DESCRIPTION
Many CVML scientists, engineers and enthusiasts do not have solid mathematical background, as it is so easy to jump into almost any CVML domain using available libraries and frameworks. This is very much true in Deep Learning and leads to a cacophony of inaccurate statements and a polyphony of ill-defined terms and concept. Therefore, a rigorous mathematical background is a must for anybody working in this area. Luckily, most ECE/CS curricula provide such foundations.
This CVML Web Module focuses on CVML Mathematical Foundations.
Mathematical Analysis for single variable and multivariate functions is the indispensable basis for all CVML domains, as, e.g., images are 2D signals (functions). Linear Algebra provides the basic mathematical tools not only for Computer Vision but also for Signals and Systems and Machine/Deep Learning. Probability Theory is very important for Signal/Image Processing and Machine Learning, since all data can be described by probabilistic forms for Data Analytics. Geometry plays an important role not only in Computer Vision, where we do 3D world modeling, but also in creating many useful data/signal representations for Data Analytics. Set theory is very useful, as data (e.g., images) can be considered as sets and training data sets are the basis for Deep Learning.
LECTURE LIST
- Mathematical Analysis
- Geometry
- Geometric Spaces
- Linear Algebra
- Set Theory
- Probability Theory
- Introduction to Statistics
- Statistical Detection
- Robust Statistics
CVML WEB LECTURE MODULE SCHEDULE
This module has been designed to be mastered within 1 month (or less), if you have proper background (at least early undergraduate student in an EE, ECE, CS, CSE or any Engineering or Exact Sciences Department).
We propose that you follow the above mentioned Lecture order. You may want to skip few Lectures that might not be of immediate interest to you for later study.
On average you can study 4 lectures per week. The related effort is as follows:
1) Lecture pdf study and filling the related understanding questionnaire: 1-2 hours per lecture (on average, depending on your background)
2) Tutorial exercise (if available): 1/2 hour on average (more if you do not have theoretical skills). We strongly recommend to try solve them yourself, before resorting to the existing solution.
3) Programming exercise (if available): 3-4 hours on average (more if you do not have good programming skills). We strongly recommend to try program them yourself, before resorting to the existing code.
The following lectures are accompanied by programming or tutorial exercises:
- Mathematical Analysis (3 Tutorial Exercises)
- Probability Theory (8 Tutorial Exercises)