Nonlinear least squares problem

  1. 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 :frown: ).

    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 Files:

  2. jcsd
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