This paper addresses the challenging problem of statistics on images by describing average and variability. We describe computational anatomy tools for building 3-D and spatio-temporal 4-D atlases of volumetric image data. The method is based on the previously published concept of unbiased atlas building, calculating the nonlinear average image of a population of images by simultaneous nonlinear deformable registration. Unlike linear averaging, the resulting center average image is sharp and encodes the average structure and geometry of the whole population. Variability is encoded in the set of deformation maps. As a new extension, longitudinal change is assessed by quantifying local deformation between atlases taken at consecutive time points. Morphological differences between groups are analyzed by the same concept but comparing group-specific atlases. Preliminary tests demonstrate that the atlas building shows excellent robustness and a very good convergence, i.e. atlases start to stabilize after 5 images only and do not show significant changes when including more than 10 volumetric images taken from the same population.