Paper
Hybrid eTFCE-GRF: Exact Cluster-Size Retrieval with Analytical p-Values for Voxel-Based Morphometry
Authors
Don Yin, Hao Chen, Takeshi Miki, Boxing Liu, Enyu Yang
Abstract
Threshold-free cluster enhancement (TFCE) integrates cluster extent across thresholds to improve voxel-wise neuroimaging inference, but permutation testing makes it prohibitively slow for large datasets. Probabilistic TFCE (pTFCE) uses analytical Gaussian random field (GRF) p-values but discretises the threshold grid. Exact TFCE (eTFCE) eliminates discretisation via a union-find data structure but still requires permutations. We combine eTFCE's union-find for exact cluster-size retrieval with pTFCE's analytical GRF inference. The union-find builds the cluster hierarchy in one pass over sorted voxels and enables exact size queries at any threshold; GRF theory then converts these sizes to analytical p-values without permutations. Validation on synthetic phantoms (64^3, 80 subjects): FWER controlled at nominal level (0/200 null rejections, 95% CI [0.0%, 1.9%]); power matches baseline pTFCE (Dice >= 0.999); smoothness error below 1%; concordance r > 0.99. On UK Biobank (N=500) and IXI (N=563), significance maps form strict subsets of reference R pTFCE, which supports conservative error control. Implemented in pytfce (pip install pytfce): baseline completes whole-brain VBM in ~5s (75x faster than R pTFCE), hybrid in ~85s (4.6x faster) with exact cluster sizes; both >1000x faster than permutation TFCE.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.11344v1</id>\n <title>Hybrid eTFCE-GRF: Exact Cluster-Size Retrieval with Analytical p-Values for Voxel-Based Morphometry</title>\n <updated>2026-03-11T22:20:03Z</updated>\n <link href='https://arxiv.org/abs/2603.11344v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.11344v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Threshold-free cluster enhancement (TFCE) integrates cluster extent across thresholds to improve voxel-wise neuroimaging inference, but permutation testing makes it prohibitively slow for large datasets. Probabilistic TFCE (pTFCE) uses analytical Gaussian random field (GRF) p-values but discretises the threshold grid. Exact TFCE (eTFCE) eliminates discretisation via a union-find data structure but still requires permutations. We combine eTFCE's union-find for exact cluster-size retrieval with pTFCE's analytical GRF inference. The union-find builds the cluster hierarchy in one pass over sorted voxels and enables exact size queries at any threshold; GRF theory then converts these sizes to analytical p-values without permutations. Validation on synthetic phantoms (64^3, 80 subjects): FWER controlled at nominal level (0/200 null rejections, 95% CI [0.0%, 1.9%]); power matches baseline pTFCE (Dice >= 0.999); smoothness error below 1%; concordance r > 0.99. On UK Biobank (N=500) and IXI (N=563), significance maps form strict subsets of reference R pTFCE, which supports conservative error control. Implemented in pytfce (pip install pytfce): baseline completes whole-brain VBM in ~5s (75x faster than R pTFCE), hybrid in ~85s (4.6x faster) with exact cluster sizes; both >1000x faster than permutation TFCE.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='eess.IV'/>\n <category scheme='http://arxiv.org/schemas/atom' term='q-bio.QM'/>\n <published>2026-03-11T22:20:03Z</published>\n <arxiv:comment>25 pages, 7 figures, 3 tables. Submitted to NeuroImage. Open-source package: https://github.com/Don-Yin/pytfce</arxiv:comment>\n <arxiv:primary_category term='eess.IV'/>\n <author>\n <name>Don Yin</name>\n </author>\n <author>\n <name>Hao Chen</name>\n </author>\n <author>\n <name>Takeshi Miki</name>\n </author>\n <author>\n <name>Boxing Liu</name>\n </author>\n <author>\n <name>Enyu Yang</name>\n </author>\n </entry>"
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