Morse-Smale Complex computation with Watershed Cut

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Abstract

The Morse-Smale complex is a useful tool to analyse the topology of an image. However, its computation is quite expensive, and several algorithms exist having some differences in the definition of the complex. On the other hand, the Watershed Cut is a morphological algorithm, which segments grayscale images. It considers that an image is an edge-weighted graph, where the weights are given by the image gradient. Lidija Comic was the first to coin a possible equivalence between the algorithms to compute the Morse-Smale complex and the Watershed Cut with specific markers on the minima and maxima of the image. In this work, we discuss about this possibility, and we propose an implementation of a modified Watershed Cut algorithm working on vertex-weighted graphs as a way to compute the Morse-Smale complex.