A Hyperelastic Two-Scale Optimization Model for Shape Matching

TL;DR

This paper introduces a shape matching algorithm for 3D surface meshes based on nonlinear elasticity theory, capable of handling large deformations by combining coarse-scale force measurement with fine-scale ICP matching.

Contribution

It proposes a novel two-scale optimization model that integrates nonlinear elasticity with shape matching, using convex approximations for efficient computation.

Findings

Effective handling of large rotations and deformations.

Combines coarse-scale force optimization with fine-scale ICP matching.

Demonstrates plausibility on diverse datasets.

Abstract

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.