Local Configurations of Digital Hyperplanes

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


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.


windows local configurations digital hyperplanes 


  1. CV97.
    J.M. Chassery & J. Vittone, Coexistence of Tricubes in Digital Naive Plane. 7th Conference on Discrete Geometry in Computer Imagery, Montpellier1997.Google Scholar
  2. D95.
    I. Debled-Renesson, Étude et reconnaissance des droites et plans discrets. Thèse de doctorat soutenue à l’Université Louis Pasteur de Strasbourg, 1995.Google Scholar
  3. F96.
    J. Françon, Sur la topologie d’un plan arithmétique. Theorical Computer Sciences 156, 1996.Google Scholar
  4. FST96.
    J. Françon, J.M. Schramm & M. Tajine, Recognizing arithmetic straight lines and planes. 6th Conference on Discrete Geometry in Computer Imagery, Lyon, 1996.Google Scholar
  5. R91.
    J.P. Reveillés, Géométrie discréte, calcul en nombre entiers et algorithmique. Thèse de doctorat soutenue à l’;Université Louis Pasteur de Strasbourg, 1991.Google Scholar
  6. R95.
    J.P. Reveillés, Combinatorial pieces in digital lines and planes. Vision Geometry IV, vol 2573 SPIE 1995.Google Scholar
  7. RY97.
    J.P. Reveillés & J. Yaacoub, Maximum area triangle operator for edge detection. Journal of electronic imaging6(4), 406–414, 1997.CrossRefGoogle Scholar
  8. S97.
    J.M. Schramm, Coplanar Tricubes. 7th Conference on Discrete Geometry in Computer Imagery, Montpellier, 1997.Google Scholar
  9. V99.
    L. Vuillon, Local configurations in discrete planes. Bull. Belg. Math. Soc. to be published 1999.Google Scholar

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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