In this paper we address the problem of registering 3D scattered data by the mean of a statistical shape model. This model is built from a training set on which a principal component analysis (PCA) is applied. A local system of reference is computed for each sample shape of the learning set, which enables to align the training set. PCA then reveals the main modes of deformation of the class of objects of interest. Furthermore, the deformation field obtained between a given shape and a reference shape is extended to a local neighborhood of these shapes by using an interpolation based on the thin-plate splines. It is then used to register objects associated with these shapes in a local and non-linear way. The data involved here are cerebral data, both anatomical (cortical sulci) and functional (MEG dipoles)