Topological analysis of shapes using Morse theory

In this paper, 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 is a Morse function defined on M. More precisely, we characterize the topology of all pairs of sub-level sets (M"y,M"x) of @f, where M"a=@f^-^1((-~,a]), for all a@?R. Classical Morse theory is used to establish a link between the topology of a pair of sub-level sets of @f and its critical points lying between the two levels.