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

### From LRDE

Line 9: | Line 9: | ||

| pages = 131 to 150 |
| 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 |

## 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} }