On Modal Modeling for Medical Images: Underconstrained Shape Description and Data Compression

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.