Mandible fractures are classified depending on their location. In clinical practice, locations are grouped into regions at different scales according to anatomical, functional and esthetic considerations. Implant design aims at defining the optimal implant for each patient. Emerging population-based techniques analyze the anatomical variability across a population and perform statistical analysis to identify an optimal set of implants. Current efforts are focused on finding clusters of patients with similar characteristics and designing one implant for each cluster. Ideally, the description of anatomical variability is directly connected to the clinical regions. This connection is what we present here, by introducing a new registration method that builds upon a tree of locally affine transformations that describes variability at different scales. We assess the accuracy of our method on 146 CT images of femurs. Two medical experts provide the ground truth by manually measuring six landmarks. We illustrate the clinical importance of our method by clustering 43 CT images of mandibles for implant design. The presented method does not require any application-specific input, which makes it attractive for the analysis of other multiscale anatomical structures. At the core of our new method lays the introduction of a new basis for stationary velocity fields. This basis has very close links to anatomical substructures. In the future, this method has the potential to discover the hidden and possibly sparse structure of the anatomy.