**Computer Vision**

Introduction to active contour model: http://en.wikipedia.org/wiki/Active_contour_model

Guillermo Sapiro's notes on PDE based image processing: http://courses.cs.washington.edu/courses/cse577/04sp/notes/sapiro2.pdf.

*It includes elementary and important differential geometry formulas for curves and surfaces, such as the celebrated elegant Serret-Frenet formulas. It has been quite useful to those who, like me, want to derive their own curve/surface evolution equations from contour/surface integral minimization problems.*

Nice introduction to Markov random field: http://www.nlpr.ia.ac.cn/users/szli/mrf_book/MRF_Book.html

Introduction to active contour, calculus of variations and level set method: Appendix-A of my thesis :) at https://repository.ntu.edu.sg/handle/10356/50709

First part of my notes on optimization models for computer vision: here

**Applied Math:**

All we need to know about calculus of variations: http://www.math.umn.edu/~olver/ln_/cv.pdf

The aurora of level set method: http://www.museth.org/Ken/Publications_files/Breen-etal_SIG04.pdf

Elegant approach to shape optimization with level set method, co-area formula, etc: ftp://ftp.math.ucla.edu/pub/camreport/cam04-02.pdf

Elegant theory of learning by kernel machines based on empirical risk minimization and function approximation: http://ttic.uchicago.edu/~smale/papers/math_foundation_of_learning.pdf

The bible book for optimization from a functional analysis point of view. The functional analysis part is quite accessible. I didn't know this book has been put online: http://math.oregonstate.edu/~show/old/142_Luenberger.pdf