Threshold-free cluster enhancement (TFCE) is widely used for cluster-based inference in neuroimaging, but existing implementations typically rely on discretized approximations that may introduce numerical variability. We present eTFCE, an efficient framework that provides a numerically exact evaluation of the TFCE integral using an optimized cluster retrieval algorithm. Across multiple datasets, eTFCE and the standard implementation produce highly consistent inference results. Voxel-wise comparisons reveal a systematic asymmetry: the standard method yields smaller p-values for more voxels, while eTFCE concentrates stronger statistical evidence within a smaller subset. These differences are primarily confined to voxels near the inference boundary and have minimal impact on overall inference. This pattern is consistent with discretization effects in standard implementations, where the TFCE integral is approximated using a finite set of threshold levels, introducing subtle biases in statistical evidence accumulation across thresholds. Furthermore, eTFCE improves computational efficiency (71.3% of runtime on average) and enables unified computation of multiple cluster-based statistics within a single permutation framework. Overall, eTFCE provides an exact, efficient, and extensible approach to nonparametric neuroimaging inference.

翻译：无阈值簇增强（TFCE）广泛应用于神经影像的基于簇的统计推断中，但现有实现通常依赖离散化近似，可能引入数值变异性。我们提出eTFCE，一种利用优化簇检索算法实现TFCE积分数值精确计算的高效框架。在多个数据集上，eTFCE与标准实现方法产生的推断结果高度一致。体素级比较揭示了系统性不对称：标准方法在更多体素上产生更小的p值，而eTFCE将更强的统计证据集中在更小子集内。这些差异主要局限于推断边界附近的体素，对整体推断影响极小。该模式与标准实现中的离散化效应一致——TFCE积分通过有限阈值层级近似计算，导致跨阈值统计证据累积中存在细微偏差。此外，eTFCE提升了计算效率（平均运行时间降至71.3%），并在单次置换框架内实现多种基于簇统计量的统一计算。总体而言，eTFCE为非参数神经影像推断提供了精确、高效且可扩展的方案。