Cubical Ripser: Software for computing persistent homology of image and volume data

TL;DR

Cubical Ripser is a highly efficient open-source software tool designed for computing persistent homology of image and volume data, combining topological analysis with neural networks for advanced image analysis.

Contribution

We present Cubical Ripser, the fastest and most memory-efficient software for persistent homology of weighted cubical complexes, with an application to image analysis integrating neural networks.

Findings

Cubical Ripser outperforms existing tools in speed and memory efficiency.

Successful integration of persistent homology with convolutional neural networks.

Open-source implementation available online.

Abstract

We introduce Cubical Ripser for computing persistent homology of image and volume data (more precisely, weighted cubical complexes). To our best knowledge, Cubical Ripser is currently the fastest and the most memory-efficient program for computing persistent homology of weighted cubical complexes. We demonstrate our software with an example of image analysis in which persistent homology and convolutional neural networks are successfully combined. Our open-source implementation is available online.