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Detection of the Discrete Convexity of Polyominoes

  • Isabelle Debled-Rennesson
  • Jean-Luc Rémy 
  • Jocelyne Rouyer-Degli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

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 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.

Keywords

Discrete Convexity Segmentation Discrete line Polyominoes Discrete tomography 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Isabelle Debled-Rennesson
    • 1
  • Jean-Luc Rémy 
    • 2
  • Jocelyne Rouyer-Degli
    • 3
  1. 1.LORIA - Laboratoire LOrrain de Recherche en Informatique et ses Applications InstitutUniversitaire de Formation des Maîtres de Lorraine Campus ScientifiqueVandœuvre-lès-Nancy
  2. 2.LORIACentre National de la Recherche Scientifique Campus ScientifiqueVandœuvre-lès-Nancy
  3. 3.LORIAUniversité Henri Poincaré, Nancy 1 Campus ScientifiqueVandœuvre-lès-Nancy

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