{"ID":3050065,"CreatedAt":"2026-06-04T02:13:16.786527022Z","UpdatedAt":"2026-06-06T11:59:53.540122282Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04801","arxiv_id":"2606.04801","title":"Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables","abstract":"We present Flash Cubical, a highly efficient computation of cubical persistence on a V-filtration for 2D and 3D images over $\\mathbb{F}_2$. 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.","short_abstract":"We present Flash Cubical, a highly efficient computation of cubical persistence on a V-filtration for 2D and 3D images over $\\mathbb{F}_2$. 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-fi...","url_abs":"https://arxiv.org/abs/2606.04801","url_pdf":"https://arxiv.org/pdf/2606.04801v1","authors":"[\"Titouan Le Breton\",\"Karol Szustakowski\",\"Marie Piraud\"]","published":"2026-06-03T12:26:52Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[]","has_code":false}