Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts
Discrete Mathematics
2022-10-06 v2 Algebraic Topology
Geometric Topology
Abstract
In this paper, we study a class of discrete Morse functions, coming from Discrete Morse Theory, that are equivalent to a class of simplicial stacks, coming from Mathematical Morphology. We show that, as in Discrete Morse Theory, we can see the gradient vector field of a simplicial stack (seen as a discrete Morse function) as the only relevant information we should consider. Last, but not the least, we also show that the Minimum Spanning Forest of the dual graph of a simplicial stack is induced by the gradient vector field of the initial function. This result allows computing a watershed-cut from a gradient vector field.
Cite
@article{arxiv.2203.11512,
title = {Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts},
author = {Nicolas Boutry and Gilles Bertrand and Laurent Najman},
journal= {arXiv preprint arXiv:2203.11512},
year = {2022}
}