MULTILEVEL SHAPE REPRESENTATION USING GLOBAL DEFORMATIONS AND LOCALLYADAPTIVE FINITE-ELEMENTS

We present a model-based method for the multi-level shape, pose estima tion and abstraction of an object's surface from range data. The surfa ce shape is estimated based on the parameters of a superquadric that i s subjected to global deformations (tapering and bending) and a varyin g number of levels of local deformations. Local deformations are imple mented using locally adaptive finite elements whose shape functions ar e piecewise cubic functions with C-1 continuity. The surface pose is e stimated based on the model's translational and rotational degrees of freedom. The algorithm first does a coarse fit, solving for a first ap proximation to the translation, rotation and global deformation parame ters and then does several passes of mesh refinement, by locally subdi viding triangles based on the distance between the given datapoints an d the model. The adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties o f conformity, non-degeneracy and smoothness are maintained. Each pass of the algorithm uses physics-based modeling techniques to iteratively adjust the global and local parameters of the model in response to fo rces that are computed from approximation errors between the model and the data. We present results demonstrating the multi-level shape repr esentation for both sparse and dense range data.