Weakly Well-Composed Cell Complexes over nD Pictures

From LRDE

Abstract

In previous work we proposed a combinatorial algorithm to “locally repair” the cubical complex that is canonically associated with a given 3D picture I. The algorithm constructs a 3D polyhedral complex which is homotopy equivalent to and whose boundary surface is a 2D manifold. A polyhedral complex satisfying these properties is called well-composed. In the present paper we extend these results to higher dimensions. We prove that for a given -dimensional picture the obtained cell complex is well-composed in a weaker sense but is still homotopy equivalent to the initial cubical complex.

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Bibtex (lrde.bib)

@Article{	  boutry.18.is,
  author	= {Nicolas Boutry and Rocio Gonzalez-Diaz and Maria-Jose
		  Jimenez},
  title		= {Weakly Well-Composed Cell Complexes over {$n$D} Pictures},
  journal	= {Information Sciences},
  volume	= {499},
  pages		= {62--83},
  month		= oct,
  year		= {2019},
  abstract	= {In previous work we proposed a combinatorial algorithm to
		  ``locally repair'' the cubical complex $Q(I)$ that is
		  canonically associated with a given 3D picture I. The
		  algorithm constructs a 3D polyhedral complex $P(I)$ which
		  is homotopy equivalent to $Q(I)$ and whose boundary surface
		  is a 2D manifold. A polyhedral complex satisfying these
		  properties is called {\it well-composed}. In the present
		  paper we extend these results to higher dimensions. We
		  prove that for a given $n$-dimensional picture the obtained
		  cell complex is well-composed in a weaker sense but is
		  still homotopy equivalent to the initial cubical complex.}
}