CurvatureEstimationTaubin estimates the curvature for a set of point neighborhoods in the cloud using Taubin Quadric Fitting. This class uses the OpenMP standard to permit parallelized feature computation. More...

#include <curvature_estimation_taubin.h>

Inheritance diagram for pcl::CurvatureEstimationTaubin< PointInT, PointOutT >:

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Public Types
typedef Feature< PointInT, PointOutT >::PointCloudOut	PointCloudOut

Public Member Functions
void	computeFeature (const Eigen::MatrixXd &samples, PointCloudOut &output)
	Estimate the curvature for a set of point neighborhoods with given centroids. More...

	CurvatureEstimationTaubin (unsigned int num_threads=0)
	Constructor. Set the number of threads to use. More...

void	estimateMedianCurvature (const std::vector< int > &indices, const Eigen::VectorXd &quadric_parameters, double &median_curvature, Eigen::Vector3d &normal, Eigen::Vector3d &curvature_axis, Eigen::Vector3d &curvature_centroid, bool is_deterministic=false)
	Estimate the median curvature for a given quadric, using the indices of the point neighborhood that the quadric is fitted to and its parameters, and return the estimated curvature, the normal axis, the curvature axis, and the curvature centroid. More...

void	fitQuadric (const std::vector< int > &indices, Eigen::VectorXd &quadric_parameters, Eigen::Vector3d &quadric_centroid, Eigen::Matrix3d &quadric_covariance_matrix)
	Fit a quadric to a given set of points, using their indices, and return the parameters of the quadric in implicit form, its centroid, and its covariance matrix. This method uses Taubin Quadric Fitting. More...

std::vector< int > const &	getNeighborhoodCentroids () const
	Get the centroid indices of each point neighborhood. More...

std::vector< std::vector< int > > const &	getNeighborhoods () const
	Get the indices of each point neighborhood. More...

void	setNumSamples (int num_samples)
	Set the number of samples (point neighborhoods). More...

void	setNumThreads (int num_threads)
	Set the number of threads used for parallelizing Taubin Quadric Fitting. More...

Static Public Member Functions
static bool	isSecondElementSmaller (const std::vector< double > &p1, const std::vector< double > &p2)
	Compares two vectors by looking at their second elements. More...

Protected Member Functions
void	computeFeature (PointCloudOut &output)
	Estimate the curvature for a set of point neighborhoods sampled from the cloud given by <setInputCloud()>, using the spatial locator in setSearchMethod(). This method creates its own set of randomly selected indices. More...

Private Member Functions
void	computeFeature (const std::vector< int > &nn_indices, int index, PointCloudOut &output)
	Estimate the curvature for a set of points, using their indices and the index of the neighborhood's centroid, and updates the output point cloud. More...

int	sign (double x)
	Get the sign of a given value (according to the sign function). More...

bool	solveGeneralizedEigenProblem (const Eigen::MatrixXd &A, const Eigen::MatrixXd &B, Eigen::MatrixXd &v, Eigen::MatrixXd &lambda)
	Solves the generalized Eigen problem A * v(j) = lambda(j) * B * v(j), where v are the Eigen vectors, and lambda are the Eigen values. The eigenvalues are stored as: (lambda(:, 1) + lambda(:, 2)*i)./lambda(:, 3). This method returns true if the Eigen problem is solved successfully. More...

void	unpackQuadric (const Eigen::VectorXd &quadric_parameters, Eigen::Vector3d &quadric_centroid, Eigen::Matrix3d &quadric_covariance_matrix)
	Unpack the quadric, using its parameters, and return the centroid and the covariance matrix of the quadric. More...

Private Attributes
std::vector< int >	neighborhood_centroids_

std::vector< std::vector< int > >	neighborhoods_

unsigned int	num_samples_

unsigned int	num_threads_

double	time_curvature

double	time_taubin

Detailed Description

template<typename PointInT, typename PointOutT>
class pcl::CurvatureEstimationTaubin< PointInT, PointOutT >

CurvatureEstimationTaubin estimates the curvature for a set of point neighborhoods in the cloud using Taubin Quadric Fitting. This class uses the OpenMP standard to permit parallelized feature computation.

Author: Andreas ten Pas

Definition at line 99 of file curvature_estimation_taubin.h.

Member Typedef Documentation

template<typename PointInT, typename PointOutT>

typedef Feature<PointInT, PointOutT>::PointCloudOut pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::PointCloudOut

Definition at line 110 of file curvature_estimation_taubin.h.

Constructor & Destructor Documentation

template<typename PointInT, typename PointOutT>

pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::CurvatureEstimationTaubin ( unsigned int num_threads = 0 )

inline

Constructor. Set the number of threads to use.

Parameters

num_threads the number of threads to use (0: automatic)

Definition at line 115 of file curvature_estimation_taubin.h.

Member Function Documentation

template<typename PointInT , typename PointOutT >

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::computeFeature	(	const Eigen::MatrixXd &	samples,
		PointCloudOut &	output
	)

Estimate the curvature for a set of point neighborhoods with given centroids.

Parameters

samples	the centroids of the neighborhoods
output	the resultant point cloud that contains the curvature, normal axes, curvature axes, and curvature centroids

Definition at line 6 of file curvature_estimation_taubin.hpp.

template<typename PointInT , typename PointOutT >

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::computeFeature ( PointCloudOut & output )

protected

Estimate the curvature for a set of point neighborhoods sampled from the cloud given by <setInputCloud()>, using the spatial locator in setSearchMethod(). This method creates its own set of randomly selected indices.

Note: If <setIndices()> is used, the set of indices is not randomly selected.

Parameters

output the resultant point cloud that contains the curvature, normal axes, curvature axes, and curvature centroids

Definition at line 129 of file curvature_estimation_taubin.hpp.

template<typename PointInT , typename PointOutT >

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::computeFeature	(	const std::vector< int > &	nn_indices,
		int	index,
		PointCloudOut &	output
	)

private

Estimate the curvature for a set of points, using their indices and the index of the neighborhood's centroid, and updates the output point cloud.

Parameters

output the resultant point cloud that contains the curvature, normal axes, curvature axes, and curvature centroids

Definition at line 212 of file curvature_estimation_taubin.hpp.

template<typename PointInT, typename PointOutT>

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::estimateMedianCurvature	(	const std::vector< int > &	indices,
		const Eigen::VectorXd &	quadric_parameters,
		double &	median_curvature,
		Eigen::Vector3d &	normal,
		Eigen::Vector3d &	curvature_axis,
		Eigen::Vector3d &	curvature_centroid,
		bool	is_deterministic = `false`
	)

inline

Estimate the median curvature for a given quadric, using the indices of the point neighborhood that the quadric is fitted to and its parameters, and return the estimated curvature, the normal axis, the curvature axis, and the curvature centroid.

Parameters

indices	the point cloud indices of the points
quadric_parameters	the quadric parameters as: a, b, c, d, e, f, g, h, i, j (ax^2 + by^2 + cz^2 + dxy + eyz + fxz + gx + hy + iz + j = 0)
median_curvature	the resultant, estimated median curvature of the quadric
normal	the normal axis of the quadric (direction vector)
curvature_axis	the curvature axis of the quadric (direction vector)
curvature_centroid	the centroid of curvature

Definition at line 294 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::fitQuadric	(	const std::vector< int > &	indices,
		Eigen::VectorXd &	quadric_parameters,
		Eigen::Vector3d &	quadric_centroid,
		Eigen::Matrix3d &	quadric_covariance_matrix
	)

inline

Fit a quadric to a given set of points, using their indices, and return the parameters of the quadric in implicit form, its centroid, and its covariance matrix. This method uses Taubin Quadric Fitting.

Parameters

indices	the point cloud indices of the points
quadric_parameters	the resultant quadric parameters as: a, b, c, d, e, f, g, h, i, j (ax^2 + by^2 + cz^2 + dxy + eyz + fxz + gx + hy + iz + j = 0)
quadric_centroid	the resultant centroid of the quadric
quadric_covariance_matrix	the resultant covariance matrix of the quadric

Definition at line 130 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

std::vector<int> const& pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::getNeighborhoodCentroids ( ) const

inline

Get the centroid indices of each point neighborhood.

Definition at line 434 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

std::vector<std::vector<int> > const& pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::getNeighborhoods ( ) const

inline

Get the indices of each point neighborhood.

Definition at line 426 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

static bool pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::isSecondElementSmaller	(	const std::vector< double > &	p1,
		const std::vector< double > &	p2
	)

inlinestatic

Compares two vectors by looking at their second elements.

Parameters

p1	the first vector to compare
p2	the second vector to compare

Definition at line 278 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::setNumSamples ( int num_samples )

inline

Set the number of samples (point neighborhoods).

Parameters

num_samples the number of samples

Definition at line 411 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::setNumThreads ( int num_threads )

inline

Set the number of threads used for parallelizing Taubin Quadric Fitting.

Parameters

num_samples the number of samples

Definition at line 419 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

int pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::sign ( double x )

inlineprivate

Get the sign of a given value (according to the sign function).

Parameters

x	the given value

Definition at line 504 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

bool pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::solveGeneralizedEigenProblem	(	const Eigen::MatrixXd &	A,
		const Eigen::MatrixXd &	B,
		Eigen::MatrixXd &	v,
		Eigen::MatrixXd &	lambda
	)

inlineprivate

Solves the generalized Eigen problem A * v(j) = lambda(j) * B * v(j), where v are the Eigen vectors, and lambda are the Eigen values. The eigenvalues are stored as: (lambda(:, 1) + lambda(:, 2)*i)./lambda(:, 3). This method returns true if the Eigen problem is solved successfully.

Parameters

A	the matrix A in the problem
B	the matrix B in the problem
v	the resultant Eigen vectors
lambda	the resultant Eigen vectors (see above)

Definition at line 522 of file curvature_estimation_taubin.h.

template<typename PointInT, typename PointOutT>

void pcl::CurvatureEstimationTaubin< PointInT, PointOutT >::unpackQuadric	(	const Eigen::VectorXd &	quadric_parameters,
		Eigen::Vector3d &	quadric_centroid,
		Eigen::Matrix3d &	quadric_covariance_matrix
	)

inlineprivate

Unpack the quadric, using its parameters, and return the centroid and the covariance matrix of the quadric.

Parameters

quadric_parameters	the resultant quadric parameters as: a, b, c, d, e, f, g, h, i, j (ax^2 + by^2 + cz^2 + dxy + eyz + fxz + gx + hy + iz + j = 0)
quadric_centroid	the resultant centroid of the quadric
quadric_covariance_matrix	the resultant covariance matrix of the quadric

Definition at line 477 of file curvature_estimation_taubin.h.