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/*
* Software License Agreement (BSD License)
*
* Point Cloud Library (PCL) - www.pointclouds.org
* Copyright (c) 2010-2012, Willow Garage, Inc.
* Copyright (c) 2012-, Open Perception, Inc.
*
* 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 the copyright holder(s) 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 OWNER 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.
*
* $Id$
*
*/
#pragma once
#include <pcl/common/utils.h>
#include <pcl/filters/voxel_grid_covariance.h>
#include <pcl/registration/registration.h>
#include <pcl/memory.h>
#include <pcl/pcl_macros.h>
#include <unsupported/Eigen/NonLinearOptimization>
namespace pcl {
/** \brief A 3D Normal Distribution Transform registration implementation for point
* cloud data. \note For more information please see <b>Magnusson, M. (2009). The
* Three-Dimensional Normal-Distributions Transform — an Efficient Representation for
* Registration, Surface Analysis, and Loop Detection. PhD thesis, Orebro University.
* Orebro Studies in Technology 36.</b>, <b>More, J., and Thuente, D. (1994). Line
* Search Algorithm with Guaranteed Sufficient Decrease In ACM Transactions on
* Mathematical Software.</b> and Sun, W. and Yuan, Y, (2006) Optimization Theory and
* Methods: Nonlinear Programming. 89-100 \note Math refactored by Todor Stoyanov.
* \author Brian Okorn (Space and Naval Warfare Systems Center Pacific)
*/
template <typename PointSource, typename PointTarget>
class NormalDistributionsTransform : public Registration<PointSource, PointTarget> {
protected:
using PointCloudSource =
typename Registration<PointSource, PointTarget>::PointCloudSource;
using PointCloudSourcePtr = typename PointCloudSource::Ptr;
using PointCloudSourceConstPtr = typename PointCloudSource::ConstPtr;
using PointCloudTarget =
typename Registration<PointSource, PointTarget>::PointCloudTarget;
using PointCloudTargetPtr = typename PointCloudTarget::Ptr;
using PointCloudTargetConstPtr = typename PointCloudTarget::ConstPtr;
using PointIndicesPtr = PointIndices::Ptr;
using PointIndicesConstPtr = PointIndices::ConstPtr;
/** \brief Typename of searchable voxel grid containing mean and covariance. */
using TargetGrid = VoxelGridCovariance<PointTarget>;
/** \brief Typename of pointer to searchable voxel grid. */
using TargetGridPtr = TargetGrid*;
/** \brief Typename of const pointer to searchable voxel grid. */
using TargetGridConstPtr = const TargetGrid*;
/** \brief Typename of const pointer to searchable voxel grid leaf. */
using TargetGridLeafConstPtr = typename TargetGrid::LeafConstPtr;
public:
using Ptr = shared_ptr<NormalDistributionsTransform<PointSource, PointTarget>>;
using ConstPtr =
shared_ptr<const NormalDistributionsTransform<PointSource, PointTarget>>;
/** \brief Constructor.
* Sets \ref outlier_ratio_ to 0.35, \ref step_size_ to 0.05 and \ref resolution_
* to 1.0
*/
NormalDistributionsTransform();
/** \brief Empty destructor */
~NormalDistributionsTransform() {}
/** \brief Provide a pointer to the input target (e.g., the point cloud that we want
* to align the input source to). \param[in] cloud the input point cloud target
*/
inline void
setInputTarget(const PointCloudTargetConstPtr& cloud) override
{
Registration<PointSource, PointTarget>::setInputTarget(cloud);
init();
}
/** \brief Set/change the voxel grid resolution.
* \param[in] resolution side length of voxels
*/
inline void
setResolution(float resolution)
{
// Prevents unnessary voxel initiations
if (resolution_ != resolution) {
resolution_ = resolution;
if (input_) {
init();
}
}
}
/** \brief Get voxel grid resolution.
* \return side length of voxels
*/
inline float
getResolution() const
{
return resolution_;
}
/** \brief Get the newton line search maximum step length.
* \return maximum step length
*/
inline double
getStepSize() const
{
return step_size_;
}
/** \brief Set/change the newton line search maximum step length.
* \param[in] step_size maximum step length
*/
inline void
setStepSize(double step_size)
{
step_size_ = step_size;
}
/** \brief Get the point cloud outlier ratio.
* \return outlier ratio
*/
inline double
getOulierRatio() const
{
return outlier_ratio_;
}
/** \brief Set/change the point cloud outlier ratio.
* \param[in] outlier_ratio outlier ratio
*/
inline void
setOulierRatio(double outlier_ratio)
{
outlier_ratio_ = outlier_ratio;
}
/** \brief Get the registration alignment probability.
* \return transformation probability
*/
inline double
getTransformationProbability() const
{
return trans_probability_;
}
/** \brief Get the number of iterations required to calculate alignment.
* \return final number of iterations
*/
inline int
getFinalNumIteration() const
{
return nr_iterations_;
}
/** \brief Convert 6 element transformation vector to affine transformation.
* \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
* \param[out] trans affine transform corresponding to given transfomation vector
*/
static void
convertTransform(const Eigen::Matrix<double, 6, 1>& x, Eigen::Affine3f& trans)
{
trans = Eigen::Translation<float, 3>(x.head<3>().cast<float>()) *
Eigen::AngleAxis<float>(float(x(3)), Eigen::Vector3f::UnitX()) *
Eigen::AngleAxis<float>(float(x(4)), Eigen::Vector3f::UnitY()) *
Eigen::AngleAxis<float>(float(x(5)), Eigen::Vector3f::UnitZ());
}
/** \brief Convert 6 element transformation vector to transformation matrix.
* \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
* \param[out] trans 4x4 transformation matrix corresponding to given transfomation
* vector
*/
static void
convertTransform(const Eigen::Matrix<double, 6, 1>& x, Eigen::Matrix4f& trans)
{
Eigen::Affine3f _affine;
convertTransform(x, _affine);
trans = _affine.matrix();
}
protected:
using Registration<PointSource, PointTarget>::reg_name_;
using Registration<PointSource, PointTarget>::getClassName;
using Registration<PointSource, PointTarget>::input_;
using Registration<PointSource, PointTarget>::indices_;
using Registration<PointSource, PointTarget>::target_;
using Registration<PointSource, PointTarget>::nr_iterations_;
using Registration<PointSource, PointTarget>::max_iterations_;
using Registration<PointSource, PointTarget>::previous_transformation_;
using Registration<PointSource, PointTarget>::final_transformation_;
using Registration<PointSource, PointTarget>::transformation_;
using Registration<PointSource, PointTarget>::transformation_epsilon_;
using Registration<PointSource, PointTarget>::transformation_rotation_epsilon_;
using Registration<PointSource, PointTarget>::converged_;
using Registration<PointSource, PointTarget>::corr_dist_threshold_;
using Registration<PointSource, PointTarget>::inlier_threshold_;
using Registration<PointSource, PointTarget>::update_visualizer_;
/** \brief Estimate the transformation and returns the transformed source (input) as
* output. \param[out] output the resultant input transformed point cloud dataset
*/
virtual void
computeTransformation(PointCloudSource& output)
{
computeTransformation(output, Eigen::Matrix4f::Identity());
}
/** \brief Estimate the transformation and returns the transformed source (input) as
* output. \param[out] output the resultant input transformed point cloud dataset
* \param[in] guess the initial gross estimation of the transformation
*/
void
computeTransformation(PointCloudSource& output,
const Eigen::Matrix4f& guess) override;
/** \brief Initiate covariance voxel structure. */
void inline init()
{
target_cells_.setLeafSize(resolution_, resolution_, resolution_);
target_cells_.setInputCloud(target_);
// Initiate voxel structure.
target_cells_.filter(true);
}
/** \brief Compute derivatives of probability function w.r.t. the transformation
* vector. \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009]. \param[out]
* score_gradient the gradient vector of the probability function w.r.t. the
* transformation vector \param[out] hessian the hessian matrix of the probability
* function w.r.t. the transformation vector \param[in] trans_cloud transformed point
* cloud \param[in] transform the current transform vector \param[in] compute_hessian
* flag to calculate hessian, unnessissary for step calculation.
*/
double
computeDerivatives(Eigen::Matrix<double, 6, 1>& score_gradient,
Eigen::Matrix<double, 6, 6>& hessian,
const PointCloudSource& trans_cloud,
const Eigen::Matrix<double, 6, 1>& transform,
bool compute_hessian = true);
/** \brief Compute individual point contirbutions to derivatives of probability
* function w.r.t. the transformation vector. \note Equation 6.10, 6.12 and 6.13
* [Magnusson 2009]. \param[in,out] score_gradient the gradient vector of the
* probability function w.r.t. the transformation vector \param[in,out] hessian the
* hessian matrix of the probability function w.r.t. the transformation vector
* \param[in] x_trans transformed point minus mean of occupied covariance voxel
* \param[in] c_inv covariance of occupied covariance voxel
* \param[in] compute_hessian flag to calculate hessian, unnessissary for step
* calculation.
*/
double
updateDerivatives(Eigen::Matrix<double, 6, 1>& score_gradient,
Eigen::Matrix<double, 6, 6>& hessian,
const Eigen::Vector3d& x_trans,
const Eigen::Matrix3d& c_inv,
bool compute_hessian = true) const;
/** \brief Precompute anglular components of derivatives.
* \note Equation 6.19 and 6.21 [Magnusson 2009].
* \param[in] transform the current transform vector
* \param[in] compute_hessian flag to calculate hessian, unnessissary for step
* calculation.
*/
void
computeAngleDerivatives(const Eigen::Matrix<double, 6, 1>& transform,
bool compute_hessian = true);
/** \brief Compute point derivatives.
* \note Equation 6.18-21 [Magnusson 2009].
* \param[in] x point from the input cloud
* \param[in] compute_hessian flag to calculate hessian, unnessissary for step
* calculation.
*/
void
computePointDerivatives(const Eigen::Vector3d& x, bool compute_hessian = true);
/** \brief Compute hessian of probability function w.r.t. the transformation vector.
* \note Equation 6.13 [Magnusson 2009].
* \param[out] hessian the hessian matrix of the probability function w.r.t. the
* transformation vector \param[in] trans_cloud transformed point cloud
*/
void
computeHessian(Eigen::Matrix<double, 6, 6>& hessian,
const PointCloudSource& trans_cloud);
/** \brief Compute hessian of probability function w.r.t. the transformation vector.
* \note Equation 6.13 [Magnusson 2009].
* \param[out] hessian the hessian matrix of the probability function w.r.t. the
* transformation vector \param[in] trans_cloud transformed point cloud \param[in]
* transform the current transform vector
*/
PCL_DEPRECATED(1, 15, "Parameter `transform` is not required")
void
computeHessian(Eigen::Matrix<double, 6, 6>& hessian,
const PointCloudSource& trans_cloud,
const Eigen::Matrix<double, 6, 1>& transform)
{
pcl::utils::ignore(transform);
computeHessian(hessian, trans_cloud);
}
/** \brief Compute individual point contirbutions to hessian of probability function
* w.r.t. the transformation vector. \note Equation 6.13 [Magnusson 2009].
* \param[in,out] hessian the hessian matrix of the probability function w.r.t. the
* transformation vector \param[in] x_trans transformed point minus mean of occupied
* covariance voxel \param[in] c_inv covariance of occupied covariance voxel
*/
void
updateHessian(Eigen::Matrix<double, 6, 6>& hessian,
const Eigen::Vector3d& x_trans,
const Eigen::Matrix3d& c_inv) const;
/** \brief Compute line search step length and update transform and probability
* derivatives using More-Thuente method. \note Search Algorithm [More, Thuente 1994]
* \param[in] transform initial transformation vector, \f$ x \f$ in Equation 1.3
* (Moore, Thuente 1994) and \f$ \vec{p} \f$ in Algorithm 2 [Magnusson 2009]
* \param[in] step_dir descent direction, \f$ p \f$ in Equation 1.3 (Moore, Thuente
* 1994) and \f$ \delta \vec{p} \f$ normalized in Algorithm 2 [Magnusson 2009]
* \param[in] step_init initial step length estimate, \f$ \alpha_0 \f$ in
* Moore-Thuente (1994) and the noramal of \f$ \delta \vec{p} \f$ in Algorithm 2
* [Magnusson 2009] \param[in] step_max maximum step length, \f$ \alpha_max \f$ in
* Moore-Thuente (1994) \param[in] step_min minimum step length, \f$ \alpha_min \f$ in
* Moore-Thuente (1994) \param[out] score final score function value, \f$ f(x + \alpha
* p) \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ score \f$ in Algorithm 2
* [Magnusson 2009] \param[in,out] score_gradient gradient of score function w.r.t.
* transformation vector, \f$ f'(x + \alpha p) \f$ in Moore-Thuente (1994) and \f$
* \vec{g} \f$ in Algorithm 2 [Magnusson 2009] \param[out] hessian hessian of score
* function w.r.t. transformation vector, \f$ f''(x + \alpha p) \f$ in Moore-Thuente
* (1994) and \f$ H \f$ in Algorithm 2 [Magnusson 2009] \param[in,out] trans_cloud
* transformed point cloud, \f$ X \f$ transformed by \f$ T(\vec{p},\vec{x}) \f$ in
* Algorithm 2 [Magnusson 2009] \return final step length
*/
double
computeStepLengthMT(const Eigen::Matrix<double, 6, 1>& transform,
Eigen::Matrix<double, 6, 1>& step_dir,
double step_init,
double step_max,
double step_min,
double& score,
Eigen::Matrix<double, 6, 1>& score_gradient,
Eigen::Matrix<double, 6, 6>& hessian,
PointCloudSource& trans_cloud);
/** \brief Update interval of possible step lengths for More-Thuente method, \f$ I \f$
* in More-Thuente (1994) \note Updating Algorithm until some value satisfies \f$
* \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$ and Modified Updating
* Algorithm from then on [More, Thuente 1994]. \param[in,out] a_l first endpoint of
* interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente (1994) \param[in,out] f_l
* value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_l)
* \f$ for Update Algorithm and \f$ \phi(\alpha_l) \f$ for Modified Update Algorithm
* \param[in,out] g_l derivative at first endpoint, \f$ g_l \f$ in Moore-Thuente
* (1994), \f$ \psi'(\alpha_l) \f$ for Update Algorithm and \f$ \phi'(\alpha_l) \f$
* for Modified Update Algorithm \param[in,out] a_u second endpoint of interval \f$ I
* \f$, \f$ \alpha_u \f$ in Moore-Thuente (1994) \param[in,out] f_u value at second
* endpoint, \f$ f_u \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_u) \f$ for Update
* Algorithm and \f$ \phi(\alpha_u) \f$ for Modified Update Algorithm \param[in,out]
* g_u derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994), \f$
* \psi'(\alpha_u) \f$ for Update Algorithm and \f$ \phi'(\alpha_u) \f$ for Modified
* Update Algorithm \param[in] a_t trial value, \f$ \alpha_t \f$ in Moore-Thuente
* (1994) \param[in] f_t value at trial value, \f$ f_t \f$ in Moore-Thuente (1994),
* \f$ \psi(\alpha_t) \f$ for Update Algorithm and \f$ \phi(\alpha_t) \f$ for Modified
* Update Algorithm \param[in] g_t derivative at trial value, \f$ g_t \f$ in
* Moore-Thuente (1994), \f$ \psi'(\alpha_t) \f$ for Update Algorithm and \f$
* \phi'(\alpha_t) \f$ for Modified Update Algorithm \return if interval converges
*/
bool
updateIntervalMT(double& a_l,
double& f_l,
double& g_l,
double& a_u,
double& f_u,
double& g_u,
double a_t,
double f_t,
double g_t) const;
/** \brief Select new trial value for More-Thuente method.
* \note Trial Value Selection [More, Thuente 1994], \f$ \psi(\alpha_k) \f$ is used
* for \f$ f_k \f$ and \f$ g_k \f$ until some value satisfies the test \f$
* \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$ then \f$
* \phi(\alpha_k) \f$ is used from then on. \note Interpolation Minimizer equations
* from Optimization Theory and Methods: Nonlinear Programming By Wenyu Sun, Ya-xiang
* Yuan (89-100). \param[in] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l
* \f$ in Moore-Thuente (1994) \param[in] f_l value at first endpoint, \f$ f_l \f$ in
* Moore-Thuente (1994) \param[in] g_l derivative at first endpoint, \f$ g_l \f$ in
* Moore-Thuente (1994) \param[in] a_u second endpoint of interval \f$ I \f$, \f$
* \alpha_u \f$ in Moore-Thuente (1994) \param[in] f_u value at second endpoint, \f$
* f_u \f$ in Moore-Thuente (1994) \param[in] g_u derivative at second endpoint, \f$
* g_u \f$ in Moore-Thuente (1994) \param[in] a_t previous trial value, \f$ \alpha_t
* \f$ in Moore-Thuente (1994) \param[in] f_t value at previous trial value, \f$ f_t
* \f$ in Moore-Thuente (1994) \param[in] g_t derivative at previous trial value, \f$
* g_t \f$ in Moore-Thuente (1994) \return new trial value
*/
double
trialValueSelectionMT(double a_l,
double f_l,
double g_l,
double a_u,
double f_u,
double g_u,
double a_t,
double f_t,
double g_t) const;
/** \brief Auxiliary function used to determine endpoints of More-Thuente interval.
* \note \f$ \psi(\alpha) \f$ in Equation 1.6 (Moore, Thuente 1994)
* \param[in] a the step length, \f$ \alpha \f$ in More-Thuente (1994)
* \param[in] f_a function value at step length a, \f$ \phi(\alpha) \f$ in
* More-Thuente (1994) \param[in] f_0 initial function value, \f$ \phi(0) \f$ in
* Moore-Thuente (1994) \param[in] g_0 initial function gradient, \f$ \phi'(0) \f$ in
* More-Thuente (1994) \param[in] mu the step length, constant \f$ \mu \f$ in
* Equation 1.1 [More, Thuente 1994] \return sufficient decrease value
*/
inline double
auxilaryFunction_PsiMT(
double a, double f_a, double f_0, double g_0, double mu = 1.e-4) const
{
return f_a - f_0 - mu * g_0 * a;
}
/** \brief Auxiliary function derivative used to determine endpoints of More-Thuente
* interval. \note \f$ \psi'(\alpha) \f$, derivative of Equation 1.6 (Moore, Thuente
* 1994) \param[in] g_a function gradient at step length a, \f$ \phi'(\alpha) \f$ in
* More-Thuente (1994) \param[in] g_0 initial function gradient, \f$ \phi'(0) \f$ in
* More-Thuente (1994) \param[in] mu the step length, constant \f$ \mu \f$ in
* Equation 1.1 [More, Thuente 1994] \return sufficient decrease derivative
*/
inline double
auxilaryFunction_dPsiMT(double g_a, double g_0, double mu = 1.e-4) const
{
return g_a - mu * g_0;
}
/** \brief The voxel grid generated from target cloud containing point means and
* covariances. */
TargetGrid target_cells_;
/** \brief The side length of voxels. */
float resolution_;
/** \brief The maximum step length. */
double step_size_;
/** \brief The ratio of outliers of points w.r.t. a normal distribution, Equation 6.7
* [Magnusson 2009]. */
double outlier_ratio_;
/** \brief The normalization constants used fit the point distribution to a normal
* distribution, Equation 6.8 [Magnusson 2009]. */
double gauss_d1_, gauss_d2_;
/** \brief The probability score of the transform applied to the input cloud,
* Equation 6.9 and 6.10 [Magnusson 2009]. */
double trans_probability_;
/** \brief Precomputed Angular Gradient
*
* The precomputed angular derivatives for the jacobian of a transformation vector,
* Equation 6.19 [Magnusson 2009].
*/
Eigen::Matrix<double, 8, 4> angular_jacobian_;
/** \brief Precomputed Angular Hessian
*
* The precomputed angular derivatives for the hessian of a transformation vector,
* Equation 6.19 [Magnusson 2009].
*/
Eigen::Matrix<double, 15, 4> angular_hessian_;
/** \brief The first order derivative of the transformation of a point w.r.t. the
* transform vector, \f$ J_E \f$ in Equation 6.18 [Magnusson 2009]. */
Eigen::Matrix<double, 3, 6> point_jacobian_;
/** \brief The second order derivative of the transformation of a point w.r.t. the
* transform vector, \f$ H_E \f$ in Equation 6.20 [Magnusson 2009]. */
Eigen::Matrix<double, 18, 6> point_hessian_;
public:
PCL_MAKE_ALIGNED_OPERATOR_NEW
};
} // namespace pcl
#include <pcl/registration/impl/ndt.hpp>
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