# Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables

arXiv: https://arxiv.org/abs/2606.04801 · HTML: https://mlsanity.com/paper/2606.04801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [Cubical Ripser: Software for computing persistent homology of image and volume data](https://mlsanity.com/paper/2005.12692/) (2020)
- [Duality in Persistent Homology of Images](https://mlsanity.com/paper/2005.04597/) (2020)

## Built on by (most cited first, 1 of 1)

- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

We present Flash Cubical, a highly efficient computation of cubical persistence on a V-filtration for 2D and 3D images over mathbbF2. The implementation is built around three core ideas. First, cubical complexes satisfy properties that allow for the computation of persistence of the highest dimension via union-find and duality. Second, pruning of certain edges allows for a fast and efficient implementation of union-find. Third, the use of a lookup table, which exploits the regularity of cubical complexes to pre-compute local information. This avoids the need to compute local information at run time. To the best of our knowledge, this is the most efficient implementation of cubical persistence with a V-filtration, both in terms of time and memory costs. Although the paper focuses on persistence for V-filtration cubical complexes, the underlying ideas generalise naturally to T-filtrations on cubical complexes and suggest promising directions for other complexes.