Shape Correspondence and Functional Maps
Channel: SmartGeometry
Date: 2017-07-27

Symposium on Geometry Processing
2017 Graduate School Lecture by Maks Ovsjanikov

http://www.lix.polytechnique.fr/~maks/

http://geometry.cs.ucl.ac.uk/SGP2017/?p=gradschool#abs_shape_correspondence

This course will introduce the audience to the techniques for computing and processing correspondences between 3D shapes based on the functional map framework. This framework, based on the idea that it is often easier to establish maps between real-valued functions, rather than points or triangles on the shapes, has recently led to significant advances in non-rigid shape matching and other related areas. Our main goal is to introduce the necessary mathematical background and to provide the computational methods based on the idea of functional maps. We will assume that the participants have knowledge of basic linear algebra and some knowledge of differential geometry, to the extent of being familiar with the concepts of a manifold. We will discuss in detail the functional approach to finding correspondences between non-rigid shapes, and mention some extensions such as the design and analysis of tangent vector fields, consistent map estimation and shape variability analysis. As part of this course, we will also provide some basic code (in MATLAB) to help in getting started with practical implementations.