rgbdodometry.cpp

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#include "precomp.hpp"

#define SHOW_DEBUG_IMAGES 0

#include "opencv2/core.hpp"
#include "opencv2/calib3d.hpp"

#if SHOW_DEBUG_IMAGES
#  include "opencv2/highgui.hpp"
#endif

#include <iostream>
#include <limits>

#if defined(HAVE_EIGEN) && EIGEN_WORLD_VERSION == 3
#  ifdef ANDROID
     template <typename Scalar> Scalar log2(Scalar v) { return std::log(v)/std::log(Scalar(2)); }
#  endif
#  if defined __GNUC__ && defined __APPLE__
#    pragma GCC diagnostic ignored "-Wshadow"
#  endif
#  include <unsupported/Eigen/MatrixFunctions>
#  include <Eigen/Dense>
#endif

using namespace cv;

inline static
void computeC_RigidBodyMotion( double* C, double dIdx, double dIdy, const Point3f& p3d, double fx, double fy )
{
    double invz  = 1. / p3d.z,
           v0 = dIdx * fx * invz,
           v1 = dIdy * fy * invz,
           v2 = -(v0 * p3d.x + v1 * p3d.y) * invz;

    C[0] = -p3d.z * v1 + p3d.y * v2;
    C[1] =  p3d.z * v0 - p3d.x * v2;
    C[2] = -p3d.y * v0 + p3d.x * v1;
    C[3] = v0;
    C[4] = v1;
    C[5] = v2;
}

inline static
void computeC_Rotation( double* C, double dIdx, double dIdy, const Point3f& p3d, double fx, double fy )
{
    double invz  = 1. / p3d.z,
           v0 = dIdx * fx * invz,
           v1 = dIdy * fy * invz,
           v2 = -(v0 * p3d.x + v1 * p3d.y) * invz;

    C[0] = -p3d.z * v1 + p3d.y * v2;
    C[1] =  p3d.z * v0 - p3d.x * v2;
    C[2] = -p3d.y * v0 + p3d.x * v1;
}

inline static
void computeC_Translation( double* C, double dIdx, double dIdy, const Point3f& p3d, double fx, double fy )
{
    double invz  = 1. / p3d.z,
           v0 = dIdx * fx * invz,
           v1 = dIdy * fy * invz,
           v2 = -(v0 * p3d.x + v1 * p3d.y) * invz;

    C[0] = v0;
    C[1] = v1;
    C[2] = v2;
}

inline static
void computeProjectiveMatrix( const Mat& ksi, Mat& Rt )
{
    CV_Assert( ksi.size() == Size(1,6) && ksi.type() == CV_64FC1 );

#if defined(HAVE_EIGEN) && EIGEN_WORLD_VERSION == 3
    const double* ksi_ptr = reinterpret_cast<const double*>(ksi.ptr(0));
    Eigen::Matrix<double,4,4> twist, g;
    twist << 0.,          -ksi_ptr[2], ksi_ptr[1],  ksi_ptr[3],
             ksi_ptr[2],  0.,          -ksi_ptr[0], ksi_ptr[4],
             -ksi_ptr[1], ksi_ptr[0],  0,           ksi_ptr[5],
             0.,          0.,          0.,          0.;
    g = twist.exp();


    eigen2cv(g, Rt);
#else
    // for infinitesimal transformation
    Rt = Mat::eye(4, 4, CV_64FC1);

    Mat R = Rt(Rect(0,0,3,3));
    Mat rvec = ksi.rowRange(0,3);

    Rodrigues( rvec, R );

    Rt.at<double>(0,3) = ksi.at<double>(3);
    Rt.at<double>(1,3) = ksi.at<double>(4);
    Rt.at<double>(2,3) = ksi.at<double>(5);
#endif
}

static
void cvtDepth2Cloud( const Mat& depth, Mat& cloud, const Mat& cameraMatrix )
{
    CV_Assert( cameraMatrix.type() == CV_64FC1 );
    const double inv_fx = 1.f/cameraMatrix.at<double>(0,0);
    const double inv_fy = 1.f/cameraMatrix.at<double>(1,1);
    const double ox = cameraMatrix.at<double>(0,2);
    const double oy = cameraMatrix.at<double>(1,2);
    cloud.create( depth.size(), CV_32FC3 );
    for( int y = 0; y < cloud.rows; y++ )
    {
        Point3f* cloud_ptr = reinterpret_cast<Point3f*>(cloud.ptr(y));
        const float* depth_prt = reinterpret_cast<const float*>(depth.ptr(y));
        for( int x = 0; x < cloud.cols; x++ )
        {
            float z = depth_prt[x];
            cloud_ptr[x].x = (float)((x - ox) * z * inv_fx);
            cloud_ptr[x].y = (float)((y - oy) * z * inv_fy);
            cloud_ptr[x].z = z;
        }
    }
}

#if SHOW_DEBUG_IMAGES
template<class ImageElemType>
static void warpImage( const Mat& image, const Mat& depth,
                       const Mat& Rt, const Mat& cameraMatrix, const Mat& distCoeff,
                       Mat& warpedImage )
{
    const Rect rect = Rect(0, 0, image.cols, image.rows);

    std::vector<Point2f> points2d;
    Mat cloud, transformedCloud;

    cvtDepth2Cloud( depth, cloud, cameraMatrix );
    perspectiveTransform( cloud, transformedCloud, Rt );
    projectPoints( transformedCloud.reshape(3,1), Mat::eye(3,3,CV_64FC1), Mat::zeros(3,1,CV_64FC1), cameraMatrix, distCoeff, points2d );

    Mat pointsPositions( points2d );
    pointsPositions = pointsPositions.reshape( 2, image.rows );

    warpedImage.create( image.size(), image.type() );
    warpedImage = Scalar::all(0);

    Mat zBuffer( image.size(), CV_32FC1, FLT_MAX );
    for( int y = 0; y < image.rows; y++ )
    {
        for( int x = 0; x < image.cols; x++ )
        {
            const Point3f p3d = transformedCloud.at<Point3f>(y,x);
            const Point p2d = pointsPositions.at<Point2f>(y,x);
            if( !cvIsNaN(cloud.at<Point3f>(y,x).z) && cloud.at<Point3f>(y,x).z > 0 &&
                rect.contains(p2d) && zBuffer.at<float>(p2d) > p3d.z )
            {
                warpedImage.at<ImageElemType>(p2d) = image.at<ImageElemType>(y,x);
                zBuffer.at<float>(p2d) = p3d.z;
            }
        }
    }
}
#endif

static inline
void set2shorts( int& dst, int short_v1, int short_v2 )
{
    unsigned short* ptr = reinterpret_cast<unsigned short*>(&dst);
    ptr[0] = static_cast<unsigned short>(short_v1);
    ptr[1] = static_cast<unsigned short>(short_v2);
}

static inline
void get2shorts( int src, int& short_v1, int& short_v2 )
{
    typedef union { int vint32; unsigned short vuint16[2]; } s32tou16;
    const unsigned short* ptr = (reinterpret_cast<s32tou16*>(&src))->vuint16;
    short_v1 = ptr[0];
    short_v2 = ptr[1];
}

static
int computeCorresp( const Mat& K, const Mat& K_inv, const Mat& Rt,
                    const Mat& depth0, const Mat& depth1, const Mat& texturedMask1, float maxDepthDiff,
                    Mat& corresps )
{
    CV_Assert( K.type() == CV_64FC1 );
    CV_Assert( K_inv.type() == CV_64FC1 );
    CV_Assert( Rt.type() == CV_64FC1 );

    corresps.create( depth1.size(), CV_32SC1 );

    Mat R = Rt(Rect(0,0,3,3)).clone();

    Mat KRK_inv = K * R * K_inv;
    const double * KRK_inv_ptr = reinterpret_cast<const double *>(KRK_inv.ptr());

    Mat Kt = Rt(Rect(3,0,1,3)).clone();
    Kt = K * Kt;
    const double * Kt_ptr = reinterpret_cast<const double *>(Kt.ptr());

    Rect r(0, 0, depth1.cols, depth1.rows);

    corresps = Scalar(-1);
    int correspCount = 0;
    for( int v1 = 0; v1 < depth1.rows; v1++ )
    {
        for( int u1 = 0; u1 < depth1.cols; u1++ )
        {
            float d1 = depth1.at<float>(v1,u1);
            if( !cvIsNaN(d1) && texturedMask1.at<uchar>(v1,u1) )
            {
                float transformed_d1 = (float)(d1 * (KRK_inv_ptr[6] * u1 + KRK_inv_ptr[7] * v1 + KRK_inv_ptr[8]) + Kt_ptr[2]);
                int u0 = cvRound((d1 * (KRK_inv_ptr[0] * u1 + KRK_inv_ptr[1] * v1 + KRK_inv_ptr[2]) + Kt_ptr[0]) / transformed_d1);
                int v0 = cvRound((d1 * (KRK_inv_ptr[3] * u1 + KRK_inv_ptr[4] * v1 + KRK_inv_ptr[5]) + Kt_ptr[1]) / transformed_d1);

                if( r.contains(Point(u0,v0)) )
                {
                    float d0 = depth0.at<float>(v0,u0);
                    if( !cvIsNaN(d0) && std::abs(transformed_d1 - d0) <= maxDepthDiff )
                    {
                        int c = corresps.at<int>(v0,u0);
                        if( c != -1 )
                        {
                            int exist_u1, exist_v1;
                            get2shorts( c, exist_u1, exist_v1);

                            float exist_d1 = (float)(depth1.at<float>(exist_v1,exist_u1) * (KRK_inv_ptr[6] * exist_u1 + KRK_inv_ptr[7] * exist_v1 + KRK_inv_ptr[8]) + Kt_ptr[2]);

                            if( transformed_d1 > exist_d1 )
                                continue;
                        }
                        else
                            correspCount++;

                        set2shorts( corresps.at<int>(v0,u0), u1, v1 );
                    }
                }
            }
        }
    }

    return correspCount;
}

static inline
void preprocessDepth( Mat depth0, Mat depth1,
                      const Mat& validMask0, const Mat& validMask1,
                      float minDepth, float maxDepth )
{
    CV_DbgAssert( depth0.size() == depth1.size() );

    for( int y = 0; y < depth0.rows; y++ )
    {
        for( int x = 0; x < depth0.cols; x++ )
        {
            float& d0 = depth0.at<float>(y,x);
            if( !cvIsNaN(d0) && (d0 > maxDepth || d0 < minDepth || d0 <= 0 || (!validMask0.empty() && !validMask0.at<uchar>(y,x))) )
                d0 = std::numeric_limits<float>::quiet_NaN();

            float& d1 = depth1.at<float>(y,x);
            if( !cvIsNaN(d1) && (d1 > maxDepth || d1 < minDepth || d1 <= 0 || (!validMask1.empty() && !validMask1.at<uchar>(y,x))) )
                d1 = std::numeric_limits<float>::quiet_NaN();
        }
    }
}

static
void buildPyramids( const Mat& image0, const Mat& image1,
                    const Mat& depth0, const Mat& depth1,
                    const Mat& cameraMatrix, int sobelSize, double sobelScale,
                    const std::vector<float>& minGradMagnitudes,
                    std::vector<Mat>& pyramidImage0, std::vector<Mat>& pyramidDepth0,
                    std::vector<Mat>& pyramidImage1, std::vector<Mat>& pyramidDepth1,
                    std::vector<Mat>& pyramid_dI_dx1, std::vector<Mat>& pyramid_dI_dy1,
                    std::vector<Mat>& pyramidTexturedMask1, std::vector<Mat>& pyramidCameraMatrix )
{
    const int pyramidMaxLevel = (int)minGradMagnitudes.size() - 1;

    buildPyramid( image0, pyramidImage0, pyramidMaxLevel );
    buildPyramid( image1, pyramidImage1, pyramidMaxLevel );

    pyramid_dI_dx1.resize( pyramidImage1.size() );
    pyramid_dI_dy1.resize( pyramidImage1.size() );
    pyramidTexturedMask1.resize( pyramidImage1.size() );

    pyramidCameraMatrix.reserve( pyramidImage1.size() );

    Mat cameraMatrix_dbl;
    cameraMatrix.convertTo( cameraMatrix_dbl, CV_64FC1 );

    for( size_t i = 0; i < pyramidImage1.size(); i++ )
    {
        Sobel( pyramidImage1[i], pyramid_dI_dx1[i], CV_16S, 1, 0, sobelSize );
        Sobel( pyramidImage1[i], pyramid_dI_dy1[i], CV_16S, 0, 1, sobelSize );

        const Mat& dx = pyramid_dI_dx1[i];
        const Mat& dy = pyramid_dI_dy1[i];

        Mat texturedMask( dx.size(), CV_8UC1, Scalar(0) );
        const float minScalesGradMagnitude2 = (float)((minGradMagnitudes[i] * minGradMagnitudes[i]) / (sobelScale * sobelScale));
        for( int y = 0; y < dx.rows; y++ )
        {
            for( int x = 0; x < dx.cols; x++ )
            {
                float m2 = (float)(dx.at<short>(y,x)*dx.at<short>(y,x) + dy.at<short>(y,x)*dy.at<short>(y,x));
                if( m2 >= minScalesGradMagnitude2 )
                    texturedMask.at<uchar>(y,x) = 255;
            }
        }
        pyramidTexturedMask1[i] = texturedMask;
        Mat levelCameraMatrix = i == 0 ? cameraMatrix_dbl : 0.5f * pyramidCameraMatrix[i-1];
        levelCameraMatrix.at<double>(2,2) = 1.;
        pyramidCameraMatrix.push_back( levelCameraMatrix );
    }

    buildPyramid( depth0, pyramidDepth0, pyramidMaxLevel );
    buildPyramid( depth1, pyramidDepth1, pyramidMaxLevel );
}

static
bool solveSystem( const Mat& C, const Mat& dI_dt, double detThreshold, Mat& ksi )
{
#if defined(HAVE_EIGEN) && EIGEN_WORLD_VERSION == 3
    Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> eC, eCt, edI_dt;
    cv2eigen(C, eC);
    cv2eigen(dI_dt, edI_dt);
    eCt = eC.transpose();

    Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> A, B, eksi;

    A = eCt * eC;
    double det = A.determinant();
    if( fabs (det) < detThreshold || cvIsNaN(det) || cvIsInf(det) )
        return false;

    B = -eCt * edI_dt;

    eksi = A.ldlt().solve(B);
    eigen2cv( eksi, ksi );

#else
    Mat A = C.t() * C;

    double det = cv::determinant(A);

    if( fabs (det) < detThreshold || cvIsNaN(det) || cvIsInf(det) )
        return false;

    Mat B = -C.t() * dI_dt;
    cv::solve( A, B, ksi, DECOMP_CHOLESKY );
#endif

    return true;
}

typedef void (*ComputeCFuncPtr)( double* C, double dIdx, double dIdy, const Point3f& p3d, double fx, double fy );

static
bool computeKsi( int transformType,
                 const Mat& image0, const Mat&  cloud0,
                 const Mat& image1, const Mat& dI_dx1, const Mat& dI_dy1,
                 const Mat& corresps, int correspsCount,
                 double fx, double fy, double sobelScale, double determinantThreshold,
                 Mat& ksi )
{
    int Cwidth = -1;
    ComputeCFuncPtr computeCFuncPtr = 0;
    if( transformType == RIGID_BODY_MOTION )
    {
        Cwidth = 6;
        computeCFuncPtr = computeC_RigidBodyMotion;
    }
    else if( transformType == ROTATION )
    {
        Cwidth = 3;
        computeCFuncPtr = computeC_Rotation;
    }
    else if( transformType == TRANSLATION )
    {
        Cwidth = 3;
        computeCFuncPtr = computeC_Translation;
    }
    else
        CV_Error(Error::StsBadFlag, "Unsupported value of transformation type flag.");

    Mat C( correspsCount, Cwidth, CV_64FC1 );
    Mat dI_dt( correspsCount, 1, CV_64FC1 );

    double sigma = 0;
    int pointCount = 0;
    for( int v0 = 0; v0 < corresps.rows; v0++ )
    {
        for( int u0 = 0; u0 < corresps.cols; u0++ )
        {
            if( corresps.at<int>(v0,u0) != -1 )
            {
                int u1, v1;
                get2shorts( corresps.at<int>(v0,u0), u1, v1 );
                double diff = static_cast<double>(image1.at<uchar>(v1,u1)) -
                              static_cast<double>(image0.at<uchar>(v0,u0));
                sigma += diff * diff;
                pointCount++;
            }
        }
    }
    sigma = std::sqrt(sigma/pointCount);

    pointCount = 0;
    for( int v0 = 0; v0 < corresps.rows; v0++ )
    {
        for( int u0 = 0; u0 < corresps.cols; u0++ )
        {
            if( corresps.at<int>(v0,u0) != -1 )
            {
                int u1, v1;
                get2shorts( corresps.at<int>(v0,u0), u1, v1 );

                double diff = static_cast<double>(image1.at<uchar>(v1,u1)) -
                              static_cast<double>(image0.at<uchar>(v0,u0));
                double w = sigma + std::abs(diff);
                w = w > DBL_EPSILON ? 1./w : 1.;

                (*computeCFuncPtr)( (double*)C.ptr(pointCount),
                                     w * sobelScale * dI_dx1.at<short int>(v1,u1),
                                     w * sobelScale * dI_dy1.at<short int>(v1,u1),
                                     cloud0.at<Point3f>(v0,u0), fx, fy);

                dI_dt.at<double>(pointCount) = w * diff;
                pointCount++;
            }
        }
    }

    Mat sln;
    bool solutionExist = solveSystem( C, dI_dt, determinantThreshold, sln );

    if( solutionExist )
    {
        ksi.create(6,1,CV_64FC1);
        ksi = Scalar(0);

        Mat subksi;
        if( transformType == RIGID_BODY_MOTION )
        {
            subksi = ksi;
        }
        else if( transformType == ROTATION )
        {
            subksi = ksi.rowRange(0,3);
        }
        else if( transformType == TRANSLATION )
        {
            subksi = ksi.rowRange(3,6);
        }

        sln.copyTo( subksi );
    }

    return solutionExist;
}

bool cv::RGBDOdometry( cv::Mat& Rt, const Mat& initRt,
                       const cv::Mat& image0, const cv::Mat& _depth0, const cv::Mat& validMask0,
                       const cv::Mat& image1, const cv::Mat& _depth1, const cv::Mat& validMask1,
                       const cv::Mat& cameraMatrix, float minDepth, float maxDepth, float maxDepthDiff,
                       const std::vector<int>& iterCounts, const std::vector<float>& minGradientMagnitudes,
                       int transformType )
{
    const int sobelSize = 3;
    const double sobelScale = 1./8;

    Mat depth0 = _depth0.clone(),
        depth1 = _depth1.clone();

    // check RGB-D input data
    CV_Assert( !image0.empty() );
    CV_Assert( image0.type() == CV_8UC1 );
    CV_Assert( depth0.type() == CV_32FC1 && depth0.size() == image0.size() );

    CV_Assert( image1.size() == image0.size() );
    CV_Assert( image1.type() == CV_8UC1 );
    CV_Assert( depth1.type() == CV_32FC1 && depth1.size() == image0.size() );

    // check masks
    CV_Assert( validMask0.empty() || (validMask0.type() == CV_8UC1 && validMask0.size() == image0.size()) );
    CV_Assert( validMask1.empty() || (validMask1.type() == CV_8UC1 && validMask1.size() == image0.size()) );

    // check camera params
    CV_Assert( cameraMatrix.type() == CV_32FC1 && cameraMatrix.size() == Size(3,3) );

    // other checks
    CV_Assert( iterCounts.empty() || minGradientMagnitudes.empty() ||
               minGradientMagnitudes.size() == iterCounts.size() );
    CV_Assert( initRt.empty() || (initRt.type()==CV_64FC1 && initRt.size()==Size(4,4) ) );

    std::vector<int> defaultIterCounts;
    std::vector<float> defaultMinGradMagnitudes;
    std::vector<int> const* iterCountsPtr = &iterCounts;
    std::vector<float> const* minGradientMagnitudesPtr = &minGradientMagnitudes;

    if( iterCounts.empty() || minGradientMagnitudes.empty() )
    {
        defaultIterCounts.resize(4);
        defaultIterCounts[0] = 7;
        defaultIterCounts[1] = 7;
        defaultIterCounts[2] = 7;
        defaultIterCounts[3] = 10;

        defaultMinGradMagnitudes.resize(4);
        defaultMinGradMagnitudes[0] = 12;
        defaultMinGradMagnitudes[1] = 5;
        defaultMinGradMagnitudes[2] = 3;
        defaultMinGradMagnitudes[3] = 1;

        iterCountsPtr = &defaultIterCounts;
        minGradientMagnitudesPtr = &defaultMinGradMagnitudes;
    }

    preprocessDepth( depth0, depth1, validMask0, validMask1, minDepth, maxDepth );

    std::vector<Mat> pyramidImage0, pyramidDepth0,
                pyramidImage1, pyramidDepth1, pyramid_dI_dx1, pyramid_dI_dy1, pyramidTexturedMask1,
                pyramidCameraMatrix;
    buildPyramids( image0, image1, depth0, depth1, cameraMatrix, sobelSize, sobelScale, *minGradientMagnitudesPtr,
                   pyramidImage0, pyramidDepth0, pyramidImage1, pyramidDepth1,
                   pyramid_dI_dx1, pyramid_dI_dy1, pyramidTexturedMask1, pyramidCameraMatrix );

    Mat resultRt = initRt.empty() ? Mat::eye(4,4,CV_64FC1) : initRt.clone();
    Mat currRt, ksi;
    for( int level = (int)iterCountsPtr->size() - 1; level >= 0; level-- )
    {
        const Mat& levelCameraMatrix = pyramidCameraMatrix[level];

        const Mat& levelImage0 = pyramidImage0[level];
        const Mat& levelDepth0 = pyramidDepth0[level];
        Mat levelCloud0;
        cvtDepth2Cloud( pyramidDepth0[level], levelCloud0, levelCameraMatrix );

        const Mat& levelImage1 = pyramidImage1[level];
        const Mat& levelDepth1 = pyramidDepth1[level];
        const Mat& level_dI_dx1 = pyramid_dI_dx1[level];
        const Mat& level_dI_dy1 = pyramid_dI_dy1[level];

        CV_Assert( level_dI_dx1.type() == CV_16S );
        CV_Assert( level_dI_dy1.type() == CV_16S );

        const double fx = levelCameraMatrix.at<double>(0,0);
        const double fy = levelCameraMatrix.at<double>(1,1);
        const double determinantThreshold = 1e-6;

        Mat corresps( levelImage0.size(), levelImage0.type() );

        // Run transformation search on current level iteratively.
        for( int iter = 0; iter < (*iterCountsPtr)[level]; iter ++ )
        {
            int correspsCount = computeCorresp( levelCameraMatrix, levelCameraMatrix.inv(), resultRt.inv(DECOMP_SVD),
                                                levelDepth0, levelDepth1, pyramidTexturedMask1[level], maxDepthDiff,
                                                corresps );

            if( correspsCount == 0 )
                break;

            bool solutionExist = computeKsi( transformType,
                                             levelImage0, levelCloud0,
                                             levelImage1, level_dI_dx1, level_dI_dy1,
                                             corresps, correspsCount,
                                             fx, fy, sobelScale, determinantThreshold,
                                             ksi );

            if( !solutionExist )
                break;

            computeProjectiveMatrix( ksi, currRt );

            resultRt = currRt * resultRt;

#if SHOW_DEBUG_IMAGES
            std::cout << "currRt " << currRt << std::endl;
            Mat warpedImage0;
            const Mat distCoeff(1,5,CV_32FC1,Scalar(0));
            warpImage<uchar>( levelImage0, levelDepth0, resultRt, levelCameraMatrix, distCoeff, warpedImage0 );

            imshow( "im0", levelImage0 );
            imshow( "wim0", warpedImage0 );
            imshow( "im1", levelImage1 );
            waitKey();
#endif
        }
    }

    Rt = resultRt;

    return !Rt.empty();
}