Elasticity-based Matching by Minimizing the Symmetric Difference of Shapes

TL;DR

This paper introduces an elastic deformation-based shape matching method that minimizes the symmetric difference between shapes using a novel cost function and convex optimization, providing an alternative to point-based matching techniques.

Contribution

It proposes a new shape matching approach based on elasticity theory and symmetric difference minimization, with a convex approximation for efficient optimization.

Findings

The method effectively matches shapes with elastic deformations.

It outperforms ICP-like algorithms in experiments.

The approach is computationally feasible through convex optimization.

Abstract

We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external boundary forces and accounts for the difference between the two shapes. Our main contribution is in proposing a cost function and an optimization procedure to minimize the symmetric difference between the deformed and the target shapes as an alternative to point matches that guide the matching in other techniques. We show how to approximate the nonlinear optimization problem by a sequence of convex problems. We demonstrate the utility of our method in experiments and compare it to an ICP-like matching algorithm.