A Hyperelastic Two-Scale Optimization Model for Shape Matching
This work addresses shape matching in computer graphics and medical imaging, but it appears incremental as it builds on existing physical models and optimization techniques without claiming major breakthroughs.
The authors tackled the problem of shape matching for 3D surface meshes by developing an algorithm based on nonlinear elasticity theory to handle large deformations, optimizing unknown boundary conditions through a heuristic convex approximation and demonstrating its plausibility on various datasets.
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 on examples taken from different datasets.