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Hausdorff Discretization and Its Comparison to Other Discretization Schemes

  • Mohamed Tajine
  • Christian Ronse
  • Daniel Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

We study the problem of discretization in a Hausdorff space followed in [WTR 98]. We recall the definitions and properties of the Hausdorff discretization of a compact set. We also study the relationship between the covering discretizations and the Hausdorff discretization. For a cellular metric every covering discretization minimizes the Hausdorff distance, and conversely, if the supercover discretization minimizes the Hausdorff distance then the metric is cellular. The supercover discretization is the Hausdorff discretization if the metric is proportional to d . We compare also the Hausdorff discretization and the Bresenham discretization [Bre 65]. Actually, the Bresenham discretization of a segment of 2 is not always a good discretization relatively to a Hausdorff metric.

Keywords

Bresenham discretization cellular metric Hausdorff metric lattice covering discretization Hausdorff discretization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Mohamed Tajine
    • 1
  • Christian Ronse
    • 1
  • Daniel Wagner
    • 1
  1. 1.(Laboratoire des Sciences de l’Image, d’Informatique et de Télédétection) Dépt. InformatiqueLSIIT UPRES-A ULP-CNRS 7005Strasbourg cedexFrance

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