Difference between revisions of "Publications/boutry.19.ismm"
From LRDE
(Created page with "{{Publication | published = true | date = 2019-03-13 | authors = Nicolas Boutry, Thierry Géraud, Laurent Najman | title = An Equivalence Relation between Morphological Dynami...") |
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| title = An Equivalence Relation between Morphological Dynamics and Persistent Homology in 1D |
| title = An Equivalence Relation between Morphological Dynamics and Persistent Homology in 1D |
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| booktitle = Mathematical Morphology and Its Application to Signal and Image Processing – Proceedings of the 14th International Symposium on Mathematical Morphology (ISMM) |
| booktitle = Mathematical Morphology and Its Application to Signal and Image Processing – Proceedings of the 14th International Symposium on Mathematical Morphology (ISMM) |
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| − | | volume = |
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| series = Lecture Notes in Computer Science Series |
| series = Lecture Notes in Computer Science Series |
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| address = Saarbrücken, Germany |
| address = Saarbrücken, Germany |
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| pages = 1 to 12 |
| pages = 1 to 12 |
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| lrdeprojects = Olena |
| lrdeprojects = Olena |
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| − | | abstract = We state in this paper a strong relation existing between Mathematical Morphology and Discrete Morse Theory when we work with 1D Morse functions. Specifically, in Mathematical Morphology, a classic way to extract robust markers for segmentation purposes, is to use the dynamics. On the other hand, in Discrete Morse Theory, a well-known tool to simplify the Morse-Smale complexes representing the topological information of a Morse function is the persistence. We show that pairing by persistence is equivalent to pairing by dynamics. |
+ | | abstract = We state in this paper a strong relation existing between Mathematical Morphology and Discrete Morse Theory when we work with 1D Morse functions. Specifically, in Mathematical Morphology, a classic way to extract robust markers for segmentation purposes, is to use the dynamics. On the other hand, in Discrete Morse Theory, a well-known tool to simplify the Morse-Smale complexes representing the topological information of a Morse function is the persistence. We show that pairing by persistence is equivalent to pairing by dynamics. Furthermoreself-duality and injectivity of these pairings are proved. |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.19.ismm.pdf |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.19.ismm.pdf |
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| lrdekeywords = Image |
| lrdekeywords = Image |
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Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>, |
Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>, |
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year = 2019, |
year = 2019, |
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| − | editor = <nowiki>{</nowiki><nowiki>}</nowiki>, |
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| − | volume = <nowiki>{</nowiki><nowiki>}</nowiki>, |
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series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>, |
series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>, |
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address = <nowiki>{</nowiki>Saarbr\"ucken, Germany<nowiki>}</nowiki>, |
address = <nowiki>{</nowiki>Saarbr\"ucken, Germany<nowiki>}</nowiki>, |
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publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>, |
publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>, |
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pages = <nowiki>{</nowiki>1--12<nowiki>}</nowiki>, |
pages = <nowiki>{</nowiki>1--12<nowiki>}</nowiki>, |
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| − | month = |
+ | month = jul, |
abstract = <nowiki>{</nowiki>We state in this paper a strong relation existing between |
abstract = <nowiki>{</nowiki>We state in this paper a strong relation existing between |
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Mathematical Morphology and Discrete Morse Theory when we |
Mathematical Morphology and Discrete Morse Theory when we |
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Revision as of 17:51, 10 April 2019
- Authors
- Nicolas Boutry, Thierry Géraud, Laurent Najman
- Where
- Mathematical Morphology and Its Application to Signal and Image Processing – Proceedings of the 14th International Symposium on Mathematical Morphology (ISMM)
- Place
- Saarbrücken, Germany
- Type
- inproceedings
- Publisher
- Springer
- Projects
- Olena
- Keywords
- Image
- Date
- 2019-03-13
Abstract
We state in this paper a strong relation existing between Mathematical Morphology and Discrete Morse Theory when we work with 1D Morse functions. Specifically, in Mathematical Morphology, a classic way to extract robust markers for segmentation purposes, is to use the dynamics. On the other hand, in Discrete Morse Theory, a well-known tool to simplify the Morse-Smale complexes representing the topological information of a Morse function is the persistence. We show that pairing by persistence is equivalent to pairing by dynamics. Furthermoreself-duality and injectivity of these pairings are proved.
Documents
Bibtex (lrde.bib)
@InProceedings{ boutry.19.ismm,
author = {Nicolas Boutry and Thierry G\'eraud and Laurent Najman},
title = {An Equivalence Relation between Morphological Dynamics and
Persistent Homology in {1D}},
booktitle = {Mathematical Morphology and Its Application to Signal and
Image Processing -- Proceedings of the 14th International
Symposium on Mathematical Morphology (ISMM)},
year = 2019,
series = {Lecture Notes in Computer Science Series},
address = {Saarbr\"ucken, Germany},
publisher = {Springer},
pages = {1--12},
month = jul,
abstract = {We state in this paper a strong relation existing between
Mathematical Morphology and Discrete Morse Theory when we
work with 1D Morse functions. Specifically, in Mathematical
Morphology, a classic way to extract robust markers for
segmentation purposes, is to use the dynamics. On the other
hand, in Discrete Morse Theory, a well-known tool to
simplify the Morse-Smale complexes representing the
topological information of a Morse function is the
persistence. We show that pairing by persistence is
equivalent to pairing by dynamics. Furthermore,
self-duality and injectivity of these pairings are
proved.}
}