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arXiv · 2510.04553

Fast Witness Persistence for MRI Volumes via Hybrid Landmarking

Jorge Leonardo Ruiz Williams
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Abstract

We introduce a scalable witness-based persistent homology pipeline for full-brain MRI volumes that couples density-aware landmark selection with a GPU-ready witness filtration. Candidates are scored by a hybrid metric that balances geometric coverage against inverse kernel density, yielding landmark sets that shrink mean pairwise distances by 30-60% over random or density-only baselines while preserving topological features. Benchmarks on BrainWeb, IXI, and synthetic manifolds execute in under ten seconds on a single NVIDIA RTX 4090 GPU, avoiding the combinatorial blow-up of Cech, Vietoris-Rips, and alpha filtrations. The package is distributed on PyPI as whale-tda (installable via pip); source and issues are hosted at https://github.com/jorgeLRW/whale. The release also exposes a fast preset (mri_deep_dive_fast) for exploratory sweeps, and ships with reproducibility-focused scripts and artifacts for drop-in use in medical imaging workflows.

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Jorge Leonardo Ruiz Williams. 2025-10-06. Fast Witness Persistence for MRI Volumes via Hybrid Landmarking. https://arxiv.org/abs/2510.04553

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