Efficient Computation of Persistent Homology for Cubical Data

  • Hubert WagnerEmail author
  • Chao Chen
  • Erald Vuçini
Part of the Mathematics and Visualization book series (MATHVISUAL)


In this paper we present an efficient framework for computation of persistent homology of cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is adapted to the setting of cubical complexes. The proposed approach enables efficient application of persistent homology in domains where the data is naturally given in a cubical form. By avoiding triangulation of the data, we significantly reduce the size of the complex. We also present a data-structure designed to compactly store and quickly manipulate cubical complexes. By means of numerical experiments, we show high speed and memory efficiency of our approach. We compare our framework to other available implementations, showing its superiority. Finally, we report performance on selected 3D and 4D data-sets.


Simplicial Complex Homology Class Cubical Data Cubical Complex Boundary Matrix 
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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This work was supported by the Austrian Science Fund (FWF) grant no. P20134-N13 and the Austrian COMET program. The first author is also supported by the Foundation for Polish Science IPP Programme “Geometry and Topology in Physical Models,” co-financed by the EU European Regional Development Fund, Operational Program Innovative Economy 2007–2013.

The authors would like to thank Prof. Herbert Edelsbrunner and Dr. Michael Kerber for fruitful discussions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Jagiellonian UniversityKrakówPoland
  2. 2.Vienna University of TechnologyViennaAustria
  3. 3.Institute of Science and TechnologyKlosterneuburgAustria
  4. 4.VRVis Center for Virtual Reality and Visualization Research-LtdViennaAustria

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