Efficient computation of persistent homology for cubical data

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