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Fast Witness Persistence for MRI Volumes via Hybrid Landmarking

Jorge Leonardo Ruiz Williams

TL;DR

This work tackles the scalability bottleneck of exact filtrations in persistent homology for full MRI volumes by proposing a hybrid landmarking strategy coupled with a GPU-accelerated lazy witness filtration. The method converts MRI data into a unit-cube point cloud with intensity weights, selects a compact landmark set using a density-aware MaxMin approach, and builds a lazy witness complex with a $k$-nearest-witness constraint, enabling efficient topological summaries while preserving $H_1$ and higher features where relevant. Key contributions include the hybrid landmarking scheme with an automatic scaling rule, a coverage-aware diagnostic suite, a modular Python distribution (whale-tda) with CLI presets for fast sweeps, and a comprehensive benchmark suite across BrainWeb, IXI, and synthetic datasets demonstrating improved coverage and scalability. The approach offers practical impact for rapid topology-aware analysis in medical imaging and beyond by avoiding the combinatorial blow-up of classical filtrations while maintaining fidelity to salient topological signatures, as evidenced by sub-second to tens-of-seconds runtimes and robust agreement with reference filtrations.

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.

Fast Witness Persistence for MRI Volumes via Hybrid Landmarking

TL;DR

This work tackles the scalability bottleneck of exact filtrations in persistent homology for full MRI volumes by proposing a hybrid landmarking strategy coupled with a GPU-accelerated lazy witness filtration. The method converts MRI data into a unit-cube point cloud with intensity weights, selects a compact landmark set using a density-aware MaxMin approach, and builds a lazy witness complex with a -nearest-witness constraint, enabling efficient topological summaries while preserving and higher features where relevant. Key contributions include the hybrid landmarking scheme with an automatic scaling rule, a coverage-aware diagnostic suite, a modular Python distribution (whale-tda) with CLI presets for fast sweeps, and a comprehensive benchmark suite across BrainWeb, IXI, and synthetic datasets demonstrating improved coverage and scalability. The approach offers practical impact for rapid topology-aware analysis in medical imaging and beyond by avoiding the combinatorial blow-up of classical filtrations while maintaining fidelity to salient topological signatures, as evidenced by sub-second to tens-of-seconds runtimes and robust agreement with reference filtrations.

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.

Paper Structure

This paper contains 13 sections, 5 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Historical Context
  3. Methods
  4. Hybrid landmark selection
  5. Automatic landmark scaling.
  6. Witness filtration
  7. Coverage metrics
  8. Relationship to classical filtrations
  9. Implementation notes
  10. Results
  11. Discussion
  12. Community contributions and artifact workflow
  13. Conclusion

Figures (1)

  • Figure 1: High-level decomposition of the Python package.