The course deals with modern methods of analysis of non-rigid surfaces, an important emerging field bringing together different disciplines of mathematics and computer science such as differential and metric geometry, numerical analysis, optimization, computer graphics, machine learning, computer vision and computational geometry. The course objective is to give theoretical and numerical tools for the analysis and comparison of surfaces from the perspective of the recent advances in the field. The first part of the course will include a brief introduction into topology, metric and Riemannian geometry as well as numerical geometry, numerical analysis and state-of-the-art tools in numerical optimization. The second part is dedicated to the representation of intrinsic geometry of surfaces. We will discuss the notion of isometric embedding, discern between local and global isometries and study different numerical methods for analysis and comparison of non-rigid surfaces. Two major emphases are spectral embeddings and multidimensional scaling. The last part of the course is dedicated to applications. We will see how many important problems can be addressed within the framework of non-rigid surface matching. We will demonstrate the 3D face recognition system based on intrinsic geometric representation of faces.

Credit points: 2.0

Time: Monday 8:30-10:30

Place: Taub 401 (seminar room on the 4th floor).