title: Threshold-free cluster enhancement: addressing problems of smoothing, threshold dependence and localisation in cluster inference.
abstract: Many image enhancement and thresholding techniques make use of spatial neighbourhood information to boost belief in extended areas of signal. The most common such approach in neuroimaging is cluster-based thresholding, which is often more sensitive than voxel-wise thresholding. However, a limitation is the need to define the initial cluster-forming threshold. This threshold is arbitrary, and yet its exact choice can have a large impact on the results, particularly at the lower (e.g., t, z < 4) cluster-forming thresholds frequently used. Furthermore, the amount of spatial pre-smoothing is also arbitrary (given that the expected signal extent is very rarely known in advance of the analysis). In the light of such problems, we propose a new method which attempts to keep the sensitivity benefits of cluster-based thresholding (and indeed the general concept of "clusters" of signal), while avoiding (or at least minimising) these problems. The method takes a raw statistic image and produces an output image in which the voxel-wise values represent the amount of cluster-like local spatial support. The method is thus referred to as "threshold-free cluster enhancement" (TFCE). We present the TFCE approach and discuss in detail ROC-based optimisation and comparisons with cluster-based and voxel-based thresholding. We find that TFCE gives generally better sensitivity than other methods over a wide range of test signal shapes and SNR values. We also show an example on a real imaging dataset, suggesting that TFCE does indeed provide not just improved sensitivity, but richer and more interpretable output than cluster-based thresholding.
authors.affiliation: FMRIB-Oxford University Centre for Functional MRI of the Brain, Department of Clinical Neurology, University of Oxford, Oxford, UK. steve@fmrib.ox.ac.uk
authors.forename: Stephen M
authors.initials: SM
authors.lastname: Smith
authors.forename: Thomas E
authors.initials: TE
authors.lastname: Nichols
mesh_terms: D000465:Algorithms; D019540:Area Under Curve; D001931:Brain Mapping / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D012372:ROC Curve