| // Copyright (c) 2022, ETH Zurich and UNC Chapel Hill. | |
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| // | |
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| // | |
| // Author: Johannes L. Schoenberger (jsch-at-demuc-dot-de) | |
| 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 <int kDim, bool kEstimateScale = true> | |
| class SimilarityTransformEstimator { | |
| public: | |
| typedef Eigen::Matrix<double, kDim, 1> X_t; | |
| typedef Eigen::Matrix<double, kDim, 1> Y_t; | |
| typedef Eigen::Matrix<double, kDim, kDim + 1> 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<M_t> Estimate(const std::vector<X_t>& src, | |
| const std::vector<Y_t>& 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<X_t>& src, | |
| const std::vector<Y_t>& dst, const M_t& matrix, | |
| std::vector<double>* residuals); | |
| }; | |
| //////////////////////////////////////////////////////////////////////////////// | |
| // Implementation | |
| //////////////////////////////////////////////////////////////////////////////// | |
| template <int kDim, bool kEstimateScale> | |
| std::vector<typename SimilarityTransformEstimator<kDim, kEstimateScale>::M_t> | |
| SimilarityTransformEstimator<kDim, kEstimateScale>::Estimate( | |
| const std::vector<X_t>& src, const std::vector<Y_t>& dst) { | |
| CHECK_EQ(src.size(), dst.size()); | |
| Eigen::Matrix<double, kDim, Eigen::Dynamic> src_mat(kDim, src.size()); | |
| Eigen::Matrix<double, kDim, Eigen::Dynamic> 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]; | |
| } | |
| const M_t model = Eigen::umeyama(src_mat, dst_mat, kEstimateScale) | |
| .topLeftCorner(kDim, kDim + 1); | |
| if (model.array().isNaN().any()) { | |
| return std::vector<M_t>{}; | |
| } | |
| return {model}; | |
| } | |
| template <int kDim, bool kEstimateScale> | |
| void SimilarityTransformEstimator<kDim, kEstimateScale>::Residuals( | |
| const std::vector<X_t>& src, const std::vector<Y_t>& dst, const M_t& matrix, | |
| std::vector<double>* 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 | |