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I am performing illumination correction using regression methods, let's say polynomial method. If we use 3rd order polynomial in 2D we will have 10 coefficients to estimate. I manually chose these coefficient values and created an illumination profile as shown below using 'once' square in MATLAB.

My question is, ignoring polynomial series, how to create similar kind of bias patterns in 2D(similar smooth but not the exact same)? I mean what are the different ways I can create such smooth surfaces?

Polynomial fitting

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If you simply want to create images like this, you could randomly create several reasonably-spaced data points in 2D space, then use 2D kriging or thin-plate-spline interpolation to fill in the the grid.

As per whuber's comment below, "reasonably-spaced" would include the four corners. I'd also think 1-3 other points inside the square, but not too many, lest you get a "smooth" image that's much busier than your target image.

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    $\begingroup$ Re "reasonably-spaced": You have to make sure you include the support points of the image (its corners) because thin-plate splines and kriging both can do dramatically terrible things outside the convex hull of the data supports. $\endgroup$ – whuber Aug 24 '17 at 15:18

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