Discrete Frontiers

  • Xavier Daragon
  • Michel Couprie
  • Gilles Bertrand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

Many applications require to extract the surface of an object from a discrete set of valued points, applications in which the topological soundness of the obtained surface is, in many case, of the utmost importance. In this paper, we introduce the notion of frontier order which provides a discrete framework for defining frontiers of arbitrary objects. A major result we obtained is a theorem which guarantees the topological soundness of such frontiers in any dimension. Furthermore, we show how frontier orders can be used to design topologically coherent ”Marching Cubes-like” algorithms.

Keywords

Binary Relation Simplicial Complex Unit Cube Discrete Surface Face Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Xavier Daragon
    • 1
  • Michel Couprie
    • 1
  • Gilles Bertrand
    • 1
  1. 1.Laboratoire A2SIÉcole Supérieure d’Ingénieurs en Électrotechnique et ÉlectroniqueNoisy le Grand CEDEXFrance

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