Discrete Morse Functions and Watersheds
Discrete Mathematics
2023-05-17 v2 Algebraic Topology
Combinatorics
Abstract
Any watershed, when defined on a stack on a normal pseudomanifold of dimension d, is a pure (d -- 1)-subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined, and can be obtained with a linear-time algorithm relying on a sequence of collapses. Last, we prove that such a watershed is the cut of the unique minimum spanning forest, rooted in the minima of the Morse stack, of the facet graph of the pseudomanifold.
Cite
@article{arxiv.2301.03840,
title = {Discrete Morse Functions and Watersheds},
author = {Gilles Bertrand and Nicolas Boutry and Laurent Najman},
journal= {arXiv preprint arXiv:2301.03840},
year = {2023}
}