maxloss.h

/*
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      names of its contributors may be used to endorse or promote products
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*/

#pragma once

#define MAXLOSS 10000000.0 // clamping of the maximal possible loss for numerical stability

#include "Hypothesis.h"

/**
 * @brief Inverts a pose hypothesis.
 * @param hyp Input pose hypothesis.
 * @return Pose hypothesis that corresponds to the inverse transformation.
 */
Hypothesis getInvHyp(const Hypothesis& hyp)
{
    cv::Mat_<double> trans = cv::Mat_<float>::eye(4, 4);

    hyp.getRotation().copyTo(trans.rowRange(0,3).colRange(0,3));
    trans(0, 3) = hyp.getTranslation().x;
    trans(1, 3) = hyp.getTranslation().y;
    trans(2, 3) = hyp.getTranslation().z;

    trans = trans.inv();

    cv::Mat_<double>invRot(3, 3);
    trans.rowRange(0,3).colRange(0,3).copyTo(invRot);
    cv::Point3d t;
    t.x = trans(0, 3);
    t.y = trans(1, 3);
    t.z = trans(2, 3);

    Hypothesis invHyp;
    invHyp.setRotation(invRot);
    invHyp.setTranslation(t);
    return invHyp;
}

/**
 * @brief Maximum of translational error (cm) and rotational error (deg) between two pose hypothesis.
 * @param h1 Pose 1.
 * @param h2 Pose 2.
 * @return Loss.
 */
double maxLoss(const Hypothesis& h1, const Hypothesis& h2)
{
    // measure loss of inverted poses (camera pose instead of scene pose)
    Hypothesis invH1 = getInvHyp(h1);
    Hypothesis invH2 = getInvHyp(h2);

    double rotErr = invH1.calcAngularDistance(invH2);
    double tErr = cv::norm(invH1.getTranslation() - invH2.getTranslation());

    return std::min(std::max(rotErr, tErr / 10), MAXLOSS);
}

/**
 * @brief Calculate the derivative of the loss w.r.t. the estimated pose.
 * @param est Estimated pose (6 DoF).
 * @param gt Ground truth pose (6 DoF).
 * @return 1x6 Jacobean.
 */
cv::Mat_<double> dLossMax(std::vector<double> est, const std::vector<double>& gt)
{
    // data conversion
    cv::Mat rod1(3, 1, CV_64F), rod2(3, 1, CV_64F);
    rod1.at<double>(0, 0) = est[0]; rod1.at<double>(1, 0) = est[1]; rod1.at<double>(2, 0) = est[2];
    rod2.at<double>(0, 0) = gt[0]; rod2.at<double>(1, 0) = gt[1]; rod2.at<double>(2, 0) = gt[2];

    cv::Mat rot1, rot2, dRod;
    cv::Rodrigues(rod1, rot1, dRod);
    cv::Rodrigues(rod2, rot2);

    // measure loss of inverted poses (camera pose instead of scene pose)
    cv::Mat_<double> invRot1 = rot1.t();
    cv::Mat_<double> invRot2 = rot2.t();

    // get the difference rotation
    cv::Mat diffRot = rot1 * invRot2;

    // calculate rotational and translational error
    double trace = cv::trace(diffRot)[0];
    trace = std::min(3.0, std::max(-1.0, trace));
    double rotErr = 180*acos((trace-1.0)/2.0)/CV_PI;

    cv::Mat_<double> invT1(3, 1);
    invT1(0, 0) = -est[3] / 10;
    invT1(1, 0) = -est[4] / 10;
    invT1(2, 0) = -est[5] / 10;
    invT1 = invRot1 * invT1;

    cv::Mat_<double> invT2(3, 1);
    invT2(0, 0) = -gt[3] / 10;
    invT2(1, 0) = -gt[4] / 10;
    invT2(2, 0) = -gt[5] / 10;
    invT2 = invRot2 * invT2;

    double tErr = cv::norm(invT1 - invT2);

    cv::Mat_<double> jacobean = cv::Mat_<double>::zeros(1, est.size());

    // clamped loss, return zero gradient if loss is bigger than threshold
    if(std::max(rotErr, tErr) > MAXLOSS)
        return jacobean;

    // zero error, abort
    if((tErr + rotErr) < EPS)
        return jacobean;

    if(tErr > rotErr)
    {
        // return gradient of translational error
        cv::Mat_<double> dDist_dInvT1(1, 3);
        for(unsigned i = 0; i < 3; i++)
            dDist_dInvT1(0, i) = (invT1(i, 0) - invT2(i, 0)) / tErr;

        cv::Mat_<double> dInvT1_dEstT(3, 3);
        dInvT1_dEstT = -invRot1;

        cv::Mat_<double> dDist_dEstT = dDist_dInvT1 * dInvT1_dEstT;
        dDist_dEstT.copyTo(jacobean.colRange(3, 6));

        cv::Mat_<double> dInvT1_dInvRot1 = cv::Mat_<double>::zeros(3, 9);
        dInvT1_dInvRot1(0, 0) = -est[3] / 10;
        dInvT1_dInvRot1(0, 3) = -est[4] / 10;
        dInvT1_dInvRot1(0, 6) = -est[5] / 10;

        dInvT1_dInvRot1(1, 1) = -est[3] / 10;
        dInvT1_dInvRot1(1, 4) = -est[4] / 10;
        dInvT1_dInvRot1(1, 7) = -est[5] / 10;

        dInvT1_dInvRot1(2, 2) = -est[3] / 10;
        dInvT1_dInvRot1(2, 5) = -est[4] / 10;
        dInvT1_dInvRot1(2, 8) = -est[5] / 10;

        dRod = dRod.t();

        cv::Mat_<double> dDist_dRod = dDist_dInvT1 * dInvT1_dInvRot1 * dRod;
        dDist_dRod.copyTo(jacobean.colRange(0, 3));
    }
    else
    {
        // return gradient of rotational error
        dRod = dRod.t();

        cv::Mat_<double> dRotDiff = cv::Mat_<double>::zeros(9, 9);
        invRot2.row(0).copyTo(dRotDiff.row(0).colRange(0, 3));
        invRot2.row(1).copyTo(dRotDiff.row(1).colRange(0, 3));
        invRot2.row(2).copyTo(dRotDiff.row(2).colRange(0, 3));

        invRot2.row(0).copyTo(dRotDiff.row(3).colRange(3, 6));
        invRot2.row(1).copyTo(dRotDiff.row(4).colRange(3, 6));
        invRot2.row(2).copyTo(dRotDiff.row(5).colRange(3, 6));

        invRot2.row(0).copyTo(dRotDiff.row(6).colRange(6, 9));
        invRot2.row(1).copyTo(dRotDiff.row(7).colRange(6, 9));
        invRot2.row(2).copyTo(dRotDiff.row(8).colRange(6, 9));

        dRotDiff = dRotDiff.t();

        cv::Mat_<double> dTrace = cv::Mat_<double>::zeros(1, 9);
        dTrace(0, 0) = 1;
        dTrace(0, 4) = 1;
        dTrace(0, 8) = 1;

        cv::Mat_<double> dAngle = (180 / CV_PI * -1 / sqrt(3 - trace * trace + 2 * trace)) * dTrace * dRotDiff * dRod;
        dAngle.copyTo(jacobean.colRange(0, 3));
    }

    if(cv::sum(cv::Mat(jacobean != jacobean))[0] > 0) //check for NaNs
        return cv::Mat_<double>::zeros(1, est.size());

    return jacobean;
}