Digitization of Partitions and Tessellations

Jean Serra; Bangalore Ravi Kiran

doi:10.1007/978-3-319-32360-2_25

Digitization of Partitions and Tessellations

Jean Serra ¹ Bangalore Ravi Kiran ²

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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 spaces our approach rests on tessellations whose classes are R-open sets. In the discrete case, the passage from partitions to tessellations is expressed by the 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 Z^2 and the centered cubic grid in 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

Type de document :

Communication dans un congrès

9th IAPR International Conference, DGCI 2016, Apr 2016, Nantes, France. Springer International Publishing, Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science ( 9647), pp.323-334, 2016, 〈dgci2016.univ-nantes.fr/page/program〉. 〈10.1007/978-3-319-32360-2_25〉

Domaine :

Informatique [cs] / Traitement des images

Informatique [cs] / Mathématique discrète [cs.DM]

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https://hal.archives-ouvertes.fr/hal-01306414
Contributeur : Bangalore Ravi Kiran <>
Soumis le : samedi 23 avril 2016 - 15:03:00
Dernière modification le : lundi 12 novembre 2018 - 10:59:58

Digitization of Partitions and Tessellations

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Digitization of Partitions and Tessellations

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