Morse connections graph for shape representation

Authors:
David Corriveau;Madjid Allili;Djemel Ziou
Affiliations:
Département d’informatique, Université de Sherbrooke, Sherbrooke, Qc, Canada;Department of Computer Science, Bishop’s University, Lennoxville, Qc, Canada;Département d’informatique, Université de Sherbrooke, Sherbrooke, Qc, Canada
Venue:
ACIVS'05 Proceedings of the 7th international conference on Advanced Concepts for Intelligent Vision Systems
Year:
2005

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Abstract

We present an algorithm for constructing efficient topological shape descriptors of three dimensional objects. Given a smooth surface S and a Morse function f defined on S, our algorithm encodes the relationship among the critical points of the function f by means of a connection graph, called the Morse Connections Graph, whose nodes represent the critical points of f. Two nodes are related by an edge if a connection is established between them. This graph structure is extremely suitable for shape comparison and shape matching and inherits the invariant properties of the given Morse function f.