# Difference between revisions of "Publications/boutry.22.jmiv"

### From LRDE

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| title = Continuous Well-Composedness implies Digital Well-Composedness in n-D |
| title = Continuous Well-Composedness implies Digital Well-Composedness in n-D |
||

| journal = Journal of Mathematical Imaging and Vision |
| journal = Journal of Mathematical Imaging and Vision |
||

− | | volume = |
+ | | volume = 64 |

− | | number = |
+ | | number = 2 |

− | | pages = |
+ | | pages = 131 to 150 |

| lrdeprojects = Olena |
| lrdeprojects = Olena |
||

− | | abstract = In this paper, we prove that when a <math>n</math>-D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological <math>(n-1)</math>-manifold, then it is digitally well-composed (DWC) |
+ | | abstract = In this paper, we prove that when a <math>n</math>-D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological <math>(n-1)</math>-manifold, then it is digitally well-composed (DWC)which means that it does not contain any critical configuration. We prove this result thanks to local homology. This paper is the sequel of a previous paper where we proved that DWCness does not imply CWCness in 4D. |

| lrdepaper = https://www.lrde.epita.fr/dload/papers/boutry.22.jmiv.pdf |
| lrdepaper = https://www.lrde.epita.fr/dload/papers/boutry.22.jmiv.pdf |
||

| lrdekeywords = Image |
| lrdekeywords = Image |
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Well-Composedness in $n$-D<nowiki>}</nowiki>, |
Well-Composedness in $n$-D<nowiki>}</nowiki>, |
||

journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>, |
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>, |
||

− | volume = <nowiki>{</nowiki><nowiki>}</nowiki>, |
+ | volume = <nowiki>{</nowiki>64<nowiki>}</nowiki>, |

− | number = <nowiki>{</nowiki><nowiki>}</nowiki>, |
+ | number = <nowiki>{</nowiki>2<nowiki>}</nowiki>, |

− | pages = <nowiki>{</nowiki><nowiki>}</nowiki>, |
+ | pages = <nowiki>{</nowiki>131--150<nowiki>}</nowiki>, |

month = jan, |
month = jan, |
||

year = <nowiki>{</nowiki>2022<nowiki>}</nowiki>, |
year = <nowiki>{</nowiki>2022<nowiki>}</nowiki>, |

## Revision as of 14:44, 10 March 2022

- Authors
- Nicolas Boutry, Rocio Gonzalez-Diaz, Laurent Najman, Thierry Géraud
- Journal
- Journal of Mathematical Imaging and Vision
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2021-11-09

## Abstract

In this paper, we prove that when a -D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological -manifold, then it is digitally well-composed (DWC)which means that it does not contain any critical configuration. We prove this result thanks to local homology. This paper is the sequel of a previous paper where we proved that DWCness does not imply CWCness in 4D.

## Documents

## Bibtex (lrde.bib)

@Article{ boutry.22.jmiv, author = {Nicolas Boutry and Rocio Gonzalez-Diaz and Laurent Najman and Thierry G\'eraud}, title = {Continuous Well-Composedness implies Digital Well-Composedness in $n$-D}, journal = {Journal of Mathematical Imaging and Vision}, volume = {64}, number = {2}, pages = {131--150}, month = jan, year = {2022}, abstract = {In this paper, we prove that when a $n$-D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological $(n-1)$-manifold, then it is digitally well-composed (DWC), which means that it does not contain any critical configuration. We prove this result thanks to local homology. This paper is the sequel of a previous paper where we proved that DWCness does not imply CWCness in 4D.}, doi = {10.1007/s10851-021-01058-8} }