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Duality in Persistent Homology of Images

arXiv 2005.04597 ↗First posted 10 May 2020math.AT cs.CG cs.CVcited by 7

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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.

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

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 0; 2024: 2; 2025: 0; 2026: 1.

7 papers.

  1. 2022Topologically faithful image segmentation via induced matching of persistence barcodescited by 48
  2. 2021A persistent homology-based topological loss for CNN-based multi-class segmentation of CMRcited by 21
  3. 2022Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmarkcited by 11
  4. 2021Persistent Homology with Improved Locality Information for more Effective Delineationcited by 10
  5. 2024Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homologycited by 7
  6. 2024Train-Free Segmentation in MRI with Cubical Persistent Homologycited by 1
  7. 2026Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tablescited by 1