Threshold Free Cluster Enhancement (TFCE) is a method for finding "clusters" in the data without having to define clusters in a binary way (e.g. with a cluster threshold). The TFCE approach aims to enhance areas of signal that exhibit some spatial contiguity. The image is passed through an algorithm which enhances the intensity within cluster-like regions more than background (noise) regions. The output image is therefore not intrinsically thresholded/clustered.
The TFCE algorithm is illustrated in the figure above. The solid curve shows a 1D profile through and example statistic image (e.g. an unthresholded t statistic image). Each voxel's TFCE score is given by the sum of the scores of all "supporting sections" underneath it; as the height h is incrementally raised from zero up to the height (signal intensity) hp of a given point p, the image is thresholded at h, and the single contiguous cluster containing p is used to define the score for that height h. This score is simply the height h (raised to some power H) multiplied by the cluster extent e (raised to some power E). Precisely, the TFCE output at voxel p is
where h0 will typically be zero, and E and H, 0.5 and 2 respectively. In practice this integral is estimated as a sum, using finite dh.
It is important to note that this kind of statistics can only be used with a permutation framework. Indeed, without a permutation framework, there's no way to obtaine p-values, either uncorrected or corrected, from a cluster-enhanced output image, since there's no standard distribution to refer to.