Object models in multiscale intrinsic coordinates via m-reps

Object descriptions used for 3D segmentation by deformable models and for statistical characterization of 3D object classes benefit from having intrinsic correspondences over deformation of the objects or multiple instances in the same object class. These correspondences apply over a variety of spatial scale levels and consequently lead to efficient segmentation and probability distributions of geometry that are trainable with an achievable number of training instances. This paper describes a figural coordinate system provided by m-reps models and shows how such coordinates not only provide the required positional correspondences, but also are intuitive and provide orientational and metric correspondences. Examples are given for the segmentation of kidneys from CT and for the statistical characterization of schizophrenia and control classes of cerebral ventricles and of hippocampus pairs.