Border operator for generalized maps

Sylvie Alayrangues (1) , Samuel Peltier (1) , Guillaume Damiand (2) , Pascal Lienhardt (1)

1 SIC
2 M2DisCo - Geometry Processing and Constrained Optimization

In this paper, we define a border operator for the 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.

Keywords: Border operation; Generalized maps; Cellular homology.

Domains: Modeling and Simulation

Sylvie Alayrangues, Samuel Peltier, Guillaume Damiand, Pascal Lienhardt. Border operator for generalized maps. 15th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI 2009), Sep 2009, Montreal, Canada. pp.300-312, ⟨10.1007/978-3-642-04397-0_26⟩. ⟨hal-00437746⟩