A Hyperelastic Two-Scale Optimization Model for Shape Matching

We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations. Deformation boundary conditions that supplement the underlying equations are usually unknown. Given an initial guess, these are optimized such that the mechanical boundary forces that are responsible for the deformation are of a simple nature. We show a heuristic way to approximate the nonlinear optimization problem by a sequence of convex problems using finite elements. The deformation cost, i.e., the forces, is measured on a coarse scale, while ICP-like matching is done on the fine scale. We demonstrate the plausibility of our algorithm through examples taken from different datasets.