Morse Homology Descriptor for Shape Characterization

Authors:
Madjid Allili;David Corriveau;Djemel Ziou
Affiliations:
Bishop's University, Canada;Université de Sherbrooke, Canada;Université de Sherbrooke, Canada
Venue:
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Year:
2004

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Abstract

In this paper, we propose a new topological method for shape description that is suitable for any multi-dimensional data set that can be modelled as a manifold.The description is obtained for all pairs (M, f), where M is a closed smooth manifold and f a Morse function defined on M.More precisely, we characterize the topology of all pairs of lower level sets (M_y, M_x) of f, where M_a = f^{-1} ((-驴, a]), for all a 驴 R.Classical Morse theory is used to establish a link between the topology of a pair of lower level sets of f and its critical points lying between the two levels.