Persistent homology and partial matching of shapes

The ability to perform not only global matching but also partial matching is investigated in computer vision and computer graphics in order to evaluate the performance ofshape 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 byshowing 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 approachin recognition tasks in the presence of partial information.