Difference between revisions of "Publications/boutry.19.ismm"

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(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
 
| 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)
⚫
| volume =
 
 
| series = Lecture Notes in Computer Science Series
  
| series = Lecture Notes in Computer Science Series
 
| address = Saarbrücken, Germany
  
| address = Saarbrücken, Germany
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| pages = 1 to 12
  
| pages = 1 to 12
 
| lrdeprojects = Olena
  
| lrdeprojects = Olena
−
| 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.
 +
| 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.
  ⚫
| volume = 12708
 
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.19.ismm.pdf
  
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.19.ismm.pdf
 
| lrdekeywords = Image
  
| lrdekeywords = Image
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| type = inproceedings
  
| type = inproceedings
 
| id = boutry.19.ismm
  
| id = boutry.19.ismm
  +
| identifier = doi:10.1007/978-3-030-20867-7_5
 
| bibtex =
 
| bibtex =
 
@InProceedings<nowiki>{</nowiki> boutry.19.ismm,
  
@InProceedings<nowiki>{</nowiki> boutry.19.ismm,
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Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>,
  
Symposium on Mathematical Morphology (ISMM)<nowiki>}</nowiki>,
 
year = 2019,
  
year = 2019,
⚫
editor = <nowiki>{</nowiki><nowiki>}</nowiki>,
  
⚫
volume = <nowiki>{</nowiki><nowiki>}</nowiki>,
  
 
series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>,
  
series = <nowiki>{</nowiki>Lecture Notes in Computer Science Series<nowiki>}</nowiki>,
 
address = <nowiki>{</nowiki>Saarbr\"ucken, Germany<nowiki>}</nowiki>,
  
address = <nowiki>{</nowiki>Saarbr\"ucken, Germany<nowiki>}</nowiki>,
 
publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>,
  
publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>,
 
pages = <nowiki>{</nowiki>1--12<nowiki>}</nowiki>,
  
pages = <nowiki>{</nowiki>1--12<nowiki>}</nowiki>,
−
month = <nowiki>{</nowiki>July<nowiki>}</nowiki>,
 +
month = jul,
  ⚫
doi = <nowiki>{</nowiki>10.1007/978-3-030-20867-7_5<nowiki>}</nowiki>,
 
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
 
Mathematical Morphology and Discrete Morse Theory when we
  
Mathematical Morphology and Discrete Morse Theory when we
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equivalent to pairing by dynamics. Furthermore,
  
equivalent to pairing by dynamics. Furthermore,
 
self-duality and injectivity of these pairings are
  
self-duality and injectivity of these pairings are
−
proved.<nowiki>}</nowiki>
 +
proved.<nowiki>}</nowiki>,
  ⚫
volume = <nowiki>{</nowiki>12708<nowiki>}</nowiki>
 
<nowiki>}</nowiki>
  
<nowiki>}</nowiki>
   

Latest revision as of 15:32, 16 December 2022

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,
  doi		= {10.1007/978-3-030-20867-7_5},
  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.},
  volume	= {12708}
}





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