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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
// 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.
//
// Author: Johannes L. Schoenberger (jsch-at-demuc-dot-de)
#include "estimators/affine_transform.h"
#include <Eigen/SVD>
#include "util/logging.h"
namespace colmap {
std::vector<AffineTransformEstimator::M_t> AffineTransformEstimator::Estimate(
const std::vector<X_t>& points1, const std::vector<Y_t>& 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<const Eigen::Matrix<double, 3, 2>> A_t(nullspace.data());
const std::vector<M_t> models = {A_t.transpose()};
return models;
}
void AffineTransformEstimator::Residuals(const std::vector<X_t>& points1,
const std::vector<Y_t>& points2,
const M_t& A,
std::vector<double>* 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
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