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

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.