Recovery of 3D Closed Surfaces from Sparse Data

Abstract

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 springs which can be considered as the analogous, in spherical coordinates, to the well-known thin plate model. The model is a representation for whole-body surfaces which has the degrees of freedom for representing fine details. We formulate the surface recovery problem as the problem of minimizing a non-quadratic energy functional. In the hypothesis of small deformations, this functional is approximated with a quadratic one which is then discretized with the finite element method. We provide steepest-descent-like algorithms both for the case of small deformations and for that of large ones. Then we introduce a representation of our model in terms of its free deformation modes. This representation is extremely concise and is therefore suited for shape analysis and recognition tasks. Finally, we report on the results of experiments with synthetic and real data which show the performance of the method