data_association.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2019, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

#include "slam-precomp.h"  // Precompiled headers

#include <mrpt/math/KDTreeCapable.h>  // For kd-tree's
#include <mrpt/math/data_utils.h>
#include <mrpt/math/distributions.h>  // for chi2inv
#include <mrpt/math/ops_matrices.h>  // extractSubmatrix
#include <mrpt/poses/CPoint2DPDFGaussian.h>
#include <mrpt/poses/CPointPDFGaussian.h>
#include <mrpt/slam/data_association.h>
#include <Eigen/Dense>
#include <memory>
#include <memory>  // unique_ptr
#include <nanoflann.hpp>  // For kd-tree's
#include <numeric>  // accumulate
#include <set>

/*
   For all data association algorithms, the individual compatibility is
   estabished by
   the chi2 test (Mahalanobis distance), but later on one of the potential
   pairings is
   picked by the metric given by the user (maha vs. match. lik.)

   Related papers:
    - Matching likelihood. See:  https://www.mrpt.org/Paper:Matching_Likelihood

    - JCBB: Joint Compatibility Branch & Bound [Neira, Tardos 2001]

*/

using namespace std;
using namespace mrpt;
using namespace mrpt::math;
using namespace mrpt::poses;
using namespace mrpt::slam;

namespace mrpt::slam
{
struct TAuxDataRecursiveJCBB
{
    /** Just to avoid recomputing them all the time. */
    size_t nPredictions, nObservations, length_O;
    std::map<size_t, size_t> currentAssociation;
};

/**  Computes the joint distance metric (mahalanobis or matching likelihood)
 * between two  a set of associations
 *
 * On "currentAssociation":  maps "ID_obs" -> "ID_pred"
 *  For each landmark ID in the observations (ID_obs), its association
 *  in the predictions, that is: ID_pred = associations[ID_obs]
 *
 */
template <typename T, TDataAssociationMetric METRIC>
double joint_pdf_metric(
    const CMatrixDynamic<T>& Z_observations_mean,
    const CMatrixDynamic<T>& Y_predictions_mean,
    const CMatrixDynamic<T>& Y_predictions_cov,
    const TAuxDataRecursiveJCBB& info, const TDataAssociationResults& aux_data)
{
    MRPT_UNUSED_PARAM(aux_data);
    // Make a list of the indices of the predictions that appear in
    // "currentAssociation":
    const size_t N = info.currentAssociation.size();
    ASSERT_(N > 0);
    std::vector<size_t> indices_pred(
        N);  // Appearance order indices in the std::maps
    std::vector<size_t> indices_obs(N);

    {
        size_t i = 0;
        for (auto it : info.currentAssociation)
        {
            indices_obs[i] = it.first;
            indices_pred[i] = it.second;
            i++;
        }
    }

    // ----------------------------------------------------------------------
    // Extract submatrix of the covariances involved here:
    //  COV = PREDICTIONS_COV(INDX,INDX) + OBSERVATIONS_COV(INDX2,INDX2)
    // ----------------------------------------------------------------------
    CMatrixDynamic<T> COV;
    mrpt::math::extractSubmatrixSymmetricalBlocksDyn(
        Y_predictions_cov,
        info.length_O,  // dims of cov. submatrices
        indices_pred, COV);

    // ----------------------------------------------------------------------
    // Mean:
    // The same for the vector of "errors" or "innovation" between predictions
    // and observations:
    // ----------------------------------------------------------------------
    Eigen::Matrix<T, Eigen::Dynamic, 1> innovations(N * info.length_O);
    T* dst_ptr = &innovations[0];
    for (auto it = info.currentAssociation.begin();
         it != info.currentAssociation.end(); ++it)
    {
        const T* pred_i_mean = &Y_predictions_mean(it->second, 0);
        const T* obs_i_mean = &Z_observations_mean(it->first, 0);

        for (unsigned int k = 0; k < info.length_O; k++)
            *dst_ptr++ = pred_i_mean[k] - obs_i_mean[k];
    }

    // Compute mahalanobis distance squared:
    const CMatrixDynamic<T> COV_inv = COV.inverse_LLt();

    const double d2 = mrpt::math::multiply_HCHt_scalar(innovations, COV_inv);

    if (METRIC == metricMaha) return d2;

    ASSERT_(METRIC == metricML);

    // Matching likelihood: The evaluation at 0 of the PDF of the difference
    // between the two Gaussians:
    const T cov_det = COV.det();
    const double ml = exp(-0.5 * d2) / (std::pow(M_2PI, info.length_O * 0.5) *
                                        std::sqrt(cov_det));
    return ml;
}

template <TDataAssociationMetric METRIC>
bool isCloser(const double v1, const double v2);

template <>
bool isCloser<metricMaha>(const double v1, const double v2)
{
    return v1 < v2;
}

template <>
bool isCloser<metricML>(const double v1, const double v2)
{
    return v1 > v2;
}

/* Based on MATLAB code by:
  University of Zaragoza
  Centro Politecnico Superior
  Robotics and Real Time Group
  Authors of the original MATLAB code:  J. Neira, J. Tardos
  C++ version: J.L. Blanco Claraco
*/
template <typename T, TDataAssociationMetric METRIC>
void JCBB_recursive(
    const mrpt::math::CMatrixDynamic<T>& Z_observations_mean,
    const mrpt::math::CMatrixDynamic<T>& Y_predictions_mean,
    const mrpt::math::CMatrixDynamic<T>& Y_predictions_cov,
    TDataAssociationResults& results, const TAuxDataRecursiveJCBB& info,
    const observation_index_t curObsIdx)
{
    // End of iteration?
    if (curObsIdx >= info.nObservations)
    {
        if (info.currentAssociation.size() > results.associations.size())
        {
            // It's a better choice since more features are matched.
            results.associations = info.currentAssociation;
            results.distance = joint_pdf_metric<T, METRIC>(
                Z_observations_mean, Y_predictions_mean, Y_predictions_cov,
                info, results);
        }
        else if (
            !info.currentAssociation.empty() &&
            info.currentAssociation.size() == results.associations.size())
        {
            // The same # of features matched than the previous best one...
            // decide by better distance:
            const double d2 = joint_pdf_metric<T, METRIC>(
                Z_observations_mean, Y_predictions_mean, Y_predictions_cov,
                info, results);

            if (isCloser<METRIC>(d2, results.distance))
            {
                results.associations = info.currentAssociation;
                results.distance = d2;
            }
        }
    }
    else  // A normal iteration:
    {
        // Iterate for all compatible landmarsk of "curObsIdx"
        const observation_index_t obsIdx = curObsIdx;

        const size_t nPreds = results.indiv_compatibility.rows();

        // Can we do it better than the current "results.associations"?
        // This can be checked by counting the potential new pairings+the so-far
        // established ones.
        //    Matlab: potentials  = pairings(compatibility.AL(i+1:end))
        // Moved up by Kasra Khosoussi
        const size_t potentials = std::accumulate(
            results.indiv_compatibility_counts.begin() + (obsIdx + 1),
            results.indiv_compatibility_counts.end(), 0);
        for (prediction_index_t predIdx = 0; predIdx < nPreds; predIdx++)
        {
            if ((info.currentAssociation.size() + potentials) >=
                results.associations.size())
            {
                // Only if predIdx is NOT already assigned:
                if (results.indiv_compatibility(predIdx, obsIdx))
                {
                    // Only if predIdx is NOT already assigned:
                    bool already_asigned = false;
                    for (auto itS : info.currentAssociation)
                    {
                        if (itS.second == predIdx)
                        {
                            already_asigned = true;
                            break;
                        }
                    }

                    if (!already_asigned)
                    {
                        // Launch a new recursive line for this hipothesis:
                        TAuxDataRecursiveJCBB new_info = info;
                        new_info.currentAssociation[curObsIdx] = predIdx;

                        results.nNodesExploredInJCBB++;

                        JCBB_recursive<T, METRIC>(
                            Z_observations_mean, Y_predictions_mean,
                            Y_predictions_cov, results, new_info,
                            curObsIdx + 1);
                    }
                }
            }
        }

        // Can we do it better than the current "results.associations"?
        if ((info.currentAssociation.size() + potentials) >=
            results.associations.size())
        {
            // Yes we can </obama>

            // star node: Ei not paired
            results.nNodesExploredInJCBB++;
            JCBB_recursive<T, METRIC>(
                Z_observations_mean, Y_predictions_mean, Y_predictions_cov,
                results, info, curObsIdx + 1);
        }
    }
}

}  // namespace mrpt::slam

/* ==================================================================================================
Computes the data-association between the prediction of a set of landmarks and
their observations, all of them with covariance matrices.
* Implemented methods include (see TDataAssociation)
*       - NN: Nearest-neighbor
*       - JCBB: Joint Compatibility Branch & Bound [Neira, Tardos 2001]
*
*  With both a Mahalanobis-distance or Matching-likelihood metric (See paper:
http://www.mrpt.org/Paper:Matching_Likelihood )
*
* \param Z_observations_mean [IN] An MxO matrix with the M observations, each
row containing the observation "mean".
* \param Y_predictions_mean [IN ] An NxO matrix with the N predictions, each row
containing the mean of one prediction.
* \param Y_predictions_cov [IN ] An N·OxN·O matrix with the full covariance
matrix of all the N predictions.

* \param predictions_mean [IN] The list of predicted locations of
landmarks/features, indexed by their ID. The 2D/3D locations are in the same
coordinate framework than "observations".
* \param predictions_cov [IN] The full covariance matrix of predictions, in
blocks of 2x2 matrices. The order of the submatrices is the appearance order of
lanmarks in "predictions_mean".
* \param results [OUT] The output data association hypothesis, and other useful
information.
* \param method [IN, optional] The selected method to make the associations.
* \param chi2quantile [IN, optional] The threshold for considering a match
between two close Gaussians for two landmarks, in the range [0,1]. It is used to
call mrpt::math::chi2inv
* \param use_kd_tree [IN, optional] Build a KD-tree to speed-up the evaluation
of individual compatibility (IC). It's perhaps more efficient to disable it for
a small number of features. (default=true).
* \param predictions_IDs [IN, optional] (default:none) An N-vector. If provided,
the resulting associations in "results.associations" will not contain prediction
indices "i", but "predictions_IDs[i]".
*
 ==================================================================================================
*/
void mrpt::slam::data_association_full_covariance(
    const mrpt::math::CMatrixDouble& Z_observations_mean,
    const mrpt::math::CMatrixDouble& Y_predictions_mean,
    const mrpt::math::CMatrixDouble& Y_predictions_cov,
    TDataAssociationResults& results, const TDataAssociationMethod method,
    const TDataAssociationMetric metric, const double chi2quantile,
    const bool DAT_ASOC_USE_KDTREE,
    const std::vector<prediction_index_t>& predictions_IDs,
    const TDataAssociationMetric compatibilityTestMetric,
    const double log_ML_compat_test_threshold)
{
    // For details on the theory, see the papers cited at the beginning of this
    // file.

    using nanoflann::KDTreeEigenMatrixAdaptor;

    MRPT_START

    results.clear();

    const size_t nPredictions = Y_predictions_mean.rows();
    const size_t nObservations = Z_observations_mean.rows();

    const size_t length_O = Z_observations_mean.cols();

    ASSERT_(nPredictions != 0);
    ASSERT_(nObservations != 0);
    ASSERT_(length_O == (size_t)Y_predictions_mean.cols());
    ASSERT_(length_O * nPredictions == (size_t)Y_predictions_cov.rows());
    ASSERT_(Y_predictions_cov.isSquare());
    ASSERT_(chi2quantile > 0 && chi2quantile < 1);
    ASSERT_(metric == metricMaha || metric == metricML);
    const double chi2thres = mrpt::math::chi2inv(chi2quantile, length_O);

    // ------------------------------------------------------------
    // Build a KD-tree of the predictions for quick look-up:
    // ------------------------------------------------------------
    using KDTreeMatrixPtr =
        std::unique_ptr<KDTreeEigenMatrixAdaptor<CMatrixDouble>>;
    KDTreeMatrixPtr kd_tree;
    const size_t N_KD_RESULTS = nPredictions;
    std::vector<double> kd_result_distances(
        DAT_ASOC_USE_KDTREE ? N_KD_RESULTS : 0);
    std::vector<CMatrixDouble::Index> kd_result_indices(
        DAT_ASOC_USE_KDTREE ? N_KD_RESULTS : 0);
    std::vector<double> kd_queryPoint(DAT_ASOC_USE_KDTREE ? length_O : 0);

    if (DAT_ASOC_USE_KDTREE)
    {
        // Construct kd-tree for the predictions:
        kd_tree = std::make_unique<KDTreeEigenMatrixAdaptor<CMatrixDouble>>(
            length_O, Y_predictions_mean);
    }

    // Initialize with the worst possible distance:
    results.distance =
        (metric == metricML) ? 0 : std::numeric_limits<double>::max();

    //-------------------------------------------
    // Compute the individual compatibility:
    //-------------------------------------------
    results.indiv_distances.resize(nPredictions, nObservations);
    results.indiv_compatibility.setSize(nPredictions, nObservations);
    results.indiv_compatibility_counts.assign(nObservations, 0);

    results.indiv_distances.fill(
        metric == metricMaha ? 1000 /*A very large Sq. Maha. Dist. */
                             : -1000 /*A very small log-likelihoo   */);
    results.indiv_compatibility.fill(false);

    CMatrixDouble pred_i_cov(length_O, length_O);

    Eigen::VectorXd diff_means_i_j(length_O);

    for (size_t j = 0; j < nObservations; ++j)
    {
        if (!DAT_ASOC_USE_KDTREE)
        {
            // Compute all the distances w/o a KD-tree
            for (size_t i = 0; i < nPredictions; ++i)
            {
                // Evaluate sqr. mahalanobis distance of obs_j -> pred_i:
                // Extract the submatrix from the diagonal:
                const size_t pred_cov_idx = i * length_O;
                pred_i_cov = Y_predictions_cov.asEigen().block(
                    pred_cov_idx, pred_cov_idx, length_O, length_O);

                for (size_t k = 0; k < length_O; k++)
                    diff_means_i_j[k] =
                        Z_observations_mean(j, k) - Y_predictions_mean(i, k);

                double d2, ml;
                // mrpt::math::productIntegralAndMahalanobisTwoGaussians(diff_means_i_j,pred_i_cov,obs_j_cov,
                // d2,ml);
                mrpt::math::mahalanobisDistance2AndLogPDF(
                    diff_means_i_j, pred_i_cov, d2, ml);

                // The distance according to the metric
                double val = (metric == metricMaha) ? d2 : ml;

                results.indiv_distances(i, j) = val;

                // Individual compatibility
                const bool IC = (compatibilityTestMetric == metricML)
                                    ? (ml > log_ML_compat_test_threshold)
                                    : (d2 < chi2thres);
                results.indiv_compatibility(i, j) = IC;
                if (IC) results.indiv_compatibility_counts[j]++;
            }
        }
        else
        {
            // Use a kd-tree and compute only the N closest ones:
            for (size_t k = 0; k < length_O; k++)
                kd_queryPoint[k] = Z_observations_mean(j, k);

            kd_tree->query(
                &kd_queryPoint[0], N_KD_RESULTS, &kd_result_indices[0],
                &kd_result_distances[0]);

            // Only compute the distances for these ones:
            for (size_t w = 0; w < N_KD_RESULTS; w++)
            {
                const size_t i = kd_result_indices[w];  // This is the index of
                // the prediction in
                // "predictions_mean"

                // Build the PDF of the prediction:
                // Extract the submatrix from the diagonal:
                const size_t pred_cov_idx = i * length_O;
                pred_i_cov = Y_predictions_cov.asEigen().block(
                    pred_cov_idx, pred_cov_idx, length_O, length_O);

                for (size_t k = 0; k < length_O; k++)
                    diff_means_i_j[k] =
                        Z_observations_mean(j, k) - Y_predictions_mean(i, k);

                double d2, ml;
                //              mrpt::math::productIntegralAndMahalanobisTwoGaussians(diff_means_i_j,pred_i_cov,obs_j_cov,
                // d2,ml);
                mrpt::math::mahalanobisDistance2AndLogPDF(
                    diff_means_i_j, pred_i_cov, d2, ml);

                if (d2 > 6 * chi2thres)
                    break;  // Since kd-tree returns the landmarks by distance
                // order, we can skip the rest

                // The distance according to the metric
                double val = (metric == metricMaha) ? d2 : ml;

                results.indiv_distances(i, j) = val;

                // Individual compatibility
                const bool IC = (compatibilityTestMetric == metricML)
                                    ? (ml > log_ML_compat_test_threshold)
                                    : (d2 < chi2thres);
                results.indiv_compatibility(i, j) = IC;
                if (IC) results.indiv_compatibility_counts[j]++;
            }
        }  // end use KD-Tree
    }  // end for

#if 0
    cout << "Distances: " << endl << results.indiv_distances << endl;
    //cout << "indiv compat: " << endl << results.indiv_compatibility << endl;
#endif

    // Do associations:
    results.associations.clear();

    switch (method)
    {
        // --------------------------
        // Nearest-neighbor
        // --------------------------
        case assocNN:
        {
            // 1) For each observation "j", make a list of the indiv. compatible
            //     predictions and their distances, sorted first the best.
            //     NOTE: distances are saved so smaller is always better,
            //            hence "metricML" are made negative.
            // -------------------------------------------------------------------
            using TListAllICs = multimap<
                double,
                pair<
                    observation_index_t, multimap<double, prediction_index_t>>>;
            TListAllICs lst_all_ICs;

            for (observation_index_t j = 0; j < nObservations; ++j)
            {
                multimap<double, prediction_index_t> ICs;

                for (prediction_index_t i = 0; i < nPredictions; ++i)
                {
                    if (results.indiv_compatibility(i, j))
                    {
                        double d2 = results.indiv_distances(i, j);
                        if (metric == metricML) d2 = -d2;
                        ICs.insert(make_pair(d2, i));
                    }
                }

                if (!ICs.empty())
                {
                    const double best_dist = ICs.begin()->first;
                    lst_all_ICs.insert(make_pair(best_dist, make_pair(j, ICs)));
                }
            }

            // 2) With that lists, start by the best one and make the
            // assignment.
            //    Remove the prediction from the list of available, and go on.
            // --------------------------------------------------------------------
            std::set<prediction_index_t> lst_already_taken_preds;

            for (auto it = lst_all_ICs.begin(); it != lst_all_ICs.end(); ++it)
            {
                const observation_index_t obs_id = it->second.first;
                const multimap<double, prediction_index_t>& lstCompats =
                    it->second.second;

                for (auto lstCompat : lstCompats)
                {
                    if (lst_already_taken_preds.find(lstCompat.second) ==
                        lst_already_taken_preds.end())
                    {
                        // It's free: make the association:
                        results.associations[obs_id] = lstCompat.second;
                        lst_already_taken_preds.insert(lstCompat.second);
                        break;
                    }
                }
            }
        }
        break;

        // ------------------------------------
        // Joint Compatibility Branch & Bound:
        // ------------------------------------
        case assocJCBB:
        {
            // Call to the recursive method:
            TAuxDataRecursiveJCBB info;
            info.nPredictions = nPredictions;
            info.nObservations = nObservations;
            info.length_O = length_O;

            if (metric == metricMaha)
                JCBB_recursive<CMatrixDouble::Scalar, metricMaha>(
                    Z_observations_mean, Y_predictions_mean, Y_predictions_cov,
                    results, info, 0);
            else
                JCBB_recursive<CMatrixDouble::Scalar, metricML>(
                    Z_observations_mean, Y_predictions_mean, Y_predictions_cov,
                    results, info, 0);
        }
        break;

        default:
            THROW_EXCEPTION("Unknown value of 'method'");
    };

    // If a mapping of prediction indices to IDs was providen, apply it now:
    // ------------------------------------------------------------------------
    if (!predictions_IDs.empty())
    {
        ASSERT_(predictions_IDs.size() == nPredictions);
        for (auto& association : results.associations)
            association.second = predictions_IDs[association.second];
    }

    MRPT_END
}

/* ==================================================================================================
                    data_association_independent_predictions
   ==================================================================================================
   */
void mrpt::slam::data_association_independent_predictions(
    const mrpt::math::CMatrixDouble& Z_observations_mean,
    const mrpt::math::CMatrixDouble& Y_predictions_mean,
    const mrpt::math::CMatrixDouble& Y_predictions_cov_stacked,
    TDataAssociationResults& results, const TDataAssociationMethod method,
    const TDataAssociationMetric metric, const double chi2quantile,
    const bool DAT_ASOC_USE_KDTREE,
    const std::vector<prediction_index_t>& predictions_IDs,
    const TDataAssociationMetric compatibilityTestMetric,
    const double log_ML_compat_test_threshold)
{
    MRPT_START

    results.clear();

    const size_t nPredictions = Y_predictions_mean.rows();
    const size_t nObservations = Z_observations_mean.rows();

    const size_t length_O = Z_observations_mean.cols();

    ASSERT_(nPredictions != 0);
    ASSERT_(nObservations != 0);
    ASSERT_(length_O == (size_t)Y_predictions_mean.cols());
    ASSERT_(
        length_O * nPredictions == (size_t)Y_predictions_cov_stacked.rows());
    ASSERT_(chi2quantile > 0 && chi2quantile < 1);
    ASSERT_(metric == metricMaha || metric == metricML);
    // const double chi2thres = mrpt::math::chi2inv( chi2quantile, length_O );

    // TODO: Optimized version!!
    CMatrixDouble Y_predictions_cov_full(
        length_O * nPredictions, length_O * nPredictions);
    CMatrixDouble COV_i(length_O, length_O);
    for (size_t i = 0; i < nPredictions; i++)
    {
        const size_t idx = i * length_O;
        COV_i =
            Y_predictions_cov_stacked.extractMatrix(length_O, length_O, idx, 0);
        Y_predictions_cov_full.insertMatrix(idx, idx, COV_i);
    }

    data_association_full_covariance(
        Z_observations_mean, Y_predictions_mean, Y_predictions_cov_full,
        results, method, metric, chi2quantile, DAT_ASOC_USE_KDTREE,
        predictions_IDs, compatibilityTestMetric, log_ML_compat_test_threshold);

    MRPT_END
}