Continuous Well-Composedness implies Digital Well-Composedness in n-D

From LRDE

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.

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Bibtex (lrde.bib)

@Article{	  boutry.21.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	= {},
  number	= {},
  pages		= {},
  month		= {},
  year		= {2021},
  doi		= {},
  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.}
}