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// 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 ETH Zurich and UNC Chapel Hill 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 HOLDERS 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
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//
// Author: Johannes L. Schoenberger (jsch-at-demuc-dot-de)
#ifndef COLMAP_SRC_ESTIMATORS_SIMILARITY_TRANSFORM_H_
#define COLMAP_SRC_ESTIMATORS_SIMILARITY_TRANSFORM_H_
#include <vector>
#include <Eigen/Core>
#include <Eigen/Geometry>
#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 <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
#endif // COLMAP_SRC_ESTIMATORS_SIMILARITY_TRANSFORM_H_
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