eTFCE: Exact Threshold-Free Cluster Enhancement via Fast Cluster Retrieval

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.