[Zurück]

H. Wagner, C. Chen, E. Vucini:
"Efficient computation of persistent homology for cubical data";
Vortrag: 4th Workshop on Topology-based Methods in Data Analysis and Visualization (TopoInVis 2011), Zürich, Schweiz; 04.04.2011 - 06.04.2011; in: "Proceedings of the 4th Workshop on Topology-based Methods in Data Analysis and Visualization (TopoInVis 2011)", (2011), S. 1 - 14.

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.

http://publik.tuwien.ac.at/files/PubDat_202404.pdf