Detection of the Discrete Convexity of Polyominoes
Identifieur interne : 001C20 ( Hal/Curation ); précédent : 001C19; suivant : 001C21Detection of the Discrete Convexity of Polyominoes
Auteurs : Isabelle Debled-Rennesson [France] ; Jean-Luc Rémy [France] ; Jocelyne Rouyer-Degli [France]Source :
Abstract
The convexity of a discrete region is a property used in numerous domains of computational imagery. We study its detection iu 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 algorithm whose correctness is proven. Correlatively, we obtain a characterisation of lower and upper convex hulls of a discrete line segment. Finally, we evoke some applications of these results to the problem of discrete tomography.
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<front><div type="abstract" xml:lang="en">The convexity of a discrete region is a property used in numerous domains of computational imagery. We study its detection iu 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 algorithm whose correctness is proven. Correlatively, we obtain a characterisation of lower and upper convex hulls of a discrete line segment. Finally, we evoke some applications of these results to the problem of discrete tomography.</div>
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