/*
Computes the likelihood of there being a player at a given location in
an image

@param img image that has been converted to HSV colorspace using bgr2hsv()
@param r row location of center of window around which to compute likelihood
@param c col location of center of window around which to compute likelihood
@param w width of region over which to compute likelihood
@param h height of region over which to compute likelihood
@param ref_histo reference histogram for a player; must have been
normalized with normalize_histogram()

@return Returns the likelihood of there being a player at location
(\a r, \a c) in \a img
*/
float likelihood( IplImage* img, int r, int c,
int w, int h, histogram* ref_histo )
{
IplImage* tmp;
histogram* histo;
float d_sq;

/* extract region around (r,c) and compute and normalize its histogram */
cvSetImageROI( img, cvRect( c - w / 2, r - h / 2, w, h ) );
tmp = cvCreateImage( cvGetSize(img), IPL_DEPTH_32F, 3 );
cvCopy( img, tmp, NULL );
cvResetImageROI( img );
histo = calc_histogram( &tmp, 1 );
cvReleaseImage( &tmp );
normalize_histogram( histo );

/* compute likelihood as e^{\lambda D^2(h, h^*)} */
d_sq = histo_dist_sq( histo, ref_histo );
free( histo );
return exp( -LAMBDA * d_sq );
}

程序首先取出對相關粒子表示的區域，然后計算其直方圖，并且歸一化。將這個直方圖和原來用戶選定區域的直方圖傳入函數histo_dist_sq進行比較，最后返回e^(-Lambda*d_sq)返回，成為這個粒子的權重。

函數histo_dist_sq的實現如下：

/*
Computes squared distance metric based on the Battacharyya similarity
coefficient between histograms.

@param h1 first histogram; should be normalized
@param h2 second histogram; should be normalized

@return Returns a squared distance based on the Battacharyya similarity
coefficient between \a h1 and \a h2
*/
float histo_dist_sq( histogram* h1, histogram* h2 )
{
float* hist1, * hist2;
float sum = 0;
int i, n;

n = h1->n;
hist1 = h1->histo;
hist2 = h2->histo;

/*
According the the Battacharyya similarity coefficient,

D = \sqrt{ 1 - \sum_1^n{ \sqrt{ h_1(i) * h_2(i) } } }
*/
for( i = 0; i < n; i++ )
sum += sqrt( hist1[i]*hist2[i] );
return 1.0 - sum;
}

采用統計學上的巴氏距離 Bhattacharyya distance，根據wiki的描述， Bhattacharyya distance 描述的是兩個離散概率分布的相似性，它通常在分類操作中被用來度量不同類型的可分離性，也就是說這個距離算式就是評定相似度的。嚴格定義為：

For discrete probability distributions p and q over the same domain X, it is defined as:

where:

is the Bhattacharyya coefficient .

該程序中的算式和這個式子略有差別。

OpenCV學習——物體跟蹤的粒子濾波算法實現之位置可能性確定