Morse homology descriptor for shape characterization

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/sub y/, M/sub x/) of f, where M/sub a/ = f/sup -1/((-/spl infin/,a]), for all a /spl isin/ 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.