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Sparse cubical complexes for efficient topology-preservation in image data — arXiv:2609.37177

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.37177
License (as archived): CC0-1.0
Archived: 2026-10-07T17:32:48.258Z
SHA-256 of the archived text: 5cd2fe75e05617d98acd04f325a38828892adcf26f6b4dfc8547a295a37777a5
Stable URL of this page: https://metraipolis.com/documento/dc_137faf2cdcaf

How to cite

Sparse cubical complexes for efficient topology-preservation in image data — arXiv:2609.37177 — arXiv (en), https://arxiv.org/abs/2609.37177 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_137faf2cdcaf (Metraipolis archive dc_137faf2cdcaf, sha256 5cd2fe75e05617d98acd04f325a38828892adcf26f6b4dfc8547a295a37777a5)

BibTeX

@misc{dc137faf2cdcaf,
  title = {Sparse cubical complexes for efficient topology-preservation in image data — arXiv:2609.37177},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.37177},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_137faf2cdcaf; sha256 5cd2fe75e05617d98acd04f325a38828892adcf26f6b4dfc8547a295a37777a5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.37177. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segmentation, where preservation of topological structures is important. However, despite its general applicability across dimensionality, domains, and target structures, the runtime cost of PH-based methods often makes their practical use infeasible. In this work, we argue that this runtime cost is largely driven by processing information that is unimportant for downstream application (e.g. as optimization objective). We propose sparse cubical filtrations as an alternative foundation for PH computation, reducing subsequent computational costs by factors of up to 100 on real datasets. We show close agreement with the optimization signal of the dense counterpart and empirically evaluate our solution's effectiveness as an optimization objective in realistic training regimes where other PH-based objectives can practically not operate (i.e., 3D data with large patch sizes). We show how our solution improves topological accuracy by up to 80\% across six diverse datasets while maintaining pixel- and region-based accuracy.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-30 in cs.LG).
Categorie arXiv: Computer Vision and Pattern Recognition (cs.CV) ; Computational Geometry (cs.CG); Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.37177 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T16:59:48.527Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).