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Computer Science > Discrete Mathematics

arXiv:2203.11512 (cs)
[Submitted on 22 Mar 2022 (v1), last revised 5 Oct 2022 (this version, v2)]

Title:Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts

Authors:Nicolas Boutry (LRDE), Gilles Bertrand (LIGM), Laurent Najman (LIGM)
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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.
Subjects: Discrete Mathematics (cs.DM); Algebraic Topology (math.AT); Geometric Topology (math.GT)
Cite as: arXiv:2203.11512 [cs.DM]
  (or arXiv:2203.11512v2 [cs.DM] for this version)
  https://doi.org/10.48550/arXiv.2203.11512
Journal reference: 2nd International Conference on Discrete Geometry and Mathematical Morphology (DGMM 2022)

Submission history

From: Laurent Najman [view email] [via CCSD proxy]
[v1] Tue, 22 Mar 2022 07:41:25 UTC (8,674 KB)
[v2] Wed, 5 Oct 2022 14:53:12 UTC (3,195 KB)
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