University of Konstanz
Graduiertenkolleg / PhD Program
Computer and Information Science

Guest Talks

title

Isometry invariant shape characterization

speaker

Dr. Facundo Memoli, Department of Mathematics, Stanford University
California, USA

date & place

Wednesday, 19.12.2007, 17:10 h
Room C252

abstract

In this talk we will describe an approach to invariant shape matching and recognition based on the Gromov-Hausdorff distance. We will provide an overview of its features and developments that lead to relating it to several pre-existing techniques used in practise. The GH distance was introduced by Gromov in the 80s in the realm of metric geometry. It essentially performs a comparison between two metric spaces. By viewing shapes as metric spaces endowed with suitable metrics, and comparing them with the GH distance one can obtain a true metric between shapes which exhibits invariance for example to rigid motions (shapes are endowed with Euclidean metrics). Having a true metric has advantages both in the theoretical and practical senses. The discretization of the GH distance leads to combinatorial optimization problems which are hard to solve . Alternatives which are structurally derived from the GH distance, and are based on mass transportation ideas provide a more computationally tractable framework.