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Convexity Preserving Contraction of Digital Sets

  • Lama TarsissiEmail author
  • David Coeurjolly
  • Yukiko Kenmochi
  • Pascal Romon
Conference paper
  • 90 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12047)

Abstract

Convexity is one of the useful geometric properties of digital sets in digital image processing. There are various applications which require deforming digital convex sets while preserving their convexity. In this article, we consider the contraction of such digital sets by removing digital points one by one. For this aim, we use some tools of combinatorics on words to detect a set of removable points and to define such convexity-preserving contraction of a digital set as an operation of re-writing its boundary word. In order to chose one of removable points for each contraction step, we present three geometrical strategies, which are related to vertex angle and area changes. We also show experimental results of applying the methods to repair some non-convex digital sets, which are obtained by rotations of convex digital sets.

Keywords

Digital convexity Digital set contraction Christoffel words Lyndon words 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Lama Tarsissi
    • 1
    • 2
    Email author
  • David Coeurjolly
    • 3
  • Yukiko Kenmochi
    • 1
  • Pascal Romon
    • 2
  1. 1.LIGM, Université Gustave Eiffel, CNRS, ESIEE ParisMarne-la-valléeFrance
  2. 2.LAMA, Université Gustave Eiffel, CNRSMarne-la-valléeFrance
  3. 3.Université de Lyon, CNRS, LIRISLyonFrance

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