Difference between revisions of "Publications/boutry.23.jmiv"
From LRDE
(Created page with "{{Publication | published = true | date = 2023-01-01 | authors = Gilles Bertrand, Nicolas Boutry, Laurent Najman | title = Discrete Morse Functions and Watersheds | journal =...") |
|||
| Line 5: | Line 5: | ||
| title = Discrete Morse Functions and Watersheds |
| title = Discrete Morse Functions and Watersheds |
||
| journal = Journal of Mathematical Imaging and Vision (Special Edition) |
| journal = Journal of Mathematical Imaging and Vision (Special Edition) |
||
| − | | volume = |
||
| − | | pages = |
||
| abstract = Any watershed, when defined on a stack on a normal pseudomanifold of dimension <math>d</math>, is a pure <math>(d-1)</math>-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. |
| abstract = Any watershed, when defined on a stack on a normal pseudomanifold of dimension <math>d</math>, is a pure <math>(d-1)</math>-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. |
||
| type = article |
| type = article |
||
| id = boutry.23.jmiv |
| id = boutry.23.jmiv |
||
| − | | identifier = doi: |
||
| bibtex = |
| bibtex = |
||
@Article<nowiki>{</nowiki> boutry.23.jmiv, |
@Article<nowiki>{</nowiki> boutry.23.jmiv, |
||
| Line 18: | Line 15: | ||
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision (Special |
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision (Special |
||
Edition)<nowiki>}</nowiki>, |
Edition)<nowiki>}</nowiki>, |
||
| − | volume = <nowiki>{</nowiki><nowiki>}</nowiki>, |
||
| − | pages = <nowiki>{</nowiki><nowiki>}</nowiki>, |
||
abstract = <nowiki>{</nowiki>Any watershed, when defined on a stack on a normal |
abstract = <nowiki>{</nowiki>Any watershed, when defined on a stack on a normal |
||
pseudomanifold of dimension $d$, is a pure |
pseudomanifold of dimension $d$, is a pure |
||
| Line 31: | Line 26: | ||
cut of the unique minimum spanning forest, rooted in the |
cut of the unique minimum spanning forest, rooted in the |
||
minima of the Morse stack, of the facet graph of the |
minima of the Morse stack, of the facet graph of the |
||
| − | pseudomanifold. <nowiki>}</nowiki> |
+ | pseudomanifold. <nowiki>}</nowiki> |
| − | doi = <nowiki>{</nowiki><nowiki>}</nowiki> |
||
<nowiki>}</nowiki> |
<nowiki>}</nowiki> |
||
Latest revision as of 16:50, 4 July 2023
- Authors
- Gilles Bertrand, Nicolas Boutry, Laurent Najman
- Journal
- Journal of Mathematical Imaging and Vision (Special Edition)
- Type
- article
- Date
- 2023-01-01
Abstract
Any watershed, when defined on a stack on a normal pseudomanifold of dimension , is a pure -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.
Bibtex (lrde.bib)
@Article{ boutry.23.jmiv,
author = {Gilles Bertrand and Nicolas Boutry and Laurent Najman},
title = {Discrete Morse Functions and Watersheds},
year = {2023},
journal = {Journal of Mathematical Imaging and Vision (Special
Edition)},
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. }
}