This blog is a follow-up of my previous blog: http://masterxinli.wordpress.com/2009/09/01/the-relationship-of-mathematics-to-image-processing/. I had sent out some cautious note about abuse of mathematics in image processing in that blog. The tone might sound a little bit overshoot; so I will “correct” myself in this blog. As I have stated in the class, mathematics “turns art into science” – so even though I maintain my position that math is only a tool, it is always a good idea to learn to use more and different tools. Here is a list of the tools relevant to image processing:
1. Euler-Lagrange equation in variational calculus.
2. EM algorithm in statistics.
3. Eigenvalues and Laplacian of a graph in spectral graph theory.
4. Convex optimization in optimization theory.
5. Finite difference method in numeral analysis.
6. Fixed-point theorem in dynamical systems.
7. LLN and heavy-tail distribution in probability theory.
8. The first fundamental form of surface in differential geometry.
9. Manifold in topology.
10. Singular value decomposition in matrix theory.
