3D ellipsoid closest fit estimation (as a way to characterize lens rolloff)

I am currently working with a number of lenses and need to be able to calculate and correct for the rolloff in an arbitrary part of the field. I have observed that the rolloff appears (by inspection) to be in the shape of a cropped ellipsoid with arbitrary position and orientation.

Does anyone know how to establish the equation for a closest fit ellipsoid to a set of data in the form of a 3D matrix of: data(y-dim, x-dim, luma-dim)?

I have spent time considering how to extrapolate the parameters by inspecting plane slices through the data, but I haven't come up with a way to get the general equation parameters.

Thanks in advance, Sean

Answer 1

[Image Analyst]

You might try gridfit: http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit I used to use John's other fitting routine but he has unfortunately removed it. You might try this alternative: http://www.mathworks.com/matlabcentral/fileexchange/13719-2d-weighted-polynomial-fitting-and-evaluation Take a blank shot (a uniform background) and then fit that to a quadratic in both directions. It makes a nice smooth model for background correcting the vignetting your lens caused.