Abstract
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, φ), where M is a closed smooth manifold and φ 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 φ, where M a = φ −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 φ and its critical points lying between the two levels.
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