Building of atlases representing average and variability of a population of images or of segmented objects is a key topic in application areas like brain mapping, deformable object segmentation and object classification. Recent developments in image averaging, i.e. constructing an image which is central within the population, focus on unbiased atlas building with nonlinear deformations. Groupwise nonlinear image averaging creates images which appear sharper than linear results. However, volumetric atlases do not explicitely carry a notion of statistics of embedded shapes. This paper compares population-based linear and non-linear image averaging on 3D objects segmented from each image and compares voxelbased versus surface-based representations. Preliminary results suggest improved locality of group average differences for the nonlinear scheme, which might lead to increased significance for hypothesis testing. Results from a clinical MRI study with sets of subcortical structures of children scanned at two years with follow-up at four years are shown.