Computing Homology Group Generators of Images Using Irregular Graph Pyramids

  • Samuel Peltier
  • Adrian Ion
  • Yll Haxhimusa
  • Walter G. Kropatsch
  • Guillaume Damiand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4538)


We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built, by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small, and a top down process is then used to deduce homology generators in any level of the pyramid, including the base level i.e. the initial image. We show that the new method produces valid homology generators and present some experimental results.


Homology Generator Homology Group Initial Image Dual Graph Smith Normal Form 
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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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Samuel Peltier
    • 1
  • Adrian Ion
    • 1
  • Yll Haxhimusa
    • 1
  • Walter G. Kropatsch
    • 1
  • Guillaume Damiand
    • 2
  1. 1.Vienna University of Technology, Faculty of Informatics, Pattern Recognition and Image Processing GroupAustria
  2. 2.University of Poitiers, SIC, FRE CNRS 2731France

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