Morphology-based hypothesis testing in discrete random fields: a non-parametric method to address the multiple-comparison problem in neuroimaging

Abstract

A new method for detecting activations in random fields, which may be useful for addressing the issue of multiple comparisons in neuroimaging, is presented. This method is based on some constructs of mathematical morphology - specifically, morphological erosions and dilations - that enable the detection of active regions in random fields possessing moderate activation levels and relatively large spatial extension, which may not be detected by the standard methods that control the family-wise error rate. The method presented here permits an appropriate control of the false positive errors, without having to adjust any threshold values, other than the significance level. The method is easily adapted to permutation-based procedures (with the usual restrictions), and therefore does not require strong assumptions about the distribution and spatio-temporal correlation structure of the data. Some examples of applications to synthetic data, including realistic fMRI simulations, as well as to real fMRI and electroencephalographic data are presented, illustrating the power of the presented technique. Comparisons with other methods that combine voxel intensity and cluster size, as well as some extensions of the method presented here based on their basic ideas are presented as well.