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2-D nonlinear curve fitting

Dear Altenbach,


Here's the file of the two phantoms.



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Message 61 of 63

Can the model be adapted to fit a superellipse?

I am using a similar model to get x_c, y_c, a, b, and rotation.

For an ellipse, the equation always has a 2 for the exponent.

In my case, I need to be able the adjust the 2 up or down slightly to fit the curve more accurately. All of my points (typically a count of 8) are on the perimeter.

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Message 62 of 63

@buckeyedave wrote:

Can the model be adapted to fit a superellipse?


A non-linear fit is a non-linear fit, so the answer is "Of course, but ...".  Gauss (of curve-fitting fame) is reputed to have said (in German, almost certainly) "With 5 parameters, I can fit an elephant; with 6, I can make him wave his trunk" (I, myself, don't really believe Gauss said this, but it illustrates that if you add enough parameters, you can exactly fit almost anything).  


Your model will have 6 parameters, and you are fitting 8 points, which may or may not be "well-placed" to allow a meaningful distinction between nearby choices of parameters (to say nothing about the possibility that there may be a little "noise" in the points, themselves).  Have you ever heard of Sensitivity Analysis?  


Bob Schor

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Message 63 of 63