The 3D Moore-Rayleigh test for the quantitative groupwise comparison of MR brain images

Non-rigid registration of MR images to a common reference image results in deformation fields, from which anatomical differences can be statistically assessed, within and between populations. Without further assumptions, nonparametric tests are required and currently the analysis of deformation fields is performed by permutation tests. For deformation fields, often the vector magnitude is chosen as test statistic, resulting in a loss of information. In this paper, we consider the three dimensional Moore-Rayleigh test as an alternative for permutation tests. This nonparametric test offers two novel features: first, it incorporates both the directions and magnitude of the deformation vectors. Second, as its distribution function is available in closed form, this test statistic can be used in a clinical setting. Using synthetic data that represents variations as commonly encountered in clinical data, we show that the Moore-Rayleigh test outperforms the classical permutation test.