SCIENCE SEMINAR
TOPOLOGICAL ANALYSIS OF SHAPES USING MORSE THEORY
Madjid Allili
Bishop's University
Monday, April 2, 2007
1:30 - 2:30 PM
Johnson 103
In computer vision, the problems of shape recognition, classification, and matching require adequate tools to represent shape properties by means of descriptors. Such descriptors allow to measure several shape characteristics of statistical, geometrical, or topological nature. We propose a novel method for shape analysis that is suitable for any multi-dimensional data set that can be modelled as a manifold. The descriptor is obtained for any pair (M,f), where M is a closed smooth manifold and f a Morse function defined on M. More precisely, we use the relative homology groups of all pairs of sub-level sets (My,Mx) of f, where Ma = f^{-1}(-infinity, a] to characterize the topological shape of M. This leads to a stable invariant tool for shape description that we call the Morse Shape Descriptor.
THIS TALK IS INTENDED FOR UNIVERSITY SCIENCE STUDENTS.
