Sparse cubical complexes for efficient topology-preservation in image data

arXiv:2609.37177 · cs.CV, cs.CG, cs.LG · Submitted 2026-09-29 · Read on arXiv

cs.CV, cs.CG, cs.LG

Submitted: 2026-09-29

Updated: 2026-09-29

Project page: https://structuralneurobiologylab.github.io/nisb

Terminology

• Persistent Homology — 15× in this paper · explained in 3 episodes
• Loss Function — 14× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Core — 7× in this paper · explained in 2 episodes
• Ablation — 4× in this paper · explained in 1 episode
• Cosine Similarity — 4× in this paper · explained in 3 episodes
• Admissibility — 3× in this paper · explained in 2 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• CVF International Conference on Computer Vision — 2× in this paper
• Consistency — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Variation of Information — 2× in this paper
• Anisotropy — 1× in this paper · explained in 3 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Conference on Computer Vision and Pattern Recognition — 1× in this paper
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Instance Segmentation — 1× in this paper · explained in 3 episodes
• Normalized Surface Distance — 1× in this paper
• Pruning — 1× in this paper · explained in 4 episodes
• Semi-supervised Learning — 1× in this paper · explained in 4 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes
• nnU-Net — 1× in this paper · explained in 2 episodes

Sources

• Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables
• Cubical Ripser: Software for computing persistent homology of image and volume data
• Analysis of the MICCAI Brain Tumor Segmentation -- Metastases (BraTS-METS) 2025 Lighthouse Challenge: Brain Metastasis Segmentation on Pre- and Post-treatment MRI
• Deep learning to achieve clinically applicable segmentation of head and neck anatomy for radiotherapy
• Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology
• Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels

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