Is it possible to formalize areas such as image processing and computer vision?

Question

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.

Answer 1

Mumford got interested; http://en.wikipedia.org/wiki/David_Mumford and http://www.amazon.com/Pattern-Theory-Stochastic-Real-World-Mathematics/dp/1568815794/ and many vision pdfs at http://www.dam.brown.edu/people/mumford/vision/papers/

Anyway, theory, such as you request, and practice are currently very far apart. You might look up "persistent homology" for example.

Answer 2

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.