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Digitization of Partitions and Tessellations

  • Jean Serra
  • B. Ravi Kiran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9647)

Abstract

We study hierarchies of partitions in a topological space where the interiors of the classes and their frontiers are simultaneously represented. In both continuous and discrete cases our approach rests on tessellations whose classes are \(\mathcal {R}\)-open sets. In the discrete case, the passage from partitions to tessellations is expressed by Alexandrov topology and yields double resolutions. A new topology is proposed to remove the ambiguities of the diagonal configurations. It leads to the triangular grid in \(\mathbb {Z}^{2}\) and the centered cubic grid in \(\mathbb {Z}^{3}\), which are the only translation invariant grids which preserve connectivity and permit the use of saliency functions.

Keywords

Tessellations Regular sets Hierarchies Khalimsky topology Simplicial complexes 3-D grids 

Notes

Acknowledgment

The authors acknowledge G. Bertrand J. Cousty and T. Geraud for their useful comments, and the two reviewers for their pertinent remarks.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.A3SI-ESIEE LIGMUniversité Paris-EstNoisy-le-GrandFrance
  2. 2.Center de Robotique, MINES ParisTechPSL-Research UniversityParisFrance

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