Nonlinear least squares problem

ciaran_hughes

Dear all,

Apologies if this is in the wrong forum.

I have a bit Nonlinear least squares fit problem. I have a pair of parametric equations (see attached, fairly nasty ).

in it, a b c x0 y0 z0 are all constant, and they are the values I want to determine from a nonlinear least squares fit to a given set of (u', v') data. (u', v') are a set of pixel locations of a curve in an image, and the equations attached describe that curve.

Now, to do a nonlinear least squares, I believe I have to get a single nonparametric function (e.g. of v' in terms of u'). To do this, I follow the standard steps of solving one of the equations in terms of t, and substitute into the other. This is where I fail.

I have even used the 'solve' function in the Symbolic Toolbox in MATLAB to solve one of the equations for t, but simply get an error.

So, my questions are:
1) Am I right in saying I must get the non-parametric equation for the curve to get a nonlinear least squares fit to the data points? I assume that I do, because t is an extra variable that I a) don't need and b) have no information for.
2) Can a nonparametric equation for this curve be obtained (from the attached equations)? Why?

Ultimately, I would like to know if I can do a nonlinear least squares fit to these parametric equations. If I can't, or if it would prove very difficult, why?

Many thanks for your time,
Ciaran

Attached Thumbnails