In this paper we present two fine and coarse approaches for the efficient registration of 3D medical images using the framework of Large Deformation Diffeomorphic Metric Mapping (LDDMM). This formalism has several important advantages since it allows large, smooth and invertible deformations and has interesting statistical properties. We first highlight the influence of the smoothing kernel in the LDDMM framework. We then show why approaches taking into account several scales simultaneously should be used for the registration of complex shapes, such as those treated in medical imaging. We then present our fine and coarse approaches and apply them to the registration of binary images as well as the longitudinal estimation of the early brain growth in preterm MR images.