【OpenCV】根据点集（轮廓）拟合圆

最小二乘法拟合圆公式推导

#include <opencv2/core/core.hpp>#include <opencv2/highgui/highgui.hpp>#include <opencv2/imgproc/imgproc.hpp>#include <opencv2/opencv.hpp>#include <vector>#include <iostream>using namespace cv;using namespace std;typedef struct Box{double x;double y;double r;}Box;Box circleLeastFit(const vector<CvPoint *> &points){Box box;box.x = 0.0f;box.y = 0.0f;box.r = 0.0f;if (points.size() < 3){return box;}int i=0;double X1=0;double Y1=0;double X2=0;double Y2=0;double X3=0;double Y3=0;double X1Y1=0;double X1Y2=0;double X2Y1=0;int Sum = points.size();for (i=0;i<Sum;i++){X1 = X1 + points[i]->x;Y1 = Y1 + points[i]->y;X2 = X2 + points[i]->x*points[i]->x;Y2 = Y2 + points[i]->y*points[i]->y;X3 = X3 + points[i]->x*points[i]->x*points[i]->x;Y3 = Y3 + points[i]->y*points[i]->y*points[i]->y;X1Y1 = X1Y1 + points[i]->x*points[i]->y;X1Y2 = X1Y2 + points[i]->x*points[i]->y*points[i]->y;X2Y1 = X2Y1 + points[i]->x*points[i]->x*points[i]->y;}double C,D,E,G,H,N;double a,b,c;N = points.size();C = N*X2 - X1*X1;D = N*X1Y1 - X1*Y1;E = N*X3 + N*X1Y2 - (X2+Y2)*X1;G = N*Y2 - Y1*Y1;H = N*X2Y1 + N*Y3 - (X2+Y2)*Y1;a = (H*D-E*G)/(C*G-D*D);b = (H*C-E*D)/(D*D-G*C);c = -(a*X1 + b*Y1 + X2 + Y2)/N;double A,B,R;A = a/(-2);B = b/(-2);R = sqrt(a*a+b*b-4*c)/2;box.x= A;box.y = B;box.r = R;return box;}//获取自定义核void f_GetElement(int **p,IplImage *src)//为什么p一定要是二级指针？？？{int length = (src->width)*(src->height);//图片大小*p = (int*)malloc(sizeof(int)*length);//动态分配内存，大小为(sizeof(int)*length)memset(*p,0,sizeof(int)*length);//初始化内存区间 p为0for(int y=0; y<src->height; y++){uchar *ptr = (uchar*)(src->imageData + y*src->widthStep);int b = y*src->widthStep;//???for(int x=0; x<src->width; x++){if(ptr[x]==255){(*p)[b+x] = 1;}else {(*p)[b+x] = 0;}}}}int main(){ IplImage* src = cvLoadImage("5.bmp",1);IplImage *gray_image = cvCreateImage(cvGetSize(src),8,1);IplImage *rgb_image = cvCreateImage(cvGetSize(src),8,3);cvZero(gray_image);cvZero(rgb_image);cvCvtColor(src,gray_image,CV_RGB2GRAY);cvCvtColor(gray_image,rgb_image,CV_GRAY2BGR);CvMemStorage *storage = cvCreateMemStorage(0);CvSeq *first_contours = NULL,*temp_contours = NULL;int n = cvFindContours(gray_image,storage,&first_contours,sizeof(CvContour), CV_RETR_LIST, CV_CHAIN_APPROX_SIMPLE);printf("n = %d\n",n);temp_contours = first_contours;for (;temp_contours != NULL; temp_contours = temp_contours->h_next){vector <CvPoint*> pt_vec;CvPoint *pt;//cvDrawContours(rgb_image, temp_contours, CV_RGB(0, 0, 255), CV_RGB(0, 0, 255), 0,2,CV_FILLED, cvPoint(0, 0)); CvRect rc =cvBoundingRect(temp_contours,0);    cvRectangle(rgb_image, cvPoint(rc.x, rc.y), cvPoint(rc.x + rc.width, rc.y + rc.height),CV_RGB(255, 0, 0), 1, 8, 0);for (int i = 0; i < temp_contours->total;i++){pt = (CvPoint *)cvGetSeqElem(temp_contours,i);pt_vec.push_back(pt);}double x = 0.0;double y = 0.0;double r = 0.0;vector<Box *>  box;Box box1;box1 = circleLeastFit(pt_vec);printf("%lf %lf %lf \n",box1.x,box1.y,box1.r);cvCircle(rgb_image,cvPoint(box1.x,box1.y),box1.r,cvScalar(155,255,0),5,8,0);cvCircle(rgb_image,cvPoint(box1.x,box1.y),5,cvScalar(155,255,155),5,8,0);} cvNamedWindow("32"); cvShowImage("32",rgb_image); cvWaitKey(0);return 0;}