class mrpt::poses::CPointPDFGaussian

A gaussian distribution for 3D points.

Also a method for bayesian fusion is provided.

CPointPDF

#include <mrpt/poses/CPointPDFGaussian.h>

class CPointPDFGaussian: public mrpt::poses::CPointPDF
{
public:
//
fields

CPoint3D mean;
mrpt::math::CMatrixDouble33 cov;

// construction

CPointPDFGaussian();
CPointPDFGaussian(const CPoint3D& init_Mean);
CPointPDFGaussian(const CPoint3D& init_Mean, const mrpt::math::CMatrixDouble33& init_Cov);

//
methods

void getMean(CPoint3D& p) const;
virtual std::tuple<cov_mat_t, type_value> getCovarianceAndMean() const;
virtual void copyFrom(const CPointPDF& o);
virtual bool saveToTextFile(const std::string& file) const;
virtual void changeCoordinatesReference(const CPose3D& newReferenceBase);
void bayesianFusion(const CPointPDFGaussian& p1, const CPointPDFGaussian& p2);
double productIntegralWith(const CPointPDFGaussian& p) const;
double productIntegralWith2D(const CPointPDFGaussian& p) const;
double productIntegralNormalizedWith(const CPointPDFGaussian& p) const;
double productIntegralNormalizedWith2D(const CPointPDFGaussian& p) const;
void drawSingleSample(CPoint3D& outSample) const;
virtual void bayesianFusion(const CPointPDF& p1, const CPointPDF& p2, const double minMahalanobisDistToDrop = 0);
double mahalanobisDistanceTo(const CPointPDFGaussian& other, bool only_2D = false) const;
};

Inherited Members

public:
// typedefs

typedef CProbabilityDensityFunction<TDATA, STATE_LEN> self_t;

//
methods

virtual void copyFrom(const CPointPDF& o) = 0;
virtual void changeCoordinatesReference(const CPose3D& newReferenceBase) = 0;

Fields

CPoint3D mean

The mean value.

mrpt::math::CMatrixDouble33 cov

The 3x3 covariance matrix.

Construction

CPointPDFGaussian()

Default constructor.

CPointPDFGaussian(const CPoint3D& init_Mean)

Constructor.

CPointPDFGaussian(const CPoint3D& init_Mean, const mrpt::math::CMatrixDouble33& init_Cov)

Constructor.

Methods

virtual std::tuple<cov_mat_t, type_value> getCovarianceAndMean() const

Returns an estimate of the pose covariance matrix (STATE_LENxSTATE_LEN cov matrix) and the mean, both at once.

virtual void copyFrom(const CPointPDF& o)

Copy operator, translating if necesary (for example, between particles and gaussian representations)

virtual bool saveToTextFile(const std::string& file) const

Save PDF’s particles to a text file, containing the 2D pose in the first line, then the covariance matrix in next 3 lines.

virtual void changeCoordinatesReference(const CPose3D& newReferenceBase)

this = p (+) this.

This can be used to convert a PDF from local coordinates to global, providing the point (newReferenceBase) from which “to project” the current pdf. Result PDF substituted the currently stored one in the object. Both the mean value and the covariance matrix are updated correctly.

void bayesianFusion(const CPointPDFGaussian& p1, const CPointPDFGaussian& p2)

Bayesian fusion of two points gauss.

distributions, then save the result in this object. The process is as follows:

• (x1,S1): Mean and variance of the p1 distribution.

• (x2,S2): Mean and variance of the p2 distribution.

• (x,S): Mean and variance of the resulting distribution.

$$S = (S_1^{-1} + S_2^{-1})^{-1}$$ $$x = S ( S_1^{-1} x_1 + S_2^{-1} x_2 )$$

double productIntegralWith(const CPointPDFGaussian& p) const

Computes the “correspondence likelihood” of this PDF with another one: This is implemented as the integral from -inf to +inf of the product of both PDF.

The resulting number is >=0.

Parameters:

 std::exception On errors like covariance matrix with null determinant, etc…

productIntegralNormalizedWith

double productIntegralWith2D(const CPointPDFGaussian& p) const

Computes the “correspondence likelihood” of this PDF with another one: This is implemented as the integral from -inf to +inf of the product of both PDF.

The resulting number is >=0. NOTE: This version ignores the “z” coordinates!!

Parameters:

 std::exception On errors like covariance matrix with null determinant, etc…

productIntegralNormalizedWith

double productIntegralNormalizedWith(const CPointPDFGaussian& p) const

Computes the “correspondence likelihood” of this PDF with another one: This is implemented as the integral from -inf to +inf of the product of both PDF.

The resulting number is in the range [0,1] Note that the resulting value is in fact

$exp( -\frac{1}{2} D^2 )$

, with $$D^2$$ being the square Mahalanobis distance between the two pdfs.

Parameters:

 std::exception On errors like covariance matrix with null determinant, etc…

productIntegralWith

double productIntegralNormalizedWith2D(const CPointPDFGaussian& p) const

Computes the “correspondence likelihood” of this PDF with another one: This is implemented as the integral from -inf to +inf of the product of both PDF.

The resulting number is in the range [0,1]. This versions ignores the “z” coordinate.

Note that the resulting value is in fact

$exp( -\frac{1}{2} D^2 )$

, with $$D^2$$ being the square Mahalanobis distance between the two pdfs.

Parameters:

 std::exception On errors like covariance matrix with null determinant, etc…

productIntegralWith

void drawSingleSample(CPoint3D& outSample) const

Draw a sample from the pdf.

virtual void bayesianFusion(
const CPointPDF& p1,
const CPointPDF& p2,
const double minMahalanobisDistToDrop = 0
)

Bayesian fusion of two point distributions (product of two distributions->new distribution), then save the result in this object (WARNING: See implementing classes to see classes that can and cannot be mixtured!)

Parameters:

 p1 The first distribution to fuse p2 The second distribution to fuse minMahalanobisDistToDrop If set to different of 0, the result of very separate Gaussian modes (that will result in negligible components) in SOGs will be dropped to reduce the number of modes in the output.
double mahalanobisDistanceTo(
const CPointPDFGaussian& other,
bool only_2D = false
) const

Returns the Mahalanobis distance from this PDF to another PDF, that is, it’s evaluation at (0,0,0)