Math in vision

I often find it difficult to understand the mathematical equations in papers, especially those published in PAMI, IJCV. Sometimes the math looks so intimidating that I only read introduction, conclusion, and skip the rest. However, as pointed out by pluskid, reading the introduction, conclusion, and the references are merely a way to convince myself of a sense of achievement, without actually thinking thoroughly.

A discussion on how to acquire the math knowledge is quite stimulating. There are several ways to meet this end, and could be summarized as follows. 

Video lectures, such as the MIT opencourseware. I learnt linear algebra from Prof. Gilbert Strang in this way.

Courses. The university graduate courses provide plenty of materials on basic concepts in this field. This course is fundamental and also recommended, so as this and this.

Textbooks. However, I often do not have the patience to read all of the pages. I normally only read the relevant parts to my current research because I forget the equations and concepts quickly without applying them. It is reported that A First Course in Linear Algebra is a good reference book. In my opinion, the books caters for Opencv are really great as they explain the math in an easy to follow way, and full of examples. 

Papers. Most papers only include advanced math but some of them cares to elaborate more. 

In short, a list of required math may be

Linear Algebra
Singular Value Decomposition
Introductory level Pattern Recognition
Principal Component Analysis
Linear Discriminant Analysis
Fourier Transform
Wavelets
Probability, Bayes rule, Maximum Likelihood, MAP
Mixtures and Expectation-Maximization Algorithm
Introductory level Statistical Learning
Support Vector Machines
Genetic Algorithms
Hidden Markov Models
Bayesian Networks
Kalman filtering

The math is critical for computer vision research as discussed here. Essentially, to solve a problem we need to choose the most effective math model to formulate it. For instance, graph theory comes in handy for segmentation. If we are not aware of the math involved, then the vision algorithm we develop may appear ad hoc.