/opencv_source/src/cv/cvoptflowgf.cpp

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#include "_cv.h"

//
// 2D dense optical flow algorithm from the following paper:
// Gunnar Farneback. "Two-Frame Motion Estimation Based on Polynomial Expansion".
// Proceedings of the 13th Scandinavian Conference on Image Analysis, Gothenburg, Sweden
//

namespace cv
{

static void
FarnebackPolyExp( const Mat& src, Mat& dst, int n, double sigma )
{
    int k, x, y;
    
    assert( src.type() == CV_32FC1 );
    int width = src.cols;
    int height = src.rows;
    AutoBuffer<float> kbuf(n*6 + 3), _row((width + n*2)*3);
    float* g = kbuf + n;
    float* xg = g + n*2 + 1;
    float* xxg = xg + n*2 + 1;
    float *row = (float*)_row + n*3;
    
    if( sigma < FLT_EPSILON )
        sigma = n*0.3;
    
    double s = 0.;
    for( x = -n; x <= n; x++ )
    {
        g[x] = (float)std::exp(-x*x/(2*sigma*sigma));
        s += g[x];
    }
    
    s = 1./s;
    for( x = -n; x <= n; x++ )
    {
        g[x] = (float)(g[x]*s);
        xg[x] = (float)(x*g[x]);
        xxg[x] = (float)(x*x*g[x]);
    }

    Mat_<double> G = Mat_<double>::zeros(6, 6);
    
    for( y = -n; y <= n; y++ )
        for( x = -n; x <= n; x++ )
        {
            G(0,0) += g[y]*g[x];
            G(1,1) += g[y]*g[x]*x*x;
            G(3,3) += g[y]*g[x]*x*x*x*x;
            G(5,5) += g[y]*g[x]*x*x*y*y;
        }
        
    //G[0][0] = 1.;
    G(2,2) = G(0,3) = G(0,4) = G(3,0) = G(4,0) = G(1,1);
    G(4,4) = G(3,3);
    G(3,4) = G(4,3) = G(5,5);

    // invG:
    // [ x        e  e    ]
    // [    y             ]
    // [       y          ]
    // [ e        z       ]
    // [ e           z    ]
    // [                u ]
    Mat_<double> invG = G.inv(DECOMP_CHOLESKY);
    double ig11 = invG(1,1), ig03 = invG(0,3), ig33 = invG(3,3), ig55 = invG(5,5);

    dst.create( height, width, CV_32FC(5));
    
    for( y = 0; y < height; y++ )
    {
        float g0 = g[0], g1, g2;
        float *srow0 = (float*)(src.data + src.step*y), *srow1 = 0;
        float *drow = (float*)(dst.data + dst.step*y);
        
        // vertical part of convolution
        for( x = 0; x < width; x++ )
        {
            row[x*3] = srow0[x]*g0;
            row[x*3+1] = row[x*3+2] = 0.f;
        }
        
        for( k = 1; k <= n; k++ )
        {
            g0 = g[k]; g1 = xg[k]; g2 = xxg[k];
            srow0 = (float*)(src.data + src.step*std::max(y-k,0));
            srow1 = (float*)(src.data + src.step*std::min(y+k,height-1));
            
            for( x = 0; x < width; x++ )
            {
                float p = srow0[x] + srow1[x];
                float t0 = row[x*3] + g0*p;
                float t1 = row[x*3+1] + g1*(srow1[x] - srow0[x]);
                float t2 = row[x*3+2] + g2*p;
                
                row[x*3] = t0;
                row[x*3+1] = t1;
                row[x*3+2] = t2;
            }
        }
        
        // horizontal part of convolution
        for( x = 0; x < n*3; x++ )
        {
            row[-1-x] = row[2-x];
            row[width*3+x] = row[width*3+x-3];
        }
        
        for( x = 0; x < width; x++ )
        {
            g0 = g[0];
            // r1 ~ 1, r2 ~ x, r3 ~ y, r4 ~ x^2, r5 ~ y^2, r6 ~ xy
            double b1 = row[x*3]*g0, b2 = 0, b3 = row[x*3+1]*g0,
                b4 = 0, b5 = row[x*3+2]*g0, b6 = 0;
            
            for( k = 1; k <= n; k++ )
            {
                double tg = row[(x+k)*3] + row[(x-k)*3];
                g0 = g[k];
                b1 += tg*g0;
                b4 += tg*xxg[k];
                b2 += (row[(x+k)*3] - row[(x-k)*3])*xg[k];
                b3 += (row[(x+k)*3+1] + row[(x-k)*3+1])*g0;
                b6 += (row[(x+k)*3+1] - row[(x-k)*3+1])*xg[k];
                b5 += (row[(x+k)*3+2] + row[(x-k)*3+2])*g0;
            }
            
            // do not store r1
            drow[x*5+1] = (float)(b2*ig11);
            drow[x*5] = (float)(b3*ig11);
            drow[x*5+3] = (float)(b1*ig03 + b4*ig33);
            drow[x*5+2] = (float)(b1*ig03 + b5*ig33);
            drow[x*5+4] = (float)(b6*ig55);
        }
    }
    
    row -= n*3;
}


/*static void
FarnebackPolyExpPyr( const Mat& src0, Vector<Mat>& pyr, int maxlevel, int n, double sigma )
{
    Vector<Mat> imgpyr;
    buildPyramid( src0, imgpyr, maxlevel );

    for( int i = 0; i <= maxlevel; i++ )
        FarnebackPolyExp( imgpyr[i], pyr[i], n, sigma );
}*/


static void
FarnebackUpdateMatrices( const Mat& _R0, const Mat& _R1, const Mat& _flow, Mat& _M, int _y0, int _y1 )
{
    const int BORDER = 5;
    static const float border[BORDER] = {0.14f, 0.14f, 0.4472f, 0.4472f, 0.4472f};

    int x, y, width = _flow.cols, height = _flow.rows;
    const float* R1 = (float*)_R1.data;
    size_t step1 = _R1.step/sizeof(R1[0]);
    
    _M.create(height, width, CV_32FC(5));

    for( y = _y0; y < _y1; y++ )
    {
        const float* flow = (float*)(_flow.data + y*_flow.step);
        const float* R0 = (float*)(_R0.data + y*_R0.step);
        float* M = (float*)(_M.data + y*_M.step);
        
        for( x = 0; x < width; x++ )
        {
            float dx = flow[x*2], dy = flow[x*2+1];
            float fx = x + dx, fy = y + dy;

#if 1
            int x1 = cvFloor(fx), y1 = cvFloor(fy);
            const float* ptr = R1 + y1*step1 + x1*5;
            float r2, r3, r4, r5, r6;

            fx -= x1; fy -= y1;
            
            if( (unsigned)x1 < (unsigned)(width-1) &&
                (unsigned)y1 < (unsigned)(height-1) )
            {
                float a00 = (1.f-fx)*(1.f-fy), a01 = fx*(1.f-fy),
                      a10 = (1.f-fx)*fy, a11 = fx*fy;

                r2 = a00*ptr[0] + a01*ptr[5] + a10*ptr[step1] + a11*ptr[step1+5];
                r3 = a00*ptr[1] + a01*ptr[6] + a10*ptr[step1+1] + a11*ptr[step1+6];
                r4 = a00*ptr[2] + a01*ptr[7] + a10*ptr[step1+2] + a11*ptr[step1+7];
                r5 = a00*ptr[3] + a01*ptr[8] + a10*ptr[step1+3] + a11*ptr[step1+8];
                r6 = a00*ptr[4] + a01*ptr[9] + a10*ptr[step1+4] + a11*ptr[step1+9];

                r4 = (R0[x*5+2] + r4)*0.5f;
                r5 = (R0[x*5+3] + r5)*0.5f;
                r6 = (R0[x*5+4] + r6)*0.25f;
            }
#else
            int x1 = cvRound(fx), y1 = cvRound(fy);
            const float* ptr = R1 + y1*step1 + x1*5;
            float r2, r3, r4, r5, r6;

            if( (unsigned)x1 < (unsigned)width &&
                (unsigned)y1 < (unsigned)height )
            {
                r2 = ptr[0];
                r3 = ptr[1];
                r4 = (R0[x*5+2] + ptr[2])*0.5f;
                r5 = (R0[x*5+3] + ptr[3])*0.5f;
                r6 = (R0[x*5+4] + ptr[4])*0.25f;
            }
#endif
            else
            {
                r2 = r3 = 0.f;
                r4 = R0[x*5+2];
                r5 = R0[x*5+3];
                r6 = R0[x*5+4]*0.5f;
            }

            r2 = (R0[x*5] - r2)*0.5f;
            r3 = (R0[x*5+1] - r3)*0.5f;

            r2 += r4*dy + r6*dx;
            r3 += r6*dy + r5*dx;

            if( (unsigned)(x - BORDER) >= (unsigned)(width - BORDER*2) ||
                (unsigned)(y - BORDER) >= (unsigned)(height - BORDER*2))
            {
                float scale = (x < BORDER ? border[x] : 1.f)*
                    (x >= width - BORDER ? border[width - x - 1] : 1.f)*
                    (y < BORDER ? border[y] : 1.f)*
                    (y >= height - BORDER ? border[height - y - 1] : 1.f);

                r2 *= scale; r3 *= scale; r4 *= scale;
                r5 *= scale; r6 *= scale;
            }

            M[x*5]   = r4*r4 + r6*r6; // G(1,1)
            M[x*5+1] = (r4 + r5)*r6;  // G(1,2)=G(2,1)
            M[x*5+2] = r5*r5 + r6*r6; // G(2,2)
            M[x*5+3] = r4*r2 + r6*r3; // h(1)
            M[x*5+4] = r6*r2 + r5*r3; // h(2)
        }
    }
}


static void
FarnebackUpdateFlow_Blur( const Mat& _R0, const Mat& _R1,
                          Mat& _flow, Mat& _M, int block_size,
                          bool update_matrices )
{
    int x, y, width = _flow.cols, height = _flow.rows;
    int m = block_size/2;
    int y0 = 0, y1;
    int min_update_stripe = std::max((1 << 10)/width, block_size);
    double scale = 1./(block_size*block_size);
    
    AutoBuffer<double> _vsum((width+m*2+2)*5);
    double* vsum = _vsum + (m+1)*5;

    // init vsum
    const float* srow0 = (const float*)_M.data;
    for( x = 0; x < width*5; x++ )
        vsum[x] = srow0[x]*(m+2);

    for( y = 1; y < m; y++ )
    {
        srow0 = (float*)(_M.data + _M.step*std::min(y,height-1));
        for( x = 0; x < width*5; x++ )
            vsum[x] += srow0[x];
    }

    // compute blur(G)*flow=blur(h)
    for( y = 0; y < height; y++ )
    {
        double g11, g12, g22, h1, h2;
        float* flow = (float*)(_flow.data + _flow.step*y);

        srow0 = (const float*)(_M.data + _M.step*std::max(y-m-1,0));
        const float* srow1 = (const float*)(_M.data + _M.step*std::min(y+m,height-1));
        
        // vertical blur
        for( x = 0; x < width*5; x++ )
            vsum[x] += srow1[x] - srow0[x];

        // update borders
        for( x = 0; x < (m+1)*5; x++ )
        {
            vsum[-1-x] = vsum[4-x];
            vsum[width*5+x] = vsum[width*5+x-5];
        }

        // init g** and h*
        g11 = vsum[0]*(m+2);
        g12 = vsum[1]*(m+2);
        g22 = vsum[2]*(m+2);
        h1 = vsum[3]*(m+2);
        h2 = vsum[4]*(m+2);

        for( x = 1; x < m; x++ )
        {
            g11 += vsum[x*5];
            g12 += vsum[x*5+1];
            g22 += vsum[x*5+2];
            h1 += vsum[x*5+3];
            h2 += vsum[x*5+4];
        }

        // horizontal blur
        for( x = 0; x < width; x++ )
        {
            g11 += vsum[(x+m)*5] - vsum[(x-m)*5 - 5];
            g12 += vsum[(x+m)*5 + 1] - vsum[(x-m)*5 - 4];
            g22 += vsum[(x+m)*5 + 2] - vsum[(x-m)*5 - 3];
            h1 += vsum[(x+m)*5 + 3] - vsum[(x-m)*5 - 2];
            h2 += vsum[(x+m)*5 + 4] - vsum[(x-m)*5 - 1];

            double g11_ = g11*scale;
            double g12_ = g12*scale;
            double g22_ = g22*scale;
            double h1_ = h1*scale;
            double h2_ = h2*scale;

            double idet = 1./(g11_*g22_ - g12_*g12_+1e-3);
            
            flow[x*2] = (float)((g11_*h2_-g12_*h1_)*idet);
            flow[x*2+1] = (float)((g22_*h1_-g12_*h2_)*idet);
        }

        y1 = y == height - 1 ? height : y - block_size;
        if( update_matrices && (y1 == height || y1 >= y0 + min_update_stripe) )
        {
            FarnebackUpdateMatrices( _R0, _R1, _flow, _M, y0, y1 );
            y0 = y1;
        }
    }
}


static void
FarnebackUpdateFlow_GaussianBlur( const Mat& _R0, const Mat& _R1,
                                  Mat& _flow, Mat& _M, int block_size,
                                  bool update_matrices )
{
    int x, y, i, width = _flow.cols, height = _flow.rows;
    int m = block_size/2;
    int y0 = 0, y1;
    int min_update_stripe = std::max((1 << 10)/width, block_size);
    double sigma = m*0.3, s = 1;
    
    AutoBuffer<float> _vsum((width+m*2+2)*5 + 16), _hsum(width*5 + 16);
    AutoBuffer<float, 4096> _kernel((m+1)*5 + 16);
    AutoBuffer<float*, 1024> _srow(m*2+1);
    float *vsum = alignPtr((float*)_vsum + (m+1)*5, 16), *hsum = alignPtr((float*)_hsum, 16);
    float* kernel = (float*)_kernel;
    const float** srow = (const float**)&_srow[0];
    kernel[0] = (float)s;

    for( i = 1; i <= m; i++ )
    {
        float t = (float)std::exp(-i*i/(2*sigma*sigma) );
        kernel[i] = t;
        s += t*2;
    }

    s = 1./s;
    for( i = 0; i <= m; i++ )
        kernel[i] = (float)(kernel[i]*s);

#if CV_SSE2
    float* simd_kernel = alignPtr(kernel + m+1, 16);
    for( i = 0; i <= m; i++ )
        _mm_store_ps(simd_kernel + i*4, _mm_set1_ps(kernel[i]));
#endif

    // compute blur(G)*flow=blur(h)
    for( y = 0; y < height; y++ )
    {
        double g11, g12, g22, h1, h2;
        float* flow = (float*)(_flow.data + _flow.step*y);

        // vertical blur
        for( i = 0; i <= m; i++ )
        {
            srow[m-i] = (const float*)(_M.data + _M.step*std::max(y-i,0));
            srow[m+i] = (const float*)(_M.data + _M.step*std::min(y+i,height-1));
        }

        x = 0;
#if CV_SSE2
        for( ; x <= width*5 - 16; x += 16 )
        {
            const float *sptr0 = srow[m], *sptr1;
            __m128 g4 = _mm_load_ps(simd_kernel);
            __m128 s0, s1, s2, s3;
            s0 = _mm_mul_ps(_mm_loadu_ps(sptr0 + x), g4);
            s1 = _mm_mul_ps(_mm_loadu_ps(sptr0 + x + 4), g4);
            s2 = _mm_mul_ps(_mm_loadu_ps(sptr0 + x + 8), g4);
            s3 = _mm_mul_ps(_mm_loadu_ps(sptr0 + x + 12), g4);

            for( i = 1; i <= m; i++ )
            {
                __m128 x0, x1;
                sptr0 = srow[m+i], sptr1 = srow[m-i];
                g4 = _mm_load_ps(simd_kernel + i*4);
                x0 = _mm_add_ps(_mm_loadu_ps(sptr0 + x), _mm_loadu_ps(sptr1 + x));
                x1 = _mm_add_ps(_mm_loadu_ps(sptr0 + x + 4), _mm_loadu_ps(sptr1 + x + 4));
                s0 = _mm_add_ps(s0, _mm_mul_ps(x0, g4));
                s1 = _mm_add_ps(s1, _mm_mul_ps(x1, g4));
                x0 = _mm_add_ps(_mm_loadu_ps(sptr0 + x + 8), _mm_loadu_ps(sptr1 + x + 8));
                x1 = _mm_add_ps(_mm_loadu_ps(sptr0 + x + 12), _mm_loadu_ps(sptr1 + x + 12));
                s2 = _mm_add_ps(s2, _mm_mul_ps(x0, g4));
                s3 = _mm_add_ps(s3, _mm_mul_ps(x1, g4));
            }
            
            _mm_store_ps(vsum + x, s0);
            _mm_store_ps(vsum + x + 4, s1);
            _mm_store_ps(vsum + x + 8, s2);
            _mm_store_ps(vsum + x + 12, s3);
        }

        for( ; x <= width*5 - 4; x += 4 )
        {
            const float *sptr0 = srow[m], *sptr1;
            __m128 g4 = _mm_load_ps(simd_kernel);
            __m128 s0 = _mm_mul_ps(_mm_loadu_ps(sptr0 + x), g4);

            for( i = 1; i <= m; i++ )
            {
                sptr0 = srow[m+i], sptr1 = srow[m-i];
                g4 = _mm_load_ps(simd_kernel + i*4);
                __m128 x0 = _mm_add_ps(_mm_loadu_ps(sptr0 + x), _mm_loadu_ps(sptr1 + x));
                s0 = _mm_add_ps(s0, _mm_mul_ps(x0, g4));
            }
            _mm_store_ps(vsum + x, s0);
        }
#endif
        for( ; x < width*5; x++ )
        {
            float s0 = srow[m][x]*kernel[0];
            for( i = 1; i <= m; i++ )
                s0 += (srow[m+i][x] + srow[m-i][x])*kernel[i];
            vsum[x] = s0;
        }

        // update borders
        for( x = 0; x < m*5; x++ )
        {
            vsum[-1-x] = vsum[4-x];
            vsum[width*5+x] = vsum[width*5+x-5];
        }

        // horizontal blur
        x = 0;
#if CV_SSE2
        for( ; x <= width*5 - 8; x += 8 )
        {
            __m128 g4 = _mm_load_ps(simd_kernel);
            __m128 s0 = _mm_mul_ps(_mm_loadu_ps(vsum + x), g4);
            __m128 s1 = _mm_mul_ps(_mm_loadu_ps(vsum + x + 4), g4);

            for( i = 1; i <= m; i++ )
            {
                g4 = _mm_load_ps(simd_kernel + i*4);
                __m128 x0 = _mm_add_ps(_mm_loadu_ps(vsum + x - i*5),
                                       _mm_loadu_ps(vsum + x + i*5));
                __m128 x1 = _mm_add_ps(_mm_loadu_ps(vsum + x - i*5 + 4),
                                       _mm_loadu_ps(vsum + x + i*5 + 4));
                s0 = _mm_add_ps(s0, _mm_mul_ps(x0, g4));
                s1 = _mm_add_ps(s1, _mm_mul_ps(x1, g4));
            }

            _mm_store_ps(hsum + x, s0);
            _mm_store_ps(hsum + x + 4, s1);
        }
#endif
        for( ; x < width*5; x++ )
        {
            float s = vsum[x]*kernel[0];
            for( i = 1; i <= m; i++ )
                s += kernel[i]*(vsum[x - i*5] + vsum[x + i*5]);
            hsum[x] = s;
        }

        for( x = 0; x < width; x++ )
        {
            g11 = hsum[x*5];
            g12 = hsum[x*5+1];
            g22 = hsum[x*5+2];
            h1 = hsum[x*5+3];
            h2 = hsum[x*5+4];

            double idet = 1./(g11*g22 - g12*g12 + 1e-3);
            
            flow[x*2] = (float)((g11*h2-g12*h1)*idet);
            flow[x*2+1] = (float)((g22*h1-g12*h2)*idet);
        }

        y1 = y == height - 1 ? height : y - block_size;
        if( update_matrices && (y1 == height || y1 >= y0 + min_update_stripe) )
        {
            FarnebackUpdateMatrices( _R0, _R1, _flow, _M, y0, y1 );
            y0 = y1;
        }
    }
}


void calcOpticalFlowFarneback( const Mat& prev0, const Mat& next0,
                               Mat& flow0, double pyr_scale, int levels, int winsize,
                               int iterations, int poly_n, double poly_sigma, int flags )
{
    const int min_size = 32;
    const Mat* img[2] = { &prev0, &next0 };
    Mat fimg;

    int i, k;
    double scale;
    Mat prevFlow, flow;

    CV_Assert( prev0.size() == next0.size() && prev0.channels() == next0.channels() &&
        prev0.channels() == 1 );
    flow0.create( prev0.size(), CV_32FC2 );

    for( k = 0, scale = 1; k < levels; k++ )
    {
        scale *= pyr_scale;
        if( prev0.cols*scale < min_size || prev0.rows*scale < min_size )
            break;
    }

    levels = k;

    for( k = levels; k >= 0; k-- )
    {
        for( i = 0, scale = 1; i < k; i++ )
            scale *= pyr_scale;

        double sigma = (1./scale-1)*0.5;
        int smooth_sz = cvRound(sigma*5)|1;
        smooth_sz = std::max(smooth_sz, 3);

        int width = cvRound(prev0.cols*scale);
        int height = cvRound(prev0.rows*scale);

        if( k > 0 )
            flow.create( height, width, CV_32FC2 );
        else
            flow = flow0;

        if( !prevFlow.data )
        {
            if( flags & OPTFLOW_USE_INITIAL_FLOW )
            {
                resize( flow0, flow, Size(width, height), 0, 0, INTER_AREA );
                flow *= scale;
            }
            else
                flow = Mat::zeros( height, width, CV_32FC2 );
        }
        else
        {
            resize( prevFlow, flow, Size(width, height), 0, 0, INTER_LINEAR );
            flow *= 1./pyr_scale;
        }

        Mat R[2], I, M;
        for( i = 0; i < 2; i++ )
        {
            img[i]->convertTo(fimg, CV_32F);
            GaussianBlur(fimg, fimg, Size(smooth_sz, smooth_sz), sigma, sigma);
            resize( fimg, I, Size(width, height), CV_INTER_LINEAR );
            FarnebackPolyExp( I, R[i], poly_n, poly_sigma );
        }
        
        FarnebackUpdateMatrices( R[0], R[1], flow, M, 0, flow.rows );

        for( i = 0; i < iterations; i++ )
        {
            if( flags & OPTFLOW_FARNEBACK_GAUSSIAN )
                FarnebackUpdateFlow_GaussianBlur( R[0], R[1], flow, M, winsize, i < iterations - 1 );
            else
                FarnebackUpdateFlow_Blur( R[0], R[1], flow, M, winsize, i < iterations - 1 );
        }

        prevFlow = flow;
    }
}

}