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我想从一张图片中提取红色的球并在图片中获取检测到的椭圆矩阵。如何从OpenCV的fitEllipse函数获取椭圆系数？
这是我的例子： 
I阈图片，发现的红球通过使用findContour（）函数的轮廓，并使用fitEllipse（）以适合的椭圆。
但我想要的是得到这个椭圆的系数。因为fitEllipse（）返回一个旋转矩形（RotatedRect），所以我需要重写这个函数。
一个椭圆可以表示为Ax^2 + By^2 + Cxy + Dx + Ey + F = 0;所以如果F是1（构造一个椭圆矩阵），我想得到u =（A，B，C，D，E，F）或u =（A，B，C，D，E）。
我读了fitEllipse（）的源代码，总共有三个SVD过程，我想我可以从这三个SVD过程的结果中得到上述系数。但是我很困惑每个SVD过程的每个结果（变量cv :: Mat x）代表什么以及为什么这里有三个SVD？
这里是这样的功能：
cv::RotatedRect cv::fitEllipse(InputArray _points)
{
Mat points = _points.getMat();
int i, n = points.checkVector(2);
int depth = points.depth();
CV_Assert(n >= 0 && (depth == CV_32F || depth == CV_32S));
RotatedRect box;
if(n < 5)
CV_Error(CV_StsBadSize, "There should be at least 5 points to fit the ellipse");
// New fitellipse algorithm, contributed by Dr. Daniel Weiss
Point2f c(0,0);
double gfp[5], rp[5], t;
const double min_eps = 1e-8;
bool is_float = depth == CV_32F;
const Point* ptsi = points.ptr<Point>();
const Point2f* ptsf = points.ptr<Point2f>();
AutoBuffer<double> _Ad(n*5), _bd(n);
double *Ad = _Ad, *bd = _bd;
// first fit for parameters A - E
Mat A(n, 5, CV_64F, Ad);
Mat b(n, 1, CV_64F, bd);
Mat x(5, 1, CV_64F, gfp);
for(i = 0; i < n; i++)
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
c += p;
}
c.x /= n;
c.y /= n;
for(i = 0; i < n; i++)
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
p -= c;
bd[i] = 10000.0; // 1.0?
Ad[i*5] = -(double)p.x * p.x; // A - C signs inverted as proposed by APP
Ad[i*5 + 1] = -(double)p.y * p.y;
Ad[i*5 + 2] = -(double)p.x * p.y;
Ad[i*5 + 3] = p.x;
Ad[i*5 + 4] = p.y;
}
solve(A, b, x, DECOMP_SVD);
// now use general-form parameters A - E to find the ellipse center:
// differentiate general form wrt x/y to get two equations for cx and cy
A = Mat(2, 2, CV_64F, Ad);
b = Mat(2, 1, CV_64F, bd);
x = Mat(2, 1, CV_64F, rp);
Ad[0] = 2 * gfp[0];
Ad[1] = Ad[2] = gfp[2];
Ad[3] = 2 * gfp[1];
bd[0] = gfp[3];
bd[1] = gfp[4];
solve(A, b, x, DECOMP_SVD);
// re-fit for parameters A - C with those center coordinates
A = Mat(n, 3, CV_64F, Ad);
b = Mat(n, 1, CV_64F, bd);
x = Mat(3, 1, CV_64F, gfp);
for(i = 0; i < n; i++)
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
p -= c;
bd[i] = 1.0;
Ad[i * 3] = (p.x - rp[0]) * (p.x - rp[0]);
Ad[i * 3 + 1] = (p.y - rp[1]) * (p.y - rp[1]);
Ad[i * 3 + 2] = (p.x - rp[0]) * (p.y - rp[1]);
}
solve(A, b, x, DECOMP_SVD);
// store angle and radii
rp[4] = -0.5 * atan2(gfp[2], gfp[1] - gfp[0]); // convert from APP angle usage
if(fabs(gfp[2]) > min_eps)
t = gfp[2]/sin(-2.0 * rp[4]);
else // ellipse is rotated by an integer multiple of pi/2
t = gfp[1] - gfp[0];
rp[2] = fabs(gfp[0] + gfp[1] - t);
if(rp[2] > min_eps)
rp[2] = std::sqrt(2.0/rp[2]);
rp[3] = fabs(gfp[0] + gfp[1] + t);
if(rp[3] > min_eps)
rp[3] = std::sqrt(2.0/rp[3]);
box.center.x = (float)rp[0] + c.x;
box.center.y = (float)rp[1] + c.y;
box.size.width = (float)(rp[2]*2);
box.size.height = (float)(rp[3]*2);
if(box.size.width > box.size.height)
{
float tmp;
CV_SWAP(box.size.width, box.size.height, tmp);
box.angle = (float)(90 + rp[4]*180/CV_PI);
}
if(box.angle < -180)
box.angle += 360;
if(box.angle > 360)
box.angle -= 360;
return box;
}
的源代码链接：https://github.com/Itseez/opencv/blob/master/modules/imgproc/src/shapedescr.cpp
