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Local Configurations of Digital Hyperplanes

  • Yan Gérard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

The aim of this article is to provide some arithmetical tools in order to study the local properties of digital hyperplanes.

With the help of the new general notion of configuration, we investigate the arrangement of the different combinatorial structures contained in a digital hyperplane. The regularity of this deployment is controlled by two arithmetical functions that we call code (I) and boundary (I) . By using these two simple tools, we prove that the local configurations in a functional digital hyperplane only depends on its normal vector and that their number is less than the size of the chosen neighborhood.

Keywords

windows local configurations digital hyperplanes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Yan Gérard
    • 1
  1. 1.Laboratoire de Logique et d’Informatique de Clermont1 (LLAIC1) IUT, Département d’InformatiqueEnsemble Universitaire des CézeauxAubière CedexFrance

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