Threshold-free cluster enhancement (TFCE) is a popular method for cluster extent inference but is computationally intensive. Existing TFCE implementations often rely on discretized approximation that introduces numerical errors. Also, we identified a long-standing scaling error in the FSL implementation of TFCE (version 6.0.7.19 and earlier). As an alternative implementation, we present eTFCE, an efficient framework that computes exact TFCE scores using an optimized cluster retrieval algorithm, which, though exact, reduces computation time by approximately 50% compared to standard approximated implementations. In addition, the proposed framework enables simultaneous computation of TFCE and generalized cluster statistics, formulated similarly to TFCE, within a single nonparametric run, with negligible additional computational cost. This, in turn, facilitates systematic method comparisons, and enables a more complete characterization of spatial activation patterns. As a result, eTFCE establishes a mathematically exact and computationally efficient framework for comprehensive and informative nonparametric inference in neuroimaging.

翻译：无阈值簇增强（TFCE）是用于簇范围推断的常用方法，但其计算强度高。现有TFCE实现通常依赖离散化近似，这会引入数值误差。此外，我们发现了FSL中TFCE实现（版本6.0.7.19及更早版本）存在长期未校正的缩放误差。作为替代方案，本文提出eTFCE——一种通过优化簇检索算法精确计算TFCE分数的高效框架。该算法虽为精确计算，但相比标准近似实现可将计算时间减少约50%。同时，该框架可在单次非参数运行中同时计算TFCE及以类似TFCE方式公式化的广义簇统计量，且仅需极少的额外计算成本。这既促进了系统性的方法比较，也能更完整地表征空间激活模式。因此，eTFCE为神经影像学中全面且信息丰富的非参数推断建立了数学精确且计算高效的框架。