/// <summary>
/// Evaluate goodness of fit.
/// </summary>
/// <remarks>
/// Calculates the average distance of all contour points to the ellipse. The distance of point to
/// an ellipse is given by calculating the point on the ellipse that is closest to the query. This calculation
/// is performed by transforming the point into a coordinate system where the ellipse is in main-pose
/// (x-axis points toward a, y-axis points toward b, the origin is the center of the ellipse). Additionally,
/// the coordinate system is crafted in such a way (non-uniform scaling) that the ellipse becomes a circle.
/// Then, the closest point is simply the closest point on the circle. This point is transformed back into
/// the world coordinate system where the distance between the query and the returned point is computed.
/// </remarks>
/// <param name="e">Ellipse</param>
/// <param name="c">Contour points</param>
/// <returns>Goodness of fit</returns>
private double GoodnessOfFit(Emgu.CV.Structure.Ellipse e, Emgu.CV.Contour<System.Drawing.Point> c) {
Matrix m = EllipseDetector.GetAffineFrame(e);
Matrix inv = m.Inverse();
List<double> distances = new List<double>();
double avg_distance = 0.0;
foreach (System.Drawing.Point p in c) {
// Bring the point into the ellipse coordinate frame
Vector x = p.ToParsley().ToHomogeneous(1.0);
Vector r = (inv.Multiply(x.ToColumnMatrix())).GetColumnVector(0);
// Find the closest point on the circle to r
// From the above scaling construction the resulting circle has radius b
Vector closest = r.ToNonHomogeneous().Normalize().Scale(e.MCvBox2D.size.Height);
// Transform the closest point back
Vector closest_in_world = (m.Multiply(closest.ToHomogeneous(1.0).ToColumnMatrix())).GetColumnVector(0);
// Calculate the squared distance between the query and the point.
avg_distance += (closest_in_world - x).ToNonHomogeneous().SquaredNorm();
}
return Math.Sqrt(avg_distance / c.Count());
}