Tensor-based morphometry (TBM) aims at showing local differences in brain volumes with respect to a common template. TBM images exhibit (especially in diseased groups) higher values in some brain regions as the lateral ventricles. More specifically, a voxelwise analysis shows a mean-variance relationship in these areas and spatially heterogeneous skewness. 



Following the approach proposed by Staicu et al. (2012) we build a model for 3-dimensional images where mean, variance, and shape functions vary smoothly across brain locations. We model the voxelwise distribution as a skew-normal and the spatial correlation using a Gaussian copula. The functional parameters are estimated on a reference population of cognitively normal subjects and the Gaussian maps can be obtained for subjects with unknown brain health condition. The aim is to use the normative maps to derive indices of deviation from the normal pattern.


In the presentation I will first describe the main features of the model, then I will briefly present some statistical approaches to outlier detection available in the multivariate and functional data analysis literature.

References:

Staicu, A. M., Crainiceanu, C. M., Reich, D. S., & Ruppert, D. (2012). Modeling functional data with spatially heterogeneous shape characteristics. Biometrics, 68(2), 331-343