Is there any inbuilt function available for surface fitting to the intensity values of a grayscale image that minimize the entropy of an Image?

I am trying to fit the surface to the intensity values of a grayscale image. For that purpose, I have decided to use the entropy of an image as a criterion function.I was wondering if there is any way I can use fit - an inbuilt function that fits the surface or optimizes the polynomial coefficients at the same time minimizing the entropy of the image.

Thanks

Answer 1

[John D'Errico]

No. Just use a general optimization tool (from the optimization toolbox), writing the objective function yourself.

The curve fitting toolbox functions will assume a minimum sum of squares of residuals criterion.

[Jay]

Thanks. I was using your code http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

It is giving me good approximation for higher order polynomials, but it uses the least squares of residuals as long as I know. Is there any possible way I can change the objective function in it? (may be by altering some steps in polyfitn function.)

[John D'Errico]

Sorry. Polyfitn uses linear algebra (linear least squares) to solve for the coefficients of the polynomial, although the polynomial itself need not be linear. The problem is linear in the unknown coefficients in terms of the estimation.

In order to change the objective to something else, the code would need to call a general optimizer. That in itself would not be the end of the world, but since the code also computes a variety of measures of fit, they would be invalidated. Essentially, a large fraction of polyfitn would need to be re-written.

[Jay]

I have one question @John. Is your polyfitn toolbox which uses QR decomposition using the brightest spot mean as a control point and try to fit the surface or it just tries to fit the data values to the surface as I am trying to correct the illumination in the digital image and after the illumination correction the color tonality of the image is similar to the brightest spot colors in a particular image?