GPU-Accelerated Computation of Persistent Homology for Topological Analysis of Image Data

arXiv:2610.10959 · cs.CV · Submitted 2026-10-07 · Read on arXiv

cs.CV

Submitted: 2026-10-07

Updated: 2026-10-07

Comments: Accepted for publication in IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI). Includes supplementary material (8 pages) after the main paper. Code: https://github.com/seravee08/GPU-Computation-of-Persistent-Homology-for-Image-Data

DOI: 10.1109/TPAMI.2026.3741473

Code: https://github.com/seravee08/GPU-Computation-of-Persist

Project page: https://topology-tool-kit.github.io

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Persistent Homology — 67× in this paper · explained in 3 episodes
• Trace — 17× in this paper · explained in 2 episodes
• Topological Order — 15× in this paper · explained in 2 episodes
• Core — 7× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Adaptation — 3× in this paper · explained in 1 episode
• U-net architecture — 3× in this paper · explained in 3 episodes
• AVERAGE PERSISTENT HOMOLOGY — 2× in this paper
• Computational Biology — 2× in this paper · explained in 2 episodes
• Point Clouds — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Segmentation Masks — 2× in this paper · explained in 2 episodes
• Topological Data Analysis (TDA) — 2× in this paper · explained in 2 episodes
• alpha — 2× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Communication Overhead — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Gaussian Random Fields — 1× in this paper
• Loss Function — 1× in this paper · explained in 2 episodes
• Point Cloud Data — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Cubical Ripser: Software for computing persistent homology of image and volume data
• Computing homology and persistent homology using iterated Morse decomposition
• Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)

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