RECOVERY OF 3D CLOSED SURFACES FROM SPARSE DATA

This paper describes a physically inspired method for the recovery of the surface of 3D solid objects from sparse data. The method is based on a model of closed elastic thin surface under the action of radial s prings which can be considered as the analogous, in spherical coordina tes, to the well-known thin plate model. The model is a representation for whole-body surfaces which has the degrees of freedom for represen ting fine details. We formulate the surface recovery problem as the pr oblem of minimizing a non-quadratic energy functional. In the hypothes is of small deformations, this functional is approximated with a quadr atic one which is then discretized with the finite element method. We provide steepest-descent-like algorithms both for the case of small de formations and for that of large ones. Then we introduce a representat ion of our model in terms of its free deformation modes. This represen tation is extremely concise and is therefore suited for shape analysis and recognition tasks. Finally, we report on the results of experimen ts with synthetic and real data which show the performance of the meth od (C) 1994 Academic Press, Inc.