Polyhedral Representation and Adjacency Graph in n-dimensional Digital Images |
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Authors: | Mohammed Khachan Patrick Chenin Hafsa Deddi |
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Affiliation: | Dépatement Informatique, Université de Poitiers, Laboratoire IRCOM-SIC, Boulevard 3-Teleport 2, BP 179, Futuroscope Cedex, 86960, Francef1;Laboratoire de Modélisation et Calcul, LMC-IMAG, 51, rue des Mathématiques, Grenoble, France, f2;Department of Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4, Canada, f3 |
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Abstract: | In this paper we generalize the concept of digital topology to arbitrary dimension n, in the context of (2n, 3n−1)-adjacency. We define an n-digital image
as an uplet (
n,
, H), where H is a finite subset of
n and
represents the adjacency relation in the whole lattice in a specific way. We give a natural and simple construction of polyhedral representation of
based on cubical-complex decomposition. We develop general properties which provide a link between connectivity in digital and Euclidean space. This enables us to use methods of continuous topology in studying properties related to the connectivity, adjacency graph, and borders connectivity in n-digital images. |
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Keywords: | Abbreviations: digital topologyAbbreviations: cubical-complexAbbreviations: sciencedirect
-polyhedronAbbreviations: adjacency graphAbbreviations: border connectivity" target="_blank">com/cache/MiamiImageURL/B6WCX-45FBSGV-S-2/0?wchp=dGLzVzb-zSkWz" alt="Image" title="Image" style="vertical-align:bottom" border="0" height=13 width="13"/>
-polyhedronAbbreviations: adjacency graphAbbreviations: border connectivity |
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