Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction

TL;DR

This paper presents a novel method for inferring physical parameters of deformable objects from sparse, correspondence-free observations by integrating finite element simulation with a Lagrangian-Eulerian optimization framework.

Contribution

It introduces a new optimization formulation that combines physics-based simulation with sparse, correspondence-free data to recover material properties and boundary conditions.

Findings

Successfully recovers material parameters from synthetic and real data.

Demonstrates robustness and convergence of the optimization scheme.

Handles various parameters like Young's modulus, Poisson ratio, and external forces.

Abstract

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable real-world data sources such as sparse observations without correspondences. We introduce a novel Lagrangian-Eulerian optimization formulation, including a cost function that penalizes differences to observations during an optimization run. This formulation matches correspondence-free, sparse observations from a single-view depth sequence with a finite element simulation of deformable bodies. In conjunction with an efficient hexahedral discretization and a stable, implicit formulation of collisions, our method can be used in demanding situation to recover a variety of material parameters, ranging from Young's modulus and Poisson ratio to gravity and stiffness damping, and even external boundaries. In a number of tests using synthetic datasets and real-world measurements, we analyse the robustness of our approach and the convergence behavior of the numerical optimization scheme.