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This paper presents a deformable model for automatically segmenting brain structures from volumetric magnetic resonance (MR) images and obtaining point correspondences, using geometric and statistical information in a hierarchical scheme. Geometric information is embedded into the model via a set of affine-invariant attribute vectors, each of which characterizes the geometric structure around a point of the model from a local to a global scale. The attribute vectors, in conjunction with the deformation mechanism of the model, warrant that the model not only deforms to nearby edges, as is customary in most deformable surface models, but also that it determines point correspondences based on geometric similarity at different scales. The proposed model is adaptive in that it initially focuses on the most reliable structures of interest, and gradually shifts 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.