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.
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Alayrangues, S., Peltier, S., Damiand, G., Lienhardt, P. (2009). Border Operator for Generalized Maps. In: Brlek, S., Reutenauer, C., Provençal, X. (eds) Discrete Geometry for Computer Imagery. DGCI 2009. Lecture Notes in Computer Science, vol 5810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04397-0_26
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DOI: https://doi.org/10.1007/978-3-642-04397-0_26
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