Difference between revisions of "Publications/boutry.21.dgmm.1"
From LRDE
(Created page with "{{Publication  published = true  date = 20210302  authors = Nicolas Boutry, Thierry Géraud, Laurent Najman  title = An Equivalence Relation between Morphological Dynami...") 

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 booktitle = Proceedings of the IAPR International Conference on Discrete Geometry and Mathematical Morphology (DGMM) 
 booktitle = Proceedings of the IAPR International Conference on Discrete Geometry and Mathematical Morphology (DGMM) 

 address = Uppsala, Sweden 
 address = Uppsala, Sweden 

+   publisher = Springer 

+   pages = 525 to 537 

 abstract = In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershedbased image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to <math>n</math>D<math>n \geq 2</math>, showing that this equality can be applied to <math>n</math>D images and not only to 1D functions. This is a step further to show how much MM and MT are related. 
 abstract = In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershedbased image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to <math>n</math>D<math>n \geq 2</math>, showing that this equality can be applied to <math>n</math>D images and not only to 1D functions. This is a step further to show how much MM and MT are related. 

+   lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.21.dgmm.1.pdf 

 lrdeprojects = Olena 
 lrdeprojects = Olena 

 lrdenewsdate = 20210302 
 lrdenewsdate = 20210302 

−   note = To appear 

 type = inproceedings 
 type = inproceedings 

 id = boutry.21.dgmm.1 
 id = boutry.21.dgmm.1 

+   identifier = doi:10.1007/9783030766573_38 

 bibtex = 
 bibtex = 

@InProceedings<nowiki>{</nowiki> boutry.21.dgmm.1, 
@InProceedings<nowiki>{</nowiki> boutry.21.dgmm.1, 

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month = <nowiki>{</nowiki>May<nowiki>}</nowiki>, 
month = <nowiki>{</nowiki>May<nowiki>}</nowiki>, 

address = <nowiki>{</nowiki>Uppsala, Sweden<nowiki>}</nowiki>, 
address = <nowiki>{</nowiki>Uppsala, Sweden<nowiki>}</nowiki>, 

+  publisher = <nowiki>{</nowiki>Springer<nowiki>}</nowiki>, 

+  pages = <nowiki>{</nowiki>525537<nowiki>}</nowiki>, 

abstract = <nowiki>{</nowiki>In Mathematical Morphology (MM), dynamics are used to 
abstract = <nowiki>{</nowiki>In Mathematical Morphology (MM), dynamics are used to 

compute markers to proceed for example to watershedbased 
compute markers to proceed for example to watershedbased 

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only to 1D functions. This is a step further to show how 
only to 1D functions. This is a step further to show how 

much MM and MT are related.<nowiki>}</nowiki>, 
much MM and MT are related.<nowiki>}</nowiki>, 

−  +  doi = <nowiki>{</nowiki>10.1007/9783030766573_38<nowiki>}</nowiki> 

<nowiki>}</nowiki> 
<nowiki>}</nowiki> 

Revision as of 20:00, 21 May 2021
 Authors
 Nicolas Boutry, Thierry Géraud, Laurent Najman
 Where
 Proceedings of the IAPR International Conference on Discrete Geometry and Mathematical Morphology (DGMM)
 Place
 Uppsala, Sweden
 Type
 inproceedings
 Publisher
 Springer
 Projects
 Olena
 Date
 20210302
Abstract
In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershedbased image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to D, showing that this equality can be applied to D images and not only to 1D functions. This is a step further to show how much MM and MT are related.
Documents
Bibtex (lrde.bib)
@InProceedings{ boutry.21.dgmm.1, author = {Nicolas Boutry and Thierry G\'eraud and Laurent Najman}, title = {An Equivalence Relation between Morphological Dynamics and Persistent Homology in {$n$D}}, booktitle = {Proceedings of the IAPR International Conference on Discrete Geometry and Mathematical Morphology (DGMM)}, year = 2021, month = {May}, address = {Uppsala, Sweden}, publisher = {Springer}, pages = {525537}, abstract = {In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershedbased image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to $n$D, $n \geq 2$, showing that this equality can be applied to $n$D images and not only to 1D functions. This is a step further to show how much MM and MT are related.}, doi = {10.1007/9783030766573_38} }