Camshift算法（2）

     这里主要介绍下MeanShift算法的迭代过程，毕竟Camshift算法是以它为核心的。MeanShift算法是一种寻找局部极值的方法。做为一种直观上的理解是它一步一步爬向最高点即爬山算法.而怎么个爬法，用计算出的重心做为下一步窗口的中心，直到窗口的位置不再变化。在理解MeanShift算法的时候，可以先不加入核函数（是计算距离对统计分布的影响）和权重函数（如人为主观的影响）。  

在Camshift算法中MeanShift是通过1阶矩除以0阶矩来计算重心的。其算法的代码如下：

CV_IMPL int
cvMeanShift( const void* imgProb, CvRect windowIn,
             CvTermCriteria criteria, CvConnectedComp* comp )
{
    CvMoments moments;
    int    i = 0, eps;
    CvMat  stub, *mat = (CvMat*)imgProb;//输入的整个图像
    CvMat  cur_win;
    CvRect cur_rect = windowIn;//当前矩形窗口初始化为输入窗口

    CV_FUNCNAME( "cvMeanShift" );

    if( comp )
        comp->rect = windowIn;//初始化联通区域

    moments.m00 = moments.m10 = moments.m01 = 0; //初始化0、1阶矩

    __BEGIN__;

    CV_CALL( mat = cvGetMat( mat, &stub ));

    if( CV_MAT_CN( mat->type ) > 1 )
        CV_ERROR( CV_BadNumChannels, cvUnsupportedFormat );

    if( windowIn.height <= 0 || windowIn.width <= 0 )
        CV_ERROR( CV_StsBadArg, "Input window has non-positive sizes" );

    if( windowIn.x < 0 || windowIn.x + windowIn.width > mat->cols ||      //x，y是指角点坐标而不是中心坐标
        windowIn.y < 0 || windowIn.y + windowIn.height > mat->rows )
        CV_ERROR( CV_StsBadArg, "Initial window is not inside the image ROI" );

    CV_CALL( criteria = cvCheckTermCriteria( criteria, 1., 100 ));//迭代的结束条件，

    eps = cvRound( criteria.epsilon * criteria.epsilon );

    for( i = 0; i < criteria.max_iter; i++ )
    {
        int dx, dy, nx, ny;
        double inv_m00;

        CV_CALL( cvGetSubRect( mat, &cur_win, cur_rect )); //cur_win指向窗口内的数据
        CV_CALL( cvMoments( &cur_win, &moments ));         //计算窗口内的各种矩

        /* Calculating center of mass */
        if( fabs(moments.m00) < DBL_EPSILON )
            break;

        inv_m00 = moments.inv_sqrt_m00*moments.inv_sqrt_m00;
        dx = cvRound( moments.m10 * inv_m00 - windowIn.width*0.5 );//中心点的坐标-宽的一半
        dy = cvRound( moments.m01 * inv_m00 - windowIn.height*0.5 );//中心点的坐标-高的一半

        nx = cur_rect.x + dx;//新的x坐标
        ny = cur_rect.y + dy;//新的y坐标

        if( nx < 0 )
            nx = 0;
        else if( nx + cur_rect.width > mat->cols )
            nx = mat->cols - cur_rect.width;

        if( ny < 0 )
            ny = 0;
        else if( ny + cur_rect.height > mat->rows )
            ny = mat->rows - cur_rect.height;

        dx = nx - cur_rect.x;//重新
        dy = ny - cur_rect.y;
        cur_rect.x = nx;     //新窗口的坐标值
        cur_rect.y = ny;

        /* Check for coverage centers mass & window */
        if( dx*dx + dy*dy < eps )    //迭代终止
            break;
    }

    __END__;

    if( comp )//返回矩形和0阶矩
    {
        comp->rect = cur_rect;
        comp->area = (float)moments.m00;
    }

    return i;  //返回迭代次数
}

Camshift算法代码：

CV_IMPL int
cvCamShift( const void* imgProb, CvRect windowIn,
            CvTermCriteria criteria,
            CvConnectedComp* _comp,
            CvBox2D* box )
{
    const int TOLERANCE = 10;
    CvMoments moments;
    double m00 = 0, m10, m01, mu20, mu11, mu02, inv_m00;
    double a, b, c, xc, yc;
    double rotate_a, rotate_c;
    double theta = 0, square;
    double cs, sn;
    double length = 0, width = 0;
    int itersUsed = 0;
    CvConnectedComp comp;
    CvMat  cur_win, stub, *mat = (CvMat*)imgProb;

    CV_FUNCNAME( "cvCamShift" );

    comp.rect = windowIn;//初始化comp

    __BEGIN__;

    CV_CALL( mat = cvGetMat( mat, &stub ));

    CV_CALL( itersUsed = cvMeanShift( mat, windowIn, criteria, &comp ));//调用meanshift计算质心
    windowIn = comp.rect;//获得新的窗口的位置

    //为了容错，窗口的四边都增大了TOLERANCE
    windowIn.x -= TOLERANCE;
    if( windowIn.x < 0 )
        windowIn.x = 0;

    windowIn.y -= TOLERANCE;
    if( windowIn.y < 0 )
        windowIn.y = 0;

    windowIn.width += 2 * TOLERANCE;
    if( windowIn.x + windowIn.width > mat->width )
        windowIn.width = mat->width - windowIn.x;

    windowIn.height += 2 * TOLERANCE;
    if( windowIn.y + windowIn.height > mat->height )
        windowIn.height = mat->height - windowIn.y;

    CV_CALL( cvGetSubRect( mat, &cur_win, windowIn ));//获得指向子窗口的数据指针

    /* Calculating moments in new center mass */
    CV_CALL( cvMoments( &cur_win, &moments ));//重新计算窗口内的各种矩

    m00 = moments.m00;
    m10 = moments.m10;
    m01 = moments.m01;
    mu11 = moments.mu11;
    mu20 = moments.mu20;
    mu02 = moments.mu02;

    if( fabs(m00) < DBL_EPSILON )
        EXIT;

    inv_m00 = 1. / m00;
    xc = cvRound( m10 * inv_m00 + windowIn.x );//新的中心坐标
    yc = cvRound( m01 * inv_m00 + windowIn.y );
    a = mu20 * inv_m00;
    b = mu11 * inv_m00;
    c = mu02 * inv_m00;

    /* Calculating width & height */
    square = sqrt( 4 * b * b + (a - c) * (a - c) );

    /* Calculating orientation */
    theta = atan2( 2 * b, a - c + square );

    /* Calculating width & length of figure */
    cs = cos( theta );
    sn = sin( theta );

    rotate_a = cs * cs * mu20 + 2 * cs * sn * mu11 + sn * sn * mu02;
    rotate_c = sn * sn * mu20 - 2 * cs * sn * mu11 + cs * cs * mu02;
    length = sqrt( rotate_a * inv_m00 ) * 4;//长与宽的计算
    width = sqrt( rotate_c * inv_m00 ) * 4;

    /* In case, when tetta is 0 or 1.57... the Length & Width may be exchanged */
    if( length < width )
    {
        double t;
        
        CV_SWAP( length, width, t );
        CV_SWAP( cs, sn, t );
        theta = CV_PI*0.5 - theta;
    }

    /* Saving results */
    //由于有宽和高的重新计算，使得能自动调整窗口大小
    if( _comp || box )
    {
        int t0, t1;
        int _xc = cvRound( xc );//取整
        int _yc = cvRound( yc );

        t0 = cvRound( fabs( length * cs ));
        t1 = cvRound( fabs( width * sn ));

        t0 = MAX( t0, t1 ) + 2;//宽的重新计算
        comp.rect.width = MIN( t0, (mat->width - _xc) * 2 );//保证宽不超出范围

        t0 = cvRound( fabs( length * sn ));
        t1 = cvRound( fabs( width * cs ));

        t0 = MAX( t0, t1 ) + 2;//高的重新计算
        comp.rect.height = MIN( t0, (mat->height - _yc) * 2 );//保证高不超出范围
        comp.rect.x = MAX( 0, _xc - comp.rect.width / 2 );
        comp.rect.y = MAX( 0, _yc - comp.rect.height / 2 );

        comp.rect.width = MIN( mat->width - comp.rect.x, comp.rect.width );
        comp.rect.height = MIN( mat->height - comp.rect.y, comp.rect.height );
        comp.area = (float) m00;
    }

    __END__;

    if( _comp )
        *_comp = comp;
    
    if( box )
    {
        box->size.height = (float)length;
        box->size.width = (float)width;
        box->angle = (float)(theta*180./CV_PI);
        box->center = cvPoint2D32f( comp.rect.x + comp.rect.width*0.5f,
                                    comp.rect.y + comp.rect.height*0.5f);
    }

    return itersUsed;
}