Persistent homology and partial matching of shapes

Abstract

The ability to perform not only global matching but also partial matching is in-vestigated in computer vision and computer graphics in order to evaluate the performance of shape descriptors. In my talk I will consider the persistent homology shape descriptor, and Iwill illustrate some results about persistence diagrams of occluded shapes and partial shapes. The main tool is a Mayer-Vietoris formula for persistent homology. Theoretical results indicate that persistence diagrams are able to detect a partial matching between shapes by showing a common subset of points both in the one-dimensional and the multi-dimensionalsetting. Experiments will be presented which outline the potential of the proposed approach in recognition tasks in the presence of partial information