椭圆检测-点到椭圆的近似距离（Rosin distance）

参考文献： P. L. Rosin, “A note on the least squares fitting of ellipses,” Pattern Recognition Letters, vol. 14, no. 10, pp. 799–808, 1993.

源码：This is the source code for the paper [Arc-support Line Segments Revisited: An Efficient and High-quality Ellipse Detection]

GitHub - AlanLuSun/High-quality-ellipse-detection: A high-quality ellipse detector based on arc-support line segments which can both accurately and efficiently detect ellipses in images.

/*----------------------------------------------------------------------------*/
/** Approximate the distance between a point and an ellipse using Rosin distance.
 */
#define DBL_MAX          1.7976931348623158e+308 // max value
inline double d_rosin(double* param, double x, double y)
{
	double ae2 = param[2] * param[2];
	double be2 = param[3] * param[3];
	x = x - param[0];
	y = y - param[1];
	double xp = x * cos(-param[4]) - y * sin(-param[4]);
	double yp = x * sin(-param[4]) + y * cos(-param[4]);
	double fe2;
	fe2 = ae2 - be2;
	double X = xp * xp;
	double Y = yp * yp;
	double delta = (X + Y + fe2) * (X + Y + fe2) - 4 * X * fe2;
	double A = (X + Y + fe2 - sqrt(delta)) / 2.0;
	double ah = sqrt(A);
	double bh2 = fe2 - A;
	double term = (A * be2 + ae2 * bh2);
	double xi = ah * sqrt(ae2 * (be2 + bh2) / term);
	double yi = param[3] * sqrt(bh2 * (ae2 - A) / term);
	double d[4], dmin;


	d[0] = dist(xp, yp, xi, yi);
	d[1] = dist(xp, yp, xi, -yi);
	d[2] = dist(xp, yp, -xi, yi);
	d[3] = dist(xp, yp, -xi, -yi);
	dmin = DBL_MAX;
	for (int i = 0; i < 4; i++)
	{
		if (d[i] <= dmin)
			dmin = d[i];
	}
	//  if (X+Y>xi*xi+yi*yi)
	//    return dmin;
	//  else return -dmin; 
	return dmin;
}