Weakly Well-Composed Cell Complexes over nD Pictures
From LRDE
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- Authors
- Nicolas Boutry, Rocio Gonzalez-Diaz, Maria-Jose Jimenez
- Journal
- Information Sciences
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2018-07-04
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.
Documents
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}, doi = {10.1016/j.ins.2018.06.005}, 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.} }