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：无阈值聚类增强（TFCE）是一种流行的聚类范围推断方法，但计算量较大。现有的TFCE实现通常依赖于离散化近似，这会引入数值误差。此外，我们发现FSL的TFCE实现（版本6.0.7.19及更早版本）中存在一个长期存在的缩放误差。作为替代实现，我们提出了eTFCE，这是一个高效框架，它使用优化的聚类检索算法计算精确的TFCE分数；尽管是精确计算，但与标准的近似实现相比，计算时间减少了约50%。此外，所提出的框架能够在单次非参数运行中同时计算TFCE和广义聚类统计量（其公式与TFCE类似），且额外计算成本可忽略不计。这反过来又促进了系统性的方法比较，并能够更完整地刻画空间激活模式。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一个数学上精确且计算高效的框架。