I present new methods for computing persistent homology for multidimensional image data. These methods are tailored for efficient handling of large -- counted in billions of voxels and beyond -- images, such as those produced by modern MicroCT scanners. First, a brief review of existing methods will be given, then new techniques will be described, including a parallel, streaming implementation. Finally, to describe limitations of current methods, we discuss worst-case bounds for topological complicatedness of images.

This presentation is part of Minisymposium “MS16 - Topological Image Analysis: Methods, Algorithms, Applications (3 parts)”
organized by: Patrizio Frosini (University of Bologna) , Massimo Ferri (University of Bologna) , Claudia Landi (University of Modena and Reggio Emilia) .

Authors:

Hubert Wagner (IST Austria)

Keywords:

algorithms, computational topology, discrete morse theory, image representation, persistent homology, streaming algorithms