Fitting an ellipse to a given set of points using Trust Region method

Ellipse fit using geometric parameters based on Trust Region minimization scheme.

This is a version of ellipse fit when applying Trust Region minimization scheme.

The most accurate and robust fit minimizes geometric (orthogonal) distances from the observed points to the fitting curve. The Trust Region algorithm requires the computation of the distances and their derivatives with respect to the ellipse parameters. So this method is generated by using implicit differentiation for computing
Jacobian matrix.

Usage: [ParG,RSS,iters] = TR_ellipse(XY,ParGIni,DeltaIni)

Child functions:
Residuals_ellipse(from previous submission) , JmatrixLMG (included in the main function)

Input:
XY:given points<XY(i,1),XY(i,2)> i=1 to n
ParGIni = [Center(1:2), Axes(1:2),Angle]'
DeltaIni: the initial size of the trust region(this is optional; if it is missing, TR sets it to 1)

Output:
ParG: parameter vector of the ellipse found
RSS: the Residual Sum of Squares (the sum of squares of the distances)
iters:# of iterations