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Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology

  • Rocio Gonzalez-Diaz
  • Adrian Ion
  • Maria Jose Jimenez
  • Regina Poyatos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6854)

Abstract

In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one for computing persistent homology [6,14,15]. We also present a decremental algorithm for computing AT-models that allows to extend the persistence computation to a wider setting. Finally, we show how to combine incremental and decremental techniques for persistent homology computation.

Keywords

Persistent homology AT-model for computing homology cell complex 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rocio Gonzalez-Diaz
    • 1
  • Adrian Ion
    • 2
    • 3
  • Maria Jose Jimenez
    • 1
  • Regina Poyatos
    • 1
  1. 1.Applied Math Dep. (I), School of Computer EngineeringUniversity of SevilleSpain
  2. 2.Pattern Recognition and Image Processing GroupVienna University of TechnologyAustria
  3. 3.Institute of Science and TechnologyAustria

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