Deformable image registration in the presence of considerable contrast differences and large-scale size and shape changes represents a significant challenge for image registration. A representative driving application is the study of early brain development in neuroimaging, which requires co-registration of images of the same subject across time or building 4-D population atlases. Growth during the first few years of development involves significant changes in size and shape of anatomical structures but also rapid changes in tissue properties due to myelination and structuring that are reflected in the multi-modal Magnetic Resonance (MR) contrast measurements. We propose a new registration method that generates a mapping between brain anatomies represented as a multi-compartment model of tissue class posterior images and geometries. We transform intensity patterns into combined probabilistic and geometric descriptors that drive the matching in a diffeomorphic framework, where distances between geometries are represented using currents which does not require geometric correspondence. We show preliminary results on the registrations of neonatal brain MRIs to two-year old infant MRIs using class posteriors and surface boundaries of structures undergoing major changes. Quantitative validation demonstrates that our proposed method generates registrations that better preserve the consistency of anatomical structures over time.