由点坐标拟合圆和计算圆度

由点坐标拟合圆和计算圆度

1.根据坐标点拟合圆
最小二乘法拟合圆

   void FitCircle(const vector<Point> pts,double& circleX,double& circleY,double& radius){circleX=0;circleY=0;radius=0;if(pts.size()<3){return;}int i=0;double X1=0,Y1=0,X2=0,Y2=0,X3=0,Y3=0;double X1Y1=0,X1Y2=0,X2Y1=0;for (i=0;i<pts.size();i++){X1+=pts.at(i).x;Y1+=pts.at(i).y;X2+=std::pow(pts.at(i).x*1.0,2);Y2+=std::pow(pts.at(i).y*1.0,2);X3+=std::pow(pts.at(i).x*1.0,3);Y3+=std::pow(pts.at(i).y*1.0,3);X1Y1+=pts.at(i).x*pts.at(i).y;X1Y2+=pts.at(i).x*std::pow(pts.at(i).y*1.0,2);X2Y1+=std::pow(pts.at(i).x*1.0,2)*pts.at(i).y;}double C,D,E,G,H,N;double a,b,c;N = pts.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;circleX = a/(-2);circleY = b/(-2);radius = std::sqrt(a*a+b*b-4*c)/2;}

2.圆度计算方式1

计算区域的面积和近似最小外接圆的面积的比值

  double CalCircularity(const vector<Point> contours,double area){double dCircular = 0;int nCount = contours.size();double dSumX = 0, dSumY = 0;for (size_t i = 0; i < nCount; i++){dSumX += contours.at(i).x;dSumY += contours.at(i).y;}double dDistSum = 0;double dtemp = 0;double meanX = dSumX * 1.0 / nCount;double meanY = dSumY * 1.0 / nCount;double dMaxDist=0;for (size_t i = 0; i < nCount; i++){dtemp = pow(contours.at(i).x - meanX, 2) + pow(contours.at(i).y - meanY, 2);dtemp=sqrt(dtemp);if (dMaxDist<dtemp){dMaxDist = dtemp;}}double dRatio = area/(dMaxDist*dMaxDist*CV_PI);dCircular = STDMIN(1,dRatio);return dCircular;}

3.圆度计算方式2
计算区域轮廓上各点到区域中心的平均距离（Distance）与这些距离的标准差（Sigma）之间的关系

 double CalRoundess(const vector<Point> contours){double dCircular = 0;int nCount = contours.size();double dSumX = 0, dSumY = 0;for (size_t i = 0; i < nCount; i++){dSumX += contours.at(i).x;dSumY += contours.at(i).y;}double dDistSum = 0;double dtemp = 0;double meanX = dSumX * 1.0 / nCount;double meanY = dSumY * 1.0 / nCount;for (size_t i = 0; i < nCount; i++){dtemp = pow(contours.at(i).x - meanX, 2) + pow(contours.at(i).y - meanY, 2);dDistSum += sqrt(dtemp);}double dMeanDist = dDistSum * 1.0 / nCount;double dSigmaSum = 0;for (size_t i = 0; i < nCount; i++){dtemp = pow(contours.at(i).x - meanX, 2) + pow(contours.at(i).y - meanY, 2);dSigmaSum +=pow( sqrt(dtemp)- dMeanDist,2);}double dMeanSigma = sqrt(dSigmaSum * 1.0 / nCount);dCircular = 1 - dMeanSigma / dMeanDist;return dCircular;}