Computer assisted imaging aims to characterize disease processes by contrasting healthy and pathological populations. The sensitivity of these analyses is hindered by the variability in the neuroanatomy of the normal population. To alleviate this shortcoming, it is necessary to define a normative range of controls. Moreover, elucidating the structure in outliers may be important in understanding diverging individuals and characterizing prodromal disease states. To address these issues, we propose a novel geometric concept called minimal convex polytope (MCP). The proposed approach is used to simultaneously capture high probability regions in datasets consisting of normal subjects, and delineate outliers, thus characterizing the main directions of deviation from the normative range. We validated our method using simulated datasets before applying it to an imaging study of elderly subjects consisting of 177 controls, 123 Alzheimer's disease (AD) and 285 mild cognitive impairment (MCI) patients. We show that cerebellar degeneration is a major type of deviation among the controls. Furthermore, our findings suggest that a subset of AD patients may be following an accelerated type of deviation that is observed among the normal population.