Class CPoint2DPDFGaussian

Inheritance Relationships

Base Type

Class Documentation

class CPoint2DPDFGaussian : public mrpt::poses::CPoint2DPDF

A gaussian distribution for 2D points. Also a method for bayesian fusion is provided.

See also

CPoint2DPDF

Public Functions

CPoint2DPDFGaussian()

Default constructor

explicit CPoint2DPDFGaussian(const CPoint2D &init_Mean)

Constructor

CPoint2DPDFGaussian(const CPoint2D &init_Mean, const mrpt::math::CMatrixDouble22 &init_Cov)

Constructor

inline void getMean(CPoint2D &p) const override

Returns an estimate of the point, (the mean, or mathematical expectation of the PDF)

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

Returns an estimate of the point covariance matrix (2x2 cov matrix) and the mean, both at once.

See also

getMean

virtual void copyFrom(const CPoint2DPDF &o) override

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

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

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) override

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 CPoint2DPDFGaussian &p1, const CPoint2DPDFGaussian &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 CPoint2DPDFGaussian &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.

See also

productIntegralNormalizedWith

Throws:

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

double productIntegralNormalizedWith(const CPoint2DPDFGaussian &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.

See also

productIntegralWith

Throws:

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

void drawSingleSample(CPoint2D &outSample) const override

Draw a sample from the pdf

virtual void bayesianFusion(const CPoint2DPDF &p1, const CPoint2DPDF &p2, const double minMahalanobisDistToDrop = 0) override

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 CPoint2DPDFGaussian &other) const

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

double mahalanobisDistanceToPoint(const double x, const double y) const

Returns the Mahalanobis distance from this PDF to some point

Public Members

CPoint2D mean

The mean value

mrpt::math::CMatrixDouble22 cov

The 2x2 covariance matrix