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.
https://hal.archives-ouvertes.fr/hal-01306414
Contributor : Bangalore Ravi Kiran
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Submitted on : Saturday, April 23, 2016 - 3:03:00 PM
Last modification on : Monday, November 12, 2018 - 10:59:58 AM
Jean Serra, Bangalore Ravi Kiran. Digitization of Partitions and Tessellations. 9th IAPR International Conference, DGCI 2016, Université Nantes, Apr 2016, Nantes, France. pp.323-334, ⟨10.1007/978-3-319-32360-2_25⟩. ⟨hal-01306414⟩
