In this paper, we present a fine and coarse approach for the multiscale registration of 3D medical images using Large Deformation Diffeomorphic Metric Mapping (LDDMM). This approach has particularly interesting properties since it estimates large, smooth and invertible optimal deformations having a rich descriptive power for the quantification of temporal changes in the images. First, we show the importance of the smoothing kernel and its influence on the final solution. We then propose a new strategy for the spatial regularization of the deformations, which uses simultaneously fine and coarse smoothing kernels. We have evaluated the approach on both 2D synthetic images as well as on 3D MR longitudinal images out of the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. Results highlight the regularizing properties of our approach for the registration of complex shapes. More importantly, the results also demonstrate its ability to measure shape variations at several scales simultaneously while keeping the desirable properties of LDDMM. This opens new perspectives for clinical applications.