This paper presents a deformable model for automatically segmenting objects from volumetric MR images and obtaining point correspondences, using geometric and statistical information in a hierarchical scheme. Geometric information is embedded into the model via an affine-invariant attribute vector, which characterizes the geometric structure around each model point from a local to a global level. Accordingly, the model deforms seeking boundary points with similar attribute vectors. This is in contrast to most deformable surface models, which adapt to nearby edges without considering the geometric structure. The proposed model is adaptive in that it initially focuses on the most reliable structures of interest, and subsequently switches focus to other structures as those become closer to their respective targets and therefore more reliable. The proposed techniques have been used to segment boundaries of the ventricles, the caudate nucleus, and the lenticular nucleus from volumetric MR images.