# Border Map: A Topological Representation for $n$D Image Analysis

Abstract : This article presents an algorithm computing a border map of an image that generalizes to the n dimension graph structures used in image analysis. Such a map represents simple and multiple adjacencies, inclusion of regions, as well as the frontier type between two adjacent regions. An algorithm computing a border map, linear to the number of elements of an image, is defined in 2D, then generalized in 3D and in nD.
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Cited literature [15 references]

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01168382
Contributor : Christophe Fiorio <>
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Yves Bertrand, Christophe Fiorio, Yann Pennaneach. Border Map: A Topological Representation for $n$D Image Analysis. DGCI: Discrete Geometry for Computer Imagery, Mar 1999, Marne-la-Vallée, France. pp.242-257, ⟨10.1007/3-540-49126-0_19⟩. ⟨lirmm-01168382⟩

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