Multiscale Discrete Geometry

  • Mouhammad Said
  • Jacques-Olivier Lachaud
  • Fabien Feschet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


This paper presents a first step in analyzing how digital shapes behave with respect to multiresolution. We first present an analysis of the covering of a standard digital straight line by a multi-resolution grid. We then study the multi-resolution of Digital Straight Segments (DSS): we provide a sublinear algorithm computing the exact characteristics of a DSS whenever it is a subset of a known standard line. We finally deduce an algorithm for computing a multiscale representation of a digital shape, based only on a DSS decomposition of its boundary.


multiscale geometry digital contours standard lines digital straight segment recognition Stern-Brocot tree multi-resolution 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mouhammad Said
    • 1
    • 2
  • Jacques-Olivier Lachaud
    • 1
  • Fabien Feschet
    • 2
  1. 1.Laboratoire de MathématiquesUMR 5127 CNRS, Université de SavoieLe Bourget du LacFrance
  2. 2.LAICUniv. Clermont-Ferrand, IUTAubière CedexFrance

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