Is it possible to formalize areas such as image processing and computer vision? Is it possible to formalize areas such as image processing?
By formalize I mean setup axioms, then derive theorems, and
reason about image processing concepts and methods formally.
I would say now image processing is pretty informal and ill-defined
without strong foundations.

I would beg to disagree.  Image processing is quite formal.  Images are treated as discrete functions in 2D, and are manipulated using very formal methods from calculus, linear algebra, and statistics.
