Computing Homology for Surfaces with Generalized Maps: Application to 3D Images

  • Guillaume Damiand
  • Samuel Peltier
  • Laurent Fuchs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4292)

Abstract

In this paper, we present an algorithm which allows to compute efficiently generators of the first homology group of a closed surface, orientable or not. Starting with an initial subdivision of a surface, we simplify it to its minimal form (minimal refers to the number of cells), while preserving its homology. Homology generators can thus be directly deduced from the minimal representation of the initial surface. Finally, we show how this algorithm can be used in a 3D labelled image in order to compute homology of each region described by its boundary.

Keywords

topological features homology generators generalized maps minimal subdivision 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Guillaume Damiand
    • 1
  • Samuel Peltier
    • 2
  • Laurent Fuchs
    • 1
  1. 1.SIC – bât. SP2MIFrance
  2. 2.PRIPVienna University of TechnologyViennaAustria

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