff1(5) = f1[2] * (f2[2] * t2[0] - f2[0] * t2[2]); ff1(6) = f1[0] * (f2[0] * t2[1] - f2[1] * t2[0]); ff1(7) = f1[1] * (f2[0] * t2[1] - f2[1] * t2[0]); ff1(8) = f1[2] * (f2[0] * t2[1] - f2[1] * t2[0]); x1P += f1[0] * f2 * ff1.transpose(); y1P += f1[1] * f2 * ff1.transpose(); z1P += f1[2] * f2 * ff1.transpose(); Eigen::Matrix ff2; ff2(0) = f2[0] * (f1[1] * t1[2] - f1[2] * t1[1]); ff2(1) = f2[1] * (f1[1] * t1[2] - f1[2] * t1[1]); ff2(2) = f2[2] * (f1[1] * t1[2] - f1[2] * t1[1]); ff2(3) = f2[0] * (f1[2] * t1[0] - f1[0] * t1[2]); ff2(4) = f2[1] * (f1[2] * t1[0] - f1[0] * t1[2]); ff2(5) = f2[2] * (f1[2] * t1[0] - f1[0] * t1[2]); ff2(6) = f2[0] * (f1[0] * t1[1] - f1[1] * t1[0]); ff2(7) = f2[1] * (f1[0] * t1[1] - f1[1] * t1[0]); ff2(8) = f2[2] * (f1[0] * t1[1] - f1[1] * t1[0]); x2P += f1[0] * f2 * ff2.transpose(); y2P += f1[1] * f2 * ff2.transpose(); z2P += f1[2] * f2 * ff2.transpose(); m11P -= ff1 * ff1.transpose(); m22P -= ff2 * ff2.transpose(); m12P -= ff2 * ff1.transpose(); } const Eigen::Vector3d initial_rotation = ComputeRotationBetweenPoints(plueckers1, plueckers2); const double kMinLambda = 0.00001; const double kMaxLambda = 0.08; const double kLambdaModifier = 2.0; const int kMaxNumIterations = 50; const bool kDisableIncrements = true; double perturbation_amplitude = 0.3; int num_random_trials = 0; Eigen::Vector3d rotation; while (num_random_trials < 5) { if (num_random_trials > 2) { perturbation_amplitude = 0.6; } if (num_random_trials == 0) { rotation = initial_rotation; } else { const Eigen::Vector3d perturbation( RandomReal(-perturbation_amplitude, perturbation_amplitude), RandomReal(-perturbation_amplitude, perturbation_amplitude), RandomReal(-perturbation_amplitude, perturbation_amplitude)); rotation = initial_rotation + perturbation; } double lambda = 0.01; int num_iterations = 0; double smallest_eigen_value = ComputeCost(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, rotation, 1); for (int iter = 0; iter < kMaxNumIterations; ++iter) { const Eigen::Vector3d jacobian = ComputeJacobian( xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, rotation, smallest_eigen_value, 1); const Eigen::Vector3d normalized_jacobian = jacobian.normalized(); Eigen::Vector3d sampling_point = rotation - lambda * normalized_jacobian; double sampling_eigen_value = ComputeCost(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, sampling_point, 1); if (num_iterations == 0 || !kDisableIncrements) { while (sampling_eigen_value < smallest_eigen_value) { smallest_eigen_value = sampling_eigen_value; if (lambda * kLambdaModifier > kMaxLambda) { break; } lambda *= kLambdaModifier; sampling_point = rotation - lambda * normalized_jacobian; sampling_eigen_value = ComputeCost(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, sampling_point, 1); } } while (sampling_eigen_value > smallest_eigen_value) { lambda /= kLambdaModifier; sampling_point = rotation - lambda * normalized_jacobian; sampling_eigen_value = ComputeCost(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, sampling_point, 1); } rotation = sampling_point; smallest_eigen_value = sampling_eigen_value; if (lambda < kMinLambda) { break; } } if (rotation.norm() < 0.01) { const double eigen_value2 = ComputeCost(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, rotation, 0); if (eigen_value2 > 0.001) { num_random_trials += 1; } else { break; } } else { break; } } const Eigen::Matrix3d R = CayleyToRotationMatrix(rotation).transpose(); const Eigen::Matrix4d G = ComposeG(xxF, yyF, zzF, xyF, yzF, zxF, x1P, y1P, z1P, x2P, y2P, z2P, m11P, m12P, m22P, rotation); const Eigen::EigenSolver eigen_solver_G(G, true); const Eigen::Matrix4cd V = eigen_solver_G.eigenvectors(); const Eigen::Matrix3x4d VV = V.real().colwise().hnormalized(); std::vector models(4); for (int i = 0; i < 4; ++i) { models[i].leftCols<3>() = R; models[i].rightCols<1>() = -R * VV.col(i); } return models; } void GR6PEstimator::Residuals(const std::vector& points1, const std::vector& points2, const M_t& proj_matrix, std::vector* residuals) { CHECK_EQ(points1.size(), points2.size()); residuals->resize(points1.size(), 0); Eigen::Matrix4d proj_matrix_homogeneous; proj_matrix_homogeneous.topRows<3>() = proj_matrix; proj_matrix_homogeneous.bottomRows<1>() = Eigen::Vector4d(0, 0, 0, 1); for (size_t i = 0; i < points1.size(); ++i) { const Eigen::Matrix3x4d& proj_matrix1 = points1[i].rel_tform; const Eigen::Matrix3x4d& proj_matrix2 = points2[i].rel_tform * proj_matrix_homogeneous; const Eigen::Matrix3d R12 = proj_matrix2.leftCols<3>() * proj_matrix1.leftCols<3>().transpose(); const Eigen::Vector3d t12 = proj_matrix2.rightCols<1>() - R12 * proj_matrix1.rightCols<1>(); const Eigen::Matrix3d E = EssentialMatrixFromPose(R12, t12); const Eigen::Vector3d Ex1 = E * points1[i].xy.homogeneous(); const Eigen::Vector3d Etx2 = E.transpose() * points2[i].xy.homogeneous(); const double x2tEx1 = points2[i].xy.homogeneous().transpose() * Ex1; (*residuals)[i] = x2tEx1 * x2tEx1 / (Ex1(0) * Ex1(0) + Ex1(1) * Ex1(1) + Etx2(0) * Etx2(0) + Etx2(1) * Etx2(1)); } } } // namespace colmap colmap-3.4/src/estimators/generalized_relative_pose.h000066400000000000000000000061141323400541200231730ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_GENERALIZED_RELATIVE_POSE_H_ #define COLMAP_SRC_ESTIMATORS_GENERALIZED_RELATIVE_POSE_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Solver for the Generalized Relative Pose problem using a minimal of 8 2D-2D // correspondences. This implementation is based on: // // "Efficient Computation of Relative Pose for Multi-Camera Systems", // Kneip and Li. CVPR 2014. // // Note that the solution to this problem is degenerate in the case of pure // translation and when all correspondences are observed from the same cameras. // // The implementation is a modified and improved version of Kneip's original // implementation in OpenGV licensed under the BSD license. class GR6PEstimator { public: // The generalized image observations of the left camera, which is composed of // the relative pose of the specific camera in the generalized camera and its // image observation. struct X_t { EIGEN_MAKE_ALIGNED_OPERATOR_NEW // The relative transformation from the generalized camera to the camera // frame of the observation. Eigen::Matrix3x4d rel_tform; // The 2D image feature observation. Eigen::Vector2d xy; }; // The normalized image feature points in the left camera. typedef X_t Y_t; // The relative transformation between the two generalized cameras. typedef Eigen::Matrix3x4d M_t; // The minimum number of samples needed to estimate a model. Note that in // theory the minimum required number of samples is 6 but Laurent Kneip showed // in his paper that using 8 samples is more stable. static const int kMinNumSamples = 8; // Estimate the most probable solution of the GR6P problem from a set of // six 2D-2D point correspondences. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the squared Sampson error between corresponding points. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& proj_matrix, std::vector* residuals); }; } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::GR6PEstimator::X_t) #endif // COLMAP_SRC_ESTIMATORS_GENERALIZED_RELATIVE_POSE_H_ colmap-3.4/src/estimators/generalized_relative_pose_test.cc000066400000000000000000000077731323400541200244040ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "base/generalized_relative_pose" #include "util/testing.h" #include #include "base/pose.h" #include "base/projection.h" #include "base/similarity_transform.h" #include "estimators/generalized_relative_pose.h" #include "optim/loransac.h" #include "util/random.h" using namespace colmap; BOOST_AUTO_TEST_CASE(Estimate) { SetPRNGSeed(0); const size_t kNumPoints = 100; std::vector points3D; for (size_t i = 0; i < kNumPoints; ++i) { points3D.emplace_back(RandomReal(-10, 10), RandomReal(-10, 10), RandomReal(-10, 10)); } for (double qx = 0; qx < 0.4; qx += 0.1) { for (double tx = 0; tx < 0.5; tx += 0.1) { const int kRefTform = 1; const int kNumTforms = 3; const std::array orig_tforms = {{ SimilarityTransform3(1, Eigen::Vector4d(1, qx, 0, 0), Eigen::Vector3d(tx, 0.1, 0)), SimilarityTransform3(1, Eigen::Vector4d(1, qx + 0.05, 0, 0), Eigen::Vector3d(tx, 0.2, 0)), SimilarityTransform3(1, Eigen::Vector4d(1, qx + 0.1, 0, 0), Eigen::Vector3d(tx, 0.3, 0)), }}; std::array rel_tforms; for (size_t i = 0; i < kNumTforms; ++i) { Eigen::Vector4d rel_qvec; Eigen::Vector3d rel_tvec; ComputeRelativePose(orig_tforms[kRefTform].Rotation(), orig_tforms[kRefTform].Translation(), orig_tforms[i].Rotation(), orig_tforms[i].Translation(), &rel_qvec, &rel_tvec); rel_tforms[i] = ComposeProjectionMatrix(rel_qvec, rel_tvec); } // Project points to cameras. std::vector points1; std::vector points2; for (size_t i = 0; i < points3D.size(); ++i) { const Eigen::Vector3d point3D_camera1 = rel_tforms[i % kNumTforms] * points3D[i].homogeneous(); Eigen::Vector3d point3D_camera2 = points3D[i]; orig_tforms[(i + 1) % kNumTforms].TransformPoint(&point3D_camera2); if (point3D_camera1.z() < 0 || point3D_camera2.z() < 0) { continue; } points1.emplace_back(); points1.back().rel_tform = rel_tforms[i % kNumTforms]; points1.back().xy = point3D_camera1.hnormalized(); points2.emplace_back(); points2.back().rel_tform = rel_tforms[(i + 1) % kNumTforms]; points2.back().xy = point3D_camera2.hnormalized(); } RANSACOptions options; options.max_error = 1e-3; LORANSAC ransac(options); const auto report = ransac.Estimate(points1, points2); BOOST_CHECK_EQUAL(report.success, true); const double matrix_diff = (orig_tforms[kRefTform].Matrix().topLeftCorner<3, 4>() - report.model) .norm(); BOOST_CHECK_LE(matrix_diff, 1e-2); std::vector residuals; GR6PEstimator::Residuals(points1, points2, report.model, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK_LE(residuals[i], options.max_error); } } } } colmap-3.4/src/estimators/homography_matrix.cc000077500000000000000000000076471323400541200216770ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/homography_matrix.h" #include #include #include #include "base/projection.h" #include "estimators/utils.h" #include "util/logging.h" namespace colmap { std::vector HomographyMatrixEstimator::Estimate( const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); const size_t N = points1.size(); // Center and normalize image points for better numerical stability. std::vector normed_points1; std::vector normed_points2; Eigen::Matrix3d points1_norm_matrix; Eigen::Matrix3d points2_norm_matrix; CenterAndNormalizeImagePoints(points1, &normed_points1, &points1_norm_matrix); CenterAndNormalizeImagePoints(points2, &normed_points2, &points2_norm_matrix); // Setup constraint matrix. Eigen::Matrix A = Eigen::MatrixXd::Zero(2 * N, 9); for (size_t i = 0, j = N; i < points1.size(); ++i, ++j) { const double s_0 = normed_points1[i](0); const double s_1 = normed_points1[i](1); const double d_0 = normed_points2[i](0); const double d_1 = normed_points2[i](1); A(i, 0) = -s_0; A(i, 1) = -s_1; A(i, 2) = -1; A(i, 6) = s_0 * d_0; A(i, 7) = s_1 * d_0; A(i, 8) = d_0; A(j, 3) = -s_0; A(j, 4) = -s_1; A(j, 5) = -1; A(j, 6) = s_0 * d_1; A(j, 7) = s_1 * d_1; A(j, 8) = d_1; } // Solve for the nullspace of the constraint matrix. Eigen::JacobiSVD> svd( A, Eigen::ComputeFullV); const Eigen::VectorXd nullspace = svd.matrixV().col(8); Eigen::Map H_t(nullspace.data()); const std::vector models = {points2_norm_matrix.inverse() * H_t.transpose() * points1_norm_matrix}; return models; } void HomographyMatrixEstimator::Residuals(const std::vector& points1, const std::vector& points2, const M_t& H, std::vector* residuals) { CHECK_EQ(points1.size(), points2.size()); residuals->resize(points1.size()); // Note that this code might not be as nice as Eigen expressions, // but it is significantly faster in various tests. const double H_00 = H(0, 0); const double H_01 = H(0, 1); const double H_02 = H(0, 2); const double H_10 = H(1, 0); const double H_11 = H(1, 1); const double H_12 = H(1, 2); const double H_20 = H(2, 0); const double H_21 = H(2, 1); const double H_22 = H(2, 2); for (size_t i = 0; i < points1.size(); ++i) { const double s_0 = points1[i](0); const double s_1 = points1[i](1); const double d_0 = points2[i](0); const double d_1 = points2[i](1); const double pd_0 = H_00 * s_0 + H_01 * s_1 + H_02; const double pd_1 = H_10 * s_0 + H_11 * s_1 + H_12; const double pd_2 = H_20 * s_0 + H_21 * s_1 + H_22; const double inv_pd_2 = 1.0 / pd_2; const double dd_0 = d_0 - pd_0 * inv_pd_2; const double dd_1 = d_1 - pd_1 * inv_pd_2; (*residuals)[i] = dd_0 * dd_0 + dd_1 * dd_1; } } } // namespace colmap colmap-3.4/src/estimators/homography_matrix.h000077500000000000000000000050201323400541200215200ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_HOMOGRAPHY_MATRIX_H_ #define COLMAP_SRC_ESTIMATORS_HOMOGRAPHY_MATRIX_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Direct linear transformation algorithm to compute the homography between // point pairs. This algorithm computes the least squares estimate for // the homography from at least 4 correspondences. class HomographyMatrixEstimator { public: typedef Eigen::Vector2d X_t; typedef Eigen::Vector2d Y_t; typedef Eigen::Matrix3d M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 4; // Estimate the projective transformation (homography). // // The number of corresponding points must be at least 4. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // // @return 3x3 homogeneous transformation matrix. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the transformation error for each corresponding point pair. // // Residuals are defined as the squared transformation error when // transforming the source to the destination coordinates. // // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param H 3x3 projective matrix. // @param residuals Output vector of residuals. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& H, std::vector* residuals); }; } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_HOMOGRAPHY_MATRIX_H_ colmap-3.4/src/estimators/homography_matrix_test.cc000077500000000000000000000033071323400541200227230ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/homography_matrix" #include "util/testing.h" #include #include #include "estimators/homography_matrix.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEstimate) { for (double x = 0; x < 10; ++x) { Eigen::Matrix3d H0; H0 << x, 0.2, 0.3, 30, 0.2, 0.1, 0.3, 20, 1; std::vector src; src.emplace_back(x, 0); src.emplace_back(1, 0); src.emplace_back(2, 1); src.emplace_back(10, 30); std::vector dst; for (size_t i = 0; i < 4; ++i) { const Eigen::Vector3d dsth = H0 * src[i].homogeneous(); dst.push_back(dsth.hnormalized()); } HomographyMatrixEstimator est_tform; const auto models = est_tform.Estimate(src, dst); std::vector residuals; est_tform.Residuals(src, dst, models[0], &residuals); for (size_t i = 0; i < 4; ++i) { BOOST_CHECK(residuals[i] < 1e-6); } } } colmap-3.4/src/estimators/pose.cc000077500000000000000000000274101323400541200170720ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/pose.h" #include "base/camera_models.h" #include "base/cost_functions.h" #include "base/essential_matrix.h" #include "base/pose.h" #include "estimators/absolute_pose.h" #include "estimators/essential_matrix.h" #include "optim/bundle_adjustment.h" #include "util/matrix.h" #include "util/misc.h" #include "util/threading.h" namespace colmap { namespace { typedef LORANSAC AbsolutePoseRANSAC; void EstimateAbsolutePoseKernel(const Camera& camera, const double focal_length_factor, const std::vector& points2D, const std::vector& points3D, const RANSACOptions& options, AbsolutePoseRANSAC::Report* report) { // Scale the focal length by the given factor. Camera scaled_camera = camera; const std::vector& focal_length_idxs = camera.FocalLengthIdxs(); for (const size_t idx : focal_length_idxs) { scaled_camera.Params(idx) *= focal_length_factor; } // Normalize image coordinates with current camera hypothesis. std::vector points2D_N(points2D.size()); for (size_t i = 0; i < points2D.size(); ++i) { points2D_N[i] = scaled_camera.ImageToWorld(points2D[i]); } // Estimate pose for given focal length. auto custom_options = options; custom_options.max_error = scaled_camera.ImageToWorldThreshold(options.max_error); AbsolutePoseRANSAC ransac(custom_options); *report = ransac.Estimate(points2D_N, points3D); } } // namespace bool EstimateAbsolutePose(const AbsolutePoseEstimationOptions& options, const std::vector& points2D, const std::vector& points3D, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec, Camera* camera, size_t* num_inliers, std::vector* inlier_mask) { options.Check(); std::vector focal_length_factors; if (options.estimate_focal_length) { // Generate focal length factors using a quadratic function, // such that more samples are drawn for small focal lengths focal_length_factors.reserve(options.num_focal_length_samples + 1); const double fstep = 1.0 / options.num_focal_length_samples; const double fscale = options.max_focal_length_ratio - options.min_focal_length_ratio; for (double f = 0; f <= 1.0; f += fstep) { focal_length_factors.push_back(options.min_focal_length_ratio + fscale * f * f); } } else { focal_length_factors.reserve(1); focal_length_factors.push_back(1); } std::vector> futures; futures.resize(focal_length_factors.size()); std::vector> reports; reports.resize(focal_length_factors.size()); ThreadPool thread_pool(std::min( options.num_threads, static_cast(focal_length_factors.size()))); for (size_t i = 0; i < focal_length_factors.size(); ++i) { futures[i] = thread_pool.AddTask( EstimateAbsolutePoseKernel, *camera, focal_length_factors[i], points2D, points3D, options.ransac_options, &reports[i]); } double focal_length_factor = 0; Eigen::Matrix3x4d proj_matrix; *num_inliers = 0; inlier_mask->clear(); // Find best model among all focal lengths. for (size_t i = 0; i < focal_length_factors.size(); ++i) { futures[i].get(); const auto report = reports[i]; if (report.success && report.support.num_inliers > *num_inliers) { *num_inliers = report.support.num_inliers; proj_matrix = report.model; *inlier_mask = report.inlier_mask; focal_length_factor = focal_length_factors[i]; } } if (*num_inliers == 0) { return false; } // Scale output camera with best estimated focal length. if (options.estimate_focal_length && *num_inliers > 0) { const std::vector& focal_length_idxs = camera->FocalLengthIdxs(); for (const size_t idx : focal_length_idxs) { camera->Params(idx) *= focal_length_factor; } } // Extract pose parameters. *qvec = RotationMatrixToQuaternion(proj_matrix.leftCols<3>()); *tvec = proj_matrix.rightCols<1>(); if (IsNaN(*qvec) || IsNaN(*tvec)) { return false; } return true; } size_t EstimateRelativePose(const RANSACOptions& ransac_options, const std::vector& points1, const std::vector& points2, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec) { RANSAC ransac(ransac_options); const auto report = ransac.Estimate(points1, points2); if (!report.success) { return 0; } std::vector inliers1(report.support.num_inliers); std::vector inliers2(report.support.num_inliers); size_t j = 0; for (size_t i = 0; i < points1.size(); ++i) { if (report.inlier_mask[i]) { inliers1[j] = points1[i]; inliers2[j] = points2[i]; j += 1; } } Eigen::Matrix3d R; std::vector points3D; PoseFromEssentialMatrix(report.model, inliers1, inliers2, &R, tvec, &points3D); *qvec = RotationMatrixToQuaternion(R); if (IsNaN(*qvec) || IsNaN(*tvec)) { return 0; } return points3D.size(); } bool RefineAbsolutePose(const AbsolutePoseRefinementOptions& options, const std::vector& inlier_mask, const std::vector& points2D, const std::vector& points3D, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec, Camera* camera) { CHECK_EQ(inlier_mask.size(), points2D.size()); CHECK_EQ(points2D.size(), points3D.size()); options.Check(); ceres::LossFunction* loss_function = new ceres::CauchyLoss(options.loss_function_scale); double* camera_params_data = camera->ParamsData(); double* qvec_data = qvec->data(); double* tvec_data = tvec->data(); std::vector points3D_copy = points3D; ceres::Problem problem; for (size_t i = 0; i < points2D.size(); ++i) { // Skip outlier observations if (!inlier_mask[i]) { continue; } ceres::CostFunction* cost_function = nullptr; switch (camera->ModelId()) { #define CAMERA_MODEL_CASE(CameraModel) \ case CameraModel::kModelId: \ cost_function = \ BundleAdjustmentCostFunction::Create(points2D[i]); \ break; CAMERA_MODEL_SWITCH_CASES #undef CAMERA_MODEL_CASE } problem.AddResidualBlock(cost_function, loss_function, qvec_data, tvec_data, points3D_copy[i].data(), camera_params_data); problem.SetParameterBlockConstant(points3D_copy[i].data()); } if (problem.NumResiduals() > 0) { // Quaternion parameterization. *qvec = NormalizeQuaternion(*qvec); ceres::LocalParameterization* quaternion_parameterization = new ceres::QuaternionParameterization; problem.SetParameterization(qvec_data, quaternion_parameterization); // Camera parameterization. if (!options.refine_focal_length && !options.refine_extra_params) { problem.SetParameterBlockConstant(camera->ParamsData()); } else { // Always set the principal point as fixed. std::vector camera_params_const; const std::vector& principal_point_idxs = camera->PrincipalPointIdxs(); camera_params_const.insert(camera_params_const.end(), principal_point_idxs.begin(), principal_point_idxs.end()); if (!options.refine_focal_length) { const std::vector& focal_length_idxs = camera->FocalLengthIdxs(); camera_params_const.insert(camera_params_const.end(), focal_length_idxs.begin(), focal_length_idxs.end()); } if (!options.refine_extra_params) { const std::vector& extra_params_idxs = camera->ExtraParamsIdxs(); camera_params_const.insert(camera_params_const.end(), extra_params_idxs.begin(), extra_params_idxs.end()); } if (camera_params_const.size() == camera->NumParams()) { problem.SetParameterBlockConstant(camera->ParamsData()); } else { ceres::SubsetParameterization* camera_params_parameterization = new ceres::SubsetParameterization( static_cast(camera->NumParams()), camera_params_const); problem.SetParameterization(camera->ParamsData(), camera_params_parameterization); } } } ceres::Solver::Options solver_options; solver_options.gradient_tolerance = options.gradient_tolerance; solver_options.max_num_iterations = options.max_num_iterations; solver_options.linear_solver_type = ceres::DENSE_QR; // The overhead of creating threads is too large. solver_options.num_threads = 1; solver_options.num_linear_solver_threads = 1; ceres::Solver::Summary summary; ceres::Solve(solver_options, &problem, &summary); if (solver_options.minimizer_progress_to_stdout) { std::cout << std::endl; } if (options.print_summary) { PrintHeading2("Pose refinement report"); PrintSolverSummary(summary); } return summary.IsSolutionUsable(); } bool RefineRelativePose(const ceres::Solver::Options& options, const std::vector& points1, const std::vector& points2, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec) { CHECK_EQ(points1.size(), points2.size()); // CostFunction assumes unit quaternions. *qvec = NormalizeQuaternion(*qvec); const double kMaxL2Error = 1.0; ceres::LossFunction* loss_function = new ceres::CauchyLoss(kMaxL2Error); ceres::Problem problem; for (size_t i = 0; i < points1.size(); ++i) { ceres::CostFunction* cost_function = RelativePoseCostFunction::Create(points1[i], points2[i]); problem.AddResidualBlock(cost_function, loss_function, qvec->data(), tvec->data()); } ceres::LocalParameterization* quaternion_parameterization = new ceres::QuaternionParameterization; problem.SetParameterization(qvec->data(), quaternion_parameterization); ceres::HomogeneousVectorParameterization* homogeneous_parameterization = new ceres::HomogeneousVectorParameterization(3); problem.SetParameterization(tvec->data(), homogeneous_parameterization); ceres::Solver::Summary summary; ceres::Solve(options, &problem, &summary); return summary.IsSolutionUsable(); } } // namespace colmap colmap-3.4/src/estimators/pose.h000077500000000000000000000166171323400541200167430ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_POSE_H_ #define COLMAP_SRC_ESTIMATORS_POSE_H_ #include #include #include #include "base/camera.h" #include "base/camera_models.h" #include "optim/loransac.h" #include "util/alignment.h" #include "util/logging.h" #include "util/threading.h" #include "util/types.h" namespace colmap { struct AbsolutePoseEstimationOptions { // Whether to estimate the focal length. bool estimate_focal_length = false; // Number of discrete samples for focal length estimation. size_t num_focal_length_samples = 30; // Minimum focal length ratio for discrete focal length sampling // around focal length of given camera. double min_focal_length_ratio = 0.2; // Maximum focal length ratio for discrete focal length sampling // around focal length of given camera. double max_focal_length_ratio = 5; // Number of threads for parallel estimation of focal length. int num_threads = ThreadPool::kMaxNumThreads; // Options used for P3P RANSAC. RANSACOptions ransac_options; void Check() const { CHECK_GT(num_focal_length_samples, 0); CHECK_GT(min_focal_length_ratio, 0); CHECK_GT(max_focal_length_ratio, 0); CHECK_LT(min_focal_length_ratio, max_focal_length_ratio); ransac_options.Check(); } }; struct AbsolutePoseRefinementOptions { // Convergence criterion. double gradient_tolerance = 1.0; // Maximum number of solver iterations. int max_num_iterations = 100; // Scaling factor determines at which residual robustification takes place. double loss_function_scale = 1.0; // Whether to refine the focal length parameter group. bool refine_focal_length = true; // Whether to refine the extra parameter group. bool refine_extra_params = true; // Whether to print final summary. bool print_summary = true; void Check() const { CHECK_GE(gradient_tolerance, 0.0); CHECK_GE(max_num_iterations, 0); CHECK_GE(loss_function_scale, 0.0); } }; // Estimate absolute pose (optionally focal length) from 2D-3D correspondences. // // Focal length estimation is performed using discrete sampling around the // focal length of the given camera. The focal length that results in the // maximal number of inliers is assigned to the given camera. // // @param options Absolute pose estimation options. // @param points2D Corresponding 2D points. // @param points3D Corresponding 3D points. // @param qvec Estimated rotation component as // unit Quaternion coefficients (w, x, y, z). // @param tvec Estimated translation component. // @param camera Camera for which to estimate pose. Modified // in-place to store the estimated focal length. // @param num_inliers Number of inliers in RANSAC. // @param inlier_mask Inlier mask for 2D-3D correspondences. // // @return Whether pose is estimated successfully. bool EstimateAbsolutePose(const AbsolutePoseEstimationOptions& options, const std::vector& points2D, const std::vector& points3D, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec, Camera* camera, size_t* num_inliers, std::vector* inlier_mask); // Estimate relative from 2D-2D correspondences. // // Pose of first camera is assumed to be at the origin without rotation. Pose // of second camera is given as world-to-image transformation, // i.e. `x2 = [R | t] * X2`. // // @param ransac_options RANSAC options. // @param points1 Corresponding 2D points. // @param points2 Corresponding 2D points. // @param qvec Estimated rotation component as // unit Quaternion coefficients (w, x, y, z). // @param tvec Estimated translation component. // // @return Number of RANSAC inliers. size_t EstimateRelativePose(const RANSACOptions& ransac_options, const std::vector& points1, const std::vector& points2, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec); // Refine absolute pose (optionally focal length) from 2D-3D correspondences. // // @param options Refinement options. // @param inlier_mask Inlier mask for 2D-3D correspondences. // @param points2D Corresponding 2D points. // @param points3D Corresponding 3D points. // @param qvec Estimated rotation component as // unit Quaternion coefficients (w, x, y, z). // @param tvec Estimated translation component. // @param camera Camera for which to estimate pose. Modified // in-place to store the estimated focal length. // // @return Whether the solution is usable. bool RefineAbsolutePose(const AbsolutePoseRefinementOptions& options, const std::vector& inlier_mask, const std::vector& points2D, const std::vector& points3D, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec, Camera* camera); // Refine relative pose of two cameras. // // Minimizes the Sampson error between corresponding normalized points using // a robust cost function, i.e. the corresponding points need not necessarily // be inliers given a sufficient initial guess for the relative pose. // // Assumes that first camera pose has projection matrix P = [I | 0], and // pose of second camera is given as transformation from world to camera system. // // Assumes that the given translation vector is normalized, and refines // the translation up to an unknown scale (i.e. refined translation vector // is a unit vector again). // // @param options Solver options. // @param points1 First set of corresponding points. // @param points2 Second set of corresponding points. // @param qvec Unit Quaternion rotation coefficients (w, x, y, z). // @param tvec 3x1 translation vector. // // @return Flag indicating if solution is usable. bool RefineRelativePose(const ceres::Solver::Options& options, const std::vector& points1, const std::vector& points2, Eigen::Vector4d* qvec, Eigen::Vector3d* tvec); } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_POSE_H_ colmap-3.4/src/estimators/similarity_transform.h000077500000000000000000000110731323400541200222450ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_SIMILARITY_TRANSFORM_H_ #define COLMAP_SRC_ESTIMATORS_SIMILARITY_TRANSFORM_H_ #include #include #include #include "base/projection.h" #include "util/alignment.h" #include "util/logging.h" #include "util/types.h" namespace colmap { // N-D similarity transform estimator from corresponding point pairs in the // source and destination coordinate systems. // // This algorithm is based on the following paper: // // S. Umeyama. Least-Squares Estimation of Transformation Parameters // Between Two Point Patterns. IEEE Transactions on Pattern Analysis and // Machine Intelligence, Volume 13 Issue 4, Page 376-380, 1991. // http://www.stanford.edu/class/cs273/refs/umeyama.pdf // // and uses the Eigen implementation. template class SimilarityTransformEstimator { public: typedef Eigen::Matrix X_t; typedef Eigen::Matrix Y_t; typedef Eigen::Matrix M_t; // The minimum number of samples needed to estimate a model. Note that // this only returns the true minimal sample in the two-dimensional case. // For higher dimensions, the system will alway be over-determined. static const int kMinNumSamples = kDim; // Estimate the similarity transform. // // @param src Set of corresponding source points. // @param dst Set of corresponding destination points. // // @return 4x4 homogeneous transformation matrix. static std::vector Estimate(const std::vector& src, const std::vector& dst); // Calculate the transformation error for each corresponding point pair. // // Residuals are defined as the squared transformation error when // transforming the source to the destination coordinates. // // @param src Set of corresponding points in the source coordinate // system as a Nx3 matrix. // @param dst Set of corresponding points in the destination // coordinate system as a Nx3 matrix. // @param matrix 4x4 homogeneous transformation matrix. // @param residuals Output vector of residuals for each point pair. static void Residuals(const std::vector& src, const std::vector& dst, const M_t& matrix, std::vector* residuals); }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// template std::vector::M_t> SimilarityTransformEstimator::Estimate( const std::vector& src, const std::vector& dst) { CHECK_EQ(src.size(), dst.size()); Eigen::Matrix src_mat(kDim, src.size()); Eigen::Matrix dst_mat(kDim, dst.size()); for (size_t i = 0; i < src.size(); ++i) { src_mat.col(i) = src[i]; dst_mat.col(i) = dst[i]; } std::vector models(1); models[0] = Eigen::umeyama(src_mat, dst_mat, kEstimateScale) .topLeftCorner(kDim, kDim + 1); return models; } template void SimilarityTransformEstimator::Residuals( const std::vector& src, const std::vector& dst, const M_t& matrix, std::vector* residuals) { CHECK_EQ(src.size(), dst.size()); residuals->resize(src.size()); for (size_t i = 0; i < src.size(); ++i) { const Y_t dst_transformed = matrix * src[i].homogeneous(); (*residuals)[i] = (dst[i] - dst_transformed).squaredNorm(); } } } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_SIMILARITY_TRANSFORM_H_ colmap-3.4/src/estimators/translation_transform.h000077500000000000000000000070111323400541200224120ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_BASE_SIMILARITY_TRANSFORM_H_ #define COLMAP_SRC_BASE_SIMILARITY_TRANSFORM_H_ #include #include #include #include "util/alignment.h" #include "util/logging.h" #include "util/types.h" namespace colmap { // Estimate a N-D translation transformation between point pairs. template class TranslationTransformEstimator { public: typedef Eigen::Matrix X_t; typedef Eigen::Matrix Y_t; typedef Eigen::Matrix M_t; // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 1; // Estimate the 2D translation transform. // // @param points1 Set of corresponding source 2D points. // @param points2 Set of corresponding destination 2D points. // // @return Translation vector. static std::vector Estimate(const std::vector& points1, const std::vector& points2); // Calculate the squared translation error. // // @param points1 Set of corresponding source 2D points. // @param points2 Set of corresponding destination 2D points. // @param translation Translation vector. // @param residuals Output vector of residuals for each point pair. static void Residuals(const std::vector& points1, const std::vector& points2, const M_t& translation, std::vector* residuals); }; //////////////////////////////////////////////////////////////////////////////// // Implementation //////////////////////////////////////////////////////////////////////////////// template std::vector::M_t> TranslationTransformEstimator::Estimate(const std::vector& points1, const std::vector& points2) { CHECK_EQ(points1.size(), points2.size()); X_t mean_src = X_t::Zero(); Y_t mean_dst = Y_t::Zero(); for (size_t i = 0; i < points1.size(); ++i) { mean_src += points1[i]; mean_dst += points2[i]; } mean_src /= points1.size(); mean_dst /= points2.size(); std::vector models(1); models[0] = mean_dst - mean_src; return models; } template void TranslationTransformEstimator::Residuals( const std::vector& points1, const std::vector& points2, const M_t& translation, std::vector* residuals) { CHECK_EQ(points1.size(), points2.size()); residuals->resize(points1.size()); for (size_t i = 0; i < points1.size(); ++i) { const M_t diff = points2[i] - points1[i] - translation; (*residuals)[i] = diff.squaredNorm(); } } } // namespace colmap #endif // COLMAP_SRC_BASE_SIMILARITY_TRANSFORM_H_ colmap-3.4/src/estimators/translation_transform_test.cc000077500000000000000000000036611323400541200236160ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/translation_transform" #include "util/testing.h" #include #include "estimators/translation_transform.h" #include "optim/ransac.h" #include "util/random.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestEstimate) { SetPRNGSeed(0); std::vector src; for (size_t i = 0; i < 100; ++i) { src.emplace_back(RandomReal(-1000.0, 1000.0), RandomReal(-1000.0, 1000.0)); } Eigen::Vector2d translation(RandomReal(-1000.0, 1000.0), RandomReal(-1000.0, 1000.0)); std::vector dst; for (size_t i = 0; i < src.size(); ++i) { dst.push_back(src[i] + translation); } const auto estimated_translation = TranslationTransformEstimator<2>::Estimate(src, dst)[0]; BOOST_CHECK_CLOSE(translation(0), estimated_translation(0), 1e-6); BOOST_CHECK_CLOSE(translation(1), estimated_translation(1), 1e-6); std::vector residuals; TranslationTransformEstimator<2>::Residuals(src, dst, estimated_translation, &residuals); for (size_t i = 0; i < residuals.size(); ++i) { BOOST_CHECK(residuals[i] < 1e-6); } } colmap-3.4/src/estimators/triangulation.cc000077500000000000000000000125131323400541200210020ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/triangulation.h" #include #include "base/projection.h" #include "base/triangulation.h" #include "estimators/essential_matrix.h" #include "optim/combination_sampler.h" #include "optim/loransac.h" #include "util/logging.h" #include "util/math.h" namespace colmap { void TriangulationEstimator::SetMinTriAngle(const double min_tri_angle) { CHECK_GE(min_tri_angle, 0); min_tri_angle_ = min_tri_angle; } void TriangulationEstimator::SetResidualType(const ResidualType residual_type) { residual_type_ = residual_type; } std::vector TriangulationEstimator::Estimate( const std::vector& point_data, const std::vector& pose_data) const { CHECK_GE(point_data.size(), 2); CHECK_EQ(point_data.size(), pose_data.size()); if (point_data.size() == 2) { // Two-view triangulation. const M_t xyz = TriangulatePoint( pose_data[0].proj_matrix, pose_data[1].proj_matrix, point_data[0].point_normalized, point_data[1].point_normalized); if (HasPointPositiveDepth(pose_data[0].proj_matrix, xyz) && HasPointPositiveDepth(pose_data[1].proj_matrix, xyz) && CalculateTriangulationAngle(pose_data[0].proj_center, pose_data[1].proj_center, xyz) >= min_tri_angle_) { return std::vector{xyz}; } } else { // Multi-view triangulation. std::vector proj_matrices; proj_matrices.reserve(point_data.size()); std::vector points; points.reserve(point_data.size()); for (size_t i = 0; i < point_data.size(); ++i) { proj_matrices.push_back(pose_data[i].proj_matrix); points.push_back(point_data[i].point_normalized); } const M_t xyz = TriangulateMultiViewPoint(proj_matrices, points); // Check for cheirality constraint. for (const auto& pose : pose_data) { if (!HasPointPositiveDepth(pose.proj_matrix, xyz)) { return std::vector(); } } // Check for sufficient triangulation angle. for (size_t i = 0; i < pose_data.size(); ++i) { for (size_t j = 0; j < i; ++j) { const double tri_angle = CalculateTriangulationAngle( pose_data[i].proj_center, pose_data[j].proj_center, xyz); if (tri_angle >= min_tri_angle_) { return std::vector{xyz}; } } } } return std::vector(); } void TriangulationEstimator::Residuals(const std::vector& point_data, const std::vector& pose_data, const M_t& xyz, std::vector* residuals) const { CHECK_EQ(point_data.size(), pose_data.size()); residuals->resize(point_data.size()); for (size_t i = 0; i < point_data.size(); ++i) { if (HasPointPositiveDepth(pose_data[i].proj_matrix, xyz)) { if (residual_type_ == ResidualType::REPROJECTION_ERROR) { (*residuals)[i] = CalculateReprojectionError(point_data[i].point, xyz, pose_data[i].proj_matrix, *pose_data[i].camera); } else if (residual_type_ == ResidualType::ANGULAR_ERROR) { (*residuals)[i] = CalculateAngularError(point_data[i].point_normalized, xyz, pose_data[i].proj_matrix); } } else { (*residuals)[i] = std::numeric_limits::max(); } } } bool EstimateTriangulation( const EstimateTriangulationOptions& options, const std::vector& point_data, const std::vector& pose_data, std::vector* inlier_mask, Eigen::Vector3d* xyz) { CHECK_NOTNULL(inlier_mask); CHECK_NOTNULL(xyz); CHECK_GE(point_data.size(), 2); CHECK_EQ(point_data.size(), pose_data.size()); options.Check(); // Robustly estimate track using LORANSAC. LORANSAC ransac(options.ransac_options); ransac.estimator.SetMinTriAngle(options.min_tri_angle); ransac.estimator.SetResidualType(options.residual_type); ransac.local_estimator.SetMinTriAngle(options.min_tri_angle); ransac.local_estimator.SetResidualType(options.residual_type); const auto report = ransac.Estimate(point_data, pose_data); if (!report.success) { return false; } *inlier_mask = report.inlier_mask; *xyz = report.model; return report.success; } } // namespace colmap colmap-3.4/src/estimators/triangulation.h000077500000000000000000000116241323400541200206460ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_TRIANGULATION_H_ #define COLMAP_SRC_ESTIMATORS_TRIANGULATION_H_ #include "base/camera.h" #include #include #include "optim/ransac.h" #include "util/alignment.h" #include "util/math.h" #include "util/types.h" namespace colmap { // Triangulation estimator to estimate 3D point from multiple observations. // The triangulation must satisfy the following constraints: // - Sufficient triangulation angle between observation pairs. // - All observations must satisfy cheirality constraint. // // An observation is composed of an image measurement and the corresponding // camera pose and calibration. class TriangulationEstimator { public: enum class ResidualType { ANGULAR_ERROR, REPROJECTION_ERROR, }; struct PointData { EIGEN_MAKE_ALIGNED_OPERATOR_NEW PointData() {} PointData(const Eigen::Vector2d& point_, const Eigen::Vector2d& point_N_) : point(point_), point_normalized(point_N_) {} // Image observation in pixels. Only needs to be set for REPROJECTION_ERROR. Eigen::Vector2d point; // Normalized image observation. Must always be set. Eigen::Vector2d point_normalized; }; struct PoseData { EIGEN_MAKE_ALIGNED_OPERATOR_NEW PoseData() : camera(nullptr) {} PoseData(const Eigen::Matrix3x4d& proj_matrix_, const Eigen::Vector3d& pose_, const Camera* camera_) : proj_matrix(proj_matrix_), proj_center(pose_), camera(camera_) {} // The projection matrix for the image of the observation. Eigen::Matrix3x4d proj_matrix; // The projection center for the image of the observation. Eigen::Vector3d proj_center; // The camera for the image of the observation. const Camera* camera; }; typedef PointData X_t; typedef PoseData Y_t; typedef Eigen::Vector3d M_t; // Specify settings for triangulation estimator. void SetMinTriAngle(const double min_tri_angle); void SetResidualType(const ResidualType residual_type); // The minimum number of samples needed to estimate a model. static const int kMinNumSamples = 2; // Estimate a 3D point from a two-view observation. // // @param point_data Image measurement. // @param point_data Camera poses. // // @return Triangulated point if successful, otherwise none. std::vector Estimate(const std::vector& point_data, const std::vector& pose_data) const; // Calculate residuals in terms of squared reprojection or angular error. // // @param point_data Image measurements. // @param point_data Camera poses. // @param xyz 3D point. // // @return Residual for each observation. void Residuals(const std::vector& point_data, const std::vector& pose_data, const M_t& xyz, std::vector* residuals) const; private: ResidualType residual_type_ = ResidualType::REPROJECTION_ERROR; double min_tri_angle_ = 0.0; }; struct EstimateTriangulationOptions { // Minimum triangulation angle in radians. double min_tri_angle = 0.0; // The employed residual type. TriangulationEstimator::ResidualType residual_type = TriangulationEstimator::ResidualType::ANGULAR_ERROR; // RANSAC options for TriangulationEstimator. RANSACOptions ransac_options; void Check() const { CHECK_GE(min_tri_angle, 0.0); ransac_options.Check(); } }; // Robustly estimate 3D point from observations in multiple views using RANSAC // and a subsequent non-linear refinement using all inliers. Returns true // if the estimated number of inliers has more than two views. bool EstimateTriangulation( const EstimateTriangulationOptions& options, const std::vector& point_data, const std::vector& pose_data, std::vector* inlier_mask, Eigen::Vector3d* xyz); } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM( colmap::TriangulationEstimator::PointData) EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM( colmap::TriangulationEstimator::PoseData) #endif // COLMAP_SRC_ESTIMATORS_TRIANGULATION_H_ colmap-3.4/src/estimators/two_view_geometry.cc000077500000000000000000000377311323400541200217110ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/two_view_geometry.h" #include "base/camera.h" #include "base/essential_matrix.h" #include "base/homography_matrix.h" #include "base/pose.h" #include "base/projection.h" #include "base/triangulation.h" #include "estimators/essential_matrix.h" #include "estimators/fundamental_matrix.h" #include "estimators/homography_matrix.h" #include "estimators/translation_transform.h" #include "optim/loransac.h" #include "optim/ransac.h" #include "util/random.h" namespace colmap { namespace { FeatureMatches ExtractInlierMatches(const FeatureMatches& matches, const size_t num_inliers, const std::vector& inlier_mask) { FeatureMatches inlier_matches(num_inliers); size_t j = 0; for (size_t i = 0; i < matches.size(); ++i) { if (inlier_mask[i]) { inlier_matches[j] = matches[i]; j += 1; } } return inlier_matches; } FeatureMatches ExtractOutlierMatches(const FeatureMatches& matches, const size_t num_inliers, const std::vector& inlier_mask) { FeatureMatches outlier_matches(matches.size() - num_inliers); size_t j = 0; for (size_t i = 0; i < matches.size(); ++i) { if (!inlier_mask[i]) { outlier_matches[j] = matches[i]; j += 1; } } return outlier_matches; } inline bool IsImagePointInBoundingBox(const Eigen::Vector2d& point, const double minx, const double maxx, const double miny, const double maxy) { return point(0) >= minx && point(0) <= maxx && point(1) >= miny && point(1) <= maxy; } } // namespace void TwoViewGeometry::Estimate(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options) { if (camera1.HasPriorFocalLength() && camera2.HasPriorFocalLength()) { EstimateCalibrated(camera1, points1, camera2, points2, matches, options); } else { EstimateUncalibrated(camera1, points1, camera2, points2, matches, options); } } void TwoViewGeometry::EstimateMultiple( const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options) { FeatureMatches remaining_matches = matches; std::vector two_view_geometries; while (true) { TwoViewGeometry two_view_geometry; two_view_geometry.Estimate(camera1, points1, camera2, points2, remaining_matches, options); if (two_view_geometry.config == ConfigurationType::DEGENERATE) { break; } if (options.multiple_ignore_watermark) { if (two_view_geometry.config != ConfigurationType::WATERMARK) { two_view_geometries.push_back(two_view_geometry); } } else { two_view_geometries.push_back(two_view_geometry); } remaining_matches = ExtractOutlierMatches( remaining_matches, two_view_geometry.inlier_matches.size(), two_view_geometry.inlier_mask); } if (two_view_geometries.empty()) { config = ConfigurationType::DEGENERATE; } else if (two_view_geometries.size() == 1) { *this = two_view_geometries[0]; } else { config = ConfigurationType::MULTIPLE; for (const auto& two_view_geometry : two_view_geometries) { inlier_matches.insert(inlier_matches.end(), two_view_geometry.inlier_matches.begin(), two_view_geometry.inlier_matches.end()); } } } void TwoViewGeometry::EstimateWithRelativePose( const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options) { // Warning: Do not change this call to another `Estimate*` method, since E is // need further down in this method. EstimateCalibrated(camera1, points1, camera2, points2, matches, options); // Extract normalized inlier points. std::vector inlier_points1_N; inlier_points1_N.reserve(inlier_matches.size()); std::vector inlier_points2_N; inlier_points2_N.reserve(inlier_matches.size()); for (const auto& match : inlier_matches) { const point2D_t idx1 = match.point2D_idx1; const point2D_t idx2 = match.point2D_idx2; inlier_points1_N.push_back(camera1.ImageToWorld(points1[idx1])); inlier_points2_N.push_back(camera2.ImageToWorld(points2[idx2])); } Eigen::Matrix3d R; std::vector points3D; if (config == CALIBRATED || config == UNCALIBRATED) { // Try to recover relative pose for calibrated and uncalibrated // configurations. In the uncalibrated case, this most likely leads to a // ill-defined reconstruction, but sometimes it succeeds anyways after e.g. // subsequent bundle-adjustment etc. PoseFromEssentialMatrix(E, inlier_points1_N, inlier_points2_N, &R, &tvec, &points3D); } else { Eigen::Vector3d n; PoseFromHomographyMatrix(H, camera1.CalibrationMatrix(), camera2.CalibrationMatrix(), inlier_points1_N, inlier_points2_N, &R, &tvec, &n, &points3D); } qvec = RotationMatrixToQuaternion(R); // Determine triangulation angle. const Eigen::Matrix3x4d proj_matrix1 = Eigen::Matrix3x4d::Identity(); const Eigen::Matrix3x4d proj_matrix2 = ComposeProjectionMatrix(R, tvec); if (points3D.empty()) { tri_angle = 0; } else { tri_angle = Median( CalculateTriangulationAngles(proj_matrix1, proj_matrix2, points3D)); } if (config == PLANAR_OR_PANORAMIC) { if (tvec.norm() == 0) { config = PANORAMIC; tri_angle = 0; } else { config = PLANAR; } } } void TwoViewGeometry::EstimateCalibrated( const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options) { options.Check(); if (matches.size() < options.min_num_inliers) { config = ConfigurationType::DEGENERATE; return; } // Extract corresponding points. std::vector matched_points1(matches.size()); std::vector matched_points2(matches.size()); std::vector matched_points1_N(matches.size()); std::vector matched_points2_N(matches.size()); for (size_t i = 0; i < matches.size(); ++i) { const point2D_t idx1 = matches[i].point2D_idx1; const point2D_t idx2 = matches[i].point2D_idx2; matched_points1[i] = points1[idx1]; matched_points2[i] = points2[idx2]; matched_points1_N[i] = camera1.ImageToWorld(points1[idx1]); matched_points2_N[i] = camera2.ImageToWorld(points2[idx2]); } // Estimate epipolar models. auto E_ransac_options = options.ransac_options; E_ransac_options.max_error = (camera1.ImageToWorldThreshold(options.ransac_options.max_error) + camera2.ImageToWorldThreshold(options.ransac_options.max_error)) / 2; LORANSAC E_ransac(E_ransac_options); const auto E_report = E_ransac.Estimate(matched_points1_N, matched_points2_N); E = E_report.model; E_num_inliers = E_report.support.num_inliers; LORANSAC F_ransac(options.ransac_options); const auto F_report = F_ransac.Estimate(matched_points1, matched_points2); F = F_report.model; F_num_inliers = F_report.support.num_inliers; // Estimate planar or panoramic model. LORANSAC H_ransac( options.ransac_options); const auto H_report = H_ransac.Estimate(matched_points1, matched_points2); H = H_report.model; H_num_inliers = H_report.support.num_inliers; if ((!E_report.success && !F_report.success && !H_report.success) || (E_num_inliers < options.min_num_inliers && F_num_inliers < options.min_num_inliers && H_num_inliers < options.min_num_inliers)) { config = ConfigurationType::DEGENERATE; return; } // Determine inlier ratios of different models. const double E_F_inlier_ratio = static_cast(E_num_inliers) / F_num_inliers; const double H_F_inlier_ratio = static_cast(H_num_inliers) / F_num_inliers; const double H_E_inlier_ratio = static_cast(H_num_inliers) / E_num_inliers; const std::vector* best_inlier_mask = nullptr; size_t num_inliers = 0; if (E_report.success && E_F_inlier_ratio > options.min_E_F_inlier_ratio && E_num_inliers >= options.min_num_inliers) { // Calibrated configuration. // Always use the model with maximum matches. if (E_num_inliers >= F_num_inliers) { num_inliers = E_num_inliers; best_inlier_mask = &E_report.inlier_mask; } else { num_inliers = F_num_inliers; best_inlier_mask = &F_report.inlier_mask; } if (H_E_inlier_ratio > options.max_H_inlier_ratio) { config = PLANAR_OR_PANORAMIC; if (H_num_inliers > num_inliers) { num_inliers = H_num_inliers; best_inlier_mask = &H_report.inlier_mask; } } else { config = ConfigurationType::CALIBRATED; } } else if (F_report.success && F_num_inliers >= options.min_num_inliers) { // Uncalibrated configuration. num_inliers = F_num_inliers; best_inlier_mask = &F_report.inlier_mask; if (H_F_inlier_ratio > options.max_H_inlier_ratio) { config = ConfigurationType::PLANAR_OR_PANORAMIC; if (H_num_inliers > num_inliers) { num_inliers = H_num_inliers; best_inlier_mask = &H_report.inlier_mask; } } else { config = ConfigurationType::UNCALIBRATED; } } else if (H_report.success && H_num_inliers >= options.min_num_inliers) { num_inliers = H_num_inliers; best_inlier_mask = &H_report.inlier_mask; config = ConfigurationType::PLANAR_OR_PANORAMIC; } else { config = ConfigurationType::DEGENERATE; return; } if (best_inlier_mask != nullptr) { inlier_matches = ExtractInlierMatches(matches, num_inliers, *best_inlier_mask); inlier_mask = *best_inlier_mask; if (options.detect_watermark && DetectWatermark(camera1, matched_points1, camera2, matched_points2, num_inliers, *best_inlier_mask, options)) { config = ConfigurationType::WATERMARK; } } } void TwoViewGeometry::EstimateUncalibrated( const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options) { options.Check(); if (matches.size() < options.min_num_inliers) { config = ConfigurationType::DEGENERATE; return; } // Extract corresponding points. std::vector matched_points1(matches.size()); std::vector matched_points2(matches.size()); for (size_t i = 0; i < matches.size(); ++i) { matched_points1[i] = points1[matches[i].point2D_idx1]; matched_points2[i] = points2[matches[i].point2D_idx2]; } // Estimate epipolar model. LORANSAC F_ransac(options.ransac_options); const auto F_report = F_ransac.Estimate(matched_points1, matched_points2); F = F_report.model; F_num_inliers = F_report.support.num_inliers; // Estimate planar or panoramic model. LORANSAC H_ransac( options.ransac_options); const auto H_report = H_ransac.Estimate(matched_points1, matched_points2); H = H_report.model; H_num_inliers = H_report.support.num_inliers; if ((!F_report.success && !H_report.success) || (F_num_inliers < options.min_num_inliers && H_num_inliers < options.min_num_inliers)) { config = ConfigurationType::DEGENERATE; return; } // Determine inlier ratios of different models. const double H_F_inlier_ratio = static_cast(H_num_inliers) / F_num_inliers; if (H_F_inlier_ratio > options.max_H_inlier_ratio) { config = ConfigurationType::PLANAR_OR_PANORAMIC; } else { config = ConfigurationType::UNCALIBRATED; } inlier_matches = ExtractInlierMatches(matches, F_num_inliers, F_report.inlier_mask); inlier_mask = F_report.inlier_mask; if (options.detect_watermark && DetectWatermark(camera1, matched_points1, camera2, matched_points2, F_num_inliers, F_report.inlier_mask, options)) { config = ConfigurationType::WATERMARK; } } bool TwoViewGeometry::DetectWatermark( const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const size_t num_inliers, const std::vector& inlier_mask, const Options& options) { options.Check(); // Check if inlier points in border region and extract inlier matches. const double diagonal1 = std::sqrt(camera1.Width() * camera1.Width() + camera1.Height() * camera1.Height()); const double diagonal2 = std::sqrt(camera2.Width() * camera2.Width() + camera2.Height() * camera2.Height()); const double minx1 = options.watermark_border_size * diagonal1; const double miny1 = minx1; const double maxx1 = camera1.Width() - minx1; const double maxy1 = camera1.Height() - miny1; const double minx2 = options.watermark_border_size * diagonal2; const double miny2 = minx2; const double maxx2 = camera2.Width() - minx2; const double maxy2 = camera2.Height() - miny2; std::vector inlier_points1(num_inliers); std::vector inlier_points2(num_inliers); size_t num_matches_in_border = 0; size_t j = 0; for (size_t i = 0; i < inlier_mask.size(); ++i) { if (inlier_mask[i]) { const auto& point1 = points1[i]; const auto& point2 = points2[i]; inlier_points1[j] = point1; inlier_points2[j] = point2; j += 1; if (!IsImagePointInBoundingBox(point1, minx1, maxx1, miny1, maxy1) && !IsImagePointInBoundingBox(point2, minx2, maxx2, miny2, maxy2)) { num_matches_in_border += 1; } } } const double matches_in_border_ratio = static_cast(num_matches_in_border) / num_inliers; if (matches_in_border_ratio < options.watermark_min_inlier_ratio) { return false; } // Check if matches follow a translational model. RANSACOptions ransac_options = options.ransac_options; ransac_options.min_inlier_ratio = options.watermark_min_inlier_ratio; LORANSAC, TranslationTransformEstimator<2>> ransac(ransac_options); const auto report = ransac.Estimate(inlier_points1, inlier_points2); const double inlier_ratio = static_cast(report.support.num_inliers) / num_inliers; return inlier_ratio >= options.watermark_min_inlier_ratio; } } // namespace colmap colmap-3.4/src/estimators/two_view_geometry.h000077500000000000000000000240271323400541200215450ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_TWO_VIEW_GEOMETRY_H_ #define COLMAP_SRC_ESTIMATORS_TWO_VIEW_GEOMETRY_H_ #include "base/camera.h" #include "feature/types.h" #include "optim/ransac.h" #include "util/alignment.h" #include "util/logging.h" namespace colmap { // Two-view geometry estimator. struct TwoViewGeometry { EIGEN_MAKE_ALIGNED_OPERATOR_NEW // The configuration of the estimated two-view geometry. enum ConfigurationType { UNDEFINED = 0, // Degenerate configuration (e.g., no overlap or not enough inliers). DEGENERATE = 1, // Essential matrix. CALIBRATED = 2, // Fundamental matrix. UNCALIBRATED = 3, // Homography, planar scene with baseline. PLANAR = 4, // Homography, pure rotation without baseline. PANORAMIC = 5, // Homography, planar or panoramic. PLANAR_OR_PANORAMIC = 6, // Watermark, pure 2D translation in image borders. WATERMARK = 7, // Multi-model configuration, i.e. the inlier matches result from multiple // individual, non-degenerate configurations. MULTIPLE = 8, }; // Estimation options. struct Options { // Minimum number of inliers for non-degenerate two-view geometry. size_t min_num_inliers = 15; // In case both cameras are calibrated, the calibration is verified by // estimating an essential and fundamental matrix and comparing their // fractions of number of inliers. If the essential matrix produces // a similar number of inliers (`min_E_F_inlier_ratio * F_num_inliers`), // the calibration is assumed to be correct. double min_E_F_inlier_ratio = 0.95; // In case an epipolar geometry can be verified, it is checked whether // the geometry describes a planar scene or panoramic view (pure rotation) // described by a homography. This is a degenerate case, since epipolar // geometry is only defined for a moving camera. If the inlier ratio of // a homography comes close to the inlier ratio of the epipolar geometry, // a planar or panoramic configuration is assumed. double max_H_inlier_ratio = 0.8; // In case of valid two-view geometry, it is checked whether the geometry // describes a pure translation in the border region of the image. If more // than a certain ratio of inlier points conform with a pure image // translation, a watermark is assumed. double watermark_min_inlier_ratio = 0.7; // Watermark matches have to be in the border region of the image. The // border region is defined as the area around the image borders and // is defined as a fraction of the image diagonal. double watermark_border_size = 0.1; // Whether to enable watermark detection. A watermark causes a pure // translation in the image space with inliers in the border region. bool detect_watermark = true; // Whether to ignore watermark models in multiple model estimation. bool multiple_ignore_watermark = true; // Options used to robustly estimate the geometry. RANSACOptions ransac_options; void Check() const { CHECK_GE(min_num_inliers, 0); CHECK_GE(min_E_F_inlier_ratio, 0); CHECK_LE(min_E_F_inlier_ratio, 1); CHECK_GE(max_H_inlier_ratio, 0); CHECK_LE(max_H_inlier_ratio, 1); CHECK_GE(watermark_min_inlier_ratio, 0); CHECK_LE(watermark_min_inlier_ratio, 1); CHECK_GE(watermark_border_size, 0); CHECK_LE(watermark_border_size, 1); ransac_options.Check(); } }; TwoViewGeometry() : config(ConfigurationType::UNDEFINED), E(Eigen::Matrix3d::Zero()), F(Eigen::Matrix3d::Zero()), H(Eigen::Matrix3d::Zero()), qvec(Eigen::Vector4d::Zero()), tvec(Eigen::Vector3d::Zero()), tri_angle(0), E_num_inliers(0), F_num_inliers(0), H_num_inliers(0) {} // Estimate two-view geometry from calibrated or uncalibrated image pair, // depending on whether a prior focal length is given or not. // // @param camera1 Camera of first image. // @param points1 Feature points in first image. // @param camera2 Camera of second image. // @param points2 Feature points in second image. // @param matches Feature matches between first and second image. // @param options Two-view geometry estimation options. void Estimate(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options); // Recursively estimate multiple configurations by removing the previous set // of inliers from the matches until not enough inliers are found. Inlier // matches are concatenated and the configuration type is `MULTIPLE` if // multiple models could be estimated. This is useful to estimate the two-view // geometry for images with large distortion or multiple rigidly moving // objects in the scene. // // Note that in case the model type is `MULTIPLE`, only the `inlier_matches` // field will be initialized. // // @param camera1 Camera of first image. // @param points1 Feature points in first image. // @param camera2 Camera of second image. // @param points2 Feature points in second image. // @param matches Feature matches between first and second image. // @param options Two-view geometry estimation options. void EstimateMultiple(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options); // Estimate two-view geometry and its relative pose from a calibrated or an // uncalibrated image pair. // // @param camera1 Camera of first image. // @param points1 Feature points in first image. // @param camera2 Camera of second image. // @param points2 Feature points in second image. // @param matches Feature matches between first and second image. // @param options Two-view geometry estimation options. void EstimateWithRelativePose(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options); // Estimate two-view geometry from calibrated image pair. // // @param camera1 Camera of first image. // @param points1 Feature points in first image. // @param camera2 Camera of second image. // @param points2 Feature points in second image. // @param matches Feature matches between first and second image. // @param options Two-view geometry estimation options. void EstimateCalibrated(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options); // Estimate two-view geometry from uncalibrated image pair. // // @param camera1 Camera of first image. // @param points1 Feature points in first image. // @param camera2 Camera of second image. // @param points2 Feature points in second image. // @param matches Feature matches between first and second image. // @param options Two-view geometry estimation options. void EstimateUncalibrated(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const FeatureMatches& matches, const Options& options); // Detect if inlier matches are caused by a watermark. // A watermark causes a pure translation in the border are of the image. static bool DetectWatermark(const Camera& camera1, const std::vector& points1, const Camera& camera2, const std::vector& points2, const size_t num_inliers, const std::vector& inlier_mask, const Options& options); // One of `ConfigurationType`. int config; // Essential matrix. Eigen::Matrix3d E; // Fundamental matrix. Eigen::Matrix3d F; // Homography matrix. Eigen::Matrix3d H; // Relative pose. Eigen::Vector4d qvec; Eigen::Vector3d tvec; // Inlier matches of the configuration. FeatureMatches inlier_matches; std::vector inlier_mask; // Median triangulation angle. double tri_angle; // Number of inliers. size_t E_num_inliers; size_t F_num_inliers; size_t H_num_inliers; }; } // namespace colmap EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION_CUSTOM(colmap::TwoViewGeometry) #endif // COLMAP_SRC_ESTIMATORS_TWO_VIEW_GEOMETRY_H_ colmap-3.4/src/estimators/utils.cc000077500000000000000000000135711323400541200172670ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include "estimators/utils.h" #include "util/logging.h" namespace colmap { void CenterAndNormalizeImagePoints(const std::vector& points, std::vector* normed_points, Eigen::Matrix3d* matrix) { // Calculate centroid Eigen::Vector2d centroid(0, 0); for (const auto point : points) { centroid += point; } centroid /= points.size(); // Root mean square error to centroid of all points double rms_mean_dist = 0; for (const auto point : points) { rms_mean_dist += (point - centroid).squaredNorm(); } rms_mean_dist = std::sqrt(rms_mean_dist / points.size()); // Compose normalization matrix const double norm_factor = std::sqrt(2.0) / rms_mean_dist; *matrix << norm_factor, 0, -norm_factor * centroid(0), 0, norm_factor, -norm_factor * centroid(1), 0, 0, 1; // Apply normalization matrix normed_points->resize(points.size()); const double M_00 = (*matrix)(0, 0); const double M_01 = (*matrix)(0, 1); const double M_02 = (*matrix)(0, 2); const double M_10 = (*matrix)(1, 0); const double M_11 = (*matrix)(1, 1); const double M_12 = (*matrix)(1, 2); const double M_20 = (*matrix)(2, 0); const double M_21 = (*matrix)(2, 1); const double M_22 = (*matrix)(2, 2); for (size_t i = 0; i < points.size(); ++i) { const double p_0 = points[i](0); const double p_1 = points[i](1); const double np_0 = M_00 * p_0 + M_01 * p_1 + M_02; const double np_1 = M_10 * p_0 + M_11 * p_1 + M_12; const double np_2 = M_20 * p_0 + M_21 * p_1 + M_22; const double inv_np_2 = 1.0 / np_2; (*normed_points)[i](0) = np_0 * inv_np_2; (*normed_points)[i](1) = np_1 * inv_np_2; } } void ComputeSquaredSampsonError(const std::vector& points1, const std::vector& points2, const Eigen::Matrix3d& E, std::vector* residuals) { CHECK_EQ(points1.size(), points2.size()); residuals->resize(points1.size()); // Note that this code might not be as nice as Eigen expressions, // but it is significantly faster in various tests const double E_00 = E(0, 0); const double E_01 = E(0, 1); const double E_02 = E(0, 2); const double E_10 = E(1, 0); const double E_11 = E(1, 1); const double E_12 = E(1, 2); const double E_20 = E(2, 0); const double E_21 = E(2, 1); const double E_22 = E(2, 2); for (size_t i = 0; i < points1.size(); ++i) { const double x1_0 = points1[i](0); const double x1_1 = points1[i](1); const double x2_0 = points2[i](0); const double x2_1 = points2[i](1); // Ex1 = E * points1[i].homogeneous(); const double Ex1_0 = E_00 * x1_0 + E_01 * x1_1 + E_02; const double Ex1_1 = E_10 * x1_0 + E_11 * x1_1 + E_12; const double Ex1_2 = E_20 * x1_0 + E_21 * x1_1 + E_22; // Etx2 = E.transpose() * points2[i].homogeneous(); const double Etx2_0 = E_00 * x2_0 + E_10 * x2_1 + E_20; const double Etx2_1 = E_01 * x2_0 + E_11 * x2_1 + E_21; // x2tEx1 = points2[i].homogeneous().transpose() * Ex1; const double x2tEx1 = x2_0 * Ex1_0 + x2_1 * Ex1_1 + Ex1_2; // Sampson distance (*residuals)[i] = x2tEx1 * x2tEx1 / (Ex1_0 * Ex1_0 + Ex1_1 * Ex1_1 + Etx2_0 * Etx2_0 + Etx2_1 * Etx2_1); } } void ComputeSquaredReprojectionError( const std::vector& points2D, const std::vector& points3D, const Eigen::Matrix3x4d& proj_matrix, std::vector* residuals) { CHECK_EQ(points2D.size(), points3D.size()); residuals->resize(points2D.size()); // Note that this code might not be as nice as Eigen expressions, // but it is significantly faster in various tests. const double P_00 = proj_matrix(0, 0); const double P_01 = proj_matrix(0, 1); const double P_02 = proj_matrix(0, 2); const double P_03 = proj_matrix(0, 3); const double P_10 = proj_matrix(1, 0); const double P_11 = proj_matrix(1, 1); const double P_12 = proj_matrix(1, 2); const double P_13 = proj_matrix(1, 3); const double P_20 = proj_matrix(2, 0); const double P_21 = proj_matrix(2, 1); const double P_22 = proj_matrix(2, 2); const double P_23 = proj_matrix(2, 3); for (size_t i = 0; i < points2D.size(); ++i) { const double X_0 = points3D[i](0); const double X_1 = points3D[i](1); const double X_2 = points3D[i](2); // Project 3D point from world to camera. const double px_2 = P_20 * X_0 + P_21 * X_1 + P_22 * X_2 + P_23; // Check if 3D point is in front of camera. if (px_2 > std::numeric_limits::epsilon()) { const double px_0 = P_00 * X_0 + P_01 * X_1 + P_02 * X_2 + P_03; const double px_1 = P_10 * X_0 + P_11 * X_1 + P_12 * X_2 + P_13; const double x_0 = points2D[i](0); const double x_1 = points2D[i](1); const double inv_px_2 = 1.0 / px_2; const double dx_0 = x_0 - px_0 * inv_px_2; const double dx_1 = x_1 - px_1 * inv_px_2; (*residuals)[i] = dx_0 * dx_0 + dx_1 * dx_1; } else { (*residuals)[i] = std::numeric_limits::max(); } } } } // namespace colmap colmap-3.4/src/estimators/utils.h000077500000000000000000000061701323400541200171260ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #ifndef COLMAP_SRC_ESTIMATORS_UTILS_H_ #define COLMAP_SRC_ESTIMATORS_UTILS_H_ #include #include #include "util/alignment.h" #include "util/types.h" namespace colmap { // Center and normalize image points. // // The points are transformed in a two-step procedure that is expressed // as a transformation matrix. The matrix of the resulting points is usually // better conditioned than the matrix of the original points. // // Center the image points, such that the new coordinate system has its // origin at the centroid of the image points. // // Normalize the image points, such that the mean distance from the points // to the coordinate system is sqrt(2). // // @param points Image coordinates. // @param normed_points Transformed image coordinates. // @param matrix 3x3 transformation matrix. void CenterAndNormalizeImagePoints(const std::vector& points, std::vector* normed_points, Eigen::Matrix3d* matrix); // Calculate the residuals of a set of corresponding points and a given // fundamental or essential matrix. // // Residuals are defined as the squared Sampson error. // // @param points1 First set of corresponding points as Nx2 matrix. // @param points2 Second set of corresponding points as Nx2 matrix. // @param E 3x3 fundamental or essential matrix. // @param residuals Output vector of residuals. void ComputeSquaredSampsonError(const std::vector& points1, const std::vector& points2, const Eigen::Matrix3d& E, std::vector* residuals); // Calculate the squared reprojection error given a set of 2D-3D point // correspondences and a projection matrix. Returns DBL_MAX if a 3D point is // behind the given camera. // // @param points2D Normalized 2D image points. // @param points3D 3D world points. // @param proj_matrix 3x4 projection matrix. // @param residuals Output vector of residuals. void ComputeSquaredReprojectionError( const std::vector& points2D, const std::vector& points3D, const Eigen::Matrix3x4d& proj_matrix, std::vector* residuals); } // namespace colmap #endif // COLMAP_SRC_ESTIMATORS_UTILS_H_ colmap-3.4/src/estimators/utils_test.cc000077500000000000000000000045511323400541200203240ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #define TEST_NAME "estimators/utils" #include "util/testing.h" #include "base/essential_matrix.h" #include "estimators/utils.h" using namespace colmap; BOOST_AUTO_TEST_CASE(TestCenterAndNormalizeImagePoints) { std::vector points; for (size_t i = 0; i < 11; ++i) { points.emplace_back(i, i); } std::vector normed_points; Eigen::Matrix3d matrix; CenterAndNormalizeImagePoints(points, &normed_points, &matrix); BOOST_CHECK_EQUAL(matrix(0, 0), 0.31622776601683794); BOOST_CHECK_EQUAL(matrix(1, 1), 0.31622776601683794); BOOST_CHECK_EQUAL(matrix(0, 2), -1.5811388300841898); BOOST_CHECK_EQUAL(matrix(1, 2), -1.5811388300841898); Eigen::Vector2d mean_point(0, 0); for (const auto& point : normed_points) { mean_point += point; } BOOST_CHECK_LT(std::abs(mean_point[0]), 1e-6); BOOST_CHECK_LT(std::abs(mean_point[1]), 1e-6); } BOOST_AUTO_TEST_CASE(TestComputeSquaredSampsonError) { std::vector points1; points1.emplace_back(0, 0); points1.emplace_back(0, 0); points1.emplace_back(0, 0); std::vector points2; points2.emplace_back(2, 0); points2.emplace_back(2, 1); points2.emplace_back(2, 2); const Eigen::Matrix3d E = EssentialMatrixFromPose(Eigen::Matrix3d::Identity(), Eigen::Vector3d(1, 0, 0)); std::vector residuals; ComputeSquaredSampsonError(points1, points2, E, &residuals); BOOST_CHECK_EQUAL(residuals.size(), 3); BOOST_CHECK_EQUAL(residuals[0], 0); BOOST_CHECK_EQUAL(residuals[1], 0.5); BOOST_CHECK_EQUAL(residuals[2], 2); } colmap-3.4/src/exe/000077500000000000000000000000001323400541200141755ustar00rootroot00000000000000colmap-3.4/src/exe/CMakeLists.txt000077500000000000000000000002351323400541200167400ustar00rootroot00000000000000set(FOLDER_NAME "exe") COLMAP_ADD_EXECUTABLE(colmap colmap.cc) if(CUDA_ENABLED) target_include_directories(colmap PUBLIC ${CUDA_INCLUDE_DIRS}) endif() colmap-3.4/src/exe/colmap.cc000077500000000000000000001606771323400541200160030ustar00rootroot00000000000000// COLMAP - Structure-from-Motion and Multi-View Stereo. // Copyright (C) 2017 Johannes L. Schoenberger // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with this program. If not, see . #include #include #include "controllers/automatic_reconstruction.h" #include "controllers/bundle_adjustment.h" #include "estimators/coordinate_frame.h" #include "feature/extraction.h" #include "feature/matching.h" #include "feature/utils.h" #include "mvs/meshing.h" #include "mvs/patch_match.h" #include "retrieval/visual_index.h" #include "ui/main_window.h" #include "util/opengl_utils.h" #include "util/version.h" using namespace colmap; #ifdef CUDA_ENABLED const bool kUseOpenGL = false; #else const bool kUseOpenGL = true; #endif int RunGraphicalUserInterface(int argc, char** argv) { OptionManager options; if (argc > 1) { options.AddAllOptions(); options.Parse(argc, argv); } #if (QT_VERSION >= QT_VERSION_CHECK(5, 6, 0)) QApplication::setAttribute(Qt::AA_EnableHighDpiScaling); #endif Q_INIT_RESOURCE(resources); QApplication app(argc, argv); MainWindow main_window(options); main_window.show(); return app.exec(); } int RunAutomaticReconstructor(int argc, char** argv) { AutomaticReconstructionController::Options reconstruction_options; std::string data_type = "individual"; std::string quality = "high"; OptionManager options; options.AddRequiredOption("workspace_path", &reconstruction_options.workspace_path); options.AddRequiredOption("image_path", &reconstruction_options.image_path); options.AddDefaultOption("vocab_tree_path", &reconstruction_options.vocab_tree_path); options.AddDefaultOption("data_type", &data_type, "{individual, video, internet}"); options.AddDefaultOption("quality", &quality, "{low, medium, high}"); options.AddDefaultOption("camera_model", &reconstruction_options.camera_model); options.AddDefaultOption("single_camera", &reconstruction_options.single_camera); options.AddDefaultOption("sparse", &reconstruction_options.sparse); options.AddDefaultOption("dense", &reconstruction_options.dense); options.AddDefaultOption("num_threads", &reconstruction_options.num_threads); options.AddDefaultOption("use_gpu", &reconstruction_options.use_gpu); options.AddDefaultOption("gpu_index", &reconstruction_options.gpu_index); options.Parse(argc, argv); StringToLower(&data_type); if (data_type == "individual") { reconstruction_options.data_type = AutomaticReconstructionController::DataType::INDIVIDUAL; } else if (data_type == "video") { reconstruction_options.data_type = AutomaticReconstructionController::DataType::VIDEO; } else if (data_type == "internet") { reconstruction_options.data_type = AutomaticReconstructionController::DataType::INTERNET; } else { LOG(FATAL) << "Invalid data type"; } StringToLower(&quality); if (quality == "low") { reconstruction_options.quality = AutomaticReconstructionController::Quality::LOW; } else if (quality == "medium") { reconstruction_options.quality = AutomaticReconstructionController::Quality::MEDIUM; } else if (quality == "high") { reconstruction_options.quality = AutomaticReconstructionController::Quality::HIGH; } else { LOG(FATAL) << "Invalid data type"; } ReconstructionManager reconstruction_manager; if (reconstruction_options.use_gpu && kUseOpenGL) { QApplication app(argc, argv); AutomaticReconstructionController controller(reconstruction_options, &reconstruction_manager); RunThreadWithOpenGLContext(&controller); } else { AutomaticReconstructionController controller(reconstruction_options, &reconstruction_manager); controller.Start(); controller.Wait(); } return EXIT_SUCCESS; } int RunBundleAdjuster(int argc, char** argv) { std::string input_path; std::string output_path; OptionManager options; options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddBundleAdjustmentOptions(); options.Parse(argc, argv); Reconstruction reconstruction; reconstruction.Read(input_path); BundleAdjustmentController ba_controller(options, &reconstruction); ba_controller.Start(); ba_controller.Wait(); reconstruction.Write(output_path); return EXIT_SUCCESS; } int RunColorExtractor(int argc, char** argv) { std::string import_path; std::string export_path; OptionManager options; options.AddImageOptions(); options.AddDefaultOption("import_path", &import_path); options.AddRequiredOption("export_path", &export_path); options.Parse(argc, argv); Reconstruction reconstruction; reconstruction.Read(import_path); reconstruction.ExtractColorsForAllImages(*options.image_path); reconstruction.Write(export_path); return EXIT_SUCCESS; } int RunDatabaseCreator(int argc, char** argv) { OptionManager options; options.AddDatabaseOptions(); options.Parse(argc, argv); Database database(*options.database_path); return EXIT_SUCCESS; } int RunDenseFuser(int argc, char** argv) { std::string workspace_path; std::string input_type = "geometric"; std::string workspace_format = "COLMAP"; std::string pmvs_option_name = "option-all"; std::string output_path; OptionManager options; options.AddRequiredOption("workspace_path", &workspace_path); options.AddDefaultOption("workspace_format", &workspace_format, "{COLMAP, PMVS}"); options.AddDefaultOption("pmvs_option_name", &pmvs_option_name); options.AddDefaultOption("input_type", &input_type, "{photometric, geometric}"); options.AddRequiredOption("output_path", &output_path); options.AddDenseFusionOptions(); options.Parse(argc, argv); StringToLower(&workspace_format); if (workspace_format != "colmap" && workspace_format != "pmvs") { std::cout << "ERROR: Invalid `workspace_format` - supported values are " "'COLMAP' or 'PMVS'." << std::endl; return EXIT_FAILURE; } StringToLower(&input_type); if (input_type != "photometric" && input_type != "geometric") { std::cout << "ERROR: Invalid input type - supported values are " "'photometric' and 'geometric'." << std::endl; return EXIT_FAILURE; } mvs::StereoFusion fuser(*options.dense_fusion, workspace_path, workspace_format, pmvs_option_name, input_type); fuser.Start(); fuser.Wait(); std::cout << "Writing output: " << output_path << std::endl; WritePlyBinary(output_path, fuser.GetFusedPoints()); return EXIT_SUCCESS; } int RunDenseMesher(int argc, char** argv) { std::string input_path; std::string output_path; OptionManager options; options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddDenseMeshingOptions(); options.Parse(argc, argv); CHECK(mvs::PoissonReconstruction(*options.dense_meshing, input_path, output_path)); return EXIT_SUCCESS; } int RunDenseStereo(int argc, char** argv) { #ifndef CUDA_ENABLED std::cerr << "ERROR: Dense stereo reconstruction requires CUDA, which is not " "available on your system." << std::endl; return EXIT_FAILURE; #else // CUDA_ENABLED std::string workspace_path; std::string workspace_format = "COLMAP"; std::string pmvs_option_name = "option-all"; OptionManager options; options.AddRequiredOption("workspace_path", &workspace_path); options.AddDefaultOption("workspace_format", &workspace_format, "{COLMAP, PMVS}"); options.AddDefaultOption("pmvs_option_name", &pmvs_option_name); options.AddDenseStereoOptions(); options.Parse(argc, argv); StringToLower(&workspace_format); if (workspace_format != "colmap" && workspace_format != "pmvs") { std::cout << "ERROR: Invalid `workspace_format` - supported values are " "'COLMAP' or 'PMVS'." << std::endl; return EXIT_FAILURE; } mvs::PatchMatchController controller(*options.dense_stereo, workspace_path, workspace_format, pmvs_option_name); controller.Start(); controller.Wait(); return EXIT_SUCCESS; #endif // CUDA_ENABLED } int RunExhaustiveMatcher(int argc, char** argv) { OptionManager options; options.AddDatabaseOptions(); options.AddExhaustiveMatchingOptions(); options.Parse(argc, argv); std::unique_ptr app; if (options.sift_matching->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } ExhaustiveFeatureMatcher feature_matcher(*options.exhaustive_matching, *options.sift_matching, *options.database_path); if (options.sift_matching->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(&feature_matcher); } else { feature_matcher.Start(); feature_matcher.Wait(); } return EXIT_SUCCESS; } int RunFeatureExtractor(int argc, char** argv) { std::string image_list_path; OptionManager options; options.AddDatabaseOptions(); options.AddImageOptions(); options.AddDefaultOption("image_list_path", &image_list_path); options.AddExtractionOptions(); options.Parse(argc, argv); ImageReaderOptions reader_options = *options.image_reader; reader_options.database_path = *options.database_path; reader_options.image_path = *options.image_path; if (!image_list_path.empty()) { reader_options.image_list = ReadTextFileLines(image_list_path); if (reader_options.image_list.empty()) { return EXIT_SUCCESS; } } if (!ExistsCameraModelWithName(options.image_reader->camera_model)) { std::cerr << "ERROR: Camera model does not exist" << std::endl; } const std::vector camera_params = CSVToVector(options.image_reader->camera_params); const int camera_model_id = CameraModelNameToId(options.image_reader->camera_model); if (camera_params.size() > 0 && !CameraModelVerifyParams(camera_model_id, camera_params)) { std::cerr << "ERROR: Invalid camera parameters" << std::endl; return EXIT_FAILURE; } std::unique_ptr app; if (options.sift_extraction->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } SiftFeatureExtractor feature_extractor(reader_options, *options.sift_extraction); if (options.sift_extraction->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(&feature_extractor); } else { feature_extractor.Start(); feature_extractor.Wait(); } return EXIT_SUCCESS; } int RunFeatureImporter(int argc, char** argv) { std::string import_path; std::string image_list_path; OptionManager options; options.AddDatabaseOptions(); options.AddImageOptions(); options.AddRequiredOption("import_path", &import_path); options.AddDefaultOption("image_list_path", &image_list_path); options.AddExtractionOptions(); options.Parse(argc, argv); ImageReaderOptions reader_options = *options.image_reader; reader_options.database_path = *options.database_path; reader_options.image_path = *options.image_path; if (!image_list_path.empty()) { reader_options.image_list = ReadTextFileLines(image_list_path); if (reader_options.image_list.empty()) { return EXIT_SUCCESS; } } const std::vector camera_params = CSVToVector(options.image_reader->camera_params); const int camera_model_id = CameraModelNameToId(options.image_reader->camera_model); if (camera_params.size() > 0 && !CameraModelVerifyParams(camera_model_id, camera_params)) { std::cerr << "ERROR: Invalid camera parameters" << std::endl; return EXIT_FAILURE; } FeatureImporter feature_importer(reader_options, import_path); feature_importer.Start(); feature_importer.Wait(); return EXIT_SUCCESS; } // Read stereo image pair names from a text file. The text file is expected to // have one image pair per line, e.g.: // // image_name1.jpg image_name2.jpg // image_name3.jpg image_name4.jpg // image_name5.jpg image_name6.jpg // ... // std::vector> ReadStereoImagePairs( const std::string& path, const Reconstruction& reconstruction) { const std::vector stereo_pair_lines = ReadTextFileLines(path); std::vector> stereo_pairs; stereo_pairs.reserve(stereo_pair_lines.size()); for (const auto& line : stereo_pair_lines) { const std::vector names = StringSplit(line, " "); CHECK_EQ(names.size(), 2); const Image* image1 = reconstruction.FindImageWithName(names[0]); const Image* image2 = reconstruction.FindImageWithName(names[1]); CHECK_NOTNULL(image1); CHECK_NOTNULL(image2); stereo_pairs.emplace_back(image1->ImageId(), image2->ImageId()); } return stereo_pairs; } int RunImageRectifier(int argc, char** argv) { std::string input_path; std::string output_path; std::string stereo_pairs_list; UndistortCameraOptions undistort_camera_options; OptionManager options; options.AddImageOptions(); options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddRequiredOption("stereo_pairs_list", &stereo_pairs_list); options.AddDefaultOption("blank_pixels", &undistort_camera_options.blank_pixels); options.AddDefaultOption("min_scale", &undistort_camera_options.min_scale); options.AddDefaultOption("max_scale", &undistort_camera_options.max_scale); options.AddDefaultOption("max_image_size", &undistort_camera_options.max_image_size); options.Parse(argc, argv); Reconstruction reconstruction; reconstruction.Read(input_path); const auto stereo_pairs = ReadStereoImagePairs(stereo_pairs_list, reconstruction); StereoImageRectifier rectifier(undistort_camera_options, reconstruction, *options.image_path, output_path, stereo_pairs); rectifier.Start(); rectifier.Wait(); return EXIT_SUCCESS; } int RunImageRegistrator(int argc, char** argv) { std::string import_path; std::string export_path; OptionManager options; options.AddDatabaseOptions(); options.AddRequiredOption("import_path", &import_path); options.AddRequiredOption("export_path", &export_path); options.AddMapperOptions(); options.Parse(argc, argv); if (!ExistsDir(import_path)) { std::cerr << "ERROR: `import_path` is not a directory" << std::endl; return EXIT_FAILURE; } if (!ExistsDir(export_path)) { std::cerr << "ERROR: `export_path` is not a directory" << std::endl; return EXIT_FAILURE; } PrintHeading1("Loading database"); DatabaseCache database_cache; { Database database(*options.database_path); Timer timer; timer.Start(); const size_t min_num_matches = static_cast(options.mapper->min_num_matches); database_cache.Load(database, min_num_matches, options.mapper->ignore_watermarks, options.mapper->image_names); std::cout << std::endl; timer.PrintMinutes(); } std::cout << std::endl; Reconstruction reconstruction; reconstruction.Read(import_path); IncrementalMapper mapper(&database_cache); mapper.BeginReconstruction(&reconstruction); const auto mapper_options = options.mapper->Mapper(); for (const auto& image : reconstruction.Images()) { if (image.second.IsRegistered()) { continue; } PrintHeading1("Registering image #" + std::to_string(image.first) + " (" + std::to_string(reconstruction.NumRegImages() + 1) + ")"); std::cout << " => Image sees " << image.second.NumVisiblePoints3D() << " / " << image.second.NumObservations() << " points" << std::endl; mapper.RegisterNextImage(mapper_options, image.first); } const bool kDiscardReconstruction = false; mapper.EndReconstruction(kDiscardReconstruction); reconstruction.Write(export_path); return EXIT_SUCCESS; } int RunImageUndistorter(int argc, char** argv) { std::string input_path; std::string output_path; std::string output_type = "COLMAP"; UndistortCameraOptions undistort_camera_options; OptionManager options; options.AddImageOptions(); options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddDefaultOption("output_type", &output_type); options.AddDefaultOption("blank_pixels", &undistort_camera_options.blank_pixels); options.AddDefaultOption("min_scale", &undistort_camera_options.min_scale); options.AddDefaultOption("max_scale", &undistort_camera_options.max_scale); options.AddDefaultOption("max_image_size", &undistort_camera_options.max_image_size); options.Parse(argc, argv); CreateDirIfNotExists(output_path); Reconstruction reconstruction; reconstruction.Read(input_path); std::unique_ptr undistorter; if (output_type == "COLMAP") { undistorter.reset(new COLMAPUndistorter(undistort_camera_options, reconstruction, *options.image_path, output_path)); } else if (output_type == "PMVS") { undistorter.reset(new PMVSUndistorter(undistort_camera_options, reconstruction, *options.image_path, output_path)); } else if (output_type == "CMP-MVS") { undistorter.reset(new CMPMVSUndistorter(undistort_camera_options, reconstruction, *options.image_path, output_path)); } else { std::cerr << "ERROR: Invalid `output_type` - supported values are " "{'COLMAP', 'PMVS', 'CMP-MVS'}." << std::endl; return EXIT_FAILURE; } undistorter->Start(); undistorter->Wait(); return EXIT_SUCCESS; } int RunMapper(int argc, char** argv) { std::string import_path; std::string export_path; std::string image_list_path; OptionManager options; options.AddDatabaseOptions(); options.AddImageOptions(); options.AddDefaultOption("import_path", &import_path); options.AddRequiredOption("export_path", &export_path); options.AddDefaultOption("image_list_path", &image_list_path); options.AddMapperOptions(); options.Parse(argc, argv); if (!ExistsDir(export_path)) { std::cerr << "ERROR: `export_path` is not a directory." << std::endl; return EXIT_FAILURE; } if (!image_list_path.empty()) { const auto image_names = ReadTextFileLines(image_list_path); options.mapper->image_names = std::set(image_names.begin(), image_names.end()); } ReconstructionManager reconstruction_manager; if (import_path != "") { if (!ExistsDir(import_path)) { std::cerr << "ERROR: `import_path` is not a directory." << std::endl; return EXIT_FAILURE; } reconstruction_manager.Read(import_path); } IncrementalMapperController mapper(options.mapper.get(), *options.image_path, *options.database_path, &reconstruction_manager); // In case a new reconstruction is started, write results of individual sub- // models to as their reconstruction finishes instead of writing all results // after all reconstructions finished. size_t prev_num_reconstructions = 0; if (import_path == "") { mapper.AddCallback( IncrementalMapperController::LAST_IMAGE_REG_CALLBACK, [&]() { // If the number of reconstructions has not changed, the last model // was discarded for some reason. if (reconstruction_manager.Size() > prev_num_reconstructions) { const std::string reconstruction_path = JoinPaths( export_path, std::to_string(prev_num_reconstructions)); const auto& reconstruction = reconstruction_manager.Get(prev_num_reconstructions); CreateDirIfNotExists(reconstruction_path); reconstruction.Write(reconstruction_path); options.Write(JoinPaths(reconstruction_path, "project.ini")); prev_num_reconstructions = reconstruction_manager.Size(); } }); } mapper.Start(); mapper.Wait(); // In case the reconstruction is continued from an existing reconstruction, do // not create sub-folders but directly write the results. if (import_path != "" && reconstruction_manager.Size() > 0) { reconstruction_manager.Get(0).Write(export_path); } return EXIT_SUCCESS; } int RunMatchesImporter(int argc, char** argv) { std::string match_list_path; std::string match_type = "pairs"; OptionManager options; options.AddDatabaseOptions(); options.AddRequiredOption("match_list_path", &match_list_path); options.AddDefaultOption("match_type", &match_type, "{'pairs', 'raw', 'inliers'}"); options.AddMatchingOptions(); options.Parse(argc, argv); std::unique_ptr app; if (options.sift_matching->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } std::unique_ptr feature_matcher; if (match_type == "pairs") { ImagePairsMatchingOptions matcher_options; matcher_options.match_list_path = match_list_path; feature_matcher.reset(new ImagePairsFeatureMatcher( matcher_options, *options.sift_matching, *options.database_path)); } else if (match_type == "raw" || match_type == "inliers") { FeaturePairsMatchingOptions matcher_options; matcher_options.match_list_path = match_list_path; matcher_options.verify_matches = match_type == "raw"; feature_matcher.reset(new FeaturePairsFeatureMatcher( matcher_options, *options.sift_matching, *options.database_path)); } else { std::cerr << "ERROR: Invalid `match_type`"; return EXIT_FAILURE; } if (options.sift_matching->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(feature_matcher.get()); } else { feature_matcher->Start(); feature_matcher->Wait(); } return EXIT_SUCCESS; } int RunModelAligner(int argc, char** argv) { std::string input_path; std::string ref_images_path; std::string output_path; int min_common_images = 3; bool robust_alignment = true; RANSACOptions ransac_options; OptionManager options; options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("ref_images_path", &ref_images_path); options.AddRequiredOption("output_path", &output_path); options.AddDefaultOption("min_common_images", &min_common_images); options.AddDefaultOption("robust_alignment", &robust_alignment); options.AddDefaultOption("robust_alignment_max_error", &ransac_options.max_error); options.Parse(argc, argv); if (robust_alignment && ransac_options.max_error <= 0) { std::cout << "ERROR: You must provide a maximum alignment error > 0" << std::endl; return EXIT_FAILURE; } std::vector ref_image_names; std::vector ref_locations; std::vector lines = ReadTextFileLines(ref_images_path); for (const auto line : lines) { std::stringstream line_parser(line); std::string image_name = ""; Eigen::Vector3d camera_position; line_parser >> image_name >> camera_position[0] >> camera_position[1] >> camera_position[2]; ref_image_names.push_back(image_name); ref_locations.push_back(camera_position); } Reconstruction reconstruction; reconstruction.Read(input_path); PrintHeading2("Aligning reconstruction"); std::cout << StringPrintf(" => Using %d reference images", ref_image_names.size()) << std::endl; bool alignment_success; if (robust_alignment) { alignment_success = reconstruction.AlignRobust( ref_image_names, ref_locations, min_common_images, ransac_options); } else { alignment_success = reconstruction.Align(ref_image_names, ref_locations, min_common_images); } if (alignment_success) { std::cout << " => Alignment succeeded" << std::endl; reconstruction.Write(output_path); std::vector errors; errors.reserve(ref_image_names.size()); for (size_t i = 0; i < ref_image_names.size(); ++i) { const Image* image = reconstruction.FindImageWithName(ref_image_names[i]); if (image != nullptr) { errors.push_back((image->ProjectionCenter() - ref_locations[i]).norm()); } } std::cout << StringPrintf(" => Alignment error: %f (mean), %f (median)", Mean(errors), Median(errors)) << std::endl; } else { std::cout << " => Alignment failed" << std::endl; } return EXIT_SUCCESS; } int RunModelAnalyzer(int argc, char** argv) { std::string path; OptionManager options; options.AddRequiredOption("path", &path); options.Parse(argc, argv); Reconstruction reconstruction; reconstruction.Read(path); std::cout << StringPrintf("Cameras: %d", reconstruction.NumCameras()) << std::endl; std::cout << StringPrintf("Images: %d", reconstruction.NumImages()) << std::endl; std::cout << StringPrintf("Registered images: %d", reconstruction.NumRegImages()) << std::endl; std::cout << StringPrintf("Points: %d", reconstruction.NumPoints3D()) << std::endl; std::cout << StringPrintf("Observations: %d", reconstruction.ComputeNumObservations()) << std::endl; std::cout << StringPrintf("Mean track length: %f", reconstruction.ComputeMeanTrackLength()) << std::endl; std::cout << StringPrintf("Mean observations per image: %f", reconstruction.ComputeMeanObservationsPerRegImage()) << std::endl; std::cout << StringPrintf("Mean reprojection error: %fpx", reconstruction.ComputeMeanReprojectionError()) << std::endl; return EXIT_SUCCESS; } int RunModelConverter(int argc, char** argv) { std::string input_path; std::string output_path; std::string output_type; OptionManager options; options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddRequiredOption("output_type", &output_type, "{'BIN', 'TXT', 'NVM', 'Bundler', 'VRML', 'PLY'}"); options.Parse(argc, argv); Reconstruction reconstruction; reconstruction.Read(input_path); StringToLower(&output_type); if (output_type == "bin") { reconstruction.WriteBinary(output_path); } else if (output_type == "txt") { reconstruction.WriteText(output_path); } else if (output_type == "nvm") { reconstruction.ExportNVM(output_path); } else if (output_type == "bundler") { reconstruction.ExportBundler(output_path + ".bundle.out", output_path + ".list.txt"); } else if (output_type == "ply") { reconstruction.ExportPLY(output_path); } else if (output_type == "vrml") { const auto base_path = output_path.substr(0, output_path.find_last_of(".")); reconstruction.ExportVRML(base_path + ".images.wrl", base_path + ".points3D.wrl", 1, Eigen::Vector3d(1, 0, 0)); } else { std::cerr << "ERROR: Invalid `output_type`" << std::endl; return EXIT_FAILURE; } return EXIT_SUCCESS; } int RunModelMerger(int argc, char** argv) { std::string input_path1; std::string input_path2; std::string output_path; int min_common_images = 3; OptionManager options; options.AddRequiredOption("input_path1", &input_path1); options.AddRequiredOption("input_path2", &input_path2); options.AddRequiredOption("output_path", &output_path); options.AddDefaultOption("min_common_images", &min_common_images); options.Parse(argc, argv); Reconstruction reconstruction1; reconstruction1.Read(input_path1); PrintHeading2("Reconstruction 1"); std::cout << StringPrintf("Images: %d", reconstruction1.NumRegImages()) << std::endl; std::cout << StringPrintf("Points: %d", reconstruction1.NumPoints3D()) << std::endl; Reconstruction reconstruction2; reconstruction2.Read(input_path2); PrintHeading2("Reconstruction 2"); std::cout << StringPrintf("Images: %d", reconstruction2.NumRegImages()) << std::endl; std::cout << StringPrintf("Points: %d", reconstruction2.NumPoints3D()) << std::endl; PrintHeading2("Merging reconstructions"); if (reconstruction1.Merge(reconstruction2, min_common_images)) { std::cout << "=> Merge succeeded" << std::endl; PrintHeading2("Merged reconstruction"); std::cout << StringPrintf("Images: %d", reconstruction1.NumRegImages()) << std::endl; std::cout << StringPrintf("Points: %d", reconstruction1.NumPoints3D()) << std::endl; } else { std::cout << "=> Merge failed" << std::endl; } reconstruction1.Write(output_path); return EXIT_SUCCESS; } int RunModelOrientationAligner(int argc, char** argv) { std::string input_path; std::string output_path; std::string method = "MANHATTAN-WORLD"; ManhattanWorldFrameEstimationOptions frame_estimation_options; OptionManager options; options.AddImageOptions(); options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddDefaultOption("method", &method, "{MANHATTAN-WORLD, IMAGE-ORIENTATION}"); options.AddDefaultOption("max_image_size", &frame_estimation_options.max_image_size); options.Parse(argc, argv); StringToLower(&method); if (method != "manhattan-world" && method != "image-orientation") { std::cout << "ERROR: Invalid `method` - supported values are " "'MANHATTAN-WORLD' or 'IMAGE-ORIENTATION'." << std::endl; return EXIT_FAILURE; } Reconstruction reconstruction; reconstruction.Read(input_path); PrintHeading1("Aligning Reconstruction"); Eigen::Matrix3d tform; if (method == "manhattan-world") { const Eigen::Matrix3d frame = EstimateManhattanWorldFrame( frame_estimation_options, reconstruction, *options.image_path); if (frame.col(0).nonZeros() == 0) { std::cout << "Only aligning vertical axis" << std::endl; tform = RotationFromUnitVectors(frame.col(1), Eigen::Vector3d(0, 1, 0)); } else if (frame.col(1).nonZeros() == 0) { tform = RotationFromUnitVectors(frame.col(0), Eigen::Vector3d(1, 0, 0)); std::cout << "Only aligning horizontal axis" << std::endl; } else { tform = frame.transpose(); std::cout << "Aligning horizontal and vertical axes" << std::endl; } } else if (method == "image-orientation") { const Eigen::Vector3d gravity_axis = EstimateGravityVectorFromImageOrientation(reconstruction); tform = RotationFromUnitVectors(gravity_axis, Eigen::Vector3d(0, 1, 0)); } else { LOG(FATAL) << "Alignment method not supported"; } std::cout << "Using the rotation matrix:" << std::endl; std::cout << tform << std::endl; reconstruction.Transform(1, RotationMatrixToQuaternion(tform), Eigen::Vector3d(0, 0, 0)); std::cout << "Writing aligned reconstruction..." << std::endl; reconstruction.Write(output_path); return EXIT_SUCCESS; } int RunSequentialMatcher(int argc, char** argv) { OptionManager options; options.AddDatabaseOptions(); options.AddSequentialMatchingOptions(); options.Parse(argc, argv); std::unique_ptr app; if (options.sift_matching->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } SequentialFeatureMatcher feature_matcher(*options.sequential_matching, *options.sift_matching, *options.database_path); if (options.sift_matching->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(&feature_matcher); } else { feature_matcher.Start(); feature_matcher.Wait(); } return EXIT_SUCCESS; } int RunPointTriangulator(int argc, char** argv) { std::string import_path; std::string export_path; OptionManager options; options.AddDatabaseOptions(); options.AddImageOptions(); options.AddRequiredOption("import_path", &import_path); options.AddRequiredOption("export_path", &export_path); options.AddMapperOptions(); options.Parse(argc, argv); if (!ExistsDir(import_path)) { std::cerr << "ERROR: `import_path` is not a directory" << std::endl; return EXIT_FAILURE; } if (!ExistsDir(export_path)) { std::cerr << "ERROR: `export_path` is not a directory" << std::endl; return EXIT_FAILURE; } const auto& mapper_options = *options.mapper; PrintHeading1("Loading database"); DatabaseCache database_cache; { Database database(*options.database_path); Timer timer; timer.Start(); const size_t min_num_matches = static_cast(mapper_options.min_num_matches); database_cache.Load(database, min_num_matches, mapper_options.ignore_watermarks, mapper_options.image_names); std::cout << std::endl; timer.PrintMinutes(); } std::cout << std::endl; Reconstruction reconstruction; reconstruction.Read(import_path); CHECK_GE(reconstruction.NumRegImages(), 2) << "Need at least two images for triangulation"; IncrementalMapper mapper(&database_cache); mapper.BeginReconstruction(&reconstruction); ////////////////////////////////////////////////////////////////////////////// // Triangulation ////////////////////////////////////////////////////////////////////////////// const auto tri_options = mapper_options.Triangulation(); for (const image_t image_id : reconstruction.RegImageIds()) { const auto& image = reconstruction.Image(image_id); PrintHeading1("Triangulating image #" + std::to_string(image_id)); const size_t num_existing_points3D = image.NumPoints3D(); std::cout << " => Image has " << num_existing_points3D << " / " << image.NumObservations() << " points" << std::endl; mapper.TriangulateImage(tri_options, image_id); std::cout << " => Triangulated " << (image.NumPoints3D() - num_existing_points3D) << " points" << std::endl; } ////////////////////////////////////////////////////////////////////////////// // Bundle adjustment ////////////////////////////////////////////////////////////////////////////// CompleteAndMergeTracks(mapper_options, &mapper); const auto ba_options = mapper_options.GlobalBundleAdjustment(); // Configure bundle adjustment. BundleAdjustmentConfig ba_config; for (const image_t image_id : reconstruction.RegImageIds()) { ba_config.AddImage(image_id); ba_config.SetConstantPose(image_id); ba_config.SetConstantCamera(reconstruction.Image(image_id).CameraId()); } for (int i = 0; i < mapper_options.ba_global_max_refinements; ++i) { // Avoid degeneracies in bundle adjustment. reconstruction.FilterObservationsWithNegativeDepth(); const size_t num_observations = reconstruction.ComputeNumObservations(); PrintHeading1("Bundle adjustment"); BundleAdjuster bundle_adjuster(ba_options, ba_config); CHECK(bundle_adjuster.Solve(&reconstruction)); size_t num_changed_observations = 0; num_changed_observations += CompleteAndMergeTracks(mapper_options, &mapper); num_changed_observations += FilterPoints(mapper_options, &mapper); const double changed = static_cast(num_changed_observations) / num_observations; std::cout << StringPrintf(" => Changed observations: %.6f", changed) << std::endl; if (changed < mapper_options.ba_global_max_refinement_change) { break; } } PrintHeading1("Extracting colors"); reconstruction.ExtractColorsForAllImages(*options.image_path); const bool kDiscardReconstruction = false; mapper.EndReconstruction(kDiscardReconstruction); reconstruction.Write(export_path); return EXIT_SUCCESS; } // Read the configuration of the camera rigs from a JSON file. The input images // of a camera rig must be named consistently to assign them to the appropriate // camera rig and the respective snapshots. // // An example configuration of a single camera rig: // [ // { // "ref_camera_id": 1, // "cameras": // [ // { // "camera_id": 1, // "image_prefix": "left1_image" // }, // { // "camera_id": 2, // "image_prefix": "left2_image" // }, // { // "camera_id": 3, // "image_prefix": "right1_image" // }, // { // "camera_id": 4, // "image_prefix": "right2_image" // } // ] // } // ] // // This file specifies the configuration for a single camera rig and that you // could potentially define multiple camera rigs. The rig is composed of 4 // cameras: all images of the first camera must have "left1_image" as a name // prefix, e.g., "left1_image_frame000.png" or "left1_image/frame000.png". // Images with the same suffix ("_frame000.png" and "/frame000.png") are // assigned to the same snapshot, i.e., they are assumed to be captured at the // same time. Only snapshots with the reference image registered will be added // to the bundle adjustment problem. The remaining images will be added with // independent poses to the bundle adjustment problem. The above configuration // could have the following input image file structure: // // /path/to/images/... // left1_image/... // frame000.png // frame001.png // frame002.png // ... // left2_image/... // frame000.png // frame001.png // frame002.png // ... // right1_image/... // frame000.png // frame001.png // frame002.png // ... // right2_image/... // frame000.png // frame001.png // frame002.png // ... // // TODO: Provide an option to manually / explicitly set the relative extrinsics // of the camera rig. At the moment, the relative extrinsics are automatically // inferred from the reconstruction. std::vector ReadCameraRigConfig( const std::string& rig_config_path, const Reconstruction& reconstruction) { boost::property_tree::ptree pt; boost::property_tree::read_json(rig_config_path.c_str(), pt); std::vector camera_rigs; for (const auto& rig_config : pt) { CameraRig camera_rig; std::vector image_prefixes; for (const auto& camera : rig_config.second.get_child("cameras")) { const int camera_id = camera.second.get("camera_id"); image_prefixes.push_back(camera.second.get("image_prefix")); camera_rig.AddCamera(camera_id, ComposeIdentityQuaternion(), Eigen::Vector3d(0, 0, 0)); } camera_rig.SetRefCameraId(rig_config.second.get("ref_camera_id")); std::unordered_map> snapshots; for (const auto image_id : reconstruction.RegImageIds()) { const auto& image = reconstruction.Image(image_id); for (const auto& image_prefix : image_prefixes) { if (StringStartsWith(image.Name(), image_prefix)) { const std::string image_suffix = StringReplace(image.Name(), image_prefix, ""); snapshots[image_suffix].push_back(image_id); } } } for (const auto& snapshot : snapshots) { bool has_ref_camera = false; for (const auto image_id : snapshot.second) { const auto& image = reconstruction.Image(image_id); if (image.CameraId() == camera_rig.RefCameraId()) { has_ref_camera = true; } } if (has_ref_camera) { camera_rig.AddSnapshot(snapshot.second); } } camera_rig.Check(reconstruction); camera_rig.ComputeRelativePoses(reconstruction); camera_rigs.push_back(camera_rig); } return camera_rigs; } int RunRigBundleAdjuster(int argc, char** argv) { std::string input_path; std::string output_path; std::string rig_config_path; OptionManager options; options.AddRequiredOption("input_path", &input_path); options.AddRequiredOption("output_path", &output_path); options.AddRequiredOption("rig_config_path", &rig_config_path); options.AddBundleAdjustmentOptions(); options.Parse(argc, argv); Reconstruction reconstruction; reconstruction.Read(input_path); PrintHeading1("Camera rig configuration"); auto camera_rigs = ReadCameraRigConfig(rig_config_path, reconstruction); BundleAdjustmentConfig config; for (size_t i = 0; i < camera_rigs.size(); ++i) { const auto& camera_rig = camera_rigs[i]; PrintHeading2(StringPrintf("Camera Rig %d", i + 1)); std::cout << StringPrintf("Cameras: %d", camera_rig.NumCameras()) << std::endl; std::cout << StringPrintf("Snapshots: %d", camera_rig.NumSnapshots()) << std::endl; // Add all registered images to the bundle adjustment configuration. for (const auto image_id : reconstruction.RegImageIds()) { config.AddImage(image_id); } } PrintHeading1("Rig bundle adjustment"); BundleAdjustmentOptions ba_options = *options.bundle_adjustment; ba_options.solver_options.minimizer_progress_to_stdout = true; RigBundleAdjuster::Options rig_ba_options; RigBundleAdjuster bundle_adjuster(ba_options, rig_ba_options, config); CHECK(bundle_adjuster.Solve(&reconstruction, &camera_rigs)); reconstruction.Write(output_path); return EXIT_SUCCESS; } int RunSpatialMatcher(int argc, char** argv) { OptionManager options; options.AddDatabaseOptions(); options.AddSpatialMatchingOptions(); options.Parse(argc, argv); std::unique_ptr app; if (options.sift_matching->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } SpatialFeatureMatcher feature_matcher(*options.spatial_matching, *options.sift_matching, *options.database_path); if (options.sift_matching->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(&feature_matcher); } else { feature_matcher.Start(); feature_matcher.Wait(); } return EXIT_SUCCESS; } int RunTransitiveMatcher(int argc, char** argv) { OptionManager options; options.AddDatabaseOptions(); options.AddTransitiveMatchingOptions(); options.Parse(argc, argv); std::unique_ptr app; if (options.sift_matching->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } TransitiveFeatureMatcher feature_matcher(*options.transitive_matching, *options.sift_matching, *options.database_path); if (options.sift_matching->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(&feature_matcher); } else { feature_matcher.Start(); feature_matcher.Wait(); } return EXIT_SUCCESS; } // Loads descriptors for training from the database. Loads all descriptors from // the database if max_num_images < 0, otherwise the descriptors of a random // subset of images are selected. FeatureDescriptors LoadRandomDatabaseDescriptors( const std::string& database_path, const int max_num_images) { Database database(database_path); DatabaseTransaction database_transaction(&database); const std::vector images = database.ReadAllImages(); FeatureDescriptors descriptors; std::vector image_ids; size_t num_descriptors = 0; if (max_num_images < 0) { // All images in the database. image_ids.resize(images.size()); std::iota(image_ids.begin(), image_ids.end(), 0); num_descriptors = database.NumDescriptors(); } else { // Random subset of images in the database. CHECK_LE(max_num_images, images.size()); RandomSampler random_sampler(max_num_images); random_sampler.Initialize(images.size()); image_ids = random_sampler.Sample(); for (const auto image_id : image_ids) { const auto& image = images.at(image_id); num_descriptors += database.NumDescriptorsForImage(image.ImageId()); } } descriptors.resize(num_descriptors, 128); size_t descriptor_row = 0; for (const auto image_id : image_ids) { const auto& image = images.at(image_id); const FeatureDescriptors image_descriptors = database.ReadDescriptors(image.ImageId()); descriptors.block(descriptor_row, 0, image_descriptors.rows(), 128) = image_descriptors; descriptor_row += image_descriptors.rows(); } CHECK_EQ(descriptor_row, num_descriptors); return descriptors; } int RunVocabTreeBuilder(int argc, char** argv) { std::string vocab_tree_path; retrieval::VisualIndex<>::BuildOptions build_options; int max_num_images = -1; OptionManager options; options.AddDatabaseOptions(); options.AddRequiredOption("vocab_tree_path", &vocab_tree_path); options.AddDefaultOption("num_visual_words", &build_options.num_visual_words); options.AddDefaultOption("branching", &build_options.branching); options.AddDefaultOption("num_iterations", &build_options.num_iterations); options.AddDefaultOption("max_num_images", &max_num_images); options.Parse(argc, argv); retrieval::VisualIndex<> visual_index; std::cout << "Loading descriptors..." << std::endl; const auto descriptors = LoadRandomDatabaseDescriptors(*options.database_path, max_num_images); std::cout << " => Loaded a total of " << descriptors.rows() << " descriptors" << std::endl; std::cout << "Building index for visual words..." << std::endl; visual_index.Build(build_options, descriptors); std::cout << " => Quantized descriptor space using " << visual_index.NumVisualWords() << " visual words" << std::endl; std::cout << "Saving index to file..." << std::endl; visual_index.Write(vocab_tree_path); return EXIT_SUCCESS; } int RunVocabTreeMatcher(int argc, char** argv) { OptionManager options; options.AddDatabaseOptions(); options.AddVocabTreeMatchingOptions(); options.Parse(argc, argv); std::unique_ptr app; if (options.sift_matching->use_gpu && kUseOpenGL) { app.reset(new QApplication(argc, argv)); } VocabTreeFeatureMatcher feature_matcher(*options.vocab_tree_matching, *options.sift_matching, *options.database_path); if (options.sift_matching->use_gpu && kUseOpenGL) { RunThreadWithOpenGLContext(&feature_matcher); } else { feature_matcher.Start(); feature_matcher.Wait(); } return EXIT_SUCCESS; } std::vector ReadVocabTreeRetrievalImageList(const std::string& path, Database* database) { std::vector images; if (path.empty()) { images.reserve(database->NumImages()); for (const auto& image : database->ReadAllImages()) { images.push_back(image); } } else { DatabaseTransaction database_transaction(database); const auto image_names = ReadTextFileLines(path); images.reserve(image_names.size()); for (const auto& image_name : image_names) { const auto image = database->ReadImageWithName(image_name); CHECK_NE(image.ImageId(), kInvalidImageId); images.push_back(image); } } return images; } int RunVocabTreeRetriever(int argc, char** argv) { std::string vocab_tree_path; std::string database_image_list_path; std::string query_image_list_path; int num_images = -1; int num_verifications = 0; int max_num_features = -1; OptionManager options; options.AddDatabaseOptions(); options.AddRequiredOption("vocab_tree_path", &vocab_tree_path); options.AddDefaultOption("database_image_list_path", &database_image_list_path); options.AddDefaultOption("query_image_list_path", &query_image_list_path); options.AddDefaultOption("num_images", &num_images); options.AddDefaultOption("num_verifications", &num_verifications); options.AddDefaultOption("max_num_features", &max_num_features); options.Parse(argc, argv); retrieval::VisualIndex<> visual_index; visual_index.Read(vocab_tree_path); Database database(*options.database_path); const auto database_images = ReadVocabTreeRetrievalImageList(database_image_list_path, &database); const auto query_images = ReadVocabTreeRetrievalImageList(query_image_list_path, &database); ////////////////////////////////////////////////////////////////////////////// // Perform image indexing ////////////////////////////////////////////////////////////////////////////// for (size_t i = 0; i < database_images.size(); ++i) { Timer timer; timer.Start(); std::cout << StringPrintf("Indexing image [%d/%d]", i + 1, database_images.size()) << std::flush; auto keypoints = database.ReadKeypoints(database_images[i].ImageId()); auto descriptors = database.ReadDescriptors(database_images[i].ImageId()); if (max_num_features > 0 && descriptors.rows() > max_num_features) { ExtractTopScaleFeatures(&keypoints, &descriptors, max_num_features); } visual_index.Add(retrieval::VisualIndex<>::IndexOptions(), database_images[i].ImageId(), keypoints, descriptors); std::cout << StringPrintf(" in %.3fs", timer.ElapsedSeconds()) << std::endl; } // Compute the TF-IDF weights, etc. visual_index.Prepare(); ////////////////////////////////////////////////////////////////////////////// // Perform image queries ////////////////////////////////////////////////////////////////////////////// retrieval::VisualIndex<>::QueryOptions query_options; query_options.max_num_images = num_images; query_options.max_num_verifications = num_verifications; std::unordered_map image_id_to_image; image_id_to_image.reserve(database_images.size()); for (const auto& image : database_images) { image_id_to_image.emplace(image.ImageId(), &image); } for (size_t i = 0; i < query_images.size(); ++i) { Timer timer; timer.Start(); std::cout << StringPrintf("Querying for image %s [%d/%d]", query_images[i].Name().c_str(), i + 1, query_images.size()) << std::flush; auto keypoints = database.ReadKeypoints(query_images[i].ImageId()); auto descriptors = database.ReadDescriptors(query_images[i].ImageId()); if (max_num_features > 0 && descriptors.rows() > max_num_features) { ExtractTopScaleFeatures(&keypoints, &descriptors, max_num_features); } std::vector image_scores; visual_index.QueryWithVerification(query_options, keypoints, descriptors, &image_scores); std::cout << StringPrintf(" in %.3fs", timer.ElapsedSeconds()) << std::endl; for (const auto& image_score : image_scores) { const auto& image = *image_id_to_image.at(image_score.image_id); std::cout << StringPrintf(" image_id=%d, image_name=%s, score=%f", image_score.image_id, image.Name().c_str(), image_score.score) << std::endl; } } return EXIT_SUCCESS; } typedef std::function command_func_t; int ShowHelp( const std::vector>& commands) { std::cout << StringPrintf( "%s -- Structure-from-Motion and Multi-View Stereo\n" " (%s)", GetVersionInfo().c_str(), GetBuildInfo().c_str()) << std::endl << std::endl; std::cout << "Usage:" << std::endl; std::cout << " colmap [command] [options]" << std::endl << std::endl; std::cout << "Documentation:" << std::endl; std::cout << " https://colmap.github.io/" << std::endl << std::endl; std::cout << "Example usage:" << std::endl; std::cout << " colmap help [ -h, --help ]" << std::endl; std::cout << " colmap gui" << std::endl; std::cout << " colmap gui -h [ --help ]" << std::endl; std::cout << " colmap automatic_reconstructor -h [ --help ]" << std::endl; std::cout << " colmap automatic_reconstructor --image_path IMAGES " "--workspace_path WORKSPACE" << std::endl; std::cout << " colmap feature_extractor --image_path IMAGES --database_path " "DATABASE" << std::endl; std::cout << " colmap exhaustive_matcher --database_path DATABASE" << std::endl; std::cout << " colmap mapper --image_path IMAGES --database_path DATABASE " "--export_path EXPORT" << std::endl; std::cout << " ..." << std::endl << std::endl; std::cout << "Available commands:" << std::endl; std::cout << " help" << std::endl; for (const auto& command : commands) { std::cout << " " << command.first << std::endl; } std::cout << std::endl; return EXIT_SUCCESS; } int main(int argc, char** argv) { InitializeGlog(argv); std::vector> commands; commands.emplace_back("gui", &RunGraphicalUserInterface); commands.emplace_back("automatic_reconstructor", &RunAutomaticReconstructor); commands.emplace_back("bundle_adjuster", &RunBundleAdjuster); commands.emplace_back("color_extractor", &RunColorExtractor); commands.emplace_back("database_creator", &RunDatabaseCreator); commands.emplace_back("dense_fuser", &RunDenseFuser); commands.emplace_back("dense_mesher", &RunDenseMesher); commands.emplace_back("dense_stereo", &RunDenseStereo); commands.emplace_back("exhaustive_matcher", &RunExhaustiveMatcher); commands.emplace_back("feature_extractor", &RunFeatureExtractor); commands.emplace_back("feature_importer", &RunFeatureImporter); commands.emplace_back("image_rectifier", &RunImageRectifier); commands.emplace_back("image_registrator", &RunImageRegistrator); commands.emplace_back("image_undistorter", &RunImageUndistorter); commands.emplace_back("mapper", &RunMapper); commands.emplace_back("matches_importer", &RunMatchesImporter); commands.emplace_back("model_aligner", &RunModelAligner); commands.emplace_back("model_analyzer", &RunModelAnalyzer); commands.emplace_back("model_converter", &RunModelConverter); commands.emplace_back("model_merger", &RunModelMerger); commands.emplace_back("model_orientation_aligner", &RunModelOrientationAligner); commands.emplace_back("point_triangulator", &RunPointTriangulator); commands.emplace_back("rig_bundle_adjuster", &RunRigBundleAdjuster); commands.emplace_back("sequential_matcher", &RunSequentialMatcher); commands.emplace_back("spatial_matcher", &RunSpatialMatcher); commands.emplace_back("transitive_matcher", &RunTransitiveMatcher); commands.emplace_back("vocab_tree_builder", &RunVocabTreeBuilder); commands.emplace_back("vocab_tree_matcher", &RunVocabTreeMatcher); commands.emplace_back("vocab_tree_retriever", &RunVocabTreeRetriever); if (argc == 1) { return ShowHelp(commands); } const std::string command = argv[1]; if (command == "help" || command == "-h" || command == "--help") { return ShowHelp(commands); } else { command_func_t matched_command_func = nullptr; for (const auto& command_func : commands) { if (command == command_func.first) { matched_command_func = command_func.second; break; } } if (matched_command_func == nullptr) { std::cerr << StringPrintf( "ERROR: Command `%s` not recognized. To list the " "available commands, run `colmap help`.", command.c_str()) << std::endl; return EXIT_FAILURE; } else { int command_argc = argc - 1; char** command_argv = &argv[1]; command_argv[0] = argv[0]; return matched_command_func(command_argc, command_argv); } } return ShowHelp(commands); } colmap-3.4/src/ext/000077500000000000000000000000001323400541200142145ustar00rootroot00000000000000colmap-3.4/src/ext/CMakeLists.txt000077500000000000000000000006071323400541200167620ustar00rootroot00000000000000set(FOLDER_NAME "ext") COLMAP_SET_THIRD_PARTY_FOLDER() if(NOT IS_MSVC) string(REPLACE "-std=c++11" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") endif() add_subdirectory(FLANN) add_subdirectory(Graclus) add_subdirectory(LSD) add_subdirectory(PBA) add_subdirectory(PoissonRecon) add_subdirectory(SiftGPU) add_subdirectory(SQLite) add_subdirectory(VLFeat) COLMAP_UNSET_THIRD_PARTY_FOLDER() colmap-3.4/src/ext/FLANN/000077500000000000000000000000001323400541200150525ustar00rootroot00000000000000colmap-3.4/src/ext/FLANN/CMakeLists.txt000066400000000000000000000002601323400541200176100ustar00rootroot00000000000000if (MSVC) set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /bigobj") endif() COLMAP_ADD_LIBRARY(flann flann.hpp flann.cpp ext/lz4.h ext/lz4.c ext/lz4hc.h ext/lz4hc.c ) colmap-3.4/src/ext/FLANN/LICENSE000066400000000000000000000031371323400541200160630ustar00rootroot00000000000000The BSD License Copyright (c) 2008-2011 Marius Muja (mariusm@cs.ubc.ca). All rights reserved. Copyright (c) 2008-2011 David G. Lowe (lowe@cs.ubc.ca). All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the "University of British Columbia" nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. colmap-3.4/src/ext/FLANN/algorithms/000077500000000000000000000000001323400541200172235ustar00rootroot00000000000000colmap-3.4/src/ext/FLANN/algorithms/all_indices.h000066400000000000000000000152731323400541200216520ustar00rootroot00000000000000/*********************************************************************** * Software License Agreement (BSD License) * * Copyright 2008-2009 Marius Muja (mariusm@cs.ubc.ca). All rights reserved. * Copyright 2008-2009 David G. Lowe (lowe@cs.ubc.ca). All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. *************************************************************************/ #ifndef FLANN_ALL_INDICES_H_ #define FLANN_ALL_INDICES_H_ #include "ext/FLANN/general.h" #include "ext/FLANN/algorithms/nn_index.h" #include "ext/FLANN/algorithms/kdtree_index.h" #include "ext/FLANN/algorithms/kdtree_single_index.h" #include "ext/FLANN/algorithms/kmeans_index.h" #include "ext/FLANN/algorithms/composite_index.h" #include "ext/FLANN/algorithms/linear_index.h" #include "ext/FLANN/algorithms/hierarchical_clustering_index.h" #include "ext/FLANN/algorithms/lsh_index.h" #include "ext/FLANN/algorithms/autotuned_index.h" #ifdef FLANN_USE_CUDA #include "ext/FLANN/algorithms/kdtree_cuda_3d_index.h" #endif namespace flann { /** * enable_if sfinae helper */ template struct enable_if{}; template struct enable_if { typedef T type; }; /** * disable_if sfinae helper */ template struct disable_if{ typedef T type; }; template struct disable_if { }; /** * Check if two type are the same */ template struct same_type { enum {value = false}; }; template struct same_type { enum {value = true}; }; #define HAS_MEMBER(member) \ template \ struct member { \ typedef char No; \ typedef long Yes; \ template static Yes test( typename C::member* ); \ template static No test( ... ); \ enum { value = sizeof (test(0))==sizeof(Yes) }; \ }; HAS_MEMBER(needs_kdtree_distance) HAS_MEMBER(needs_vector_space_distance) HAS_MEMBER(is_kdtree_distance) HAS_MEMBER(is_vector_space_distance) struct DummyDistance { typedef float ElementType; typedef float ResultType; template ResultType operator()(Iterator1 a, Iterator2 b, size_t size, ResultType /*worst_dist*/ = -1) const { return ResultType(0); } template inline ResultType accum_dist(const U& a, const V& b, int) const { return ResultType(0); } }; /** * Checks if an index and a distance can be used together */ template