This paper provides analytical methods for characterizing the variation of the shape of neuroanatomically significant substructures of the brain in an ensemble of brain images. The focus of this paper is on the neuro-anatomical variation of the “shape” of 2-dimensional surfaces in the brain. Brain surfaces are studied by building templates that are smooth sub-manifolds of the underlying coordinate system of the brain. Variation of the shape in populations is quantified via defining Gaassian random vector fields on these sub-manifolds. Methods for the empirical construction of Ganssian random vector fields for representing the variations of the substructures are presented. As an example, using these methods we characterize the shape of the hippocampus in a population of normal controls and schizophrenic brains. Results from a recently completed study comparing shapes of the hippocampus in a group of matched schizophrenic and normal control subjects are presented. Bayesian hypothesis test is formulated to cluster the normal and schizophrenic hippocampi in the population of 20 individuals.