mrpt::poses::CPose3DQuatPDFGaussian Class Reference

Declares a class that represents a Probability Density function (PDF) of a 3D pose using a quaternion $p(\mathbf{x}) = [x ~ y ~ z ~ qr ~ qx ~ qy ~ qz]^\top$ . More...

#include <mrpt/poses/CPose3DQuatPDFGaussian.h>

Inheritance diagram for mrpt::poses::CPose3DQuatPDFGaussian:

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List of all members.

Public Member Functions
	CPose3DQuatPDFGaussian ()
	Default constructor - set all values to zero.
	CPose3DQuatPDFGaussian (bool, bool)
	Constructor which left all the member uninitialized, for using when speed is critical - as argument, use UNINITIALIZED_QUATERNION.
	CPose3DQuatPDFGaussian (const CPose3DQuat &init_Mean)
	Constructor from a default mean value, covariance equals to zero.
	CPose3DQuatPDFGaussian (const CPose3DQuat &init_Mean, const CMatrixDouble77 &init_Cov)
	Constructor with mean and covariance.
	CPose3DQuatPDFGaussian (const CPosePDFGaussian &o)
	Constructor from a Gaussian 2D pose PDF (sets to 0 the missing variables).
	CPose3DQuatPDFGaussian (const CPose3DPDFGaussian &o)
	Constructor from an equivalent Gaussian in Euler angles representation.
void	getMean (CPose3DQuat &mean_pose) const
	Returns an estimate of the pose, (the mean, or mathematical expectation of the PDF).
void	getCovarianceAndMean (CMatrixDouble77 &cov, CPose3DQuat &mean_point) const
	Returns an estimate of the pose covariance matrix (7x7 cov matrix) and the mean, both at once.
void	copyFrom (const CPose3DQuatPDF &o)
	Copy operator, translating if necesary (for example, between particles and gaussian representations).
void	copyFrom (const CPosePDF &o)
	Copy operator, translating if necesary (for example, between particles and gaussian representations).
void	copyFrom (const CPose3DPDFGaussian &o)
	Copy operator, translating if necesary (for example, between particles and gaussian representations).
void	saveToTextFile (const std::string &file) const
	Save the PDF to a text file, containing the 3D pose in the first line (x y z qr qx qy qz), then the covariance matrix in the next 7 lines.
void	changeCoordinatesReference (const CPose3DQuat &newReferenceBase)
	This can be used to convert a PDF from local coordinates to global, providing the point (newReferenceBase) from which "to project" the current pdf.
void	changeCoordinatesReference (const CPose3D &newReferenceBase)
	This can be used to convert a PDF from local coordinates to global, providing the point (newReferenceBase) from which "to project" the current pdf.
void	drawSingleSample (CPose3DQuat &outPart) const
	Draws a single sample from the distribution.
void	drawManySamples (size_t N, std::vector< vector_double > &outSamples) const
	Draws a number of samples from the distribution, and saves as a list of 1x7 vectors, where each row contains a (x,y,z,qr,qx,qy,qz) datum.
void	bayesianFusion (const CPose3DQuatPDF &p1, const CPose3DQuatPDF &p2)
	Bayesian fusion of two points gauss.
void	inverse (CPose3DQuatPDF &o) const
	Returns a new PDF such as: NEW_PDF = (0,0,0) - THIS_PDF.
CPose3DQuatPDFGaussian	operator- () const
	Unary - operator, returns the PDF of the inverse pose.
void	operator+= (const CPose3DQuat &Ap)
	Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated).
void	operator+= (const CPose3DQuatPDFGaussian &Ap)
	Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated) (see formulas in jacobiansPoseComposition ).
void	operator-= (const CPose3DQuatPDFGaussian &Ap)
	Makes: thisPDF = thisPDF - Ap, where "-" is pose inverse composition (both the mean, and the covariance matrix are updated).
double	evaluatePDF (const CPose3DQuat &x) const
	Evaluates the PDF at a given point.
double	evaluateNormalizedPDF (const CPose3DQuat &x) const
	Evaluates the ratio PDF(x) / PDF(MEAN), that is, the normalized PDF in the range [0,1].
double	mahalanobisDistanceTo (const CPose3DQuatPDFGaussian &theOther)
	Computes the Mahalanobis distance between the centers of two Gaussians.
Static Public Member Functions
static void	jacobiansPoseComposition (const CPose3DQuat &x, const CPose3DQuat &u, CMatrixDouble77 &df_dx, CMatrixDouble77 &df_du, CPose3DQuat *out_x_oplus_u=NULL)
	This static method computes the two Jacobians of a pose composition operation $f(x,u)= x u$.
Public Attributes
CPose3DQuat	mean
	The mean value.
CMatrixDouble77	cov
	The 7x7 covariance matrix.
Protected Member Functions
void	assureSymmetry ()
	Assures the symmetry of the covariance matrix (eventually certain operations in the math-coprocessor lead to non-symmetric matrixes!).

Detailed Description

Declares a class that represents a Probability Density function (PDF) of a 3D pose using a quaternion $p(\mathbf{x}) = [x ~ y ~ z ~ qr ~ qx ~ qy ~ qz]^\top$ .

This class implements that PDF using a mono-modal Gaussian distribution. See mrpt::poses::CPose3DQuatPDF for more details, or mrpt::poses::CPose3DPDF for classes based on Euler angles instead.

Uncertainty of pose composition operations ( $y = x \oplus u$ ) is implemented in the methods "CPose3DQuatPDFGaussian::operator+=" and "CPose3DQuatPDFGaussian::jacobiansPoseComposition".

For further details on implemented methods and the theory behind them, see the report: * "6D poses as Euler angles, transformation matrices and quaternions: equivalences, compositions and uncertainty", Jose-Luis Blanco (Technical Report), 2010.

See also:: CPose3DQuat, CPose3DQuatPDF, CPose3DPDF

Definition at line 57 of file CPose3DQuatPDFGaussian.h.

Constructor & Destructor Documentation

mrpt::poses::CPose3DQuatPDFGaussian::CPose3DQuatPDFGaussian ( )

Default constructor - set all values to zero.

mrpt::poses::CPose3DQuatPDFGaussian::CPose3DQuatPDFGaussian	(	bool	,
		bool
	)

Constructor which left all the member uninitialized, for using when speed is critical - as argument, use UNINITIALIZED_QUATERNION.

mrpt::poses::CPose3DQuatPDFGaussian::CPose3DQuatPDFGaussian ( const CPose3DQuat & init_Mean ) [explicit]

Constructor from a default mean value, covariance equals to zero.

mrpt::poses::CPose3DQuatPDFGaussian::CPose3DQuatPDFGaussian	(	const CPose3DQuat &	init_Mean,
		const CMatrixDouble77 &	init_Cov
	)

Constructor with mean and covariance.

mrpt::poses::CPose3DQuatPDFGaussian::CPose3DQuatPDFGaussian ( const CPosePDFGaussian & o ) [explicit]

Constructor from a Gaussian 2D pose PDF (sets to 0 the missing variables).

mrpt::poses::CPose3DQuatPDFGaussian::CPose3DQuatPDFGaussian ( const CPose3DPDFGaussian & o ) [explicit]

Constructor from an equivalent Gaussian in Euler angles representation.

Member Function Documentation

void mrpt::poses::CPose3DQuatPDFGaussian::assureSymmetry ( ) [protected]

Assures the symmetry of the covariance matrix (eventually certain operations in the math-coprocessor lead to non-symmetric matrixes!).

void mrpt::poses::CPose3DQuatPDFGaussian::bayesianFusion	(	const CPose3DQuatPDF &	p1,
		const CPose3DQuatPDF &	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 = (S1^-1 + S2^-1)^-1; x = S * ( S1^-1*x1 + S2^-1*x2 );

void mrpt::poses::CPose3DQuatPDFGaussian::changeCoordinatesReference ( const CPose3D & newReferenceBase ) [virtual]

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.

Implements mrpt::utils::CProbabilityDensityFunction< CPose3DQuat, 7 >.

void mrpt::poses::CPose3DQuatPDFGaussian::changeCoordinatesReference ( const CPose3DQuat & newReferenceBase )

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.

void mrpt::poses::CPose3DQuatPDFGaussian::copyFrom ( const CPose3DPDFGaussian & o )

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

void mrpt::poses::CPose3DQuatPDFGaussian::copyFrom ( const CPosePDF & o )

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

void mrpt::poses::CPose3DQuatPDFGaussian::copyFrom ( const CPose3DQuatPDF & o )

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

void mrpt::poses::CPose3DQuatPDFGaussian::drawManySamples	(	size_t	N,
		std::vector< vector_double > &	outSamples
	)			const `[virtual]`

Draws a number of samples from the distribution, and saves as a list of 1x7 vectors, where each row contains a (x,y,z,qr,qx,qy,qz) datum.

Reimplemented from mrpt::utils::CProbabilityDensityFunction< CPose3DQuat, 7 >.

void mrpt::poses::CPose3DQuatPDFGaussian::drawSingleSample ( CPose3DQuat & outPart ) const [virtual]

Draws a single sample from the distribution.

Implements mrpt::utils::CProbabilityDensityFunction< CPose3DQuat, 7 >.

double mrpt::poses::CPose3DQuatPDFGaussian::evaluateNormalizedPDF ( const CPose3DQuat & x ) const

Evaluates the ratio PDF(x) / PDF(MEAN), that is, the normalized PDF in the range [0,1].

double mrpt::poses::CPose3DQuatPDFGaussian::evaluatePDF ( const CPose3DQuat & x ) const

Evaluates the PDF at a given point.

void mrpt::poses::CPose3DQuatPDFGaussian::getCovarianceAndMean	(	CMatrixDouble77 &	cov,
		CPose3DQuat &	mean_point
	)			const

Returns an estimate of the pose covariance matrix (7x7 cov matrix) and the mean, both at once.

See also:: getMean

void mrpt::poses::CPose3DQuatPDFGaussian::getMean ( CPose3DQuat & mean_pose ) const [virtual]

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

See also:: getCovariance

Implements mrpt::utils::CProbabilityDensityFunction< CPose3DQuat, 7 >.

void mrpt::poses::CPose3DQuatPDFGaussian::inverse ( CPose3DQuatPDF & o ) const

Returns a new PDF such as: NEW_PDF = (0,0,0) - THIS_PDF.

static void mrpt::poses::CPose3DQuatPDFGaussian::jacobiansPoseComposition	(	const CPose3DQuat &	x,
		const CPose3DQuat &	u,
		CMatrixDouble77 &	df_dx,
		CMatrixDouble77 &	df_du,
		CPose3DQuat *	out_x_oplus_u = `NULL`
	)			`[static]`

This static method computes the two Jacobians of a pose composition operation $f(x,u)= x u$.

Parameters:

out_x_oplus_u

If set to !=NULL, the result of "x+u" will be stored here (it will be computed internally anyway). To see the mathematical derivation of the formulas, refer to the technical report here:

http://www.mrpt.org/Probability_Density_Distributions_Over_Spatial_Representations

double mrpt::poses::CPose3DQuatPDFGaussian::mahalanobisDistanceTo ( const CPose3DQuatPDFGaussian & theOther )

Computes the Mahalanobis distance between the centers of two Gaussians.

The variables with a variance exactly equal to 0 are not taken into account in the process, but "infinity" is returned if the corresponding elements are not exactly equal.

void mrpt::poses::CPose3DQuatPDFGaussian::operator+= ( const CPose3DQuatPDFGaussian & Ap )

Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated) (see formulas in jacobiansPoseComposition ).

void mrpt::poses::CPose3DQuatPDFGaussian::operator+= ( const CPose3DQuat & Ap )

Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the mean, and the covariance matrix are updated).

CPose3DQuatPDFGaussian mrpt::poses::CPose3DQuatPDFGaussian::operator- ( ) const [inline]

Unary - operator, returns the PDF of the inverse pose.

Definition at line 152 of file CPose3DQuatPDFGaussian.h.

References UNINITIALIZED_QUATERNION.

void mrpt::poses::CPose3DQuatPDFGaussian::operator-= ( const CPose3DQuatPDFGaussian & Ap )

Makes: thisPDF = thisPDF - Ap, where "-" is pose inverse composition (both the mean, and the covariance matrix are updated).

void mrpt::poses::CPose3DQuatPDFGaussian::saveToTextFile ( const std::string & file ) const [virtual]

Save the PDF to a text file, containing the 3D pose in the first line (x y z qr qx qy qz), then the covariance matrix in the next 7 lines.

Implements mrpt::utils::CProbabilityDensityFunction< CPose3DQuat, 7 >.

Member Data Documentation

CMatrixDouble77 mrpt::poses::CPose3DQuatPDFGaussian::cov

The 7x7 covariance matrix.

Definition at line 90 of file CPose3DQuatPDFGaussian.h.

CPose3DQuat mrpt::poses::CPose3DQuatPDFGaussian::mean

The mean value.

Definition at line 87 of file CPose3DQuatPDFGaussian.h.

mrpt::poses::CPose3DQuatPDFGaussian Class Reference

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation