# Duality in Persistent Homology of Images

arXiv: https://arxiv.org/abs/2005.04597 · HTML: https://mlsanity.com/paper/2005.04597/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2020.

## Built on by (most cited first, 7 of 7)

- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark](https://mlsanity.com/paper/2206.13932/) (2022)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology](https://mlsanity.com/paper/2407.04683/) (2024)
- [Train-Free Segmentation in MRI with Cubical Persistent Homology](https://mlsanity.com/paper/2401.01160/) (2024)
- [Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables](https://mlsanity.com/paper/2606.04801/) (2026)

## Abstract (arXiv)

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.