Combinatorial View of Digital Convexity

  • Srečko Brlek
  • Jacques-Olivier Lachaud
  • X. Provençal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)


The notion of convexity translates non-trivially from Euclidean geometry to discrete geometry, and detecting if a discrete region of the plane is convex requires analysis. In this paper we study digital convexity from the combinatorics on words point of view, and provide a fast optimal algorithm checking digital convexity of polyominoes coded by the contour word. The result is based on the Lyndon factorization of the contour word, and the recognition of Christoffel factors that are approximations of digital lines.


Digital Convexity Lyndon words Christoffel words 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Srečko Brlek
    • 1
  • Jacques-Olivier Lachaud
    • 2
  • X. Provençal
    • 1
  1. 1.Laboratoire de Combinatoire et d’Informatique MathématiqueUniversité du Québec à MontréalMontréalCanada
  2. 2.Laboratoire de Mathématiques, UMR 5127 CNRSUniversité de SavoieLe Bourget du LacFrance

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