Functional Maps: A Flexible Representation for Learning and Computing Correspondence

Abstract: Notions of similarity and correspondence between shapes, understood in a broad sense as domain or signal geometry, proximity or connectivity (e.g. images, point clouds, meshes or graphs), is central to many tasks in shape analysis, geometry processing, and computer vision. The goal of this course is to familiarize the audience with the functional map framework, a set of recent techniques that greatly facilitate the computation of correspondences between geometric data by formulating them as mappings between functions rather than points or triangles. In this course, we will provide a unifying treatment of the mathematical background of these techniques and cover the most relevant computational methods proposed in the recent years. Particular attention will be given to the integration of the functional map framework into deep learning pipelines. The effectiveness and flexibility of the functional map representation will be shown in various applications to 3D computer vision, geometry processing, and machine learning problems.