OpenCV最小二成拟合椭圆算法
//传入样本点，返回椭圆的5个参数
vector<double> getEllipsepar(vector<CvPoint> vec_point)
{
vector<double> vec_result;
double x3y1 = 0,x1y3= 0,x2y2= 0,yyy4= 0, xxx3= 0,xxx2= 0,x2y1= 0,yyy3= 0,x1y2= 0 ,yyy2= 0,x1y1= 0,xxx1= 0,yyy1= 0;
int N = vec_point.size();
cout << N << endl;
for (int m_i = 0;m_i < N ;++m_i )
{
double xi = vec_point[m_i].x ;
double yi = vec_point[m_i].y;
x3y1 += xi*xi*xi*yi ;
x1y3 += xi*yi*yi*yi;
x2y2 += xi*xi*yi*yi; ;
yyy4 +=yi*yi*yi*yi;
xxx3 += xi*xi*xi ;
xxx2 += xi*xi ;
x2y1 += xi*xi*yi;
x1y2 += xi*yi*yi;
yyy2 += yi*yi;
x1y1 += xi*yi;
xxx1 += xi;
yyy1 += yi;
yyy3 += yi*yi*yi;
}
long double resul1 = -(x3y1);
long double resul2 = -(x2y2);
long double resul3 = -(xxx3);
long double resul4 = -(x2y1);
long double resul5 = -(xxx2);
long double B1 = x1y3, C1 = x2y1, D1 = x1y2, E1 = x1y1, A1 = x2y2;
long double B2 = yyy4, C2 = x1y2, D2 = yyy3, E2 = yyy2, A2 = x1y3;
long double B3 = x1y2, C3 = xxx2, D3 = x1y1, E3 = xxx1, A3 = x2y1;
long double B4 = yyy3, C4 = x1y1, D4 = yyy2, E4 = yyy1, A4 = x1y2;
long double B5 = yyy2, C5 = xxx1, D5 = yyy1, E5 = N, A5 = x1y1;
//
CvMat* Ma = cvCreateMat(5,5,CV_64FC1);
CvMat* Md = cvCreateMat(5,1,CV_64FC1);
CvMat* Mb = cvCreateMat(5,1,CV_64FC1);
//
cvmSet(Mb,0,0,resul1);
cvmSet(Mb,1,0,resul2);
cvmSet(Mb,2,0,resul3);
cvmSet(Mb,3,0,resul4);
cvmSet(Mb,4,0,resul5);
cvmSet(Ma,0,0,A1);
cvmSet(Ma,0,1,B1);
cvmSet(Ma,0,2,C1);
cvmSet(Ma,0,3,D1);
cvmSet(Ma,0,4,E1);
cvmSet(Ma,1,0,A2);
cvmSet(Ma,1,1,B2);
cvmSet(Ma,1,2,C2);
cvmSet(Ma,1,3,D2);
cvmSet(Ma,1,4,E2);
cvmSet(Ma,2,0,A3);
cvmSet(Ma,2,1,B3);
cvmSet(Ma,2,2,C3);
cvmSet(Ma,2,3,D3);
cvmSet(Ma,2,4,E3);
cvmSet(Ma,3,0,A4);
cvmSet(Ma,3,1,B4);
cvmSet(Ma,3,2,C4);
cvmSet(Ma,3,3,D4);
cvmSet(Ma,3,4,E4);
cvmSet(Ma,4,0,A5);
cvmSet(Ma,4,1,B5);
cvmSet(Ma,4,2,C5);
cvmSet(Ma,4,3,D5);
cvmSet(Ma,4,4,E5);
cvSolve(Ma, Mb, Md);
long double A = cvmGet(Md,0,0);
long double B = cvmGet(Md,1,0);
long double C = cvmGet(Md,2,0);
long double D = cvmGet(Md,3,0);
long double E = cvmGet(Md,4,0);
double XC = (2*B*C - A*D) /(A*A-4*B);
double YC =(2*D-A*D)/(A*A-4*B);
long double fenzi = 2*(A*C*D-B*C*C-D*D+4*E*B-A*A*E);
long double fenmu =(A*A-4*B) * (B- sqrt(A*A+ (1-B) * (1-B) ) +1);
long double femmu2 =(A*A-4*B) * (B+ sqrt(A*A+ (1-B) * (1-B) ) +1);
double XA =sqrt(fabs(fenzi/fenmu));
double XB =sqrt(fabs(fenzi/femmu2));
double Xtheta =atan(sqrt((XA*XA-XB*XB*B)/(XA*XA*B-XB*XB))+0.0001)*180/3.1415926;
vec_result.push_back(XC);
vec_result.push_back(YC);
vec_result.push_back(XA);
vec_result.push_back(XB);
vec_result.push_back(Xtheta);
return vec_result;
}