Border operator for generalized maps

Authors:
Sylvie Alayrangues;Samuel Peltier;Guillaume Damiand;Pascal Lienhardt
Affiliations:
XLIM-SIC, Université de Poitiers, CNRS, Futuroscope Chasseneuil Cedex, France;XLIM-SIC, Université de Poitiers, CNRS, Futuroscope Chasseneuil Cedex, France;Université de Lyon, CNRS, LIRIS, UMR, France;XLIM-SIC, Université de Poitiers, CNRS, Futuroscope Chasseneuil Cedex, France
Venue:
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Year:
2009

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Abstract

In this paper, we define a border operator for generalized maps, a data structure for representing cellular quasi-manifolds. The interest of this work lies in the optimization of homology computation, by using a model with less cells than models in which cells are regular ones as tetrahedra and cubes. For instance, generalized maps have been used for representing segmented images. We first define a face operator to retrieve the faces of any cell, then deduce the border operator and prove that it satisfies the required property : border of border is void. At last, we study the links between the cellular homology defined from our border operator and the classical simplicial homology.