Duality in Persistent Homology of Images

Abstract

We derive the relationship between the persistent homology barcodes of two dual filtered CW complexes. Applied to greyscale digital images, we obtain an algorithm to convert barcodes between the two different (dual) topological models of pixel connectivity.

This is an extended abstract for the SoCG Young Researchers Forum 2020

Cited by in corpus (2)

• Cubical Ripser: Software for computing persistent homology of image and volume data
• U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology