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Convexity-Preserving Rigid Motions of 2D Digital Objects

  • Phuc Ngo
  • Yukiko Kenmochi
  • Isabelle Debled-Rennesson
  • Nicolas Passat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10502)

Abstract

Rigid motions on \(\mathbb {R}^2\) are isometric and thus preserve the geometry and topology of objects. However, this important property is generally lost when considering digital objects defined on \(\mathbb {Z}^2\), due to the digitization process from \(\mathbb {R}^2\) to \(\mathbb {Z}^2\). In this article, we focus on the convexity property of digital objects, and propose an approach for rigid motions of digital objects which preserves this convexity. The method is extended to non-convex objects, based on the concavity tree representation.

Keywords

Digital rigid motion Digital convexity Half-plane representation Concavity tree Quasi-regularity 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Phuc Ngo
    • 1
  • Yukiko Kenmochi
    • 2
  • Isabelle Debled-Rennesson
    • 1
  • Nicolas Passat
    • 3
  1. 1.Université de Lorraine, LORIA, UMR, 7503Villers-lès-NancyFrance
  2. 2.Université Paris-Est, LIGM, CNRSParisFrance
  3. 3.Université de Reims Champagne-Ardenne, CReSTICReimsFrance

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