CPointPDFGaussian.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2020, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */
#pragma once

#include <mrpt/math/CMatrixF.h>
#include <mrpt/poses/CPointPDF.h>

namespace mrpt::poses
{
/** A gaussian distribution for 3D points. Also a method for bayesian fusion is
 * provided.
 *
 * \sa CPointPDF
 * \ingroup poses_pdf_grp
 */
class CPointPDFGaussian : public CPointPDF
{
    DEFINE_SERIALIZABLE(CPointPDFGaussian, mrpt::poses)
    DEFINE_SCHEMA_SERIALIZABLE()

   public:
    /** Default constructor
     */
    CPointPDFGaussian();

    /** Constructor
     */
    CPointPDFGaussian(const CPoint3D& init_Mean);

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

    /** The mean value */
    CPoint3D mean;
    /** The 3x3 covariance matrix */
    mrpt::math::CMatrixDouble33 cov;

    void getMean(CPoint3D& p) const override;
    std::tuple<cov_mat_t, type_value> getCovarianceAndMean() const override
    {
        return {cov, mean};
    }

    /** Copy operator, translating if necesary (for example, between particles
     * and gaussian representations) */
    void copyFrom(const CPointPDF& o) 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. */
    bool saveToTextFile(const std::string& file) const 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 changeCoordinatesReference(const CPose3D& newReferenceBase) override;

    /** Bayesian fusion of two points gauss. distributions, then save the result
     *in this object.
     *  The process is as follows:<br>
     *      - (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<sup>-1</sup> + S2<sup>-1</sup>)<sup>-1</sup>;
     *    x = S * ( S1<sup>-1</sup>*x1 + S2<sup>-1</sup>*x2 );
     */
    void bayesianFusion(
        const CPointPDFGaussian& p1, const CPointPDFGaussian& p2);

    /** 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.
     * \sa productIntegralNormalizedWith
     * \exception std::exception On errors like covariance matrix with null
     * determinant, etc...
     */
    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.
     * NOTE: This version ignores the "z" coordinates!!
     * \sa productIntegralNormalizedWith
     * \exception std::exception On errors like covariance matrix with null
     * determinant, etc...
     */
    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 in the range [0,1]
     *  Note that the resulting value is in fact
     *  \f[ exp( -\frac{1}{2} D^2 ) \f]
     *  , with \f$ D^2 \f$ being the square Mahalanobis distance between the
     * two pdfs.
     * \sa productIntegralWith
     * \exception std::exception On errors like covariance matrix with null
     * determinant, etc...
     */
    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]. This versions ignores the
     * "z" coordinate.
     *
     *  Note that the resulting value is in fact
     *  \f[ exp( -\frac{1}{2} D^2 ) \f]
     *  , with \f$ D^2 \f$ being the square Mahalanobis distance between the
     * two pdfs.
     * \sa productIntegralWith
     * \exception std::exception On errors like covariance matrix with null
     * determinant, etc...
     */
    double productIntegralNormalizedWith2D(const CPointPDFGaussian& p) const;

    /** Draw a sample from the pdf */
    void drawSingleSample(CPoint3D& outSample) const 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!)
     * \param p1 The first distribution to fuse
     * \param p2 The second distribution to fuse
     * \param 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.
     */
    void bayesianFusion(
        const CPointPDF& p1, const CPointPDF& p2,
        const double minMahalanobisDistToDrop = 0) override;

    /** Returns the Mahalanobis distance from this PDF to another PDF, that is,
     * it's evaluation at (0,0,0) */
    double mahalanobisDistanceTo(
        const CPointPDFGaussian& other, bool only_2D = false) const;

};  // End of class def.
}  // namespace mrpt::poses