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TBM images are smooth, but they exhibit (especially in diseased groups) higher values in some brain regions called lateral ventricles. More specifically, our voxelwise analysis shows both a mean\u2013variance relationship in these areas and evidence of spatially dependent skewness. We propose a model for three\u2010dimensional imaging data where mean, variance and skewness functions vary smoothly across brain locations. We model the voxelwise distributions as skew\u2010normal. We illustrate an interpolation\u2010based approach to obtain smooth parameter functions based on a subset of voxels. The effects of age and sex are estimated on a reference population of cognitively normal subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI) data set and mapped across the whole brain. The three parameter functions allow transforming each TBM image (in the reference population as well as in a test set) into a normative map based on Gaussian distributions. 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