PointToPointWithCov.cpp

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/*

Copyright (c) 2010--2012,
François Pomerleau and Stephane Magnenat, ASL, ETHZ, Switzerland
You can contact the authors at <f dot pomerleau at gmail dot com> and
<stephane at magnenat dot net>

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#include "ErrorMinimizersImpl.h"
#include "PointMatcherPrivate.h"
#include "Eigen/SVD"

using namespace Eigen;

template<typename T>
PointToPointWithCovErrorMinimizer<T>::PointToPointWithCovErrorMinimizer(const Parameters& params):
        PointToPointErrorMinimizer<T>("PointToPointWithCovErrorMinimizer", availableParameters(), params),
        sensorStdDev(Parametrizable::get<T>("sensorStdDev"))
{
}

template<typename T>
typename PointMatcher<T>::TransformationParameters PointToPointWithCovErrorMinimizer<T>::compute(const ErrorElements& mPts_const)
{
        ErrorElements mPts = mPts_const;
        typename PointMatcher<T>::TransformationParameters result = PointToPointErrorMinimizer<T>::compute_in_place(mPts);
        
        this->covMatrix = this->estimateCovariance(mPts, result);
        
        return result;
}

//TODO: rewrite this using ErrorElements struct
template<typename T>
typename PointToPointWithCovErrorMinimizer<T>::Matrix PointToPointWithCovErrorMinimizer<T>::estimateCovariance(const ErrorElements& mPts, const TransformationParameters& transformation)
{
        const int max_nbr_point = mPts.reading.getNbPoints();
        
        Matrix covariance(Matrix::Zero(6,6));
        Matrix J_hessian(Matrix::Zero(6,6));
        Matrix d2J_dReadingdX(Matrix::Zero(6, max_nbr_point));
        Matrix d2J_dReferencedX(Matrix::Zero(6, max_nbr_point));
        
        Vector reading_point(Vector::Zero(3));
        Vector reference_point(Vector::Zero(3));
        Vector normal(3);
        Vector reading_direction(Vector::Zero(3));
        Vector reference_direction(Vector::Zero(3));
        
        normal << 1.0, 1.0, 1.0;    // Used for point-to-point computation
        
        T beta = -asin(transformation(2,0));
        T alpha = atan2(transformation(2,1), transformation(2,2));
        T gamma = atan2(transformation(1,0)/cos(beta), transformation(0,0)/cos(beta));
        T t_x = transformation(0,3);
        T t_y = transformation(1,3);
        T t_z = transformation(2,3);
        
        Vector tmp_vector_6(Vector::Zero(6));
        
        int valid_points_count = 0;
        
        //TODO: add missing const
        for(int i = 0; i < max_nbr_point; ++i)
        {
                //if (outlierWeights(0,i) > 0.0)
                {
                        reading_point = mPts.reading.features.block(0,i,3,1);
                        //int reference_idx = matches.ids(0,i);
                        reference_point = mPts.reference.features.block(0,i,3,1);
                        
                        T reading_range = reading_point.norm();
                        reading_direction = reading_point / reading_range;
                        T reference_range = reference_point.norm();
                        reference_direction = reference_point / reference_range;
                        
                        T n_alpha = normal(2)*reading_direction(1) - normal(1)*reading_direction(2);
                        T n_beta = normal(0)*reading_direction(2) - normal(2)*reading_direction(0);
                        T n_gamma = normal(1)*reading_direction(0) - normal(0)*reading_direction(1);
                        
                        T E = normal(0)*(reading_point(0) - gamma*reading_point(1) + beta*reading_point(2) + t_x - reference_point(0));
                        E +=  normal(1)*(gamma*reading_point(0) + reading_point(1) - alpha*reading_point(2) + t_y - reference_point(1));
                        E +=  normal(2)*(-beta*reading_point(0) + alpha*reading_point(1) + reading_point(2) + t_z - reference_point(2));
                        
                        T N_reading = normal(0)*(reading_direction(0) - gamma*reading_direction(1) + beta*reading_direction(2));
                        N_reading +=  normal(1)*(gamma*reading_direction(0) + reading_direction(1) - alpha*reading_direction(2));
                        N_reading +=  normal(2)*(-beta*reading_direction(0) + alpha*reading_direction(1) + reading_direction(2));
                        
                        T N_reference = -(normal(0)*reference_direction(0) + normal(1)*reference_direction(1) + normal(2)*reference_direction(2));
                        
                        // update the hessian and d2J/dzdx
                        tmp_vector_6 << normal(0), normal(1), normal(2), reading_range * n_alpha, reading_range * n_beta, reading_range * n_gamma;
                        
                        J_hessian += tmp_vector_6 * tmp_vector_6.transpose();
                        
                        tmp_vector_6 << normal(0) * N_reading, normal(1) * N_reading, normal(2) * N_reading, n_alpha * (E + reading_range * N_reading), n_beta * (E + reading_range * N_reading), n_gamma * (E + reading_range * N_reading);
                        
                        d2J_dReadingdX.block(0,valid_points_count,6,1) = tmp_vector_6;
                        
                        tmp_vector_6 << normal(0) * N_reference, normal(1) * N_reference, normal(2) * N_reference, reference_range * n_alpha * N_reference, reference_range * n_beta * N_reference, reference_range * n_gamma * N_reference;
                        
                        d2J_dReferencedX.block(0,valid_points_count,6,1) = tmp_vector_6;
                        
                        valid_points_count++;
                } // if (outlierWeights(0,i) > 0.0)
        }
        
        Matrix d2J_dZdX(Matrix::Zero(6, 2 * valid_points_count));
        d2J_dZdX.block(0,0,6,valid_points_count) = d2J_dReadingdX.block(0,0,6,valid_points_count);
        d2J_dZdX.block(0,valid_points_count,6,valid_points_count) = d2J_dReferencedX.block(0,0,6,valid_points_count);
        
        Matrix inv_J_hessian = J_hessian.inverse();
        
        covariance = d2J_dZdX * d2J_dZdX.transpose();
        covariance = inv_J_hessian * covariance * inv_J_hessian;
        
        return (sensorStdDev * sensorStdDev) * covariance;
}

template<typename T>
typename PointToPointWithCovErrorMinimizer<T>::Matrix PointToPointWithCovErrorMinimizer<T>::getCovariance() const
{
        return covMatrix;
}

template struct PointToPointWithCovErrorMinimizer<float>;
template struct PointToPointWithCovErrorMinimizer<double>;