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[opencv] / cv / src / cvfundam.cpp

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#include "_cv.h"

/* Evaluation of Fundamental Matrix from point correspondences.
   The original code has been written by Valery Mosyagin */

/* The algorithms (except for RANSAC) and the notation have been taken from
   Zhengyou Zhang's research report
   "Determining the Epipolar Geometry and its Uncertainty: A Review"
   that can be found at http://www-sop.inria.fr/robotvis/personnel/zzhang/zzhang-eng.html */

/************************************** 7-point algorithm *******************************/
static int
icvFMatrix_7Point( const CvPoint2D64f* m0, const CvPoint2D64f* m1, double* fmatrix )
{
    double a[7*9], w[7], v[9*9], c[4], r[3];
    double* f1, *f2;
    double t0, t1, t2;
    CvMat A = cvMat( 7, 9, CV_64F, a );
    CvMat V = cvMat( 9, 9, CV_64F, v );
    CvMat W = cvMat( 7, 1, CV_64F, w );
    CvMat coeffs = cvMat( 1, 4, CV_64F, c );
    CvMat roots = cvMat( 1, 3, CV_64F, r );
    int i, k, n;

    assert( m0 && m1 && fmatrix );

    // form a linear system: i-th row of A(=a) represents
    // the equation: (m1[i], 1)'*F*(m0[i], 1) = 0
    for( i = 0; i < 7; i++ )
    {
        double x0 = m0[i].x, y0 = m0[i].y;
        double x1 = m1[i].x, y1 = m1[i].y;

        a[i*9+0] = x1*x0;
        a[i*9+1] = x1*y0;
        a[i*9+2] = x1;
        a[i*9+3] = y1*x0;
        a[i*9+4] = y1*y0;
        a[i*9+5] = y1;
        a[i*9+6] = x0;
        a[i*9+7] = y0;
        a[i*9+8] = 1;
    }

    // A*(f11 f12 ... f33)' = 0 is singular (7 equations for 9 variables), so
    // the solution is linear subspace of dimensionality 2.
    // => use the last two singular vectors as a basis of the space
    // (according to SVD properties)
    cvSVD( &A, &W, 0, &V, CV_SVD_MODIFY_A + CV_SVD_V_T );
    f1 = v + 7*9;
    f2 = v + 8*9;

    // f1, f2 is a basis => lambda*f1 + mu*f2 is an arbitrary f. matrix.
    // as it is determined up to a scale, normalize lambda & mu (lambda + mu = 1),
    // so f ~ lambda*f1 + (1 - lambda)*f2.
    // use the additional constraint det(f) = det(lambda*f1 + (1-lambda)*f2) to find lambda.
    // it will be a cubic equation.
    // find c - polynomial coefficients.
    for( i = 0; i < 9; i++ )
        f1[i] -= f2[i];

    t0 = f2[4]*f2[8] - f2[5]*f2[7];
    t1 = f2[3]*f2[8] - f2[5]*f2[6];
    t2 = f2[3]*f2[7] - f2[4]*f2[6];

    c[3] = f2[0]*t0 - f2[1]*t1 + f2[2]*t2;

    c[2] = f1[0]*t0 - f1[1]*t1 + f1[2]*t2 -
           f1[3]*(f2[1]*f2[8] - f2[2]*f2[7]) +
           f1[4]*(f2[0]*f2[8] - f2[2]*f2[6]) -
           f1[5]*(f2[0]*f2[7] - f2[1]*f2[6]) +
           f1[6]*(f2[1]*f2[5] - f2[2]*f2[4]) -
           f1[7]*(f2[0]*f2[5] - f2[2]*f2[3]) +
           f1[8]*(f2[0]*f2[4] - f2[1]*f2[3]);

    t0 = f1[4]*f1[8] - f1[5]*f1[7];
    t1 = f1[3]*f1[8] - f1[5]*f1[6];
    t2 = f1[3]*f1[7] - f1[4]*f1[6];

    c[1] = f2[0]*t0 - f2[1]*t1 + f2[2]*t2 -
           f2[3]*(f1[1]*f1[8] - f1[2]*f1[7]) +
           f2[4]*(f1[0]*f1[8] - f1[2]*f1[6]) -
           f2[5]*(f1[0]*f1[7] - f1[1]*f1[6]) +
           f2[6]*(f1[1]*f1[5] - f1[2]*f1[4]) -
           f2[7]*(f1[0]*f1[5] - f1[2]*f1[3]) +
           f2[8]*(f1[0]*f1[4] - f1[1]*f1[3]);

    c[0] = f1[0]*t0 - f1[1]*t1 + f1[2]*t2;

    // solve the cubic equation; there can be 1 to 3 roots ...
    n = cvSolveCubic( &coeffs, &roots );

    if( n < 1 || n > 3 )
        return n;

    for( k = 0; k < n; k++, fmatrix += 9 )
    {
        // for each root form the fundamental matrix
        double lambda = r[k], mu = 1.;
        double s = f1[8]*r[k] + f2[8];

        // normalize each matrix, so that F(3,3) (~fmatrix[8]) == 1
        if( fabs(s) > DBL_EPSILON )
        {
            mu = 1./s;
            lambda *= mu;
            fmatrix[8] = 1.;
        }
        else
            fmatrix[8] = 0.;

        for( i = 0; i < 8; i++ )
            fmatrix[i] = f1[i]*lambda + f2[i]*mu;
    }

    return n;
}


/*************************************** 8-point algorithm ******************************/
static int
icvFMatrix_8Point( const CvPoint2D64f* m0, const CvPoint2D64f* m1,
                   const uchar* mask, int count, double* fmatrix )
{
    int result = 0;
    CvMat* A = 0;

    double w[9], v[9*9];
    CvMat W = cvMat( 1, 9, CV_64F, w);
    CvMat V = cvMat( 9, 9, CV_64F, v);
    CvMat U, F0, TF;

    int i, good_count = 0;
    CvPoint2D64f m0c = {0,0}, m1c = {0,0};
    double t, scale0 = 0, scale1 = 0;
    double* a;
    int a_step;

    CV_FUNCNAME( "icvFMatrix_8Point" );

    __BEGIN__;

    assert( m0 && m1 && fmatrix );

    // compute centers and average distances for each of the two point sets
    for( i = 0; i < count; i++ )
        if( !mask || mask[i] )
        {
            double x = m0[i].x, y = m0[i].y;
            m0c.x += x; m0c.y += y;

            x = m1[i].x, y = m1[i].y;
            m1c.x += x; m1c.y += y;
            good_count++;
        }

    if( good_count < 8 )
        EXIT;

    // calculate the normalizing transformations for each of the point sets:
    // after the transformation each set will have the mass center at the coordinate origin
    // and the average distance from the origin will be ~sqrt(2).
    t = 1./good_count;
    m0c.x *= t; m0c.y *= t;
    m1c.x *= t; m1c.y *= t;

    for( i = 0; i < count; i++ )
        if( !mask || mask[i] )
        {
            double x = m0[i].x - m0c.x, y = m0[i].y - m0c.y;
            scale0 += sqrt(x*x + y*y);

            x = fabs(m1[i].x - m1c.x), y = fabs(m1[i].y - m1c.y);
            scale1 += sqrt(x*x + y*y);
        }

    scale0 *= t;
    scale1 *= t;

    if( scale0 < FLT_EPSILON || scale1 < FLT_EPSILON )
        EXIT;

    scale0 = sqrt(2.)/scale0;
    scale1 = sqrt(2.)/scale1;

    CV_CALL( A = cvCreateMat( good_count, 9, CV_64F ));
    a = A->data.db;
    a_step = A->step / sizeof(a[0]);

    // form a linear system: for each selected pair of points m0 & m1,
    // the row of A(=a) represents the equation: (m1, 1)'*F*(m0, 1) = 0
    for( i = 0; i < count; i++ )
    {
        if( !mask || mask[i] )
        {
            double x0 = (m0[i].x - m0c.x)*scale0;
            double y0 = (m0[i].y - m0c.y)*scale0;
            double x1 = (m1[i].x - m1c.x)*scale1;
            double y1 = (m1[i].y - m1c.y)*scale1;

            a[0] = x1*x0;
            a[1] = x1*y0;
            a[2] = x1;
            a[3] = y1*x0;
            a[4] = y1*y0;
            a[5] = y1;
            a[6] = x0;
            a[7] = y0;
            a[8] = 1;
            a += a_step;
        }
    }

    cvSVD( A, &W, 0, &V, CV_SVD_MODIFY_A + CV_SVD_V_T );

    for( i = 0; i < 8; i++ )
    {
        if( fabs(w[i]) < FLT_EPSILON )
            break;
    }

    if( i < 7 )
        EXIT;

    F0 = cvMat( 3, 3, CV_64F, v + 9*8 ); // take the last column of v as a solution of Af = 0

    // make F0 singular (of rank 2) by decomposing it with SVD,
    // zeroing the last diagonal element of W and then composing the matrices back.

    // use v as a temporary storage for different 3x3 matrices
    W = U = V = TF = F0;
    W.data.db = v;
    U.data.db = v + 9;
    V.data.db = v + 18;
    TF.data.db = v + 27;

    cvSVD( &F0, &W, &U, &V, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T );
    W.data.db[8] = 0.;

    // F0 <- U*diag([W(1), W(2), 0])*V'
    cvGEMM( &U, &W, 1., 0, 0., &TF, CV_GEMM_A_T );
    cvGEMM( &TF, &V, 1., 0, 0., &F0, 0/*CV_GEMM_B_T*/ );

    // apply the transformation that is inverse
    // to what we used to normalize the point coordinates
    {
        double tt0[] = { scale0, 0, -scale0*m0c.x, 0, scale0, -scale0*m0c.y, 0, 0, 1 };
        double tt1[] = { scale1, 0, -scale1*m1c.x, 0, scale1, -scale1*m1c.y, 0, 0, 1 };
        CvMat T0, T1;
        T0 = T1 = F0;
        T0.data.db = tt0;
        T1.data.db = tt1;

        // F0 <- T1'*F0*T0
        cvGEMM( &T1, &F0, 1., 0, 0., &TF, CV_GEMM_A_T );
        F0.data.db = fmatrix;
        cvGEMM( &TF, &T0, 1., 0, 0., &F0, 0 );

        // make F(3,3) = 1
        if( fabs(F0.data.db[8]) > FLT_EPSILON )
            cvScale( &F0, &F0, 1./F0.data.db[8] );
    }

    result = 1;

    __END__;

    cvReleaseMat( &A );
    return result;
}


CV_IMPL int
cvRANSACUpdateNumIters( double p, double ep,
                        int model_points, int max_iters )
{
    int result = 0;
    
    CV_FUNCNAME( "cvRANSACUpdateNumIters" );

    __BEGIN__;
    
    double num, denom;
    
    if( model_points <= 0 )
        CV_ERROR( CV_StsOutOfRange, "the number of model points should be positive" );

    p = MAX(p, 0.);
    p = MIN(p, 1.);
    ep = MAX(ep, 0.);
    ep = MIN(ep, 1.);

    // avoid inf's & nan's
    num = MAX(1. - p, DBL_MIN);
    denom = 1. - pow(1. - ep,model_points);
    if( denom < DBL_MIN )
        EXIT;

    num = log(num);
    denom = log(denom);
    
    result = denom >= 0 || -num >= max_iters*(-denom) ?
        max_iters : cvRound(num/denom);

    __END__;

    return result;
}


/************************************ RANSAC algorithm **********************************/
static int
icvFMatrix_RANSAC( const CvPoint2D64f* m0, const CvPoint2D64f* m1,
                   uchar* mask, int count, double* fmatrix,
                   double threshold, double p,
                   unsigned rng_seed, int use_8point )
{
    int result = 0;

    const int max_random_iters = 1000;
    const int sample_size = 7;
    uchar* curr_mask = 0;
    uchar* temp_mask = 0;

    CV_FUNCNAME( "icvFMatrix_RANSAC" );

    __BEGIN__;

    double ff[9*3];
    CvRNG rng = cvRNG(rng_seed);
    int i, j, k, sample_count, max_samples = 500;
    int best_good_count = 0;

    assert( m0 && m1 && fmatrix && 0 < p && p < 1 && threshold > 0 );

    threshold *= threshold;

    CV_CALL( curr_mask = (uchar*)cvAlloc( count ));
    if( !mask && use_8point )
    {
        CV_CALL( temp_mask = (uchar*)cvAlloc( count ));
        mask = temp_mask;
    }

    // find the best fundamental matrix (giving the least backprojection error)
    // by picking at most <max_samples> 7-tuples of corresponding points
    // <max_samples> may be updated (decreased) within the loop based on statistics of outliers
    for( sample_count = 0; sample_count < max_samples; sample_count++ )
    {
        int idx[sample_size], n;
        CvPoint2D64f ms0[sample_size], ms1[sample_size];

        // choose random <sample_size> (=7) points
        for( i = 0; i < sample_size; i++ )
        {
            for( k = 0; k < max_random_iters; k++ )
            {
                idx[i] = cvRandInt(&rng) % count;
                for( j = 0; j < i; j++ )
                    if( idx[j] == idx[i] )
                        break;
                if( j == i )
                {
                    ms0[i] = m0[idx[i]];
                    ms1[i] = m1[idx[i]];
                    break;
                }
            }
            if( k >= max_random_iters )
                break;
        }

        if( i < sample_size )
            continue;

        // find 1 or 3 fundamental matrices out of the 7 point correspondences
        n = icvFMatrix_7Point( ms0, ms1, ff );

        if( n < 1 || n > 3 )
            continue;

        // for each matrix calculate the backprojection error
        // (distance to the corresponding epipolar lines) for each point and thus find
        // the number of in-liers.
        for( k = 0; k < n; k++ )
        {
            const double* f = ff + k*9;
            int good_count = 0;

            for( i = 0; i < count; i++ )
            {
                double d0, d1, s0, s1;

                double a = f[0]*m0[i].x + f[1]*m0[i].y + f[2];
                double b = f[3]*m0[i].x + f[4]*m0[i].y + f[5];
                double c = f[6]*m0[i].x + f[7]*m0[i].y + f[8];

                s1 = a*a + b*b;
                d1 = m1[i].x*a + m1[i].y*b + c;

                a = f[0]*m1[i].x + f[3]*m1[i].y + f[6];
                b = f[1]*m1[i].x + f[4]*m1[i].y + f[7];
                c = f[2]*m1[i].x + f[5]*m1[i].y + f[8];

                s0 = a*a + b*b;
                d0 = m0[i].x*a + m0[i].y*b + c;

                curr_mask[i] = d1*d1 < threshold*s1 && d0*d0 < threshold*s0;
                good_count += curr_mask[i];
            }

            if( good_count > MAX( best_good_count, 6 ) )
            {
                // update the current best fundamental matrix and "goodness" flags
                if( mask )
                    memcpy( mask, curr_mask, count );
                memcpy( fmatrix, f, 9*sizeof(f[0]));
                best_good_count = good_count;
                
                max_samples = cvRANSACUpdateNumIters( p,
                    (double)(count - good_count)/count, 7, max_samples );
                if( max_samples == 0 )
                    break;
            }
        }
    }

    if( best_good_count < 7 )
        EXIT;

    result = 1;

    // optionally, use 8-point algorithm to compute fundamental matrix using only the in-liers
    if( best_good_count >= 8 && use_8point )
        result = icvFMatrix_8Point( m0, m1, mask, count, fmatrix );

    __END__;

    cvFree( &temp_mask );
    cvFree( &curr_mask );

    return result;
}


/***************************** Least Median of Squares algorithm ************************/

static CV_IMPLEMENT_QSORT( icvSortDistances, int, CV_LT )

/* the algorithm is quite similar to RANSAC, but here we choose the matrix that gives
   the least median of d(m0[i], F'*m1[i])^2 + d(m1[i], F*m0[i])^2 (0<=i<count),
   instead of choosing the matrix that gives the least number of outliers (as it is done in RANSAC) */
static int
icvFMatrix_LMedS( const CvPoint2D64f* m0, const CvPoint2D64f* m1,
                  uchar* mask, int count, double* fmatrix,
                  double threshold, double p,
                  unsigned rng_seed, int use_8point )
{
    int result = 0;

    const int max_random_iters = 1000;
    const int sample_size = 7;

    float* dist = 0;
    uchar* curr_mask = 0;
    uchar* temp_mask = 0;

    CV_FUNCNAME( "icvFMatrix_LMedS" );

    __BEGIN__;

    double ff[9*3];
    CvRNG rng = cvRNG(rng_seed);
    int i, j, k, sample_count, max_samples = 500;
    double least_median = DBL_MAX, median;
    int best_good_count = 0;

    assert( m0 && m1 && fmatrix && 0 < p && p < 1 && threshold > 0 );

    threshold *= threshold;

    CV_CALL( curr_mask = (uchar*)cvAlloc( count ));
    CV_CALL( dist = (float*)cvAlloc( count*sizeof(dist[0]) ));

    if( !mask && use_8point )
    {
        CV_CALL( temp_mask = (uchar*)cvAlloc( count ));
        mask = temp_mask;
    }

    // find the best fundamental matrix (giving the least backprojection error)
    // by picking at most <max_samples> 7-tuples of corresponding points
    // <max_samples> may be updated (decreased) within the loop based on statistics of outliers
    for( sample_count = 0; sample_count < max_samples; sample_count++ )
    {
        int idx[sample_size], n;
        CvPoint2D64f ms0[sample_size], ms1[sample_size];

        // choose random <sample_size> (=7) points
        for( i = 0; i < sample_size; i++ )
        {
            for( k = 0; k < max_random_iters; k++ )
            {
                idx[i] = cvRandInt(&rng) % count;
                for( j = 0; j < i; j++ )
                    if( idx[j] == idx[i] )
                        break;
                if( j == i )
                {
                    ms0[i] = m0[idx[i]];
                    ms1[i] = m1[idx[i]];
                    break;
                }
            }
            if( k >= max_random_iters )
                break;
        }

        if( i < sample_size )
            continue;

        // find 1 or 3 fundamental matrix out of the 7 point correspondences
        n = icvFMatrix_7Point( ms0, ms1, ff );

        if( n < 1 || n > 3 )
            continue;

        // for each matrix calculate the backprojection error
        // (distance to the corresponding epipolar lines) for each point and thus find
        // the number of in-liers.
        for( k = 0; k < n; k++ )
        {
            const double* f = ff + k*9;
            int good_count = 0;

            for( i = 0; i < count; i++ )
            {
                double d0, d1, s;

                double a = f[0]*m0[i].x + f[1]*m0[i].y + f[2];
                double b = f[3]*m0[i].x + f[4]*m0[i].y + f[5];
                double c = f[6]*m0[i].x + f[7]*m0[i].y + f[8];

                s = 1./(a*a + b*b);
                d1 = m1[i].x*a + m1[i].y*b + c;
                d1 = s*d1*d1;

                a = f[0]*m1[i].x + f[3]*m1[i].y + f[6];
                b = f[1]*m1[i].x + f[4]*m1[i].y + f[7];
                c = f[2]*m1[i].x + f[5]*m1[i].y + f[8];

                s = 1./(a*a + b*b);
                d0 = m0[i].x*a + m0[i].y*b + c;
                d0 = s*d0*d0;

                curr_mask[i] = d1 < threshold && d0 < threshold;
                good_count += curr_mask[i];

                dist[i] = (float)(d0 + d1);
            }

            icvSortDistances( (int*)dist, count, 0 );
            median = (double)dist[count/2];

            if( median < least_median )
            {
                double ep, lp, lep;
                int new_max_samples;

                // update the current best fundamental matrix and "goodness" flags
                if( mask )
                    memcpy( mask, curr_mask, count );
                memcpy( fmatrix, f, 9*sizeof(f[0]));
                least_median = median;
                best_good_count = good_count;

                // try to update (decrease) <max_samples>
                ep = (double)(count - good_count)/count;
                lp = log(1. - p);
                lep = log(1. - pow(ep,7.));
                if( lp < lep || lep >= 0 )
                    break;
                else
                {
                    new_max_samples = cvRound(lp/lep);
                    max_samples = MIN( new_max_samples, max_samples );
                }
            }
        }
    }

    if( best_good_count < 7 )
        EXIT;

    result = 1;

    // optionally, use 8-point algorithm to compute fundamental matrix using only the in-liers
    if( best_good_count >= 8 && use_8point )
        result = icvFMatrix_8Point( m0, m1, mask, count, fmatrix );

    __END__;

    cvFree( &temp_mask );
    cvFree( &curr_mask );
    cvFree( &dist );

    return result;
}


CV_IMPL int
cvFindFundamentalMat( const CvMat* points0, const CvMat* points1,
                      CvMat* fmatrix, int method,
                      double param1, double param2, CvMat* status )
{
    const unsigned rng_seed = 0xffffffff;
    int result = 0;
    int pt_alloc_flag[2] = { 0, 0 };
    int i, k;
    CvPoint2D64f* pt[2] = { 0, 0 };
    CvMat* _status = 0;

    CV_FUNCNAME( "cvFindFundamentalMat" );

    __BEGIN__;

    int count, dims;
    int depth, cn;
    uchar* status_data = 0;
    double fmatrix_data0[9*3];
    double* fmatrix_data = 0;

    if( !CV_IS_MAT(points0) )
        CV_ERROR( !points0 ? CV_StsNullPtr : CV_StsBadArg, "points0 is not a valid matrix" );

    if( !CV_IS_MAT(points1) )
        CV_ERROR( !points1 ? CV_StsNullPtr : CV_StsBadArg, "points1 is not a valid matrix" );

    if( !CV_ARE_TYPES_EQ(points0, points1) )
        CV_ERROR( CV_StsUnmatchedFormats, "The matrices of points should have the same data type" );

    if( !CV_ARE_SIZES_EQ(points0, points1) )
        CV_ERROR( CV_StsUnmatchedSizes, "The matrices of points should have the same size" );

    depth = CV_MAT_DEPTH(points0->type);
    cn = CV_MAT_CN(points0->type);
    if( depth != CV_32S && depth != CV_32F && depth != CV_64F || cn != 1 && cn != 2 && cn != 3 )
        CV_ERROR( CV_StsUnsupportedFormat, "The format of point matrices is unsupported" );

    if( points0->rows > points0->cols )
    {
        dims = cn*points0->cols;
        count = points0->rows;
    }
    else
    {
        if( points0->rows > 1 && cn > 1 || points0->rows == 1 && cn == 1 )
            CV_ERROR( CV_StsBadSize, "The point matrices do not have a proper layout (2xn, 3xn, nx2 or nx3)" );
        dims = cn * points0->rows;
        count = points0->cols;
    }

    if( dims != 2 && dims != 3 )
        CV_ERROR( CV_StsOutOfRange, "The dimensionality of points must be 2 or 3" );

    if( method == CV_FM_7POINT && count != 7 ||
        method != CV_FM_7POINT && count < 7 + (method == CV_FM_8POINT) )
        CV_ERROR( CV_StsOutOfRange,
        "The number of points must be 7 for 7-point algorithm, "
        ">=8 for 8-point algorithm and >=7 for other algorithms" );

    if( !CV_IS_MAT(fmatrix) )
        CV_ERROR( !fmatrix ? CV_StsNullPtr : CV_StsBadArg, "fmatrix is not a valid matrix" );

    if( CV_MAT_TYPE(fmatrix->type) != CV_32FC1 && CV_MAT_TYPE(fmatrix->type) != CV_64FC1 )
        CV_ERROR( CV_StsUnsupportedFormat, "fundamental matrix must have 32fC1 or 64fC1 type" );

    if( fmatrix->cols != 3 || (fmatrix->rows != 3 && (method != CV_FM_7POINT || fmatrix->rows != 9)))
        CV_ERROR( CV_StsBadSize, "fundamental matrix must be 3x3 or 3x9 (for 7-point method only)" );

    fmatrix_data = fmatrix->data.db;
    if( !CV_IS_MAT_CONT(fmatrix->type) || CV_MAT_TYPE(fmatrix->type) != CV_64FC1 ||
        method == CV_FM_7POINT && fmatrix->rows != 9 )
        fmatrix_data = fmatrix_data0;

    if( status )
    {
        if( !CV_IS_MAT(status) )
            CV_ERROR( CV_StsBadArg, "The output status is not a valid matrix" );

        if( status->cols != 1 && status->rows != 1 || status->cols + status->rows - 1 != count )
            CV_ERROR( CV_StsUnmatchedSizes,
            "The status matrix must have the same size as the point matrices" );

        if( method == CV_FM_7POINT || method == CV_FM_8POINT )
            cvSet( status, cvScalarAll(1.) );
        else
        {
            status_data = status->data.ptr;
            if( !CV_IS_MAT_CONT(status->type) || !CV_IS_MASK_ARR(status) )
            {
                CV_CALL( _status = cvCreateMat( status->rows, status->cols, CV_8UC1 ));
                status_data = _status->data.ptr;
            }
        }
    }

    for( k = 0; k < 2; k++ )
    {
        const CvMat* spt = k == 0 ? points0 : points1;
        CvPoint2D64f* dpt = pt[k] = (CvPoint2D64f*)spt->data.db;
        int plane_stride, stride, elem_size;

        if( CV_IS_MAT_CONT(spt->type) && CV_MAT_DEPTH(spt->type) == CV_64F &&
            dims == 2 && (spt->rows == 1 || spt->rows == count) )
            continue;

        elem_size = CV_ELEM_SIZE(depth);

        if( spt->rows == dims )
        {
            plane_stride = spt->step / elem_size;
            stride = 1;
        }
        else
        {
            plane_stride = 1;
            stride = spt->rows == 1 ? dims : spt->step / elem_size;
        }

        CV_CALL( dpt = pt[k] = (CvPoint2D64f*)cvAlloc( count*sizeof(dpt[0]) ));
        pt_alloc_flag[k] = 1;

        if( depth == CV_32F )
        {
            const float* xp = spt->data.fl;
            const float* yp = xp + plane_stride;
            const float* zp = dims == 3 ? yp + plane_stride : 0;

            for( i = 0; i < count; i++ )
            {
                double x = *xp, y = *yp;
                xp += stride;
                yp += stride;
                if( dims == 3 )
                {
                    double z = *zp;
                    zp += stride;
                    z = z ? 1./z : 1.;
                    x *= z;
                    y *= z;
                }
                dpt[i].x = x;
                dpt[i].y = y;
            }
        }
        else
        {
            const double* xp = spt->data.db;
            const double* yp = xp + plane_stride;
            const double* zp = dims == 3 ? yp + plane_stride : 0;

            for( i = 0; i < count; i++ )
            {
                double x = *xp, y = *yp;
                xp += stride;
                yp += stride;
                if( dims == 3 )
                {
                    double z = *zp;
                    zp += stride;
                    z = z ? 1./z : 1.;
                    x *= z;
                    y *= z;
                }
                dpt[i].x = x;
                dpt[i].y = y;
            }
        }
    }

    if( method == CV_FM_7POINT )
        result = icvFMatrix_7Point( pt[0], pt[1], fmatrix_data );
    else if( method == CV_FM_8POINT )
        result = icvFMatrix_8Point( pt[0], pt[1], 0, count, fmatrix_data );
    else
    {
        if( param1 < 0 )
            CV_ERROR( CV_StsOutOfRange, "param1 (threshold) must be > 0" );

        if( param2 < 0 || param2 > 1 )
            CV_ERROR( CV_StsOutOfRange, "param2 (confidence level) must be between 0 and 1" );

        if( param2 < DBL_EPSILON || param2 > 1 - DBL_EPSILON )
            param2 = 0.99;

        if( method < CV_FM_RANSAC_ONLY )
            result = icvFMatrix_LMedS( pt[0], pt[1], status_data, count, fmatrix_data,
                                       param1, param2, rng_seed, method & CV_FM_8POINT );
        else
            result = icvFMatrix_RANSAC( pt[0], pt[1], status_data, count, fmatrix_data,
                                        param1, param2, rng_seed, method & CV_FM_8POINT );
    }

    if( result && fmatrix->data.db != fmatrix_data )
    {
        CvMat hdr;
        cvZero( fmatrix );
        hdr = cvMat( MIN(fmatrix->rows, result*3), fmatrix->cols, CV_64F, fmatrix_data );
        cvConvert( &hdr, fmatrix );
    }

    if( status && status_data && status->data.ptr != status_data )
        cvConvert( _status, status );

    __END__;

    cvReleaseMat( &_status );
    for( k = 0; k < 2; k++ )
        if( pt_alloc_flag[k] )
            cvFree( &pt[k] );

    return result;
}


CV_IMPL void
cvComputeCorrespondEpilines( const CvMat* points, int pointImageID,
                             const CvMat* fmatrix, CvMat* lines )
{
    CV_FUNCNAME( "cvComputeCorrespondEpilines" );

    __BEGIN__;

    int abc_stride, abc_plane_stride, abc_elem_size;
    int plane_stride, stride, elem_size;
    int i, dims, count, depth, cn, abc_dims, abc_count, abc_depth, abc_cn;
    uchar *ap, *bp, *cp;
    const uchar *xp, *yp, *zp;
    double f[9];
    CvMat F = cvMat( 3, 3, CV_64F, f );

    if( !CV_IS_MAT(points) )
        CV_ERROR( !points ? CV_StsNullPtr : CV_StsBadArg, "points parameter is not a valid matrix" );

    depth = CV_MAT_DEPTH(points->type);
    cn = CV_MAT_CN(points->type);
    if( depth != CV_32F && depth != CV_64F || cn != 1 && cn != 2 && cn != 3 )
        CV_ERROR( CV_StsUnsupportedFormat, "The format of point matrix is unsupported" );

    if( points->rows > points->cols )
    {
        dims = cn*points->cols;
        count = points->rows;
    }
    else
    {
        if( points->rows > 1 && cn > 1 || points->rows == 1 && cn == 1 )
            CV_ERROR( CV_StsBadSize, "The point matrix does not have a proper layout (2xn, 3xn, nx2 or nx3)" );
        dims = cn * points->rows;
        count = points->cols;
    }

    if( dims != 2 && dims != 3 )
        CV_ERROR( CV_StsOutOfRange, "The dimensionality of points must be 2 or 3" );

    if( !CV_IS_MAT(fmatrix) )
        CV_ERROR( !fmatrix ? CV_StsNullPtr : CV_StsBadArg, "fmatrix is not a valid matrix" );

    if( CV_MAT_TYPE(fmatrix->type) != CV_32FC1 && CV_MAT_TYPE(fmatrix->type) != CV_64FC1 )
        CV_ERROR( CV_StsUnsupportedFormat, "fundamental matrix must have 32fC1 or 64fC1 type" );

    if( fmatrix->cols != 3 || fmatrix->rows != 3 )
        CV_ERROR( CV_StsBadSize, "fundamental matrix must be 3x3" );

    if( !CV_IS_MAT(lines) )
        CV_ERROR( !lines ? CV_StsNullPtr : CV_StsBadArg, "lines parameter is not a valid matrix" );

    abc_depth = CV_MAT_DEPTH(lines->type);
    abc_cn = CV_MAT_CN(lines->type);
    if( abc_depth != CV_32F && abc_depth != CV_64F || abc_cn != 1 && abc_cn != 3 )
        CV_ERROR( CV_StsUnsupportedFormat, "The format of the matrix of lines is unsupported" );

    if( lines->rows > lines->cols )
    {
        abc_dims = abc_cn*lines->cols;
        abc_count = lines->rows;
    }
    else
    {
        if( lines->rows > 1 && abc_cn > 1 || lines->rows == 1 && abc_cn == 1 )
            CV_ERROR( CV_StsBadSize, "The lines matrix does not have a proper layout (3xn or nx3)" );
        abc_dims = abc_cn * lines->rows;
        abc_count = lines->cols;
    }

    if( abc_dims != 3 )
        CV_ERROR( CV_StsOutOfRange, "The lines matrix does not have a proper layout (3xn or nx3)" );

    if( abc_count != count )
        CV_ERROR( CV_StsUnmatchedSizes, "The numbers of points and lines are different" );

    elem_size = CV_ELEM_SIZE(depth);
    abc_elem_size = CV_ELEM_SIZE(abc_depth);

    if( points->rows == dims )
    {
        plane_stride = points->step;
        stride = elem_size;
    }
    else
    {
        plane_stride = elem_size;
        stride = points->rows == 1 ? dims*elem_size : points->step;
    }

    if( lines->rows == 3 )
    {
        abc_plane_stride = lines->step;
        abc_stride = abc_elem_size;
    }
    else
    {
        abc_plane_stride = abc_elem_size;
        abc_stride = lines->rows == 1 ? 3*abc_elem_size : lines->step;
    }

    CV_CALL( cvConvert( fmatrix, &F ));
    if( pointImageID == 2 )
        cvTranspose( &F, &F );

    xp = points->data.ptr;
    yp = xp + plane_stride;
    zp = dims == 3 ? yp + plane_stride : 0;

    ap = lines->data.ptr;
    bp = ap + abc_plane_stride;
    cp = bp + abc_plane_stride;

    for( i = 0; i < count; i++ )
    {
        double x, y, z = 1.;
        double a, b, c, nu;

        if( depth == CV_32F )
        {
            x = *(float*)xp; y = *(float*)yp;
            if( zp )
                z = *(float*)zp, zp += stride;
        }
        else
        {
            x = *(double*)xp; y = *(double*)yp;
            if( zp )
                z = *(double*)zp, zp += stride;
        }

        xp += stride; yp += stride;

        a = f[0]*x + f[1]*y + f[2]*z;
        b = f[3]*x + f[4]*y + f[5]*z;
        c = f[6]*x + f[7]*y + f[8]*z;
        nu = a*a + b*b;
        nu = nu ? 1./sqrt(nu) : 1.;
        a *= nu; b *= nu; c *= nu;

        if( abc_depth == CV_32F )
        {
            *(float*)ap = (float)a;
            *(float*)bp = (float)b;
            *(float*)cp = (float)c;
        }
        else
        {
            *(double*)ap = a;
            *(double*)bp = b;
            *(double*)cp = c;
        }

        ap += abc_stride;
        bp += abc_stride;
        cp += abc_stride;
    }

    __END__;
}


CV_IMPL void
cvConvertPointsHomogenious( const CvMat* src, CvMat* dst )
{
    CvMat* temp = 0;
    CvMat* denom = 0;

    CV_FUNCNAME( "cvConvertPointsHomogenious" );

    __BEGIN__;

    int i, s_count, s_dims, d_count, d_dims;
    CvMat _src, _dst, _ones;
    CvMat* ones = 0;

    if( !CV_IS_MAT(src) )
        CV_ERROR( !src ? CV_StsNullPtr : CV_StsBadArg,
        "The input parameter is not a valid matrix" );

    if( !CV_IS_MAT(dst) )
        CV_ERROR( !dst ? CV_StsNullPtr : CV_StsBadArg,
        "The output parameter is not a valid matrix" );

    if( src == dst || src->data.ptr == dst->data.ptr )
    {
        if( src != dst && (!CV_ARE_TYPES_EQ(src, dst) || !CV_ARE_SIZES_EQ(src,dst)) )
            CV_ERROR( CV_StsBadArg, "Invalid inplace operation" );
        EXIT;
    }

    if( src->rows > src->cols )
    {
        if( !((src->cols > 1) ^ (CV_MAT_CN(src->type) > 1)) )
            CV_ERROR( CV_StsBadSize, "Either the number of channels or columns or rows must be =1" );

        s_dims = CV_MAT_CN(src->type)*src->cols;
        s_count = src->rows;
    }
    else
    {
        if( !((src->rows > 1) ^ (CV_MAT_CN(src->type) > 1)) )
            CV_ERROR( CV_StsBadSize, "Either the number of channels or columns or rows must be =1" );

        s_dims = CV_MAT_CN(src->type)*src->rows;
        s_count = src->cols;
    }

    if( src->rows == 1 || src->cols == 1 )
        src = cvReshape( src, &_src, 1, s_count );

    if( dst->rows > dst->cols )
    {
        if( !((dst->cols > 1) ^ (CV_MAT_CN(dst->type) > 1)) )
            CV_ERROR( CV_StsBadSize,
            "Either the number of channels or columns or rows in the input matrix must be =1" );

        d_dims = CV_MAT_CN(dst->type)*dst->cols;
        d_count = dst->rows;
    }
    else
    {
        if( !((dst->rows > 1) ^ (CV_MAT_CN(dst->type) > 1)) )
            CV_ERROR( CV_StsBadSize,
            "Either the number of channels or columns or rows in the output matrix must be =1" );

        d_dims = CV_MAT_CN(dst->type)*dst->rows;
        d_count = dst->cols;
    }

    if( dst->rows == 1 || dst->cols == 1 )
        dst = cvReshape( dst, &_dst, 1, d_count );

    if( s_count != d_count )
        CV_ERROR( CV_StsUnmatchedSizes, "Both matrices must have the same number of points" );

    if( CV_MAT_DEPTH(src->type) < CV_32F || CV_MAT_DEPTH(dst->type) < CV_32F )
        CV_ERROR( CV_StsUnsupportedFormat,
        "Both matrices must be floating-point (single or double precision)" );

    if( s_dims < 2 || s_dims > 4 || d_dims < 2 || d_dims > 4 )
        CV_ERROR( CV_StsOutOfRange,
        "Both input and output point dimensionality must be 2, 3 or 4" );

    if( s_dims < d_dims - 1 || s_dims > d_dims + 1 )
        CV_ERROR( CV_StsUnmatchedSizes,
        "The dimensionalities of input and output point sets differ too much" );

    if( s_dims == d_dims - 1 )
    {
        if( d_count == dst->rows )
        {
            ones = cvGetSubRect( dst, &_ones, cvRect( s_dims, 0, 1, d_count ));
            dst = cvGetSubRect( dst, &_dst, cvRect( 0, 0, s_dims, d_count ));
        }
        else
        {
            ones = cvGetSubRect( dst, &_ones, cvRect( 0, s_dims, d_count, 1 ));
            dst = cvGetSubRect( dst, &_dst, cvRect( 0, 0, d_count, s_dims ));
        }
    }

    if( s_dims <= d_dims )
    {
        if( src->rows == dst->rows && src->cols == dst->cols )
        {
            if( CV_ARE_TYPES_EQ( src, dst ) )
                cvCopy( src, dst );
            else
                cvConvert( src, dst );
        }
        else
        {
            if( !CV_ARE_TYPES_EQ( src, dst ))
            {
                CV_CALL( temp = cvCreateMat( src->rows, src->cols, dst->type ));
                cvConvert( src, temp );
                src = temp;
            }
            cvTranspose( src, dst );
        }

        if( ones )
            cvSet( ones, cvRealScalar(1.) );
    }
    else
    {
        int s_plane_stride, s_stride, d_plane_stride, d_stride, elem_size;

        if( !CV_ARE_TYPES_EQ( src, dst ))
        {
            CV_CALL( temp = cvCreateMat( src->rows, src->cols, dst->type ));
            cvConvert( src, temp );
            src = temp;
        }

        elem_size = CV_ELEM_SIZE(src->type);

        if( s_count == src->cols )
            s_plane_stride = src->step / elem_size, s_stride = 1;
        else
            s_stride = src->step / elem_size, s_plane_stride = 1;

        if( d_count == dst->cols )
            d_plane_stride = dst->step / elem_size, d_stride = 1;
        else
            d_stride = dst->step / elem_size, d_plane_stride = 1;

        CV_CALL( denom = cvCreateMat( 1, d_count, dst->type ));

        if( CV_MAT_DEPTH(dst->type) == CV_32F )
        {
            const float* xs = src->data.fl;
            const float* ys = xs + s_plane_stride;
            const float* zs = 0;
            const float* ws = xs + (s_dims - 1)*s_plane_stride;

            float* iw = denom->data.fl;

            float* xd = dst->data.fl;
            float* yd = xd + d_plane_stride;
            float* zd = 0;

            if( d_dims == 3 )
            {
                zs = ys + s_plane_stride;
                zd = yd + d_plane_stride;
            }

            for( i = 0; i < d_count; i++, ws += s_stride )
            {
                float t = *ws;
                iw[i] = t ? t : 1.f;
            }

            cvDiv( 0, denom, denom );

            if( d_dims == 3 )
                for( i = 0; i < d_count; i++ )
                {
                    float w = iw[i];
                    float x = *xs * w, y = *ys * w, z = *zs * w;
                    xs += s_stride; ys += s_stride; zs += s_stride;
                    *xd = x; *yd = y; *zd = z;
                    xd += d_stride; yd += d_stride; zd += d_stride;
                }
            else
                for( i = 0; i < d_count; i++ )
                {
                    float w = iw[i];
                    float x = *xs * w, y = *ys * w;
                    xs += s_stride; ys += s_stride;
                    *xd = x; *yd = y;
                    xd += d_stride; yd += d_stride;
                }
        }
        else
        {
            const double* xs = src->data.db;
            const double* ys = xs + s_plane_stride;
            const double* zs = 0;
            const double* ws = xs + (s_dims - 1)*s_plane_stride;

            double* iw = denom->data.db;

            double* xd = dst->data.db;
            double* yd = xd + d_plane_stride;
            double* zd = 0;

            if( d_dims == 3 )
            {
                zs = ys + s_plane_stride;
                zd = yd + d_plane_stride;
            }

            for( i = 0; i < d_count; i++, ws += s_stride )
            {
                double t = *ws;
                iw[i] = t ? t : 1.;
            }

            cvDiv( 0, denom, denom );

            if( d_dims == 3 )
                for( i = 0; i < d_count; i++ )
                {
                    double w = iw[i];
                    double x = *xs * w, y = *ys * w, z = *zs * w;
                    xs += s_stride; ys += s_stride; zs += s_stride;
                    *xd = x; *yd = y; *zd = z;
                    xd += d_stride; yd += d_stride; zd += d_stride;
                }
            else
                for( i = 0; i < d_count; i++ )
                {
                    double w = iw[i];
                    double x = *xs * w, y = *ys * w;
                    xs += s_stride; ys += s_stride;
                    *xd = x; *yd = y;
                    xd += d_stride; yd += d_stride;
                }
        }
    }

    __END__;

    cvReleaseMat( &denom );
    cvReleaseMat( &temp );
}

/* End of file. */