Robust Fitting of Subdivision Surfaces for Smooth Shape Analysis

Most shape analysis methods use meshes to discretize the shape and functions on it by piecewise linear functions. Fine meshes are then necessary to represent smooth shapes and compute accurate curvatures or Laplace-Beltrami eigenfunctions at large computational costs. We avoid this bottleneck by representing smooth shapes as subdivision surfaces and using the subdivision scheme to parametrize smooth surface functions with few control parameters. We propose a model to fit a subdivision surface to input samples that, unlike previous methods, can be applied to noisy and partial scans from depth sensors. The task is formulated as an optimization problem with robust data terms and solved with a sequential quadratic program that outperforms the solvers previously used to fit subdivision surfaces to noisy data. Our experiments show that the compression of a subdivision representation does not affect the accuracy of the Laplace-Beltrami operator and allows to compute shape descriptors, geodesics, and shape matchings at a fraction of the computational cost of mesh representations.