CDifodo.cpp

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/* +---------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)               |
   |                          http://www.mrpt.org/                             |
   |                                                                           |
   | Copyright (c) 2005-2017, Individual contributors, see AUTHORS file        |
   | See: http://www.mrpt.org/Authors - All rights reserved.                   |
   | Released under BSD License. See details in http://www.mrpt.org/License    |
   +---------------------------------------------------------------------------+ */

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

#include <mrpt/vision/CDifodo.h>
#include <mrpt/utils/utils_defs.h>
#include <mrpt/utils/CTicTac.h>
#include <mrpt/utils/round.h>

using namespace mrpt;
using namespace mrpt::vision;
using namespace mrpt::math;
using namespace std;
using namespace Eigen;
using mrpt::utils::round;
using mrpt::math::square;

CDifodo::CDifodo()
{
        rows = 60;
        cols = 80;
        fovh = M_PIf*58.6f/180.0f;
        fovv = M_PIf*45.6f/180.0f;
        cam_mode = 1;                   // (1 - 640 x 480, 2 - 320 x 240, 4 - 160 x 120)
        downsample = 1;
        ctf_levels = 1;
        width = 640/(cam_mode*downsample);
        height = 480/(cam_mode*downsample);
        fast_pyramid = true;

        //Resize pyramid
    const unsigned int pyr_levels = round(log(float(width/cols))/log(2.f)) + ctf_levels;
    depth.resize(pyr_levels);
    depth_old.resize(pyr_levels);
    depth_inter.resize(pyr_levels);
        depth_warped.resize(pyr_levels);
    xx.resize(pyr_levels);
    xx_inter.resize(pyr_levels);
    xx_old.resize(pyr_levels);
        xx_warped.resize(pyr_levels);
    yy.resize(pyr_levels);
    yy_inter.resize(pyr_levels);
    yy_old.resize(pyr_levels);
        yy_warped.resize(pyr_levels);
        transformations.resize(pyr_levels);

        for (unsigned int i = 0; i<pyr_levels; i++)
    {
        unsigned int s = pow(2.f,int(i));
        cols_i = width/s; rows_i = height/s;
        depth[i].resize(rows_i, cols_i);
        depth_inter[i].resize(rows_i, cols_i);
        depth_old[i].resize(rows_i, cols_i);
        depth[i].assign(0.0f);
        depth_old[i].assign(0.0f);
        xx[i].resize(rows_i, cols_i);
        xx_inter[i].resize(rows_i, cols_i);
        xx_old[i].resize(rows_i, cols_i);
        xx[i].assign(0.0f);
        xx_old[i].assign(0.0f);
        yy[i].resize(rows_i, cols_i);
        yy_inter[i].resize(rows_i, cols_i);
        yy_old[i].resize(rows_i, cols_i);
        yy[i].assign(0.0f);
        yy_old[i].assign(0.0f);
                transformations[i].resize(4,4);

                if (cols_i <= cols)
                {
                        depth_warped[i].resize(rows_i,cols_i);
                        xx_warped[i].resize(rows_i,cols_i);
                        yy_warped[i].resize(rows_i,cols_i);
                }
    }

        depth_wf.setSize(height,width);

        fps = 30.f;             //In Hz

        previous_speed_const_weight = 0.05f;
        previous_speed_eig_weight = 0.5f;
        kai_loc_old.assign(0.f);
        num_valid_points = 0;

        //Compute gaussian mask
        VectorXf v_mask(4);
        v_mask(0) = 1.f; v_mask(1) = 2.f; v_mask(2) = 2.f; v_mask(3) = 1.f;
        for (unsigned int i = 0; i<4; i++)
                for (unsigned int j = 0; j<4; j++)
                        f_mask(i,j) = v_mask(i)*v_mask(j)/36.f;

        //Compute gaussian mask
        float v_mask2[5] = {1,4,6,4,1};
        for (unsigned int i = 0; i<5; i++)
                for (unsigned int j = 0; j<5; j++)
                        g_mask[i][j] = v_mask2[i]*v_mask2[j]/256.f;
}

void CDifodo::buildCoordinatesPyramid()
{
        const float max_depth_dif = 0.1f;

        //Push coordinates back
        depth_old.swap(depth);
        xx_old.swap(xx);
        yy_old.swap(yy);

        //The number of levels of the pyramid does not match the number of levels used
        //in the odometry computation (because we might want to finish with lower resolutions)

        unsigned int pyr_levels = round(log(float(width/cols))/log(2.f)) + ctf_levels;

        //Generate levels
        for (unsigned int i = 0; i<pyr_levels; i++)
        {
                unsigned int s = pow(2.f,int(i));
                cols_i = width/s;
                rows_i = height/s;
                const int rows_i2 = 2*rows_i;
                const int cols_i2 = 2*cols_i;
                const int i_1 = i-1;

                if (i == 0)
                        depth[i].swap(depth_wf);

                //                              Downsampling
                //-----------------------------------------------------------------------------
                else
                {
                        for (unsigned int u = 0; u < cols_i; u++)
                        for (unsigned int v = 0; v < rows_i; v++)
                        {
                                const int u2 = 2*u;
                                const int v2 = 2*v;
                                const float dcenter = depth[i_1](v2,u2);

                                //Inner pixels
                                if ((v>0)&&(v<rows_i-1)&&(u>0)&&(u<cols_i-1))
                                {
                                        if (dcenter > 0.f)
                                        {
                                                float sum = 0.f;
                                                float weight = 0.f;

                                                for (int l = -2; l<3; l++)
                                                for (int k = -2; k<3; k++)
                                                {
                                                        const float abs_dif = abs(depth[i_1](v2+k,u2+l)-dcenter);
                                                        if (abs_dif < max_depth_dif)
                                                        {
                                                                const float aux_w = g_mask[2+k][2+l]*(max_depth_dif - abs_dif);
                                                                weight += aux_w;
                                                                sum += aux_w*depth[i_1](v2+k,u2+l);
                                                        }
                                                }
                                                depth[i](v,u) = sum/weight;
                                        }
                                        else
                                        {
                                                float min_depth = 10.f;
                                                for (int l = -2; l<3; l++)
                                                for (int k = -2; k<3; k++)
                                                {
                                                        const float d = depth[i_1](v2+k,u2+l);
                                                        if ((d > 0.f)&&(d < min_depth))
                                                                min_depth = d;
                                                }

                                                if (min_depth < 10.f)
                                                        depth[i](v,u) = min_depth;
                                                else
                                                        depth[i](v,u) = 0.f;
                                        }
                                }

                                //Boundary
                                else
                                {
                                        if (dcenter > 0.f)
                                        {
                                                float sum = 0.f;
                                                float weight = 0.f;

                                                for (int l = -2; l<3; l++)
                                                for (int k = -2; k<3; k++)
                                                {
                                                        const int indv = v2+k,indu = u2+l;
                                                        if ((indv>=0)&&(indv<rows_i2)&&(indu>=0)&&(indu<cols_i2))
                                                        {
                                                                const float abs_dif = abs(depth[i_1](indv,indu)-dcenter);
                                                                if (abs_dif < max_depth_dif)
                                                                {
                                                                        const float aux_w = g_mask[2+k][2+l]*(max_depth_dif - abs_dif);
                                                                        weight += aux_w;
                                                                        sum += aux_w*depth[i_1](indv,indu);
                                                                }
                                                        }
                                                }
                                                depth[i](v,u) = sum/weight;
                                        }
                                        else
                                        {
                                                float min_depth = 10.f;
                                                for (int l = -2; l<3; l++)
                                                for (int k = -2; k<3; k++)
                                                {
                                                        const int indv = v2+k,indu = u2+l;
                                                        if ((indv>=0)&&(indv<rows_i2)&&(indu>=0)&&(indu<cols_i2))
                                                        {
                                                                const float d = depth[i_1](indv,indu);
                                                                if ((d > 0.f)&&(d < min_depth))
                                                                        min_depth = d;
                                                        }
                                                }

                                                if (min_depth < 10.f)
                                                        depth[i](v,u) = min_depth;
                                                else
                                                        depth[i](v,u) = 0.f;
                                        }
                                }
                        }
                }

                //Calculate coordinates "xy" of the points
                const float inv_f_i = 2.f*tan(0.5f*fovh)/float(cols_i);
                const float disp_u_i = 0.5f*(cols_i-1);
                const float disp_v_i = 0.5f*(rows_i-1);

                for (unsigned int u = 0; u < cols_i; u++)
                for (unsigned int v = 0; v < rows_i; v++)
                if (depth[i](v,u) > 0.f)
                {
                        xx[i](v,u) = (u - disp_u_i)*depth[i](v,u)*inv_f_i;
                        yy[i](v,u) = (v - disp_v_i)*depth[i](v,u)*inv_f_i;
                }
                else
                {
                        xx[i](v,u) = 0.f;
                        yy[i](v,u) = 0.f;
                }
        }
}

void CDifodo::buildCoordinatesPyramidFast()
{
        const float max_depth_dif = 0.1f;
        
        //Push coordinates back
        depth_old.swap(depth);
        xx_old.swap(xx);
        yy_old.swap(yy);

        //The number of levels of the pyramid does not match the number of levels used
        //in the odometry computation (because we might want to finish with lower resolutions)

        unsigned int pyr_levels = round(log(float(width/cols))/log(2.f)) + ctf_levels;

        //Generate levels
        for (unsigned int i = 0; i<pyr_levels; i++)
        {
                unsigned int s = pow(2.f,int(i));
                cols_i = width/s;
                rows_i = height/s;
                //const int rows_i2 = 2*rows_i;
                //const int cols_i2 = 2*cols_i;
                const int i_1 = i-1;

                if (i == 0)
                        depth[i].swap(depth_wf);

                //                              Downsampling
                //-----------------------------------------------------------------------------
                else
                {
                        for (unsigned int u = 0; u < cols_i; u++)
                                for (unsigned int v = 0; v < rows_i; v++)
                                {
                                        const int u2 = 2*u;
                                        const int v2 = 2*v;
                                        
                                        //Inner pixels
                                        if ((v>0)&&(v<rows_i-1)&&(u>0)&&(u<cols_i-1))
                                        {
                                                const Matrix4f d_block = depth[i_1].block<4,4>(v2-1,u2-1);
                                                float depths[4] = {d_block(5),d_block(6),d_block(9),d_block(10)};
                                                float dcenter;

                                                //Sort the array (try to find a good/representative value)
                                                for (signed char k = 2; k>=0; k--)
                                                if (depths[k+1] < depths[k])
                                                        std::swap(depths[k+1],depths[k]);
                                                for (unsigned char k = 1; k<3; k++)
                                                if (depths[k] > depths[k+1])
                                                        std::swap(depths[k+1],depths[k]);
                                                if (depths[2] < depths[1])
                                                        dcenter = depths[1];
                                                else
                                                        dcenter = depths[2];
                                                
                                                if (dcenter > 0.f)
                                                {       
                                                        float sum = 0.f;
                                                        float weight = 0.f;

                                                        for (unsigned char k = 0; k<16; k++)
                                                        {
                                                                const float abs_dif = abs(d_block(k) - dcenter);
                                                                if (abs_dif < max_depth_dif)
                                                                {
                                                                        const float aux_w = f_mask(k)*(max_depth_dif - abs_dif);
                                                                        weight += aux_w;
                                                                        sum += aux_w*d_block(k);
                                                                }
                                                        }
                                                        depth[i](v,u) = sum/weight;
                                                }
                                                else
                                                        depth[i](v,u) = 0.f;

                    }

                    //Boundary
                                        else
                                        {
                                                const Matrix2f d_block = depth[i_1].block<2,2>(v2,u2);
                                                const float new_d = 0.25f*d_block.sumAll();
                                                if (new_d < 0.4f)
                                                        depth[i](v,u) = 0.f;
                                                else
                                                        depth[i](v,u) = new_d;
                                        }
                                }
        }

        //Calculate coordinates "xy" of the points
                const float inv_f_i = 2.f*tan(0.5f*fovh)/float(cols_i);
        const float disp_u_i = 0.5f*(cols_i-1);
        const float disp_v_i = 0.5f*(rows_i-1);

        for (unsigned int u = 0; u < cols_i; u++) 
                        for (unsigned int v = 0; v < rows_i; v++)
                if (depth[i](v,u) > 0.f)
                                {
                                        xx[i](v,u) = (u - disp_u_i)*depth[i](v,u)*inv_f_i;
                                        yy[i](v,u) = (v - disp_v_i)*depth[i](v,u)*inv_f_i;
                                }
                                else
                                {
                                        xx[i](v,u) = 0.f;
                                        yy[i](v,u) = 0.f;
                                }
    }
}

void CDifodo::performWarping()
{
        //Camera parameters (which also depend on the level resolution)
        const float f = float(cols_i)/(2.f*tan(0.5f*fovh));
        const float disp_u_i = 0.5f*float(cols_i-1);
    const float disp_v_i = 0.5f*float(rows_i-1);

        //Rigid transformation estimated up to the present level
        Matrix4f acu_trans; 
        acu_trans.setIdentity();
        for (unsigned int i=1; i<=level; i++)
                acu_trans = transformations[i-1]*acu_trans;

        MatrixXf wacu(rows_i,cols_i);
        wacu.assign(0.f);
        depth_warped[image_level].assign(0.f);

        const float cols_lim = float(cols_i-1);
        const float rows_lim = float(rows_i-1);

        //                                              Warping loop
        //---------------------------------------------------------
        for (unsigned int j = 0; j<cols_i; j++)
                for (unsigned int i = 0; i<rows_i; i++)
                {               
                        const float z = depth[image_level](i,j);
                        
                        if (z > 0.f)
                        {
                                //Transform point to the warped reference frame
                                const float depth_w = acu_trans(0,0)*z + acu_trans(0,1)*xx[image_level](i,j) + acu_trans(0,2)*yy[image_level](i,j) + acu_trans(0,3);
                                const float x_w = acu_trans(1,0)*z + acu_trans(1,1)*xx[image_level](i,j) + acu_trans(1,2)*yy[image_level](i,j) + acu_trans(1,3);
                                const float y_w = acu_trans(2,0)*z + acu_trans(2,1)*xx[image_level](i,j) + acu_trans(2,2)*yy[image_level](i,j) + acu_trans(2,3);

                                //Calculate warping
                                const float uwarp = f*x_w/depth_w + disp_u_i;
                                const float vwarp = f*y_w/depth_w + disp_v_i;

                                //The warped pixel (which is not integer in general) contributes to all the surrounding ones
                                if (( uwarp >= 0.f)&&( uwarp < cols_lim)&&( vwarp >= 0.f)&&( vwarp < rows_lim))
                                {
                                        const int uwarp_l = uwarp;
                                        const int uwarp_r = uwarp_l + 1;
                                        const int vwarp_d = vwarp;
                                        const int vwarp_u = vwarp_d + 1;
                                        const float delta_r = float(uwarp_r) - uwarp;
                                        const float delta_l = uwarp - float(uwarp_l);
                                        const float delta_u = float(vwarp_u) - vwarp;
                                        const float delta_d = vwarp - float(vwarp_d);

                                        //Warped pixel very close to an integer value
                                        if (abs(round(uwarp) - uwarp) + abs(round(vwarp) - vwarp) < 0.05f)
                                        {
                                                depth_warped[image_level](round(vwarp), round(uwarp)) += depth_w;
                                                wacu(round(vwarp), round(uwarp)) += 1.f;
                                        }
                                        else
                                        {
                                                const float w_ur = square(delta_l) + square(delta_d);
                                                depth_warped[image_level](vwarp_u,uwarp_r) += w_ur*depth_w;
                                                wacu(vwarp_u,uwarp_r) += w_ur;

                                                const float w_ul = square(delta_r) + square(delta_d);
                                                depth_warped[image_level](vwarp_u,uwarp_l) += w_ul*depth_w;
                                                wacu(vwarp_u,uwarp_l) += w_ul;

                                                const float w_dr = square(delta_l) + square(delta_u);
                                                depth_warped[image_level](vwarp_d,uwarp_r) += w_dr*depth_w;
                                                wacu(vwarp_d,uwarp_r) += w_dr;

                                                const float w_dl = square(delta_r) + square(delta_u);
                                                depth_warped[image_level](vwarp_d,uwarp_l) += w_dl*depth_w;
                                                wacu(vwarp_d,uwarp_l) += w_dl;
                                        }
                                }
                        }
                }

        //Scale the averaged depth and compute spatial coordinates
    const float inv_f_i = 1.f/f;
        for (unsigned int u = 0; u<cols_i; u++)
                for (unsigned int v = 0; v<rows_i; v++)
                {       
                        if (wacu(v,u) > 0.f)
                        {
                                depth_warped[image_level](v,u) /= wacu(v,u);
                                xx_warped[image_level](v,u) = (u - disp_u_i)*depth_warped[image_level](v,u)*inv_f_i;
                                yy_warped[image_level](v,u) = (v - disp_v_i)*depth_warped[image_level](v,u)*inv_f_i;
                        }
                        else
                        {
                                depth_warped[image_level](v,u) = 0.f;
                                xx_warped[image_level](v,u) = 0.f;
                                yy_warped[image_level](v,u) = 0.f;
                        }
                }
}

void CDifodo::calculateCoord()
{       
        null.resize(rows_i, cols_i);
        null.assign(false);
        num_valid_points = 0;
        
        for (unsigned int u = 0; u < cols_i; u++)
                for (unsigned int v = 0; v < rows_i; v++)
                {
                        if ((depth_old[image_level](v,u)) == 0.f || (depth_warped[image_level](v,u) == 0.f))
                        {
                                depth_inter[image_level](v,u) = 0.f;
                                xx_inter[image_level](v,u) = 0.f;
                                yy_inter[image_level](v,u) = 0.f;
                                null(v, u) = true;
                        }
                        else
                        {
                                depth_inter[image_level](v,u) = 0.5f*(depth_old[image_level](v,u) + depth_warped[image_level](v,u));
                                xx_inter[image_level](v,u) = 0.5f*(xx_old[image_level](v,u) + xx_warped[image_level](v,u));
                                yy_inter[image_level](v,u) = 0.5f*(yy_old[image_level](v,u) + yy_warped[image_level](v,u));
                                null(v, u) = false;
                                if ((u>0)&&(v>0)&&(u<cols_i-1)&&(v<rows_i-1))
                                        num_valid_points++;
                        }
                }
}

void CDifodo::calculateDepthDerivatives()
{
        dt.resize(rows_i,cols_i); dt.assign(0.f);
        du.resize(rows_i,cols_i); du.assign(0.f);
        dv.resize(rows_i,cols_i); dv.assign(0.f);

    //Compute connectivity
        MatrixXf rx_ninv(rows_i,cols_i);
        MatrixXf ry_ninv(rows_i,cols_i);
    rx_ninv.assign(1.f); ry_ninv.assign(1.f);

        for (unsigned int u = 0; u < cols_i-1; u++)
        for (unsigned int v = 0; v < rows_i; v++)
                        if (null(v,u) == false)
                        {
                                rx_ninv(v,u) = sqrtf(square(xx_inter[image_level](v,u+1) - xx_inter[image_level](v,u))
                                                                        + square(depth_inter[image_level](v,u+1) - depth_inter[image_level](v,u)));
                        }

        for (unsigned int u = 0; u < cols_i; u++)
        for (unsigned int v = 0; v < rows_i-1; v++)
                        if (null(v,u) == false)
                        {
                                ry_ninv(v,u) = sqrtf(square(yy_inter[image_level](v+1,u) - yy_inter[image_level](v,u))
                                                                        + square(depth_inter[image_level](v+1,u) - depth_inter[image_level](v,u)));
                        }


    //Spatial derivatives
    for (unsigned int v = 0; v < rows_i; v++)
    {
        for (unsigned int u = 1; u < cols_i-1; u++)
                        if (null(v,u) == false)
                                du(v,u) = (rx_ninv(v,u-1)*(depth_inter[image_level](v,u+1)-depth_inter[image_level](v,u)) + rx_ninv(v,u)*(depth_inter[image_level](v,u) - depth_inter[image_level](v,u-1)))/(rx_ninv(v,u)+rx_ninv(v,u-1));

                du(v,0) = du(v,1);
                du(v,cols_i-1) = du(v,cols_i-2);
    }

    for (unsigned int u = 0; u < cols_i; u++)
    {
        for (unsigned int v = 1; v < rows_i-1; v++)
                        if (null(v,u) == false)
                                dv(v,u) = (ry_ninv(v-1,u)*(depth_inter[image_level](v+1,u)-depth_inter[image_level](v,u)) + ry_ninv(v,u)*(depth_inter[image_level](v,u) - depth_inter[image_level](v-1,u)))/(ry_ninv(v,u)+ry_ninv(v-1,u));

                dv(0,u) = dv(1,u);
                dv(rows_i-1,u) = dv(rows_i-2,u);
    }

        //Temporal derivative
        for (unsigned int u = 0; u < cols_i; u++)
                for (unsigned int v = 0; v < rows_i; v++)
                        if (null(v,u) == false)
                                dt(v,u) = fps*(depth_warped[image_level](v,u) - depth_old[image_level](v,u));
}

void CDifodo::computeWeights()
{
        weights.resize(rows_i, cols_i);
        weights.assign(0.f);

        //Obtain the velocity associated to the rigid transformation estimated up to the present level
        Matrix<float,6,1> kai_level = kai_loc_old;

        Matrix4f acu_trans;
        acu_trans.setIdentity();
        for (unsigned int i=0; i<level; i++)
                acu_trans = transformations[i]*acu_trans;

        //Alternative way to compute the log
        CMatrixDouble44 mat_aux = acu_trans.cast<double>();
        poses::CPose3D aux(mat_aux);
        CArrayDouble<6> kai_level_acu = aux.ln()*fps;
        kai_level -= kai_level_acu.cast<float>();

        //Parameters for the measurement error
        const float f_inv = float(cols_i)/(2.f*tan(0.5f*fovh));
        const float kz2 = 8.122e-12f;  //square(1.425e-5) / 25
        
        //Parameters for linearization error
        const float kduv = 20e-5f;
        const float kdt = kduv/square(fps);
        const float k2dt = 5e-6f;
        const float k2duv = 5e-6f;
        
        for (unsigned int u = 1; u < cols_i-1; u++)
                for (unsigned int v = 1; v < rows_i-1; v++)
                        if (null(v,u) == false)
                        {
                                //                                      Compute measurment error (simplified)
                                //-----------------------------------------------------------------------
                                const float z = depth_inter[image_level](v,u);
                                const float inv_d = 1.f/z;
                                //const float dycomp = du2(v,u)*f_inv_y*inv_d;
                                //const float dzcomp = dv2(v,u)*f_inv_z*inv_d;
                                const float z2 = z*z;
                                const float z4 = z2*z2;

                                //const float var11 = kz2*z4;
                                //const float var12 = kz2*xx_inter[image_level](v,u)*z2*depth_inter[image_level](v,u);
                                //const float var13 = kz2*yy_inter[image_level](v,u)*z2*depth_inter[image_level](v,u);
                                //const float var22 = kz2*square(xx_inter[image_level](v,u))*z2;
                                //const float var23 = kz2*xx_inter[image_level](v,u)*yy_inter[image_level](v,u)*z2;
                                //const float var33 = kz2*square(yy_inter[image_level](v,u))*z2;
                                const float var44 = kz2*z4*square(fps);
                                const float var55 = kz2*z4*0.25f;
                                const float var66 = var55;

                                //const float j1 = -2.f*inv_d*inv_d*(xx_inter[image_level](v,u)*dycomp + yy_inter[image_level](v,u)*dzcomp)*(kai_level[0] + yy_inter[image_level](v,u)*kai_level[4] - xx_inter[image_level](v,u)*kai_level[5])
                                //                              + inv_d*dycomp*(kai_level[1] - yy_inter[image_level](v,u)*kai_level[3]) + inv_d*dzcomp*(kai_level[2] + xx_inter[image_level](v,u)*kai_level[3]);
                                //const float j2 = inv_d*dycomp*(kai_level[0] + yy_inter[image_level](v,u)*kai_level[4] - 2.f*xx_inter[image_level](v,u)*kai_level[5]) - dzcomp*kai_level[3];
                                //const float j3 = inv_d*dzcomp*(kai_level[0] + 2.f*yy_inter[image_level](v,u)*kai_level[4] - xx_inter[image_level](v,u)*kai_level[5]) + dycomp*kai_level[3];

                                const float j4 = 1.f;
                                const float j5 =  xx_inter[image_level](v,u)*inv_d*inv_d*f_inv*(kai_level[0] + yy_inter[image_level](v,u)*kai_level[4] - xx_inter[image_level](v,u)*kai_level[5]) 
                                                           + inv_d*f_inv*(-kai_level[1] - z*kai_level[5] + yy_inter[image_level](v,u)*kai_level[3]);
                                const float j6 = yy_inter[image_level](v,u)*inv_d*inv_d*f_inv*(kai_level[0] + yy_inter[image_level](v,u)*kai_level[4] - xx_inter[image_level](v,u)*kai_level[5])
                                                           + inv_d*f_inv*(-kai_level[2] + z*kai_level[4] - xx_inter[image_level](v,u)*kai_level[3]);

                                //error_measurement(v,u) = j1*(j1*var11+j2*var12+j3*var13) + j2*(j1*var12+j2*var22+j3*var23)
                                //                                              +j3*(j1*var13+j2*var23+j3*var33) + j4*j4*var44 + j5*j5*var55 + j6*j6*var66;

                                const float error_m = j4*j4*var44 + j5*j5*var55 + j6*j6*var66;

                                
                                //                                      Compute linearization error
                                //-----------------------------------------------------------------------
                                const float ini_du = depth_old[image_level](v,u+1) - depth_old[image_level](v,u-1);
                                const float ini_dv = depth_old[image_level](v+1,u) - depth_old[image_level](v-1,u);
                                const float final_du = depth_warped[image_level](v,u+1) - depth_warped[image_level](v,u-1);
                                const float final_dv = depth_warped[image_level](v+1,u) - depth_warped[image_level](v-1,u);

                                const float dut = ini_du - final_du;
                                const float dvt = ini_dv - final_dv;
                                const float duu = du(v,u+1) - du(v,u-1);
                                const float dvv = dv(v+1,u) - dv(v-1,u);
                                const float dvu = dv(v,u+1) - dv(v,u-1); //Completely equivalent to compute duv

                                const float error_l = kdt*square(dt(v,u)) + kduv*(square(du(v,u)) + square(dv(v,u))) + k2dt*(square(dut) + square(dvt))
                                                                                        + k2duv*(square(duu) + square(dvv) + square(dvu));

                                //Weight
                                weights(v,u) = sqrt(1.f/(error_m + error_l));
                        }

        //Normalize weights in the range [0,1]
        const float inv_max = 1.f/weights.maximum();
        weights = inv_max*weights;
}

void CDifodo::solveOneLevel()
{
        MatrixXf A(num_valid_points,6);
        MatrixXf B(num_valid_points,1);
        unsigned int cont = 0;

        //Fill the matrix A and the vector B
        //The order of the unknowns is (vz, vx, vy, wz, wx, wy)
        //The points order will be (1,1), (1,2)...(1,cols-1), (2,1), (2,2)...(row-1,cols-1).

        const float f_inv = float(cols_i)/(2.f*tan(0.5f*fovh));

        for (unsigned int u = 1; u < cols_i-1; u++)
                for (unsigned int v = 1; v < rows_i-1; v++)
                        if (null(v,u) == false)
                        {
                                // Precomputed expressions
                                const float d = depth_inter[image_level](v,u);
                                const float inv_d = 1.f/d;
                                const float x = xx_inter[image_level](v,u);
                                const float y = yy_inter[image_level](v,u);
                                const float dycomp = du(v,u)*f_inv*inv_d;
                                const float dzcomp = dv(v,u)*f_inv*inv_d;
                                const float tw = weights(v,u);

                                //Fill the matrix A
                                A(cont, 0) = tw*(1.f + dycomp*x*inv_d + dzcomp*y*inv_d);
                                A(cont, 1) = tw*(-dycomp);
                                A(cont, 2) = tw*(-dzcomp);
                                A(cont, 3) = tw*(dycomp*y - dzcomp*x);
                                A(cont, 4) = tw*(y + dycomp*inv_d*y*x + dzcomp*(y*y*inv_d + d));
                                A(cont, 5) = tw*(-x - dycomp*(x*x*inv_d + d) - dzcomp*inv_d*y*x);
                                B(cont,0) = tw*(-dt(v,u));

                                cont++;
                        }
        
        //Solve the linear system of equations using weighted least squares
        MatrixXf AtA, AtB;
        AtA.multiply_AtA(A);
        AtB.multiply_AtB(A,B);
        MatrixXf Var = AtA.ldlt().solve(AtB);

        //Covariance matrix calculation 
        MatrixXf res = -B;
        for (unsigned int k = 0; k<6; k++)
                res += Var(k)*A.col(k);

        est_cov = (1.f/float(num_valid_points-6))*AtA.inverse()*res.squaredNorm();

        //Update last velocity in local coordinates
        kai_loc_level = Var;
}

void CDifodo::odometryCalculation()
{
        //Clock to measure the runtime
        utils::CTicTac clock;
        clock.Tic();

        //Build the gaussian pyramid
        if (fast_pyramid)       buildCoordinatesPyramidFast();
        else                            buildCoordinatesPyramid();

        //Coarse-to-fines scheme
    for (unsigned int i=0; i<ctf_levels; i++)
    {
                //Previous computations
                transformations[i].setIdentity();

                level = i;
                unsigned int s = pow(2.f,int(ctf_levels-(i+1)));
        cols_i = cols/s; rows_i = rows/s;
        image_level = ctf_levels - i + round(log(float(width/cols))/log(2.f)) - 1;

                //1. Perform warping
                if (i == 0)
                {
                        depth_warped[image_level] = depth[image_level];
                        xx_warped[image_level] = xx[image_level];
                        yy_warped[image_level] = yy[image_level];
                }
                else
                        performWarping();

                //2. Calculate inter coords and find null measurements
                calculateCoord();

                //3. Compute derivatives
                calculateDepthDerivatives();

                //4. Compute weights
                computeWeights();

                //5. Solve odometry
                if (num_valid_points > 6)
                        solveOneLevel();

                //6. Filter solution
                filterLevelSolution();
        }

        //Update poses
        poseUpdate();

        //Save runtime
        execution_time = 1000.f*clock.Tac();   
}

void CDifodo::filterLevelSolution()
{
        //              Calculate Eigenvalues and Eigenvectors
        //----------------------------------------------------------
        SelfAdjointEigenSolver<MatrixXf> eigensolver(est_cov);
        if (eigensolver.info() != Success) 
        { 
                printf("\n Eigensolver couldn't find a solution. Pose is not updated");
                return;
        }
        
        //First, we have to describe both the new linear and angular velocities in the "eigenvector" basis
        //-------------------------------------------------------------------------------------------------
        Matrix<float,6,6> Bii;
        Matrix<float,6,1> kai_b;
        Bii = eigensolver.eigenvectors();
        kai_b = Bii.colPivHouseholderQr().solve(kai_loc_level);

        //Second, we have to describe both the old linear and angular velocities in the "eigenvector" basis
        //-------------------------------------------------------------------------------------------------
        Matrix<float,6,1> kai_loc_sub = kai_loc_old;

        //Important: we have to substract the previous levels' solutions from the old velocity.
        Matrix4f acu_trans;
        acu_trans.setIdentity();
        for (unsigned int i=0; i<level; i++)
                acu_trans = transformations[i]*acu_trans;

        CMatrixDouble44 mat_aux = acu_trans.cast<double>();
        poses::CPose3D aux(mat_aux);
        CArrayDouble<6> kai_level_acu = aux.ln()*fps;
        kai_loc_sub -= kai_level_acu.cast<float>();

        //Matrix<float, 4, 4> log_trans = fps*acu_trans.log();
        //kai_loc_sub(0) -= log_trans(0,3); kai_loc_sub(1) -= log_trans(1,3); kai_loc_sub(2) -= log_trans(2,3);
        //kai_loc_sub(3) += log_trans(1,2); kai_loc_sub(4) -= log_trans(0,2); kai_loc_sub(5) += log_trans(0,1);

        //Transform that local representation to the "eigenvector" basis
        Matrix<float,6,1> kai_b_old;
        kai_b_old = Bii.colPivHouseholderQr().solve(kai_loc_sub);

        //                                                                      Filter velocity
        //--------------------------------------------------------------------------------
        const float cf = previous_speed_eig_weight*expf(-int(level)), df = previous_speed_const_weight*expf(-int(level));
        Matrix<float,6,1> kai_b_fil;
        for (unsigned int i=0; i<6; i++)
                kai_b_fil(i) = (kai_b(i) + (cf*eigensolver.eigenvalues()(i,0) + df)*kai_b_old(i))/(1.f + cf*eigensolver.eigenvalues()(i) + df);

        //Transform filtered velocity to the local reference frame 
        Matrix<float, 6, 1> kai_loc_fil = Bii.inverse().colPivHouseholderQr().solve(kai_b_fil);

        //Compute the rigid transformation
        mrpt::math::CArrayDouble<6> aux_vel = kai_loc_fil.cast<double>()/fps;
        poses::CPose3D aux1, aux2; 
        CMatrixDouble44 trans;
        aux2 = aux1.exp(aux_vel);
        aux2.getHomogeneousMatrix(trans);
        transformations[level] = trans.cast<float>();
}

void CDifodo::poseUpdate()
{
        //First, compute the overall transformation
        //---------------------------------------------------
        Matrix4f acu_trans;
        acu_trans.setIdentity();
        for (unsigned int i=1; i<=ctf_levels; i++)
                acu_trans = transformations[i-1]*acu_trans;


        //Compute the new estimates in the local and absolutes reference frames
        //---------------------------------------------------------------------
        CMatrixDouble44 mat_aux = acu_trans.cast<double>();
        poses::CPose3D aux(mat_aux);
        CArrayDouble<6> kai_level_acu = aux.ln()*fps;
        kai_loc = kai_level_acu.cast<float>();

        //---------------------------------------------------------------------------------------------
        //Directly from Eigen:
        //- Eigen 3.1.0 needed for Matrix::log()
        //- The line "#include <unsupported/Eigen/MatrixFunctions>" should be uncommented (CDifodo.h)
        //
        //Matrix<float, 4, 4> log_trans = fps*acu_trans.log();
        //kai_loc(0) = log_trans(0,3); kai_loc(1) = log_trans(1,3); kai_loc(2) = log_trans(2,3);
        //kai_loc(3) = -log_trans(1,2); kai_loc(4) = log_trans(0,2); kai_loc(5) = -log_trans(0,1);
        //---------------------------------------------------------------------------------------------

        CMatrixDouble33 inv_trans;
        CMatrixFloat31 v_abs, w_abs;

        cam_pose.getRotationMatrix(inv_trans);
        v_abs = inv_trans.cast<float>()*kai_loc.topRows(3);
        w_abs = inv_trans.cast<float>()*kai_loc.bottomRows(3);
        kai_abs.topRows<3>() = v_abs;
        kai_abs.bottomRows<3>() = w_abs;        


        //                                              Update poses
        //-------------------------------------------------------       
        cam_oldpose = cam_pose;
        CMatrixDouble44 aux_acu = acu_trans;
        poses::CPose3D pose_aux(aux_acu);
        cam_pose = cam_pose + pose_aux;


        //Compute the velocity estimate in the new ref frame (to be used by the filter in the next iteration)
        //---------------------------------------------------------------------------------------------------
        cam_pose.getRotationMatrix(inv_trans);
        kai_loc_old.topRows<3>() = inv_trans.inverse().cast<float>()*kai_abs.topRows(3);
        kai_loc_old.bottomRows<3>() = inv_trans.inverse().cast<float>()*kai_abs.bottomRows(3);
}

void CDifodo::setFOV(float new_fovh, float new_fovv)
{
        fovh = M_PI*new_fovh/180.0;
        fovv = M_PI*new_fovv/180.0;
}

void CDifodo::getPointsCoord(MatrixXf &x, MatrixXf &y, MatrixXf &z)
{
        x.resize(rows,cols);
        y.resize(rows,cols);
        z.resize(rows,cols);

        z = depth_inter[0];
        x = xx_inter[0];
        y = yy_inter[0];
}

void CDifodo::getDepthDerivatives(MatrixXf &cur_du, MatrixXf &cur_dv, MatrixXf &cur_dt)
{
        cur_du.resize(rows,cols);
        cur_dv.resize(rows,cols);
        cur_dt.resize(rows,cols);

        cur_du = du;
        cur_dv = dv;
        cur_dt = dt;
}

void CDifodo::getWeights(MatrixXf &w)
{
        w.resize(rows,cols);
        w = weights;
}