提出混合方法，实现无阈值聚类增强的精确簇大小检索与解析p值计算。
Hybrid eTFCE-GRF: Exact Cluster-Size Retrieval with Analytical p-Values for Voxel-Based Morphometry
- 结合联合查找结构与解析高斯随机场理论，避免离散化和置换检验
- 在合成数据与真实脑影像上验证，误差低于1%，统计功效接近基准方法
- 比传统置换检验快75倍以上，适合大规模脑形态测量分析
无阈值聚类增强（TFCE）通过整合不同阈值下的簇扩展性提升体素级神经影像推断能力，但置换检验使其在大数据集上难以应用。概率性TFCE（pTFCE）采用解析高斯随机场（GRF）p值，但需离散化阈值网格；精确TFCE（eTFCE）通过并查集结构消除离散化，但仍依赖置换。本文将eTFCE的并查集用于精确簇大小检索，结合pTFCE的解析GRF推断。并查集单次遍历排序体素构建簇层次结构，支持任意阈值下精确大小查询；随后利用GRF理论将这些大小转化为解析p值，无需置换。在合成幻影数据（64³，80名受试者）上验证：族错误率（FWER）控制在名义水平（0/200次零假设拒绝，95%置信区间[0.0%, 1.9%]）；效能与基线pTFCE相当（Dice ≥ 0.999）；平滑误差<1%；一致性相关系数r > 0.99。在英国生物银行（N=500）与IXI数据集（N=563）中，显著性图严格包含于参考的pTFCE结果，表明保守误差控制。已开源至pytfce（pip install pytfce）：基线全脑VBM耗时约5秒（比R pTFCE快75倍），混合方法约85秒（快4.6倍），且具备精确簇大小；二者均比置换TFCE快逾1000倍。
原文摘要 · Abstract (English)
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.
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