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), 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.
 
| 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.
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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 12:54, 13 February 2022

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}
}