Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction (1910.01812v1)

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.

• The paper introduces a novel Lagrangian-Eulerian optimization framework to infer material parameters and boundary conditions from sparse observational data.
• It employs hexahedral discretization and a differentiable, gradient-based solver to efficiently manage parameters like Young’s modulus and gravity.
• Results on synthetic and real-world datasets demonstrate robust performance in elasticity simulation, paving the way for advancements in biomechanics and computer vision.

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

The paper "Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction" presents a novel framework to infer material parameters and boundary conditions of deformable objects using sparse observations from real-world data. The authors introduce an optimization approach leveraging a Lagrangian-Eulerian framework to tackle inverse problems inherent in elasticity simulations.

Problem Statement

The primary focus of this research is the estimation of physical material parameters and boundary conditions of homogeneous deformable objects based on sparse observational data, notably devoid of spatial correspondence between observations and model points. Traditional methods for estimating such parameters usually demand controlled experimental settings or dense data, which is not feasible in many practical scenarios involving real-world interactions. This work focuses on addressing the challenges posed in these scenarios.

Methodology

A novel Lagrangian-Eulerian optimization framework is proposed, which includes a cost function penalizing discrepancies between observations and simulations. The integration of correspondence-free sparse observations from depth sequences with finite element simulations of deformable bodies serves as the foundation of this framework.

1. Cost Function Design: The cost function is crafted to minimize the difference between observed motion and simulated deformation without relying on explicit correspondences. This is achieved by matching observations to a simulation grid via a cost function sensitive to the surface geometry dictating the object’s deformation.
2. Simulation Approach: The approach employs a hexahedral discretization for numerical simulation. An implicit formulation is used for handling collisions, critical for incorporating real-world scenarios with interactions caused by gravitational forces and external conditions.
3. Gradient-Based Optimization: The method utilizes a differentiable solver, allowing the direct computation of gradients utilizing the adjoint method, which provides more reliable results compared to traditional finite difference approaches. This makes it efficient for handling multiple parameters simultaneously, such as the Young’s modulus, Poisson ratio, and gravity, along with external boundary constraints.

Results and Evaluation

The efficacy of the outlined approach is demonstrated through a range of tests, both on synthetic datasets, providing a controlled environment for validation against known parameters, and on live captures of real-world objects. The results indicate robust performance in estimating material parameters, demonstrating the capability of the method in navigating complex interaction scenarios, such as collisions and varying material behaviors.

Implications and Future Directions

The practical implication of this research is particularly profound in fields requiring accurate material modeling from limited data, such as biomechanics, computer vision, and animation. Further development could include incorporating more complex material models and collision dynamics, potentially broadening the utility of the framework in comprehensive material analysis and object reconstruction tasks. Additionally, this framework opens pathways for integrating physical simulations into AI models, assisting in predictive modeling and enhancing the interpretability of machine learning systems in physical contexts.

In essence, this research offers a promising advancement in elasticity simulations, providing a groundbreaking approach that circumvents the need for dense observational data, thereby optimizing material parameter estimation in real-world applications.