# Difference between revisions of "Publications/boutry.20.iwcia2"

### From LRDE

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| publisher = Springer |
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− | | abstract = In this paper, we prove that the two flavours of well-composedness called Continuous Well-Composedness (shortly CWCness), stating that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical |
+ | | abstract = In this paper, we prove that the two flavours of well-composedness called Continuous Well-Composedness (shortly CWCness), stating that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical configurationare not equivalent in dimension 4. To prove this, we exhibit the example of a configuration of 8 tesseracts (4D cubes) sharing a common corner (vertex), which is DWC but not CWC. This result is surprising since we know that CWCness and DWCness are equivalent in 2D and 3D. To reach our goal, we use local homology. |

| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.20.iwcia2.pdf |
| lrdepaper = http://www.lrde.epita.fr/dload/papers/boutry.20.iwcia2.pdf |
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| lrdeprojects = Olena |
| lrdeprojects = Olena |

## Revision as of 18:20, 9 November 2020

- Authors
- Nicolas Boutry, Rocio Gonzalez-Diaz, Laurent Najman, Thierry Géraud
- Where
- Combinatorial Image Analysis: Proceedings of the 20th International Workshop, IWCIA 2020, Novi Sad, Serbia, July 16–18, 2020
- Type
- inproceedings
- Publisher
- Springer
- Projects
- Olena
- Date
- 2020-07-21

## Abstract

In this paper, we prove that the two flavours of well-composedness called Continuous Well-Composedness (shortly CWCness), stating that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical configurationare not equivalent in dimension 4. To prove this, we exhibit the example of a configuration of 8 tesseracts (4D cubes) sharing a common corner (vertex), which is DWC but not CWC. This result is surprising since we know that CWCness and DWCness are equivalent in 2D and 3D. To reach our goal, we use local homology.

## Documents

## Bibtex (lrde.bib)

@InProceedings{ boutry.20.iwcia2, author = {Nicolas Boutry and Rocio Gonzalez-Diaz and Laurent Najman and Thierry G\'eraud}, title = {A {4D} Counter-Example Showing that {DWCness} Does Not Imply {CWCness} in $n$-{D}}, booktitle = {Combinatorial Image Analysis: Proceedings of the 20th International Workshop, IWCIA 2020, Novi Sad, Serbia, July 16--18, 2020}, year = 2020, editor = {T. Lukic and R. P. Barneva and V. Brimkov and L. Comic and N. Sladoje}, volume = {12148}, series = {Lecture Notes in Computer Science}, pages = {73--87}, publisher = {Springer}, abstract = {In this paper, we prove that the two flavours of well-composedness called Continuous Well-Composedness (shortly CWCness), stating that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical configuration, are not equivalent in dimension 4. To prove this, we exhibit the example of a configuration of 8 tesseracts (4D cubes) sharing a common corner (vertex), which is DWC but not CWC. This result is surprising since we know that CWCness and DWCness are equivalent in 2D and 3D. To reach our goal, we use local homology.} }