Seminars/Colloquia/Invited Talks

Seminars

Peter Michor

The Hamiltonian of Metrics on Curve and Shape

PLACE:	Clark 314
EVENT:	CIS Seminar
DATE:	October 19, 2005
TIME:	3:00 - 4:00

Abstract

This work arose by the need in pattern recognition to find good metrics on the space of shapes, i.e., the space of regular smooth curves in the plane, viewed as the orbit space of immersions from S¹ to the plane modulo the group of diffeomorphisms of S¹, acting as reparameterizations, or various completions of this. We look for Riemannian metrics. The usual L²-metric leads to vanishing geodesic distance on shape space. The Hamiltonian approach for various metrics has been particularly successful since it also allows the computation of various conserved momenta. In this talk I will give an overview on various metrics, their geodesic equations, and some of their properties.