We have previously described modal analysis, an efficient, physically-based solution for recovering, tracking, and recognizing solid models from 2-D and 3-D sensor data. The underlying representation consists of two levels: modal deformations, which describe the overall shape of a solid, and displacement maps, which employ a multiscale wavelet representation to provide local and fine surface detail. This paper addresses the problem of recovering modal models in the underconstrained case of fitting a 3-D model to contours found in medical slice and X-ray data. We will describe an extension which can be used to incorporate measurement uncertainty while estimating the modal deformation parameters. Finally, we give details about how to compress dense 3-D point data from surfaces, by use of displacement maps and wavelets.

We describe a new method for establishing correspondence, computing canonical descriptions, and recognizing objects that is based on the idea of describing objects by their generalized symmetries, as defined by the object's vibration or deformation modes. The resulting modal description is useful for object classification, where object similarities are computed in terms of the amounts of modal deformation energy needed to align the two objects. In general, modes provide a global-to-local ordering of shape deformation which allows us to select which types of deformations are to be used in object alignment and comparison. In contrast to previous methods [14, 30, 17] we are able to compute the object's deformation modes directly from available image information, rather than requiring the computation of correspondence with an initial or prototype shape. This results in greater generality and accuracy, and is applicable to data of any dimensionality.