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

Abstract

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.

Figures (4)

• Figure 1: Illustration of Algorithm \ref{['alg']} for constructing a directed rooted forest. (a) Input undirected graph with $9$ nodes, ordered by non-ascending statistic values (or non-descending $p$-values). (b) Output directed rooted forest after applying the 2D edge-connectivity (or $4$-connectivity) criterion.
• Figure 2: Comparison of eTFCE and FSL’s default TFCE on auditory data. Panels show results before (left) and after (right) scaling error correction. The TFCE scores are displayed in the top row, and the log-transformed FWER-corrected $p$-values ($-\log_{10}(p)$) are shown in the bottom row, derived from $5000$ sign-flipping randomizations. The red dashed lines correspond to the identity line.
• Figure 3: Comparison of eTFCE and FSL's default TFCE for $6$ cognitive task contrasts from the Human Connectome Project. The log-transformed FWER-corrected $p$-values ($-\log_{10}(p)$, based on $5000$ randomizations) are shown. (a) Results before applying scaling error correction to FSL's TFCE. (b) Results after applying scaling error correction to FSL's TFCE, which ensures a fair comparison with eTFCE. The red dashed lines indicate the identity line, and the six contrasts are: Emotional (faces vs shapes), Gambling (punish vs reward), Language (math vs story), Relational (matching vs relational), Social (ToM vs random), and WM (2-back vs 1-back).
• Figure 4: Example visualization of integrated inference on two task contrasts with distinct spatial activation profiles. (a) Auditory discrimination task (vocal $>$ non-vocal), where CEI identifies focal, high-intensity activation as well as additional spatially distinct clusters (see black arrows), while most TFCE-specific voxels are distributed along the boundaries of, or adjacent to, shared clusters. (b) HCP working memory task (2-back $>$ 1-back), where multiple bilaterally symmetric clusters distributed across regions are detected by both methods. All CEI-significant clusters are also identified by TFCE, which further reveals additional subcortical activation (see black arrows).