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Detection of the Discrete Convexity of Polyominoes

Isabelle Debled-Rennesson 1 Jean-Luc Rémy 1 Jocelyne Rouyer-Degli 1
1 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The convexity of a discrete region is a property used in numerous domains of computational imagery. We study its detection in the particular case of polyominoes. We present a first method, directly relying on its definition. A second method, which is based on techniques for segmentation of curves in discrete lines, leads to a very simple, linear algorithm, whose correction is proven. Correlatively, we obtain a characterisation of lower and upper frontiers of the convex hull of a discrete line segment. Finally, we evoke some applications of these results to the problem of discrete tomography.
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Submitted on : Tuesday, September 26, 2006 - 9:37:57 AM
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  • HAL Id : inria-00099507, version 1



Isabelle Debled-Rennesson, Jean-Luc Rémy, Jocelyne Rouyer-Degli. Detection of the Discrete Convexity of Polyominoes. Discrete Applied Mathematics, Elsevier, 2003, 125 (1), pp.115-133. ⟨inria-00099507⟩



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