meanshift 与 camshift 跟踪算法比较
MeanShift Algorithm
思想很简单：利用概率密度的梯度爬升来寻找局部最优...具体参考文献：
[1]The Estimation of the Gradient of a Density Function, with Applications in Pattern Recognition (1975)
[2]Mean shift, mode seeking, and clustering (1995)
[3]Mean Shift: a robust approach toward feature space analysis (2002)
[4]Real-time tracking of non-rigid objects using mean shift (2000)
[5]Mean-shift Blob Tracking through Scale Space (2003)
[6]An algorithm for data-driven bandwidth selection(2003)
对于OpenCV的Meanshift算法 貌似只是简化成了一个重心跟踪法，没有引入核函数与巴氏系数....
怪不得跟踪的效果那么差...
具体计算过程如下：
1.计算区域内0阶矩
for(int i=0;i
2.区域内1阶矩：
for(int i=0;i
M10+=i*I(i,j);
M01+=j*I(i,j);
}
3.则Mass Center为：
Xc=M10/M00; Yc=M01/M00
具体的CVMEANSHIFT算法可以分为以下4步：
1.选择窗的大小和初始位置.
2.计算此时窗口内的Mass Center.
3.调整窗口的中心到Mass Center.
4.重复2和3，直到窗口中心"会聚"，即每次窗口移动的距离小于一定的阈值，或者迭代次数达到设定值。
int cvMeanShift(IplImage* imgprob,CvRect windowIn,
CvTermCriteria criteria,CvConnectedComp* out);
函数说明： 需要的参数为： 1.IplImage* imgprob：2D概率分布图像，传入； 2.CvRect windowIn：初始的窗口，传入； 3.CvTermCriteria criteria：停止迭代的标准，传入； 4.CvConnectedComp* out:查询结果，传出。 (注：构造CvTermCriteria变量需要三个参数，一个是类型，另一个是迭代的最大次数，最后一个表示特定的阈值。例如可以这样构造criteria：criteria=cvTermCriteria(CV_TERMCRIT_ITER|CV_TERMCRIT_EPS,10,0.1)。) Parameters: imgProb - 2D object probability distribution windowIn - CvRect of CAMSHIFT Window intial size numIters - If CAMSHIFT iterates this many times, stop windowOut - Location, height and width of converged CAMSHIFT window len - If != NULL, return equivalent len width - If != NULL, return equivalent width itersUsed - Returns number of iterations CAMSHIFT took to converge Returns: The function itself returns the area found int cvMeanShift( const void* imgProb, CvRect windowIn, CvTermCriteria criteria, CvConnectedComp* comp ) { CvMoments moments; int i = 0, eps; CvMat stub, *mat = (CvMat*)imgProb; CvMat cur_win; CvRect cur_rect = windowIn; CV_FUNCNAME( "cvMeanShift" ); if( comp ) comp->rect = windowIn; moments.m00 = moments.m10 = moments.m01 = 0; __BEGIN__; CV_CALL( mat = cvGetMat( mat, &stub )); 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 || 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 )); 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 )); CV_CALL( cvMoments( &cur_win, &moments )); 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 ); dy = cvRound( moments.m01 * inv_m00 - windowIn.height*0.5 ); nx = cur_rect.x + dx; ny = cur_rect.y + dy; 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; dy = ny - cur_rect.y; cur_rect.x = nx; cur_rect.y = ny; if( dx*dx + dy*dy < eps ) break; } __END__; if( comp ) { comp->rect = cur_rect; comp->area = (float)moments.m00; } return i; }
Camshift Algorithm
它是MeanShift算法的改进，称为连续自适应的MeanShift算法，CamShift算法的全称是"Continuously Apaptive Mean-SHIFT"，它的基本思想是视频图像的所有帧作MeanShift运算，并将上一帧的结果（即Search Window的中心和大小）作为下一帧MeanShift算法的Search Window的初始值，如此迭代下去。
Camshift 是由Meanshift 推倒而來 Meanshift主要是用在單張影像上，但
是獨立一張影像分析對追蹤而言並無意義，Camshift 就是利用MeanShift的方
法，對影像串列進行分析。
(1) 首先在影像串列中選擇ㄧ區域。
(2) 計算此區域的顏色2D機率分布。
(3) 用MeanShift演算法來收斂欲追蹤的區域。
(4) 集中收斂的區域，並標示之。
(5) 每個frame重複(3)(4)。
Camshift 关键就在于当目标的大小发生改变的时候，此算法可以自适应调整目标区域继续跟踪。没什么多说的，给出源码吧，里面有部分代码是计算代码执行时间的，不需要的可以去掉。
如果要详细了解，去看下这篇参考文献吧：
Bradski, Computer Video Face Tracking for use in a Perceptual User Interface. Intel Technology Journal, Q2, 1998.
函数说明： Parameters: imgProb - 2D object probability distribution windowIn - CvRect of CAMSHIFT Window intial size criteria - criteria of stop finding window windowOut - Location, height and width of converged CAMSHIFT window orientation - If != NULL, return distribution orientation len - If != NULL, return equivalent len width - If != NULL, return equivalent width area - sum of all elements in result window itersUsed - Returns number of iterations CAMSHIFT took to converge Returns: The function itself returns the area found int cvCamShift( const void* imgProb, CvRect windowIn, CvTermCriteria criteria, CvConnectedComp* _comp, CvBox2D* box ) { QueryPerformanceFrequency(&freq); QueryPerformanceCounter(&start1); 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; __BEGIN__; CV_CALL( mat = cvGetMat( mat, &stub )); CV_CALL( itersUsed = cvMeanShift( mat, windowIn, criteria, &comp )); windowIn = comp.rect; 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 )); CV_CALL( cvMoments( &cur_win, &moments )); 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 ); yc = cvRound( m01 * inv_m00 + windowIn.y ); a = mu20 * inv_m00; b = mu11 * inv_m00; c = mu02 * inv_m00; square = sqrt( 4 * b * b + (a - c) * (a - c) ); theta = atan2( 2 * b, a - c + square ); 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; width = sqrt( rotate_c * inv_m00 ) * 4; if( length < width ) { double t; CV_SWAP( length, width, t ); CV_SWAP( cs, sn, t ); theta = CV_PI*0.5 - theta; } if( _comp || box ) { int t0, t1; int _xc = cvRound( xc ); int _yc = cvRound( yc ); t0 = cvRound( fabs( length * cs )); t1 = cvRound( fabs( width * sn )); t0 = MAX( t0, t1 ) + 2; comp.rect.width = MIN( t0, (mat->width - _xc) * 2 ); t0 = cvRound( fabs( length * sn )); t1 = cvRound( fabs( width * cs )); t0 = MAX( t0, t1 ) + 2; comp.rect.height = MIN( t0, (mat->height - _yc) * 2 ); 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); } QueryPerformanceCounter(&end1); time_origin<<(double)(end1.QuadPart - start1.QuadPart) / (double)freq.QuadPart<
对于OPENCV中的CAMSHIFT例子，是通过计算目标HSV空间下的HUE分量直方图，通过直方图反向投影得到目标像素的概率分布，然后通过调用CV库中的CAMSHIFT算法，自动跟踪并调整目标窗口的中心位置与大小。
这个算法对于纯色物体在黑白背景下的跟踪效果是很好的，但是如果背景的颜色与目标相近，或者目标附近有与目标的色调相近的算法比较物体，则CAMSHIFT会自动将其包括在内，导致跟踪窗口扩大，甚至有时会将跟踪窗口扩大到整个视频框架。
昨天看Learning OpenCV 看完了第十章，课后习题里有题就是将camshift改成meanshift算法比较一下结果，我自己改了一下，用meanshift的矩形框跟踪物体，由于meanshift不会改变核窗口的大小，所以矩形框当然是不变的...
与camshift比较了一下，由于都是通过H直方图反向投影的算法，实际是大差不差的，实验证明，对于较远的小的目标，使用meanshift算法比较好，因为目标大小一般不变，而且窗口不容易受外界影响，对于近距离的目标，尺寸会与镜头距离的远近而改变的，使用camshift可以自适应的改变。
Learning OpenCV 中也提到了可以使用两种方法结合来加强跟踪的鲁棒性，我个人觉得这两种方法其实没什么根本区别，也就不存在什么结合的问题了 呵呵。
下面是修改的代码 选取目标采用了蓝色方框 跟踪的目标采用了红色方框
//--------------------------------------------------------------------------- #include