921 lines
37 KiB
C++
921 lines
37 KiB
C++
/*
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* Software License Agreement (BSD License)
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*
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* Point Cloud Library (PCL) - www.pointclouds.org
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* Copyright (c) 2010, Willow Garage, Inc.
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* Copyright (c) 2012-, Open Perception, Inc.
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*
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above
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* copyright notice, this list of conditions and the following
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* disclaimer in the documentation and/or other materials provided
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* with the distribution.
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* * Neither the name of the copyright holder(s) nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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* $Id$
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*
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*/
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#ifndef PCL_REGISTRATION_IMPL_GICP_HPP_
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#define PCL_REGISTRATION_IMPL_GICP_HPP_
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#include <pcl/registration/exceptions.h>
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namespace pcl {
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template <typename PointSource, typename PointTarget, typename Scalar>
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template <typename PointT>
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void
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GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::computeCovariances(
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typename pcl::PointCloud<PointT>::ConstPtr cloud,
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const typename pcl::search::KdTree<PointT>::Ptr kdtree,
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MatricesVector& cloud_covariances)
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{
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if (k_correspondences_ > static_cast<int>(cloud->size())) {
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PCL_ERROR("[pcl::GeneralizedIterativeClosestPoint::computeCovariances] Number or "
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"points in cloud (%lu) is less than k_correspondences_ (%lu)!\n",
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cloud->size(),
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k_correspondences_);
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return;
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}
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Eigen::Vector3d mean;
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pcl::Indices nn_indices(k_correspondences_);
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std::vector<float> nn_dist_sq(k_correspondences_);
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// We should never get there but who knows
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if (cloud_covariances.size() < cloud->size())
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cloud_covariances.resize(cloud->size());
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auto matrices_iterator = cloud_covariances.begin();
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for (auto points_iterator = cloud->begin(); points_iterator != cloud->end();
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++points_iterator, ++matrices_iterator) {
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const PointT& query_point = *points_iterator;
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Eigen::Matrix3d& cov = *matrices_iterator;
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// Zero out the cov and mean
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cov.setZero();
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mean.setZero();
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// Search for the K nearest neighbours
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kdtree->nearestKSearch(query_point, k_correspondences_, nn_indices, nn_dist_sq);
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// Find the covariance matrix
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for (int j = 0; j < k_correspondences_; j++) {
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// de-mean neighbourhood to avoid inaccuracies when far away from origin
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const double ptx = (*cloud)[nn_indices[j]].x - query_point.x,
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pty = (*cloud)[nn_indices[j]].y - query_point.y,
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ptz = (*cloud)[nn_indices[j]].z - query_point.z;
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mean[0] += ptx;
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mean[1] += pty;
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mean[2] += ptz;
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cov(0, 0) += ptx * ptx;
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cov(1, 0) += pty * ptx;
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cov(1, 1) += pty * pty;
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cov(2, 0) += ptz * ptx;
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cov(2, 1) += ptz * pty;
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cov(2, 2) += ptz * ptz;
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}
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mean /= static_cast<double>(k_correspondences_);
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// Get the actual covariance
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for (int k = 0; k < 3; k++)
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for (int l = 0; l <= k; l++) {
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cov(k, l) /= static_cast<double>(k_correspondences_);
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cov(k, l) -= mean[k] * mean[l];
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cov(l, k) = cov(k, l);
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}
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// Compute the SVD (covariance matrix is symmetric so U = V')
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Eigen::JacobiSVD<Eigen::Matrix3d> svd(cov, Eigen::ComputeFullU);
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cov.setZero();
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Eigen::Matrix3d U = svd.matrixU();
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// Reconstitute the covariance matrix with modified singular values using the column
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// // vectors in V.
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for (int k = 0; k < 3; k++) {
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Eigen::Vector3d col = U.col(k);
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double v = 1.; // biggest 2 singular values replaced by 1
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if (k == 2) // smallest singular value replaced by gicp_epsilon
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v = gicp_epsilon_;
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cov += v * col * col.transpose();
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}
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}
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}
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template <typename PointSource, typename PointTarget, typename Scalar>
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void
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GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::getRDerivatives(
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double phi,
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double theta,
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double psi,
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Eigen::Matrix3d& dR_dPhi,
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Eigen::Matrix3d& dR_dTheta,
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Eigen::Matrix3d& dR_dPsi) const
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{
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const double cphi = std::cos(phi), sphi = std::sin(phi);
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const double ctheta = std::cos(theta), stheta = std::sin(theta);
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const double cpsi = std::cos(psi), spsi = std::sin(psi);
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dR_dPhi(0, 0) = 0.;
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dR_dPhi(1, 0) = 0.;
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dR_dPhi(2, 0) = 0.;
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dR_dPhi(0, 1) = sphi * spsi + cphi * cpsi * stheta;
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dR_dPhi(1, 1) = -cpsi * sphi + cphi * spsi * stheta;
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dR_dPhi(2, 1) = cphi * ctheta;
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dR_dPhi(0, 2) = cphi * spsi - cpsi * sphi * stheta;
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dR_dPhi(1, 2) = -cphi * cpsi - sphi * spsi * stheta;
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dR_dPhi(2, 2) = -ctheta * sphi;
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dR_dTheta(0, 0) = -cpsi * stheta;
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dR_dTheta(1, 0) = -spsi * stheta;
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dR_dTheta(2, 0) = -ctheta;
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dR_dTheta(0, 1) = cpsi * ctheta * sphi;
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dR_dTheta(1, 1) = ctheta * sphi * spsi;
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dR_dTheta(2, 1) = -sphi * stheta;
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dR_dTheta(0, 2) = cphi * cpsi * ctheta;
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dR_dTheta(1, 2) = cphi * ctheta * spsi;
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dR_dTheta(2, 2) = -cphi * stheta;
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dR_dPsi(0, 0) = -ctheta * spsi;
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dR_dPsi(1, 0) = cpsi * ctheta;
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dR_dPsi(2, 0) = 0.;
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dR_dPsi(0, 1) = -cphi * cpsi - sphi * spsi * stheta;
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dR_dPsi(1, 1) = -cphi * spsi + cpsi * sphi * stheta;
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dR_dPsi(2, 1) = 0.;
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dR_dPsi(0, 2) = cpsi * sphi - cphi * spsi * stheta;
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dR_dPsi(1, 2) = sphi * spsi + cphi * cpsi * stheta;
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dR_dPsi(2, 2) = 0.;
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}
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template <typename PointSource, typename PointTarget, typename Scalar>
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void
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GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::computeRDerivative(
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const Vector6d& x, const Eigen::Matrix3d& dCost_dR_T, Vector6d& g) const
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{
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Eigen::Matrix3d dR_dPhi;
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Eigen::Matrix3d dR_dTheta;
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Eigen::Matrix3d dR_dPsi;
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getRDerivatives(x[3], x[4], x[5], dR_dPhi, dR_dTheta, dR_dPsi);
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g[3] = (dR_dPhi * dCost_dR_T).trace();
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g[4] = (dR_dTheta * dCost_dR_T).trace();
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g[5] = (dR_dPsi * dCost_dR_T).trace();
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}
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template <typename PointSource, typename PointTarget, typename Scalar>
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void
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GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::getR2ndDerivatives(
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double phi,
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double theta,
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double psi,
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Eigen::Matrix3d& ddR_dPhi_dPhi,
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Eigen::Matrix3d& ddR_dPhi_dTheta,
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Eigen::Matrix3d& ddR_dPhi_dPsi,
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Eigen::Matrix3d& ddR_dTheta_dTheta,
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Eigen::Matrix3d& ddR_dTheta_dPsi,
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Eigen::Matrix3d& ddR_dPsi_dPsi) const
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{
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const double sphi = std::sin(phi), stheta = std::sin(theta), spsi = std::sin(psi);
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const double cphi = std::cos(phi), ctheta = std::cos(theta), cpsi = std::cos(psi);
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ddR_dPhi_dPhi(0, 0) = 0.0;
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ddR_dPhi_dPhi(1, 0) = 0.0;
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ddR_dPhi_dPhi(2, 0) = 0.0;
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ddR_dPhi_dPhi(0, 1) = -cpsi * stheta * sphi + spsi * cphi;
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ddR_dPhi_dPhi(1, 1) = -cpsi * cphi - spsi * stheta * sphi;
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ddR_dPhi_dPhi(2, 1) = -ctheta * sphi;
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ddR_dPhi_dPhi(0, 2) = -spsi * sphi - cpsi * stheta * cphi;
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ddR_dPhi_dPhi(1, 2) = -spsi * stheta * cphi + cpsi * sphi;
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ddR_dPhi_dPhi(2, 2) = -ctheta * cphi;
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ddR_dPhi_dTheta(0, 0) = 0.0;
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ddR_dPhi_dTheta(1, 0) = 0.0;
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ddR_dPhi_dTheta(2, 0) = 0.0;
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ddR_dPhi_dTheta(0, 1) = cpsi * ctheta * cphi;
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ddR_dPhi_dTheta(1, 1) = spsi * ctheta * cphi;
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ddR_dPhi_dTheta(2, 1) = -stheta * cphi;
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ddR_dPhi_dTheta(0, 2) = -cpsi * ctheta * sphi;
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ddR_dPhi_dTheta(1, 2) = -spsi * ctheta * sphi;
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ddR_dPhi_dTheta(2, 2) = stheta * sphi;
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ddR_dPhi_dPsi(0, 0) = 0.0;
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ddR_dPhi_dPsi(1, 0) = 0.0;
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ddR_dPhi_dPsi(2, 0) = 0.0;
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ddR_dPhi_dPsi(0, 1) = -spsi * stheta * cphi + cpsi * sphi;
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ddR_dPhi_dPsi(1, 1) = spsi * sphi + cpsi * stheta * cphi;
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ddR_dPhi_dPsi(2, 1) = 0.0;
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ddR_dPhi_dPsi(0, 2) = cpsi * cphi + spsi * stheta * sphi;
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ddR_dPhi_dPsi(1, 2) = -cpsi * stheta * sphi + spsi * cphi;
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ddR_dPhi_dPsi(2, 2) = 0.0;
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ddR_dTheta_dTheta(0, 0) = -cpsi * ctheta;
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ddR_dTheta_dTheta(1, 0) = -spsi * ctheta;
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ddR_dTheta_dTheta(2, 0) = stheta;
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ddR_dTheta_dTheta(0, 1) = -cpsi * stheta * sphi;
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ddR_dTheta_dTheta(1, 1) = -spsi * stheta * sphi;
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ddR_dTheta_dTheta(2, 1) = -ctheta * sphi;
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ddR_dTheta_dTheta(0, 2) = -cpsi * stheta * cphi;
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ddR_dTheta_dTheta(1, 2) = -spsi * stheta * cphi;
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ddR_dTheta_dTheta(2, 2) = -ctheta * cphi;
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ddR_dTheta_dPsi(0, 0) = spsi * stheta;
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ddR_dTheta_dPsi(1, 0) = -cpsi * stheta;
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ddR_dTheta_dPsi(2, 0) = 0.0;
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ddR_dTheta_dPsi(0, 1) = -spsi * ctheta * sphi;
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ddR_dTheta_dPsi(1, 1) = cpsi * ctheta * sphi;
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ddR_dTheta_dPsi(2, 1) = 0.0;
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ddR_dTheta_dPsi(0, 2) = -spsi * ctheta * cphi;
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ddR_dTheta_dPsi(1, 2) = cpsi * ctheta * cphi;
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ddR_dTheta_dPsi(2, 2) = 0.0;
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ddR_dPsi_dPsi(0, 0) = -cpsi * ctheta;
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ddR_dPsi_dPsi(1, 0) = -spsi * ctheta;
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ddR_dPsi_dPsi(2, 0) = 0.0;
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ddR_dPsi_dPsi(0, 1) = -cpsi * stheta * sphi + spsi * cphi;
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ddR_dPsi_dPsi(1, 1) = -cpsi * cphi - spsi * stheta * sphi;
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ddR_dPsi_dPsi(2, 1) = 0.0;
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ddR_dPsi_dPsi(0, 2) = -spsi * sphi - cpsi * stheta * cphi;
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ddR_dPsi_dPsi(1, 2) = -spsi * stheta * cphi + cpsi * sphi;
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ddR_dPsi_dPsi(2, 2) = 0.0;
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}
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template <typename PointSource, typename PointTarget, typename Scalar>
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void
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GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
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estimateRigidTransformationBFGS(const PointCloudSource& cloud_src,
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const pcl::Indices& indices_src,
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const PointCloudTarget& cloud_tgt,
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const pcl::Indices& indices_tgt,
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Matrix4& transformation_matrix)
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{
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// need at least min_number_correspondences_ samples
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if (indices_src.size() < min_number_correspondences_) {
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PCL_THROW_EXCEPTION(
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NotEnoughPointsException,
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"[pcl::GeneralizedIterativeClosestPoint::estimateRigidTransformationBFGS] Need "
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"at least "
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<< min_number_correspondences_
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<< " points to estimate a transform! "
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"Source and target have "
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<< indices_src.size() << " points!");
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return;
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}
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// Set the initial solution
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Vector6d x = Vector6d::Zero();
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// translation part
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x[0] = transformation_matrix(0, 3);
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x[1] = transformation_matrix(1, 3);
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x[2] = transformation_matrix(2, 3);
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// rotation part (Z Y X euler angles convention)
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// see: https://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
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x[3] = std::atan2(transformation_matrix(2, 1), transformation_matrix(2, 2));
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x[4] = asin(-transformation_matrix(2, 0));
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x[5] = std::atan2(transformation_matrix(1, 0), transformation_matrix(0, 0));
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// Set temporary pointers
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tmp_src_ = &cloud_src;
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tmp_tgt_ = &cloud_tgt;
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tmp_idx_src_ = &indices_src;
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tmp_idx_tgt_ = &indices_tgt;
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// Optimize using BFGS
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OptimizationFunctorWithIndices functor(this);
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BFGS<OptimizationFunctorWithIndices> bfgs(functor);
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bfgs.parameters.sigma = 0.01;
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bfgs.parameters.rho = 0.01;
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bfgs.parameters.tau1 = 9;
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bfgs.parameters.tau2 = 0.05;
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bfgs.parameters.tau3 = 0.5;
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bfgs.parameters.order = 3;
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int inner_iterations_ = 0;
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int result = bfgs.minimizeInit(x);
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result = BFGSSpace::Running;
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do {
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inner_iterations_++;
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result = bfgs.minimizeOneStep(x);
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if (result) {
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break;
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}
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result = bfgs.testGradient();
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} while (result == BFGSSpace::Running && inner_iterations_ < max_inner_iterations_);
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if (result == BFGSSpace::NoProgress || result == BFGSSpace::Success ||
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inner_iterations_ == max_inner_iterations_) {
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PCL_DEBUG("[pcl::registration::TransformationEstimationBFGS::"
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"estimateRigidTransformation]");
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PCL_DEBUG("BFGS solver finished with exit code %i \n", result);
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transformation_matrix.setIdentity();
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applyState(transformation_matrix, x);
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}
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else
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PCL_THROW_EXCEPTION(
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SolverDidntConvergeException,
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"[pcl::" << getClassName()
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<< "::TransformationEstimationBFGS::estimateRigidTransformation] BFGS "
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"solver didn't converge!");
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}
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template <typename PointSource, typename PointTarget, typename Scalar>
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void
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GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
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estimateRigidTransformationNewton(const PointCloudSource& cloud_src,
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const pcl::Indices& indices_src,
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const PointCloudTarget& cloud_tgt,
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const pcl::Indices& indices_tgt,
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Matrix4& transformation_matrix)
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{
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// need at least min_number_correspondences_ samples
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if (indices_src.size() < min_number_correspondences_) {
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PCL_THROW_EXCEPTION(NotEnoughPointsException,
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"[pcl::GeneralizedIterativeClosestPoint::"
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"estimateRigidTransformationNewton] Need "
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"at least "
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<< min_number_correspondences_
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<< " points to estimate a transform! "
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"Source and target have "
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<< indices_src.size() << " points!");
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return;
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}
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// Set the initial solution
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Vector6d x = Vector6d::Zero();
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// translation part
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x[0] = transformation_matrix(0, 3);
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x[1] = transformation_matrix(1, 3);
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x[2] = transformation_matrix(2, 3);
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// rotation part (Z Y X euler angles convention)
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// see: https://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
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x[3] = std::atan2(transformation_matrix(2, 1), transformation_matrix(2, 2));
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x[4] = std::asin(
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std::min<double>(1.0, std::max<double>(-1.0, -transformation_matrix(2, 0))));
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x[5] = std::atan2(transformation_matrix(1, 0), transformation_matrix(0, 0));
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// Set temporary pointers
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tmp_src_ = &cloud_src;
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tmp_tgt_ = &cloud_tgt;
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tmp_idx_src_ = &indices_src;
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tmp_idx_tgt_ = &indices_tgt;
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// Optimize using Newton
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OptimizationFunctorWithIndices functor(this);
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Eigen::Matrix<double, 6, 6> hessian;
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Eigen::Matrix<double, 6, 1> gradient;
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double current_x_value = functor(x);
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functor.dfddf(x, gradient, hessian);
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Eigen::Matrix<double, 6, 1> delta;
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int inner_iterations_ = 0;
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do {
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++inner_iterations_;
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// compute descent direction from hessian and gradient. Take special measures if
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// hessian is not positive-definite (positive Eigenvalues)
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Eigen::SelfAdjointEigenSolver<Eigen::Matrix<double, 6, 6>> eigensolver(hessian);
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Eigen::Matrix<double, 6, 6> inverted_eigenvalues =
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Eigen::Matrix<double, 6, 6>::Zero();
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for (int i = 0; i < 6; ++i) {
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const double ev = eigensolver.eigenvalues()[i];
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if (ev < 0)
|
|
inverted_eigenvalues(i, i) = 1.0 / eigensolver.eigenvalues()[5];
|
|
else
|
|
inverted_eigenvalues(i, i) = 1.0 / ev;
|
|
}
|
|
delta = eigensolver.eigenvectors() * inverted_eigenvalues *
|
|
eigensolver.eigenvectors().transpose() * gradient;
|
|
|
|
// simple line search to guarantee a decrease in the function value
|
|
double alpha = 1.0;
|
|
double candidate_x_value;
|
|
bool improvement_found = false;
|
|
for (int i = 0; i < 10; ++i, alpha /= 2) {
|
|
Vector6d candidate_x = x - alpha * delta;
|
|
candidate_x_value = functor(candidate_x);
|
|
if (candidate_x_value < current_x_value) {
|
|
PCL_DEBUG("[estimateRigidTransformationNewton] Using stepsize=%g, function "
|
|
"value previously: %g, now: %g, "
|
|
"improvement: %g\n",
|
|
alpha,
|
|
current_x_value,
|
|
candidate_x_value,
|
|
current_x_value - candidate_x_value);
|
|
x = candidate_x;
|
|
current_x_value = candidate_x_value;
|
|
improvement_found = true;
|
|
break;
|
|
}
|
|
}
|
|
if (!improvement_found) {
|
|
PCL_DEBUG("[estimateRigidTransformationNewton] finishing because no progress\n");
|
|
break;
|
|
}
|
|
functor.dfddf(x, gradient, hessian);
|
|
if (gradient.head<3>().norm() < translation_gradient_tolerance_ &&
|
|
gradient.tail<3>().norm() < rotation_gradient_tolerance_) {
|
|
PCL_DEBUG("[estimateRigidTransformationNewton] finishing because gradient below "
|
|
"threshold: translation: %g<%g, rotation: %g<%g\n",
|
|
gradient.head<3>().norm(),
|
|
translation_gradient_tolerance_,
|
|
gradient.tail<3>().norm(),
|
|
rotation_gradient_tolerance_);
|
|
break;
|
|
}
|
|
} while (inner_iterations_ < max_inner_iterations_);
|
|
PCL_DEBUG("[estimateRigidTransformationNewton] solver finished after %i iterations "
|
|
"(of max %i)\n",
|
|
inner_iterations_,
|
|
max_inner_iterations_);
|
|
transformation_matrix.setIdentity();
|
|
applyState(transformation_matrix, x);
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
inline double
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
|
|
OptimizationFunctorWithIndices::operator()(const Vector6d& x)
|
|
{
|
|
Matrix4 transformation_matrix = gicp_->base_transformation_;
|
|
gicp_->applyState(transformation_matrix, x);
|
|
double f = 0;
|
|
int m = static_cast<int>(gicp_->tmp_idx_src_->size());
|
|
for (int i = 0; i < m; ++i) {
|
|
// The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_src =
|
|
(*gicp_->tmp_src_)[(*gicp_->tmp_idx_src_)[i]].getVector4fMap();
|
|
// The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_tgt =
|
|
(*gicp_->tmp_tgt_)[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap();
|
|
Eigen::Vector4f p_trans_src(transformation_matrix.template cast<float>() * p_src);
|
|
// Estimate the distance (cost function)
|
|
// The last coordinate is still guaranteed to be set to 1.0
|
|
// The d here is the negative of the d in the paper
|
|
Eigen::Vector3d d(p_trans_src[0] - p_tgt[0],
|
|
p_trans_src[1] - p_tgt[1],
|
|
p_trans_src[2] - p_tgt[2]);
|
|
Eigen::Vector3d Md(gicp_->mahalanobis((*gicp_->tmp_idx_src_)[i]) * d);
|
|
// increment= d'*Md/num_matches = d'*M*d/num_matches (we postpone
|
|
// 1/num_matches after the loop closes)
|
|
f += static_cast<double>(d.transpose() * Md);
|
|
}
|
|
return f / m;
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
inline void
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
|
|
OptimizationFunctorWithIndices::df(const Vector6d& x, Vector6d& g)
|
|
{
|
|
Matrix4 transformation_matrix = gicp_->base_transformation_;
|
|
gicp_->applyState(transformation_matrix, x);
|
|
// Zero out g
|
|
g.setZero();
|
|
// Eigen::Vector3d g_t = g.head<3> ();
|
|
// the transpose of the derivative of the cost function w.r.t rotation matrix
|
|
Eigen::Matrix3d dCost_dR_T = Eigen::Matrix3d::Zero();
|
|
int m = static_cast<int>(gicp_->tmp_idx_src_->size());
|
|
for (int i = 0; i < m; ++i) {
|
|
// The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_src =
|
|
(*gicp_->tmp_src_)[(*gicp_->tmp_idx_src_)[i]].getVector4fMap();
|
|
// The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_tgt =
|
|
(*gicp_->tmp_tgt_)[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap();
|
|
|
|
Eigen::Vector4f p_trans_src(transformation_matrix.template cast<float>() * p_src);
|
|
// The last coordinate is still guaranteed to be set to 1.0
|
|
// The d here is the negative of the d in the paper
|
|
Eigen::Vector3d d(p_trans_src[0] - p_tgt[0],
|
|
p_trans_src[1] - p_tgt[1],
|
|
p_trans_src[2] - p_tgt[2]);
|
|
// Md = M*d
|
|
Eigen::Vector3d Md(gicp_->mahalanobis((*gicp_->tmp_idx_src_)[i]) * d);
|
|
// Increment translation gradient
|
|
// g.head<3> ()+= 2*M*d/num_matches (we postpone 2/num_matches after the loop
|
|
// closes)
|
|
g.head<3>() += Md;
|
|
// Increment rotation gradient
|
|
p_trans_src = gicp_->base_transformation_.template cast<float>() * p_src;
|
|
Eigen::Vector3d p_base_src(p_trans_src[0], p_trans_src[1], p_trans_src[2]);
|
|
dCost_dR_T += p_base_src * Md.transpose();
|
|
}
|
|
g.head<3>() *= 2.0 / m;
|
|
dCost_dR_T *= 2.0 / m;
|
|
gicp_->computeRDerivative(x, dCost_dR_T, g);
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
inline void
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
|
|
OptimizationFunctorWithIndices::fdf(const Vector6d& x, double& f, Vector6d& g)
|
|
{
|
|
Matrix4 transformation_matrix = gicp_->base_transformation_;
|
|
gicp_->applyState(transformation_matrix, x);
|
|
f = 0;
|
|
g.setZero();
|
|
// the transpose of the derivative of the cost function w.r.t rotation matrix
|
|
Eigen::Matrix3d dCost_dR_T = Eigen::Matrix3d::Zero();
|
|
const int m = static_cast<int>(gicp_->tmp_idx_src_->size());
|
|
for (int i = 0; i < m; ++i) {
|
|
// The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_src =
|
|
(*gicp_->tmp_src_)[(*gicp_->tmp_idx_src_)[i]].getVector4fMap();
|
|
// The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_tgt =
|
|
(*gicp_->tmp_tgt_)[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap();
|
|
Eigen::Vector4f p_trans_src(transformation_matrix.template cast<float>() * p_src);
|
|
// The last coordinate is still guaranteed to be set to 1.0
|
|
// The d here is the negative of the d in the paper
|
|
Eigen::Vector3d d(p_trans_src[0] - p_tgt[0],
|
|
p_trans_src[1] - p_tgt[1],
|
|
p_trans_src[2] - p_tgt[2]);
|
|
// Md = M*d
|
|
Eigen::Vector3d Md(gicp_->mahalanobis((*gicp_->tmp_idx_src_)[i]) * d);
|
|
// Increment total error
|
|
f += static_cast<double>(d.transpose() * Md);
|
|
// Increment translation gradient
|
|
// g.head<3> ()+= 2*M*d/num_matches (we postpone 2/num_matches after the loop
|
|
// closes)
|
|
g.head<3>() += Md;
|
|
p_trans_src = gicp_->base_transformation_.template cast<float>() * p_src;
|
|
Eigen::Vector3d p_base_src(p_trans_src[0], p_trans_src[1], p_trans_src[2]);
|
|
// Increment rotation gradient
|
|
dCost_dR_T += p_base_src * Md.transpose();
|
|
}
|
|
f /= static_cast<double>(m);
|
|
g.head<3>() *= (2.0 / m);
|
|
dCost_dR_T *= 2.0 / m;
|
|
gicp_->computeRDerivative(x, dCost_dR_T, g);
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
inline void
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
|
|
OptimizationFunctorWithIndices::dfddf(const Vector6d& x,
|
|
Vector6d& gradient,
|
|
Matrix6d& hessian)
|
|
{
|
|
Matrix4 transformation_matrix = gicp_->base_transformation_;
|
|
gicp_->applyState(transformation_matrix, x);
|
|
const Eigen::Matrix4f transformation_matrix_float =
|
|
transformation_matrix.template cast<float>();
|
|
const Eigen::Matrix4f base_transformation_float =
|
|
gicp_->base_transformation_.template cast<float>();
|
|
// Zero out gradient and hessian
|
|
gradient.setZero();
|
|
hessian.setZero();
|
|
// Helper matrices
|
|
Eigen::Matrix3d dR_dPhi;
|
|
Eigen::Matrix3d dR_dTheta;
|
|
Eigen::Matrix3d dR_dPsi;
|
|
gicp_->getRDerivatives(x[3], x[4], x[5], dR_dPhi, dR_dTheta, dR_dPsi);
|
|
Eigen::Matrix3d ddR_dPhi_dPhi;
|
|
Eigen::Matrix3d ddR_dPhi_dTheta;
|
|
Eigen::Matrix3d ddR_dPhi_dPsi;
|
|
Eigen::Matrix3d ddR_dTheta_dTheta;
|
|
Eigen::Matrix3d ddR_dTheta_dPsi;
|
|
Eigen::Matrix3d ddR_dPsi_dPsi;
|
|
gicp_->getR2ndDerivatives(x[3],
|
|
x[4],
|
|
x[5],
|
|
ddR_dPhi_dPhi,
|
|
ddR_dPhi_dTheta,
|
|
ddR_dPhi_dPsi,
|
|
ddR_dTheta_dTheta,
|
|
ddR_dTheta_dPsi,
|
|
ddR_dPsi_dPsi);
|
|
Eigen::Matrix3d dCost_dR_T = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d dCost_dR_T1 = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d dCost_dR_T2 = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d dCost_dR_T3 = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d dCost_dR_T1b = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d dCost_dR_T2b = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d dCost_dR_T3b = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d hessian_rot_phi = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d hessian_rot_theta = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix3d hessian_rot_psi = Eigen::Matrix3d::Zero();
|
|
Eigen::Matrix<double, 9, 6> hessian_rot_tmp = Eigen::Matrix<double, 9, 6>::Zero();
|
|
|
|
int m = static_cast<int>(gicp_->tmp_idx_src_->size());
|
|
for (int i = 0; i < m; ++i) {
|
|
// The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
const auto& src_idx = (*gicp_->tmp_idx_src_)[i];
|
|
Vector4fMapConst p_src = (*gicp_->tmp_src_)[src_idx].getVector4fMap();
|
|
// The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
|
|
Vector4fMapConst p_tgt =
|
|
(*gicp_->tmp_tgt_)[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap();
|
|
Eigen::Vector4f p_trans_src(transformation_matrix_float * p_src);
|
|
// The last coordinate is still guaranteed to be set to 1.0
|
|
// The d here is the negative of the d in the paper
|
|
const Eigen::Vector3d d(p_trans_src[0] - p_tgt[0],
|
|
p_trans_src[1] - p_tgt[1],
|
|
p_trans_src[2] - p_tgt[2]);
|
|
const Eigen::Matrix3d& M = gicp_->mahalanobis(src_idx);
|
|
const Eigen::Vector3d Md(M * d); // Md = M*d
|
|
gradient.head<3>() += Md; // translation gradient
|
|
hessian.block<3, 3>(0, 0) += M; // translation-translation hessian
|
|
p_trans_src = base_transformation_float * p_src;
|
|
const Eigen::Vector3d p_base_src(p_trans_src[0], p_trans_src[1], p_trans_src[2]);
|
|
dCost_dR_T.noalias() += p_base_src * Md.transpose();
|
|
dCost_dR_T1b += p_base_src[0] * M;
|
|
dCost_dR_T2b += p_base_src[1] * M;
|
|
dCost_dR_T3b += p_base_src[2] * M;
|
|
hessian_rot_tmp.noalias() +=
|
|
Eigen::Map<const Eigen::Matrix<double, 9, 1>>{M.data()} *
|
|
(Eigen::Matrix<double, 1, 6>() << p_base_src[0] * p_base_src[0],
|
|
p_base_src[0] * p_base_src[1],
|
|
p_base_src[0] * p_base_src[2],
|
|
p_base_src[1] * p_base_src[1],
|
|
p_base_src[1] * p_base_src[2],
|
|
p_base_src[2] * p_base_src[2])
|
|
.finished();
|
|
}
|
|
gradient.head<3>() *= 2.0 / m; // translation gradient
|
|
dCost_dR_T *= 2.0 / m;
|
|
gicp_->computeRDerivative(x, dCost_dR_T, gradient); // rotation gradient
|
|
hessian.block<3, 3>(0, 0) *= 2.0 / m; // translation-translation hessian
|
|
// translation-rotation hessian
|
|
dCost_dR_T1.row(0) = dCost_dR_T1b.col(0);
|
|
dCost_dR_T1.row(1) = dCost_dR_T2b.col(0);
|
|
dCost_dR_T1.row(2) = dCost_dR_T3b.col(0);
|
|
dCost_dR_T2.row(0) = dCost_dR_T1b.col(1);
|
|
dCost_dR_T2.row(1) = dCost_dR_T2b.col(1);
|
|
dCost_dR_T2.row(2) = dCost_dR_T3b.col(1);
|
|
dCost_dR_T3.row(0) = dCost_dR_T1b.col(2);
|
|
dCost_dR_T3.row(1) = dCost_dR_T2b.col(2);
|
|
dCost_dR_T3.row(2) = dCost_dR_T3b.col(2);
|
|
dCost_dR_T1 *= 2.0 / m;
|
|
dCost_dR_T2 *= 2.0 / m;
|
|
dCost_dR_T3 *= 2.0 / m;
|
|
hessian(3, 0) = (dR_dPhi * dCost_dR_T1).trace();
|
|
hessian(4, 0) = (dR_dTheta * dCost_dR_T1).trace();
|
|
hessian(5, 0) = (dR_dPsi * dCost_dR_T1).trace();
|
|
hessian(3, 1) = (dR_dPhi * dCost_dR_T2).trace();
|
|
hessian(4, 1) = (dR_dTheta * dCost_dR_T2).trace();
|
|
hessian(5, 1) = (dR_dPsi * dCost_dR_T2).trace();
|
|
hessian(3, 2) = (dR_dPhi * dCost_dR_T3).trace();
|
|
hessian(4, 2) = (dR_dTheta * dCost_dR_T3).trace();
|
|
hessian(5, 2) = (dR_dPsi * dCost_dR_T3).trace();
|
|
hessian.block<3, 3>(0, 3) = hessian.block<3, 3>(3, 0).transpose();
|
|
// rotation-rotation hessian
|
|
int lookup[3][3] = {{0, 1, 2}, {1, 3, 4}, {2, 4, 5}};
|
|
for (int l = 0; l < 3; ++l) {
|
|
for (int i = 0; i < 3; ++i) {
|
|
double phi_tmp = 0.0, theta_tmp = 0.0, psi_tmp = 0.0;
|
|
for (int j = 0; j < 3; ++j) {
|
|
for (int k = 0; k < 3; ++k) {
|
|
phi_tmp += hessian_rot_tmp(3 * j + i, lookup[l][k]) * dR_dPhi(j, k);
|
|
theta_tmp += hessian_rot_tmp(3 * j + i, lookup[l][k]) * dR_dTheta(j, k);
|
|
psi_tmp += hessian_rot_tmp(3 * j + i, lookup[l][k]) * dR_dPsi(j, k);
|
|
}
|
|
}
|
|
hessian_rot_phi(i, l) = phi_tmp;
|
|
hessian_rot_theta(i, l) = theta_tmp;
|
|
hessian_rot_psi(i, l) = psi_tmp;
|
|
}
|
|
}
|
|
hessian_rot_phi *= 2.0 / m;
|
|
hessian_rot_theta *= 2.0 / m;
|
|
hessian_rot_psi *= 2.0 / m;
|
|
hessian(3, 3) = (dR_dPhi.transpose() * hessian_rot_phi).trace() +
|
|
(ddR_dPhi_dPhi * dCost_dR_T).trace();
|
|
hessian(3, 4) = (dR_dPhi.transpose() * hessian_rot_theta).trace() +
|
|
(ddR_dPhi_dTheta * dCost_dR_T).trace();
|
|
hessian(3, 5) = (dR_dPhi.transpose() * hessian_rot_psi).trace() +
|
|
(ddR_dPhi_dPsi * dCost_dR_T).trace();
|
|
hessian(4, 4) = (dR_dTheta.transpose() * hessian_rot_theta).trace() +
|
|
(ddR_dTheta_dTheta * dCost_dR_T).trace();
|
|
hessian(4, 5) = (dR_dTheta.transpose() * hessian_rot_psi).trace() +
|
|
(ddR_dTheta_dPsi * dCost_dR_T).trace();
|
|
hessian(5, 5) = (dR_dPsi.transpose() * hessian_rot_psi).trace() +
|
|
(ddR_dPsi_dPsi * dCost_dR_T).trace();
|
|
hessian(4, 3) = hessian(3, 4);
|
|
hessian(5, 3) = hessian(3, 5);
|
|
hessian(5, 4) = hessian(4, 5);
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
inline BFGSSpace::Status
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
|
|
OptimizationFunctorWithIndices::checkGradient(const Vector6d& g)
|
|
{
|
|
auto translation_epsilon = gicp_->translation_gradient_tolerance_;
|
|
auto rotation_epsilon = gicp_->rotation_gradient_tolerance_;
|
|
|
|
if ((translation_epsilon < 0.) || (rotation_epsilon < 0.))
|
|
return BFGSSpace::NegativeGradientEpsilon;
|
|
|
|
// express translation gradient as norm of translation parameters
|
|
auto translation_grad = g.head<3>().norm();
|
|
|
|
// express rotation gradient as a norm of rotation parameters
|
|
auto rotation_grad = g.tail<3>().norm();
|
|
|
|
if ((translation_grad < translation_epsilon) && (rotation_grad < rotation_epsilon))
|
|
return BFGSSpace::Success;
|
|
|
|
return BFGSSpace::Running;
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
inline void
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::
|
|
computeTransformation(PointCloudSource& output, const Matrix4& guess)
|
|
{
|
|
pcl::IterativeClosestPoint<PointSource, PointTarget, Scalar>::initComputeReciprocal();
|
|
// Difference between consecutive transforms
|
|
double delta = 0;
|
|
// Get the size of the source point cloud
|
|
const std::size_t N = indices_->size();
|
|
// Set the mahalanobis matrices to identity
|
|
mahalanobis_.resize(N, Eigen::Matrix3d::Identity());
|
|
// Compute target cloud covariance matrices
|
|
if ((!target_covariances_) || (target_covariances_->empty())) {
|
|
target_covariances_.reset(new MatricesVector);
|
|
computeCovariances<PointTarget>(target_, tree_, *target_covariances_);
|
|
}
|
|
// Compute input cloud covariance matrices
|
|
if ((!input_covariances_) || (input_covariances_->empty())) {
|
|
input_covariances_.reset(new MatricesVector);
|
|
computeCovariances<PointSource>(input_, tree_reciprocal_, *input_covariances_);
|
|
}
|
|
|
|
base_transformation_ = Matrix4::Identity();
|
|
nr_iterations_ = 0;
|
|
converged_ = false;
|
|
double dist_threshold = corr_dist_threshold_ * corr_dist_threshold_;
|
|
pcl::Indices nn_indices(1);
|
|
std::vector<float> nn_dists(1);
|
|
|
|
pcl::transformPointCloud(output, output, guess);
|
|
|
|
while (!converged_) {
|
|
std::size_t cnt = 0;
|
|
pcl::Indices source_indices(indices_->size());
|
|
pcl::Indices target_indices(indices_->size());
|
|
|
|
// guess corresponds to base_t and transformation_ to t
|
|
Eigen::Matrix4d transform_R = Eigen::Matrix4d::Zero();
|
|
for (std::size_t i = 0; i < 4; i++)
|
|
for (std::size_t j = 0; j < 4; j++)
|
|
for (std::size_t k = 0; k < 4; k++)
|
|
transform_R(i, j) += static_cast<double>(transformation_(i, k)) *
|
|
static_cast<double>(guess(k, j));
|
|
|
|
Eigen::Matrix3d R = transform_R.topLeftCorner<3, 3>();
|
|
|
|
for (std::size_t i = 0; i < N; i++) {
|
|
PointSource query = output[i];
|
|
query.getVector4fMap() =
|
|
transformation_.template cast<float>() * query.getVector4fMap();
|
|
|
|
if (!searchForNeighbors(query, nn_indices, nn_dists)) {
|
|
PCL_ERROR("[pcl::%s::computeTransformation] Unable to find a nearest neighbor "
|
|
"in the target dataset for point %d in the source!\n",
|
|
getClassName().c_str(),
|
|
(*indices_)[i]);
|
|
return;
|
|
}
|
|
|
|
// Check if the distance to the nearest neighbor is smaller than the user imposed
|
|
// threshold
|
|
if (nn_dists[0] < dist_threshold) {
|
|
Eigen::Matrix3d& C1 = (*input_covariances_)[i];
|
|
Eigen::Matrix3d& C2 = (*target_covariances_)[nn_indices[0]];
|
|
Eigen::Matrix3d& M = mahalanobis_[i];
|
|
// M = R*C1
|
|
M = R * C1;
|
|
// temp = M*R' + C2 = R*C1*R' + C2
|
|
Eigen::Matrix3d temp = M * R.transpose();
|
|
temp += C2;
|
|
// M = temp^-1
|
|
M = temp.inverse();
|
|
source_indices[cnt] = static_cast<int>(i);
|
|
target_indices[cnt] = nn_indices[0];
|
|
cnt++;
|
|
}
|
|
}
|
|
// Resize to the actual number of valid correspondences
|
|
source_indices.resize(cnt);
|
|
target_indices.resize(cnt);
|
|
/* optimize transformation using the current assignment and Mahalanobis metrics*/
|
|
previous_transformation_ = transformation_;
|
|
// optimization right here
|
|
try {
|
|
rigid_transformation_estimation_(
|
|
output, source_indices, *target_, target_indices, transformation_);
|
|
/* compute the delta from this iteration */
|
|
delta = 0.;
|
|
for (int k = 0; k < 4; k++) {
|
|
for (int l = 0; l < 4; l++) {
|
|
double ratio = 1;
|
|
if (k < 3 && l < 3) // rotation part of the transform
|
|
ratio = 1. / rotation_epsilon_;
|
|
else
|
|
ratio = 1. / transformation_epsilon_;
|
|
double c_delta =
|
|
ratio * std::abs(previous_transformation_(k, l) - transformation_(k, l));
|
|
if (c_delta > delta)
|
|
delta = c_delta;
|
|
}
|
|
}
|
|
} catch (PCLException& e) {
|
|
PCL_DEBUG("[pcl::%s::computeTransformation] Optimization issue %s\n",
|
|
getClassName().c_str(),
|
|
e.what());
|
|
break;
|
|
}
|
|
nr_iterations_++;
|
|
|
|
if (update_visualizer_ != nullptr) {
|
|
PointCloudSourcePtr input_transformed(new PointCloudSource);
|
|
pcl::transformPointCloud(output, *input_transformed, transformation_);
|
|
update_visualizer_(*input_transformed, source_indices, *target_, target_indices);
|
|
}
|
|
|
|
// Check for convergence
|
|
if (nr_iterations_ >= max_iterations_ || delta < 1) {
|
|
converged_ = true;
|
|
PCL_DEBUG("[pcl::%s::computeTransformation] Convergence reached. Number of "
|
|
"iterations: %d out of %d. Transformation difference: %f\n",
|
|
getClassName().c_str(),
|
|
nr_iterations_,
|
|
max_iterations_,
|
|
(transformation_ - previous_transformation_).array().abs().sum());
|
|
previous_transformation_ = transformation_;
|
|
}
|
|
else
|
|
PCL_DEBUG("[pcl::%s::computeTransformation] Convergence failed\n",
|
|
getClassName().c_str());
|
|
}
|
|
final_transformation_ = previous_transformation_ * guess;
|
|
|
|
PCL_DEBUG("Transformation "
|
|
"is:\n\t%5f\t%5f\t%5f\t%5f\n\t%5f\t%5f\t%5f\t%5f\n\t%5f\t%5f\t%5f\t%5f\n\t%"
|
|
"5f\t%5f\t%5f\t%5f\n",
|
|
final_transformation_(0, 0),
|
|
final_transformation_(0, 1),
|
|
final_transformation_(0, 2),
|
|
final_transformation_(0, 3),
|
|
final_transformation_(1, 0),
|
|
final_transformation_(1, 1),
|
|
final_transformation_(1, 2),
|
|
final_transformation_(1, 3),
|
|
final_transformation_(2, 0),
|
|
final_transformation_(2, 1),
|
|
final_transformation_(2, 2),
|
|
final_transformation_(2, 3),
|
|
final_transformation_(3, 0),
|
|
final_transformation_(3, 1),
|
|
final_transformation_(3, 2),
|
|
final_transformation_(3, 3));
|
|
|
|
// Transform the point cloud
|
|
pcl::transformPointCloud(*input_, output, final_transformation_);
|
|
}
|
|
|
|
template <typename PointSource, typename PointTarget, typename Scalar>
|
|
void
|
|
GeneralizedIterativeClosestPoint<PointSource, PointTarget, Scalar>::applyState(
|
|
Matrix4& t, const Vector6d& x) const
|
|
{
|
|
// Z Y X euler angles convention
|
|
Matrix3 R = (AngleAxis(static_cast<Scalar>(x[5]), Vector3::UnitZ()) *
|
|
AngleAxis(static_cast<Scalar>(x[4]), Vector3::UnitY()) *
|
|
AngleAxis(static_cast<Scalar>(x[3]), Vector3::UnitX()))
|
|
.toRotationMatrix();
|
|
Matrix4 T = Matrix4::Identity();
|
|
T.template block<3, 3>(0, 0) = R;
|
|
T.template block<3, 1>(0, 3) = Vector3(
|
|
static_cast<Scalar>(x[0]), static_cast<Scalar>(x[1]), static_cast<Scalar>(x[2]));
|
|
t = T * t;
|
|
}
|
|
|
|
} // namespace pcl
|
|
|
|
#endif // PCL_REGISTRATION_IMPL_GICP_HPP_
|