Instructors :

Prof. Yanxi Liu, Dr. Martin Oswald

Teaching assistants :

Ian Cherabier

Lectures :

Thursdays from 09:15-11:00 in CHN D 44

Exercises :

Thursdays from 11:15-12:00 in CHN D 44

You may find additional information on the previous course webpage.

Course Abstract:

Regularity is an essential and ubiquitous concept in nature, science, and art. Numerous biological, natural, or man-made structures exhibit regularities, abstracted by symmetries, as a fundamental design principle or as an essential aspect of their function. This course concentrates on rigorous theory (group theory), keen observations, and computational (automatic) discovery of patterns in various data forms in our daily life and our research.

Group theory, the ultimate mathematical theory for symmetry will not be textbook-learned only but practiced on real-world digitized data sets. The course abandons the classical definition-theorem-proof model, instead, relies heavily on your senses and intuitions, both visual and tactile, resulting in a solid understanding of group theory that you can touch! The key challenge of turning the concept of mathematical symmetry/regularity into a computationally useful tool is to figure out how to apply the concise group theory to the noisy albeit often near-regular real-world. So far, a robust, general symmetry (covering all types of symmetries) detection algorithm for real-world digital data (images or otherwise) remains to be elusive. This challenge leads to the unique role this course will explore "computational symmetry" (Liu 2000).

Computation forms the key component of this course which links theory and applications. Students will witness effective computational models with concrete applications in robotics, computer vision, computer graphics, and medical image analysis. The emphasis is on hands-on computational experience and on producing state of the art, publishable research projects. During the semester, we shall start with intuition, learn the basic mathematical concepts and develop state of the art computer algorithms for real-world problems. Our goal is to build “bridges” connecting symmetry, symmetry group theory, general and specific regularities, and real-world applications.

Lecture Syllabus (Tentative) :
Date Topic
Sep 22, 2016 Introduction of Regularity and Symmetry
Sep 29, 2016 - Symmetry groups. Classical mathematical definitions.
- Cyclic, Dihedral, Frieze groups.
Oct 06, 2016 Wallpaper Groups
Oct 13, 2016 No lecture and exercises
Oct 27, 2016 Symmetry Detection / Digital Papercutting
Nov 03, 2016 Student Term Project Presentation
Nov 10, 2016 - Student Term Project Presentation (continued)
- Human and Animal Perception of Patterns
Nov 17, 2016 Symmetry Groups in Spatiotemporal Data
Nov 24, 2016 Student Term Project Mid-Term Presentations
Dec 01, 2016 Student Term Project Mid-Term Presentations (continued)
Dec 08, 2016 Quantified regularity in Biomedical Image Applications
Dec 15, 2016 - Introduction to Pattern Theory
- Exercise: finish pattern sorting game
Dec 22, 2016 Student Term Project Final Presentations / Discussions
Course Material :

The course is managed through the course management system moodle. All lecture material will be shared there, and further, all homework and exercises will be submitted through this system. Homework is generally to be submitted at the latest the night before the next lecture, i.e., Wednesday midnight.

Course Grading :
  • Written Homework: 30%
  • Presentations/Discussions: 20%
  • Term Project: 50%
References :

We will use a combination of state-of-the-art research articles and a few books. Some of them are listed below. On-line versions of relevant chapters will be provided to the students.

Semester Index