linefit.cpp

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#include "precomp.hpp"

namespace cv
{

static const double eps = 1e-6;

static void fitLine2D_wods( const Point2f* points, int count, float *weights, float *line )
{
    double x = 0, y = 0, x2 = 0, y2 = 0, xy = 0, w = 0;
    double dx2, dy2, dxy;
    int i;
    float t;

    // Calculating the average of x and y...
    if( weights == 0 )
    {
        for( i = 0; i < count; i += 1 )
        {
            x += points[i].x;
            y += points[i].y;
            x2 += points[i].x * points[i].x;
            y2 += points[i].y * points[i].y;
            xy += points[i].x * points[i].y;
        }
        w = (float) count;
    }
    else
    {
        for( i = 0; i < count; i += 1 )
        {
            x += weights[i] * points[i].x;
            y += weights[i] * points[i].y;
            x2 += weights[i] * points[i].x * points[i].x;
            y2 += weights[i] * points[i].y * points[i].y;
            xy += weights[i] * points[i].x * points[i].y;
            w += weights[i];
        }
    }

    x /= w;
    y /= w;
    x2 /= w;
    y2 /= w;
    xy /= w;

    dx2 = x2 - x * x;
    dy2 = y2 - y * y;
    dxy = xy - x * y;

    t = (float) atan2( 2 * dxy, dx2 - dy2 ) / 2;
    line[0] = (float) cos( t );
    line[1] = (float) sin( t );

    line[2] = (float) x;
    line[3] = (float) y;
}

static void fitLine3D_wods( const Point3f * points, int count, float *weights, float *line )
{
    int i;
    float w0 = 0;
    float x0 = 0, y0 = 0, z0 = 0;
    float x2 = 0, y2 = 0, z2 = 0, xy = 0, yz = 0, xz = 0;
    float dx2, dy2, dz2, dxy, dxz, dyz;
    float *v;
    float n;
    float det[9], evc[9], evl[3];

    memset( evl, 0, 3*sizeof(evl[0]));
    memset( evc, 0, 9*sizeof(evl[0]));

    if( weights )
    {
        for( i = 0; i < count; i++ )
        {
            float x = points[i].x;
            float y = points[i].y;
            float z = points[i].z;
            float w = weights[i];


            x2 += x * x * w;
            xy += x * y * w;
            xz += x * z * w;
            y2 += y * y * w;
            yz += y * z * w;
            z2 += z * z * w;
            x0 += x * w;
            y0 += y * w;
            z0 += z * w;
            w0 += w;
        }
    }
    else
    {
        for( i = 0; i < count; i++ )
        {
            float x = points[i].x;
            float y = points[i].y;
            float z = points[i].z;

            x2 += x * x;
            xy += x * y;
            xz += x * z;
            y2 += y * y;
            yz += y * z;
            z2 += z * z;
            x0 += x;
            y0 += y;
            z0 += z;
        }
        w0 = (float) count;
    }

    x2 /= w0;
    xy /= w0;
    xz /= w0;
    y2 /= w0;
    yz /= w0;
    z2 /= w0;

    x0 /= w0;
    y0 /= w0;
    z0 /= w0;

    dx2 = x2 - x0 * x0;
    dxy = xy - x0 * y0;
    dxz = xz - x0 * z0;
    dy2 = y2 - y0 * y0;
    dyz = yz - y0 * z0;
    dz2 = z2 - z0 * z0;

    det[0] = dz2 + dy2;
    det[1] = -dxy;
    det[2] = -dxz;
    det[3] = det[1];
    det[4] = dx2 + dz2;
    det[5] = -dyz;
    det[6] = det[2];
    det[7] = det[5];
    det[8] = dy2 + dx2;

    // Searching for a eigenvector of det corresponding to the minimal eigenvalue
    Mat _det( 3, 3, CV_32F, det );
    Mat _evc( 3, 3, CV_32F, evc );
    Mat _evl( 3, 1, CV_32F, evl );
    eigen( _det, _evl, _evc );
    i = evl[0] < evl[1] ? (evl[0] < evl[2] ? 0 : 2) : (evl[1] < evl[2] ? 1 : 2);

    v = &evc[i * 3];
    n = (float) std::sqrt( (double)v[0] * v[0] + (double)v[1] * v[1] + (double)v[2] * v[2] );
    n = (float)MAX(n, eps);
    line[0] = v[0] / n;
    line[1] = v[1] / n;
    line[2] = v[2] / n;
    line[3] = x0;
    line[4] = y0;
    line[5] = z0;
}

static double calcDist2D( const Point2f* points, int count, float *_line, float *dist )
{
    int j;
    float px = _line[2], py = _line[3];
    float nx = _line[1], ny = -_line[0];
    double sum_dist = 0.;

    for( j = 0; j < count; j++ )
    {
        float x, y;

        x = points[j].x - px;
        y = points[j].y - py;

        dist[j] = (float) fabs( nx * x + ny * y );
        sum_dist += dist[j];
    }

    return sum_dist;
}

static double calcDist3D( const Point3f* points, int count, float *_line, float *dist )
{
    int j;
    float px = _line[3], py = _line[4], pz = _line[5];
    float vx = _line[0], vy = _line[1], vz = _line[2];
    double sum_dist = 0.;

    for( j = 0; j < count; j++ )
    {
        float x, y, z;
        double p1, p2, p3;

        x = points[j].x - px;
        y = points[j].y - py;
        z = points[j].z - pz;

        p1 = vy * z - vz * y;
        p2 = vz * x - vx * z;
        p3 = vx * y - vy * x;

        dist[j] = (float) std::sqrt( p1*p1 + p2*p2 + p3*p3 );
        sum_dist += dist[j];
    }

    return sum_dist;
}

static void weightL1( float *d, int count, float *w )
{
    int i;

    for( i = 0; i < count; i++ )
    {
        double t = fabs( (double) d[i] );
        w[i] = (float)(1. / MAX(t, eps));
    }
}

static void weightL12( float *d, int count, float *w )
{
    int i;

    for( i = 0; i < count; i++ )
    {
        w[i] = 1.0f / (float) std::sqrt( 1 + (double) (d[i] * d[i] * 0.5) );
    }
}


static void weightHuber( float *d, int count, float *w, float _c )
{
    int i;
    const float c = _c <= 0 ? 1.345f : _c;

    for( i = 0; i < count; i++ )
    {
        if( d[i] < c )
            w[i] = 1.0f;
        else
            w[i] = c/d[i];
    }
}


static void weightFair( float *d, int count, float *w, float _c )
{
    int i;
    const float c = _c == 0 ? 1 / 1.3998f : 1 / _c;

    for( i = 0; i < count; i++ )
    {
        w[i] = 1 / (1 + d[i] * c);
    }
}

static void weightWelsch( float *d, int count, float *w, float _c )
{
    int i;
    const float c = _c == 0 ? 1 / 2.9846f : 1 / _c;

    for( i = 0; i < count; i++ )
    {
        w[i] = (float) std::exp( -d[i] * d[i] * c * c );
    }
}


/* Takes an array of 2D points, type of distance (including user-defined
 distance specified by callbacks, fills the array of four floats with line
 parameters A, B, C, D, where (A, B) is the normalized direction vector,
 (C, D) is the point that belongs to the line. */

static void fitLine2D( const Point2f * points, int count, int dist,
                      float _param, float reps, float aeps, float *line )
{
    double EPS = count*FLT_EPSILON;
    void (*calc_weights) (float *, int, float *) = 0;
    void (*calc_weights_param) (float *, int, float *, float) = 0;
    int i, j, k;
    float _line[6], _lineprev[6];
    float rdelta = reps != 0 ? reps : 1.0f;
    float adelta = aeps != 0 ? aeps : 0.01f;
    double min_err = DBL_MAX, err = 0;
    RNG rng((uint64)-1);

    memset( line, 0, 4*sizeof(line[0]) );

    switch (dist)
    {
    case CV_DIST_L2:
        return fitLine2D_wods( points, count, 0, line );

    case CV_DIST_L1:
        calc_weights = weightL1;
        break;

    case CV_DIST_L12:
        calc_weights = weightL12;
        break;

    case CV_DIST_FAIR:
        calc_weights_param = weightFair;
        break;

    case CV_DIST_WELSCH:
        calc_weights_param = weightWelsch;
        break;

    case CV_DIST_HUBER:
        calc_weights_param = weightHuber;
        break;

    /*case DIST_USER:
     calc_weights = (void ( * )(float *, int, float *)) _PFP.fp;
     break;*/
    default:
        CV_Error(CV_StsBadArg, "Unknown distance type");
    }

    AutoBuffer<float> wr(count*2);
    float *w = wr, *r = w + count;

    for( k = 0; k < 20; k++ )
    {
        int first = 1;
        for( i = 0; i < count; i++ )
            w[i] = 0.f;

        for( i = 0; i < MIN(count,10); )
        {
            j = rng.uniform(0, count);
            if( w[j] < FLT_EPSILON )
            {
                w[j] = 1.f;
                i++;
            }
        }

        fitLine2D_wods( points, count, w, _line );
        for( i = 0; i < 30; i++ )
        {
            double sum_w = 0;

            if( first )
            {
                first = 0;
            }
            else
            {
                double t = _line[0] * _lineprev[0] + _line[1] * _lineprev[1];
                t = MAX(t,-1.);
                t = MIN(t,1.);
                if( fabs(acos(t)) < adelta )
                {
                    float x, y, d;

                    x = (float) fabs( _line[2] - _lineprev[2] );
                    y = (float) fabs( _line[3] - _lineprev[3] );

                    d = x > y ? x : y;
                    if( d < rdelta )
                        break;
                }
            }
            /* calculate distances */
            err = calcDist2D( points, count, _line, r );
            if( err < EPS )
                break;

            /* calculate weights */
            if( calc_weights )
                calc_weights( r, count, w );
            else
                calc_weights_param( r, count, w, _param );

            for( j = 0; j < count; j++ )
                sum_w += w[j];

            if( fabs(sum_w) > FLT_EPSILON )
            {
                sum_w = 1./sum_w;
                for( j = 0; j < count; j++ )
                    w[j] = (float)(w[j]*sum_w);
            }
            else
            {
                for( j = 0; j < count; j++ )
                    w[j] = 1.f;
            }

            /* save the line parameters */
            memcpy( _lineprev, _line, 4 * sizeof( float ));

            /* Run again... */
            fitLine2D_wods( points, count, w, _line );
        }

        if( err < min_err )
        {
            min_err = err;
            memcpy( line, _line, 4 * sizeof(line[0]));
            if( err < EPS )
                break;
        }
    }
}


/* Takes an array of 3D points, type of distance (including user-defined
 distance specified by callbacks, fills the array of four floats with line
 parameters A, B, C, D, E, F, where (A, B, C) is the normalized direction vector,
 (D, E, F) is the point that belongs to the line. */
static void fitLine3D( Point3f * points, int count, int dist,
                       float _param, float reps, float aeps, float *line )
{
    double EPS = count*FLT_EPSILON;
    void (*calc_weights) (float *, int, float *) = 0;
    void (*calc_weights_param) (float *, int, float *, float) = 0;
    int i, j, k;
    float _line[6]={0,0,0,0,0,0}, _lineprev[6]={0,0,0,0,0,0};
    float rdelta = reps != 0 ? reps : 1.0f;
    float adelta = aeps != 0 ? aeps : 0.01f;
    double min_err = DBL_MAX, err = 0;
    RNG rng((uint64)-1);

    switch (dist)
    {
    case CV_DIST_L2:
        return fitLine3D_wods( points, count, 0, line );

    case CV_DIST_L1:
        calc_weights = weightL1;
        break;

    case CV_DIST_L12:
        calc_weights = weightL12;
        break;

    case CV_DIST_FAIR:
        calc_weights_param = weightFair;
        break;

    case CV_DIST_WELSCH:
        calc_weights_param = weightWelsch;
        break;

    case CV_DIST_HUBER:
        calc_weights_param = weightHuber;
        break;

    default:
        CV_Error(CV_StsBadArg, "Unknown distance");
    }

    AutoBuffer<float> buf(count*2);
    float *w = buf, *r = w + count;

    for( k = 0; k < 20; k++ )
    {
        int first = 1;
        for( i = 0; i < count; i++ )
            w[i] = 0.f;

        for( i = 0; i < MIN(count,10); )
        {
            j = rng.uniform(0, count);
            if( w[j] < FLT_EPSILON )
            {
                w[j] = 1.f;
                i++;
            }
        }

        fitLine3D_wods( points, count, w, _line );
        for( i = 0; i < 30; i++ )
        {
            double sum_w = 0;

            if( first )
            {
                first = 0;
            }
            else
            {
                double t = _line[0] * _lineprev[0] + _line[1] * _lineprev[1] + _line[2] * _lineprev[2];
                t = MAX(t,-1.);
                t = MIN(t,1.);
                if( fabs(acos(t)) < adelta )
                {
                    float x, y, z, ax, ay, az, dx, dy, dz, d;

                    x = _line[3] - _lineprev[3];
                    y = _line[4] - _lineprev[4];
                    z = _line[5] - _lineprev[5];
                    ax = _line[0] - _lineprev[0];
                    ay = _line[1] - _lineprev[1];
                    az = _line[2] - _lineprev[2];
                    dx = (float) fabs( y * az - z * ay );
                    dy = (float) fabs( z * ax - x * az );
                    dz = (float) fabs( x * ay - y * ax );

                    d = dx > dy ? (dx > dz ? dx : dz) : (dy > dz ? dy : dz);
                    if( d < rdelta )
                        break;
                }
            }
            /* calculate distances */
            err = calcDist3D( points, count, _line, r );
            //if( err < FLT_EPSILON*count )
            //    break;

            /* calculate weights */
            if( calc_weights )
                calc_weights( r, count, w );
            else
                calc_weights_param( r, count, w, _param );

            for( j = 0; j < count; j++ )
                sum_w += w[j];

            if( fabs(sum_w) > FLT_EPSILON )
            {
                sum_w = 1./sum_w;
                for( j = 0; j < count; j++ )
                    w[j] = (float)(w[j]*sum_w);
            }
            else
            {
                for( j = 0; j < count; j++ )
                    w[j] = 1.f;
            }

            /* save the line parameters */
            memcpy( _lineprev, _line, 6 * sizeof( float ));

            /* Run again... */
            fitLine3D_wods( points, count, w, _line );
        }

        if( err < min_err )
        {
            min_err = err;
            memcpy( line, _line, 6 * sizeof(line[0]));
            if( err < EPS )
                break;
        }
    }
}

}

void cv::fitLine( InputArray _points, OutputArray _line, int distType,
                 double param, double reps, double aeps )
{
    CV_INSTRUMENT_REGION()

    Mat points = _points.getMat();

    float linebuf[6]={0.f};
    int npoints2 = points.checkVector(2, -1, false);
    int npoints3 = points.checkVector(3, -1, false);

    CV_Assert( npoints2 >= 0 || npoints3 >= 0 );

    if( points.depth() != CV_32F || !points.isContinuous() )
    {
        Mat temp;
        points.convertTo(temp, CV_32F);
        points = temp;
    }

    if( npoints2 >= 0 )
        fitLine2D( points.ptr<Point2f>(), npoints2, distType,
                   (float)param, (float)reps, (float)aeps, linebuf);
    else
        fitLine3D( points.ptr<Point3f>(), npoints3, distType,
                   (float)param, (float)reps, (float)aeps, linebuf);

    Mat(npoints2 >= 0 ? 4 : 6, 1, CV_32F, linebuf).copyTo(_line);
}


CV_IMPL void
cvFitLine( const CvArr* array, int dist, double param,
           double reps, double aeps, float *line )
{
    CV_Assert(line != 0);

    cv::AutoBuffer<double> buf;
    cv::Mat points = cv::cvarrToMat(array, false, false, 0, &buf);
    cv::Mat linemat(points.checkVector(2) >= 0 ? 4 : 6, 1, CV_32F, line);

    cv::fitLine(points, linemat, dist, param, reps, aeps);
}

/* End of file. */