Effective persistent homology of digital images

TL;DR

This paper introduces algorithms combining effective homology, persistent homology, and discrete vector fields for digital image processing, implemented in Kenzo, demonstrating good performance on real images from public datasets.

Contribution

It presents a novel integration of three computational topology methods into algorithms for digital image analysis, implemented in the Kenzo system.

Findings

Algorithms perform well on actual images

Effective homology enhances digital image processing

Implementation in Kenzo system proves practical

Abstract

In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been implemented as extensions of the Kenzo system and have shown a good performance when applied on some actual images extracted from a public dataset.