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

arXiv: https://arxiv.org/abs/1910.01812 · HTML: https://mlsanity.com/paper/1910.01812/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2019.

## Built on by (most cited first, 12 of 12)

- [Virtual Elastic Objects](https://mlsanity.com/paper/2201.04623/) (2022)
- [DiffCloud: Real-to-Sim from Point Clouds with Differentiable Simulation and Rendering of Deformable Objects](https://mlsanity.com/paper/2204.03139/) (2022)
- [φ-SfT: Shape-from-Template with a Physics-Based Deformation Model](https://mlsanity.com/paper/2203.11938/) (2022)
- [Neural Implicit Representations for Physical Parameter Inference from a Single Video](https://mlsanity.com/paper/2204.14030/) (2022)
- [Global Transport for Fluid Reconstruction with Learned Self-Supervision](https://mlsanity.com/paper/2104.06031/) (2021)
- [DiffSDFSim: Differentiable Rigid-Body Dynamics With Implicit Shapes](https://mlsanity.com/paper/2111.15318/) (2021)
- [Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systems](https://mlsanity.com/paper/2410.01376/) (2024)
- [HMDO: Markerless Multi-view Hand Manipulation Capture with Deformable Objects](https://mlsanity.com/paper/2301.07652/) (2023)
- [One-shot recognition of any material anywhere using contrastive learning with physics-based rendering](https://mlsanity.com/paper/2212.00648/) (2022)
- [Thin-Shell-SfT: Fine-Grained Monocular Non-rigid 3D Surface Tracking with Neural Deformation Fields](https://mlsanity.com/paper/2503.19976/) (2025)
- [Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields](https://mlsanity.com/paper/2107.06028/) (2021)
- [Image-Guided Shape-from-Template Using Mesh Inextensibility Constraints](https://mlsanity.com/paper/2507.22699/) (2025)

## Abstract (arXiv)

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.