How to perform surface fitting in two dimensional case of image?

I am reading the csaps and tpaps docs in Matlab documentation. I understand most of the things, except one. In the case of two-dimensional case of image surface fitting, hows the panelized sum of square formulation look like?

And hows the thin plate spline(tpaps) is different from cubic Smoothing spline(csaps) in the case of a 2D grayscale image?

Answer 1

[Chris Perkins]

While it looks like you got your question answered in the below stack exchange article, for anyone else who has the same question, the difference between the "csaps" and "tpaps" functions are explained in the following post:

https://stats.stackexchange.com/questions/295904/how-does-the-cubic-smoothing-spline-works-in-2d-case