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Published in:
2020 | OriginalPaper | Chapter
Euler Well-Composedness
Authors : Nicolas Boutry, Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Eduardo Paluzo-Hildago
Published in: Combinatorial Image Analysis
Publisher: Springer International Publishing
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Abstract
In this paper, we define a new flavour of well-composedness, called Euler well-composedness, in the general setting of regular cell complexes: A regular cell complex is Euler well-composed if the Euler characteristic of the link of each boundary vertex is 1. A cell decomposition of a picture I is a pair of regular cell complexes \(\big (K(I),K(\bar{I})\big )\) such that K(I) (resp. \(K(\bar{I})\)) is a topological and geometrical model representing I (resp. its complementary, \(\bar{I}\)). Then, a cell decomposition of a picture I is self-dual Euler well-composed if both K(I) and \(K(\bar{I})\) are Euler well-composed. We prove in this paper that, first, self-dual Euler well-composedness is equivalent to digital well-composedness in dimension 2 and 3, and second, in dimension 4, self-dual Euler well-composedness implies digital well-composedness, though the converse is not true.