Mathematics of computer vision: course
This is an introduction into the mathematics of computer vision and digital image analysis: topology and geometry. (For a more advanced approach see Introductory algebraic topology: course, more math here.)
The exposition is geared towards CS students and potential and current math majors. The material is self-contained beyond high school math (no calculus). Special attention is paid to the algorithmic implementation of the mathematics. A variety of applications is considered in detail.
Calculus I, computer language preferred but not required.
A large part of the lectures is now a part of a draft of a book called Topology Illustrated.
Introduction: analysis of visual information and Examples of image analysis
- Digital images
- Topology and geometry of binary images
- Topology and geometry of gray scale images
- 3D image analysis
- Miscellaneous topics
- Analysis of color images and other multi-parameter images
- Robustness of image analysis
- What is the difference between binary and gray scale images?
- How do you count holes in a binary image?
C++, Java, or MATLAB
- Modification of the algorithms (construction of the topology graph, analysis of the topology graph);
- Implementation of the algorithms (motion, color, stereo, 3D, etc);
- Practical applications of the algorithms (based on Pixcavator SDK or CHomP).
Software: Pixcavator Student Edition (free)