Efficient topological descriptor for shape representation

In a recent paper, we have introduced a topological descriptor for shape representation based on classical Morse theory. More precisely, given a manifold M and a Morse function f on M, we build an invariant (Morse Shape Descriptor (MSD)) of the manifold from the ranks of relative homology groups of all pairs of lower levels of the function f. While the MSD is a robust invariant with very nice properties, its application requires time consuming computations of homology groups. We present a new and computationally efficient method to capture the essential of the information given by the MSD.