void evaluateSVDSolver(const Eigen::MatrixXd& A, const Eigen::VectorXd& b,
const Eigen::VectorXd& x) {
// const double before = aslam::calibration::Timestamp::now();
const Eigen::JacobiSVD<Eigen::MatrixXd> svd(A,
Eigen::ComputeThinU | Eigen::ComputeThinV);
Eigen::VectorXd x_est = svd.solve(b);
// const double after = aslam::calibration::Timestamp::now();
// const double error = (b - A * x_est).norm();
// std::cout << std::fixed << std::setprecision(18) << "error: " << error
// << " est_diff: " << (x - x_est).norm() << " time: " << after - before
// << std::endl;
// std::cout << "estimated rank: " << svd.nonzeroSingularValues() << std::endl;
// std::cout << "estimated rank deficiency: "
// << A.cols() - svd.nonzeroSingularValues() << std::endl;
}
template<typename PointSource, typename PointTarget> void
pcl::NormalDistributionsTransform<PointSource, PointTarget>::computeTransformation (PointCloudSource &output, const Eigen::Matrix4f &guess)
{
nr_iterations_ = 0;
converged_ = false;
double gauss_c1, gauss_c2, gauss_d3;
// Initializes the guassian fitting parameters (eq. 6.8) [Magnusson 2009]
gauss_c1 = 10 * (1 - outlier_ratio_);
gauss_c2 = outlier_ratio_ / pow (resolution_, 3);
gauss_d3 = -log (gauss_c2);
gauss_d1_ = -log ( gauss_c1 + gauss_c2 ) - gauss_d3;
gauss_d2_ = -2 * log ((-log ( gauss_c1 * exp ( -0.5 ) + gauss_c2 ) - gauss_d3) / gauss_d1_);
if (guess != Eigen::Matrix4f::Identity ())
{
// Initialise final transformation to the guessed one
final_transformation_ = guess;
// Apply guessed transformation prior to search for neighbours
transformPointCloud (output, output, guess);
}
// Initialize Point Gradient and Hessian
point_gradient_.setZero ();
point_gradient_.block<3, 3>(0, 0).setIdentity ();
point_hessian_.setZero ();
Eigen::Transform<float, 3, Eigen::Affine, Eigen::ColMajor> eig_transformation;
eig_transformation.matrix () = final_transformation_;
// Convert initial guess matrix to 6 element transformation vector
Eigen::Matrix<double, 6, 1> p, delta_p, score_gradient;
Eigen::Vector3f init_translation = eig_transformation.translation ();
Eigen::Vector3f init_rotation = eig_transformation.rotation ().eulerAngles (0, 1, 2);
p << init_translation (0), init_translation (1), init_translation (2),
init_rotation (0), init_rotation (1), init_rotation (2);
Eigen::Matrix<double, 6, 6> hessian;
double score = 0;
double delta_p_norm;
// Calculate derivates of initial transform vector, subsequent derivative calculations are done in the step length determination.
score = computeDerivatives (score_gradient, hessian, output, p);
while (!converged_)
{
// Store previous transformation
previous_transformation_ = transformation_;
// Solve for decent direction using newton method, line 23 in Algorithm 2 [Magnusson 2009]
Eigen::JacobiSVD<Eigen::Matrix<double, 6, 6> > sv (hessian, Eigen::ComputeFullU | Eigen::ComputeFullV);
// Negative for maximization as opposed to minimization
delta_p = sv.solve (-score_gradient);
//Calculate step length with guarnteed sufficient decrease [More, Thuente 1994]
delta_p_norm = delta_p.norm ();
if (delta_p_norm == 0 || delta_p_norm != delta_p_norm)
{
trans_probability_ = score / static_cast<double> (input_->points.size ());
converged_ = delta_p_norm == delta_p_norm;
return;
}
delta_p.normalize ();
delta_p_norm = computeStepLengthMT (p, delta_p, delta_p_norm, step_size_, transformation_epsilon_ / 2, score, score_gradient, hessian, output);
delta_p *= delta_p_norm;
transformation_ = (Eigen::Translation<float, 3> (static_cast<float> (delta_p (0)), static_cast<float> (delta_p (1)), static_cast<float> (delta_p (2))) *
Eigen::AngleAxis<float> (static_cast<float> (delta_p (3)), Eigen::Vector3f::UnitX ()) *
Eigen::AngleAxis<float> (static_cast<float> (delta_p (4)), Eigen::Vector3f::UnitY ()) *
Eigen::AngleAxis<float> (static_cast<float> (delta_p (5)), Eigen::Vector3f::UnitZ ())).matrix ();
p = p + delta_p;
// Update Visualizer (untested)
if (update_visualizer_ != 0)
update_visualizer_ (output, std::vector<int>(), *target_, std::vector<int>() );
if (nr_iterations_ > max_iterations_ ||
(nr_iterations_ && (std::fabs (delta_p_norm) < transformation_epsilon_)))
{
converged_ = true;
}
nr_iterations_++;
}
// Store transformation probability. The realtive differences within each scan registration are accurate
// but the normalization constants need to be modified for it to be globally accurate
trans_probability_ = score / static_cast<double> (input_->points.size ());
}