Abstract
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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Berger, A. H., Fontana, M., Rueckert, D., Paetzold, J. C., Lux, L., & Bauer, U. (2026). Sparse cubical complexes for efficient topology-preservation in image data. https://omanscience.com/en/articles/sparse-cubical-complexes-for-efficient-topology-preservation-in-image-data
MLA 9
Berger, Alexander H., et al. "Sparse cubical complexes for efficient topology-preservation in image data." https://omanscience.com/en/articles/sparse-cubical-complexes-for-efficient-topology-preservation-in-image-data.
Chicago (author–date)
Berger, Alexander H., Marco Fontana, Daniel Rueckert, Johannes C. Paetzold, Laurin Lux, and Ulrich Bauer. 2026. "Sparse cubical complexes for efficient topology-preservation in image data." https://omanscience.com/en/articles/sparse-cubical-complexes-for-efficient-topology-preservation-in-image-data.
Harvard
Berger, A. H., Fontana, M., Rueckert, D., Paetzold, J. C., Lux, L. and Bauer, U. (2026) 'Sparse cubical complexes for efficient topology-preservation in image data', Available at: https://omanscience.com/en/articles/sparse-cubical-complexes-for-efficient-topology-preservation-in-image-data.
Vancouver
Berger AH, Fontana M, Rueckert D, Paetzold JC, Lux L, Bauer U. Sparse cubical complexes for efficient topology-preservation in image data. https://omanscience.com/en/articles/sparse-cubical-complexes-for-efficient-topology-preservation-in-image-data
IEEE
A. H. Berger, M. Fontana, D. Rueckert, J. C. Paetzold, L. Lux, and U. Bauer, "Sparse cubical complexes for efficient topology-preservation in image data," https://omanscience.com/en/articles/sparse-cubical-complexes-for-efficient-topology-preservation-in-image-data.