Duality in Persistent Homology of Images
arXiv:2005.04597v216 citations
AI Analysis
This addresses a theoretical and computational issue in topological data analysis for image processing, but it appears incremental as it builds on existing duality concepts.
The paper tackled the problem of relating persistent homology barcodes for dual filtered CW complexes, resulting in an algorithm that converts barcodes between dual topological models for greyscale digital images.
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.