The 3D Moore-Rayleigh Test for the Quantitative Groupwise Comparison of MR Brain Images. A.E.H. Scheenstra 1, 2 , M. Muskulus 5 , M. Staring 1, 2 , A.M.J.V. van den Maagdenberg 3, 4 , S. Verduyn Lunel 5 , J.H.C.Reiber 1, 2 , L. van der Weerd 1, 4 , and J. Dijkstra 1, 2 1 Department of Radiology, 2 Division of Image Processing, 3 Department of Neurology, 4 Department of Anatomy and Embryology, Leiden University Medical Center, Postbus 9600, 2300 RC , Leiden, the Netherlands 5 Leiden University, Mathematical Institute, Leiden, The Netherlands Abstract. 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. 1 1 Introduction Mice have been used in genetic research as models for a variety of diseases occurring in the human population. They allow researchers to study the devel- opment of genetic diseases, to improve early diagnoses and subsequent treat- ment. Non-invasive imaging techniques, e.g. MRI, allow localized investigation of 3D anatomical structures of interest [1]. This provides a useful tool for in vivo structural and functional phenotyping, especially in the brain [2]. Since the introduction of non-rigid registration of brain images, a variety of new applica- tions for brain research have emerged. Non-rigid registration is used in clinical practice to register MR images taken from different biological populations to a common average. The resulting deformation fields indicate and localize differ- ences between pairs of images. Their second order statistics are stored in atlases to characterize variability within a population (intra-group variability) [3,4]. 1 J.L. Prince, D.L. Pham and K.J. Meyers (Eds.): IPMI 2009, LNCS 5636, pp 564 – 575, 2009. c ⃝ Springer-Verlag Berlin Heidelberg 2009