Chapter

Topological Methods in Data Analysis and Visualization II

Part of the series Mathematics and Visualization pp 91-106

Date:

Efficient Computation of Persistent Homology for Cubical Data

  • Hubert WagnerAffiliated withJagiellonian UniversityVienna University of Technology Email author 
  • , Chao ChenAffiliated withInstitute of Science and TechnologyVienna University of Technology
  • , Erald VuçiniAffiliated withVRVis Center for Virtual Reality and Visualization Research-LtdVienna University of Technology

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Abstract

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.