轉(zhuǎn)自：http://blog.csdn.net/lxiaoxiaot/article/details/6539834

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不規(guī)則區(qū)域的矩，表示把一個歸一化的灰度級圖像函數(shù)理解為一個二維隨機(jī)變量的概率密度。

?????? 這個隨機(jī)變量的屬性可以用統(tǒng)計特征--矩（Moments）來描述。通過假設(shè)非零的像素值表示區(qū)域，矩可以用于二值或灰度級的區(qū)域描述。

?????? M_pq = sigma(i)sigma(j) i^p?j^q?f(i,j)

?????? 其中x,y,i,j是區(qū)域點的坐標(biāo)（在數(shù)字圖像中的像素坐標(biāo)）。

?????? 令Xc,Yc表示區(qū)域重心的坐標(biāo)，則：

????????????? Xc = M₁₀/M₀₀;

????????????? Yc = M₀₁/M₀₀;

?????? 在二值圖像的情況下，M₀₀表示區(qū)域的面積。

?????? OpenCV中可以使用函數(shù)cvMoments來計算二值圖像的矩信息。

?????? 使用函數(shù)cvGetSpatialMoment獲得指定維的矩信息。

?????? 例如：

?????? // 計算二值化圖像imgYellowThresh中物體的重心坐標(biāo)

??????? CvMoments *moments = (CvMoments*)malloc(sizeof(CvMoments));

cvMoments(imgYellowThresh, moments, 1); ? // The actual moment values double moment10 = cvGetSpatialMoment(moments, 1, 0); double moment01 = cvGetSpatialMoment(moments, 0, 1); double area = cvGetSpatialMoment(moments, 0, 0);

???????? // 計算重心

???????? posX = moment10 / area;

???????? posY = moment01 / area;

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轉(zhuǎn)自：http://blog.163.com/forever_871226/blog/static/34424308201141851736984/

/** 計算二值圖像的重心
* @param[in] src? 輸入的待處理圖像
* @param[out] center 重心坐標(biāo)
* @retval 0? 操作成功
* @retval -1 操作失敗
* @note 輸入圖像是二值化圖像
* @note xc=M10/M00, yc=M01/M00, 其中 Mx_order,y_order=SUMx,y(I(x,y)*x^x_order*y^y_order)
*/
static int aoiGravityCenter(IplImage *src, CvPoint &center)
{
?//if(!src)
?// return GRAVITYCENTER__SRC_IS_NULL;
?double m00, m10, m01;
?CvMoments moment;
?cvMoments( src, &moment, 1);
?m00 = cvGetSpatialMoment( &moment, 0, 0 );
?if( m00 == 0)
? return 1;
?m10 = cvGetSpatialMoment( &moment, 1, 0 );
?m01 = cvGetSpatialMoment( &moment, 0, 1 );
?center.x = (int) (m10/m00);
?center.y = (int) (m01/m00);
?return 0;
}

轉(zhuǎn)自：http://www.opencv.org.cn/forum/viewtopic.php?p=1016

#include "cv.h"
#include "highgui.h"

void main( int argc, char** argv )
{
IplImage* src;
CvMoments moments;
CvMat *region;
CvPoint pt1,pt2;
double m00 = 0, m10, m01, mu20, mu11, mu02, inv_m00;
double a, b, c;
int xc, yc;
// 第一條命令行參數(shù)確定了圖像的文件名。
if( (src=cvLoadImage("two.bmp", 0))!= 0)
//if( (src=cvLoadImage("fbb.jpg", 0))!= 0)
//if( argc == 2 && (src=cvLoadImage(argv[1], 0))!= 0)
{
IplImage* dst = cvCreateImage( cvGetSize(src), 8, 3 );
CvMemStorage* storage = cvCreateMemStorage(0);
CvSeq* contour = 0;

cvThreshold( src, src, 100, 255, CV_THRESH_BINARY );//100 is the thredhold
cvNot( src, src );
cvNamedWindow( "Source", 1 );
cvShowImage( "Source", src );

//cvFindContours( src, storage, &contour, sizeof(CvContour), CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE,cvPoint(0,0) );

cvFindContours( src, storage, &contour, sizeof(CvContour),CV_RETR_TREE, CV_CHAIN_APPROX_SIMPLE, cvPoint(0,0) );
cvZero( dst );

for( ; contour != 0; contour = contour->h_next )
{
//CvScalar color = CV_RGB( rand()&255, rand()&255, rand()&255 );
CvScalar color = CV_RGB( 255, 0,0 );
/* 用1替代 CV_FILLED 所指示的輪廓外形 */
cvDrawContours( dst, contour, color, color, -1, CV_FILLED, 8,cvPoint(0,0) );//you can change 1 to CV_FILLED
contour = cvApproxPoly( contour, sizeof(CvContour), storage, CV_POLY_APPROX_DP, 3, 1 );
//CvRect* r = (CvRect*)cvGetSeqElem( contour,1);
region=(CvMat*)contour;
cvMoments( region, &moments,0 );
//cvMoments( &contour, &moments,0 );
// cvDrawContours( cnt_img, _contours, CV_RGB(255,0,0), CV_RGB(0,255,0), _levels, 3, CV_AA, cvPoint(0,0) ); CV_FILLED

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

//if( fabs(m00) < DBL_EPSILON )break;

inv_m00 = 1. / m00;
xc = cvRound( m10 * inv_m00 );
yc = cvRound( m01 * inv_m00 );
a = mu20 * inv_m00;
b = mu11 * inv_m00;
c = mu02 * inv_m00;
/
pt1.x=xc-1;pt1.y=yc;
pt2.x=xc+1;pt2.y=yc;
cvLine( dst, pt1, pt2, CV_RGB(0,255,0), 2, CV_AA, 0 );
pt1.x=xc;pt1.y=yc-1;
pt2.x=xc;pt2.y=yc+1;
cvLine( dst, pt1, pt2, CV_RGB(0,255,0), 2, CV_AA, 0 );
}

cvNamedWindow( "Components", 1 );
cvShowImage( "Components", dst );
cvWaitKey(0);
}
}