Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians (2403.09434v3)

Abstract: Reconstructing and simulating elastic objects from visual observations is crucial for applications in computer vision and robotics. Existing methods, such as 3D Gaussians, model 3D appearance and geometry, but lack the ability to estimate physical properties for objects and simulate them. The core challenge lies in integrating an expressive yet efficient physical dynamics model. We propose Spring-Gaus, a 3D physical object representation for reconstructing and simulating elastic objects from videos of the object from multiple viewpoints. In particular, we develop and integrate a 3D Spring-Mass model into 3D Gaussian kernels, enabling the reconstruction of the visual appearance, shape, and physical dynamics of the object. Our approach enables future prediction and simulation under various initial states and environmental properties. We evaluate Spring-Gaus on both synthetic and real-world datasets, demonstrating accurate reconstruction and simulation of elastic objects. Project page: https://zlicheng.com/spring_gaus/.

Integrating 3D Gaussians with Physics-based Simulation for Elastic Object Reconstruction and Simulation

Introduction

The accurate reconstruction and simulation of elastic objects from visual observations play a pivotal role in advancing computer vision and robotics applications. Traditional methods have excelled in capturing 3D appearances and geometries, yet often stumble when tasked with simulating physical properties or heterogeneously constitutive objects. Addressing these challenges, we introduce the Spring-Gaus framework, a novel integration of 3D Gaussians with physics-based simulation. Through leveraging a 3D Spring-Mass model, Spring-Gaus enables individual point-level optimization of physical parameters while maintaining a separate learning paradigm for physics and appearance. This dichotomy not only augments sample efficiency and generalization capabilities but also withstands sensitivity issues related to particle distribution in simulations. Below, we dissect the areas where Spring-Gaus marks its innovation, the quantitative strides it achieves, and its broader implications in modeling elastic object dynamics.

Methodology

Spring-Gaus is crafted around the delicate balance of accurately rendering elastic objects' deformations while inferring their intrinsic physical properties. The approach pivots on two primary phases: static reconstruction utilizing the first frame of a video series for anchoring object positioning and dynamic reconstruction extending this static base into the domain of motion and physical interaction.

• Static Scene Reconstruction distills a complex visual input into a simplified yet accurate representation through isotropic 3D Gaussian kernels.
• Dynamic Scene Reconstruction delves deeper, employing a mass-spring system for each point to simulate dynamic deformations, utilizing volume sampling to bridge abstract points (Gaussians) with physically anchored ones (mass-spring anchors).

A notable innovation within Spring-Gaus is the utilization of a soft vector $\eta$, which dynamically modulates the influence and count of spring connections based on a granular optimization at each anchor point. This mechanism offers adaptability and fine-grained control over the deformation behaviors, surpassing traditional hard-coded or globally applied rules.

Experiments and Evaluation

Spring-Gaus was rigorously tested against both synthetic and real-world datasets, with a particular focus on synthetic datasets featuring elastic objects under various deformation scenarios. The framework demonstrated a remarkable fidelity in reconstructing and simulating elastic objects, outperforming existing benchmarks across several metrics:

• Accuracy of Reconstruction and Simulation: Through the adoption of specialized metrics like Chamfer Distance (CD) and Earth Mover's Distance (EMD), Spring-Gaus showcased a significant reduction in error and an improvement in detail capture compared to leading alternatives like PAC-NeRF.
• Ability to Predict Future States: Evaluating the framework's predictive robustness, it adeptly anticipated future deformations and environmental interactions, further evidenced by superior PSNR and SSIM scores.

Implications and Future Work

The implications of Spring-Gaus extend beyond its immediate improvements in elasticity simulation. Firstly, the framework presents new opportunities for creating simulated environments where digital objects not only look realistic but also behave in accordance with physics. This capability can enhance virtual and augmented reality experiences, making them more immersive and interactive.

Secondly, Spring-Gaus opens new avenues in robotics, where understanding and predicting the behavior of materials can significantly impact manipulation strategies. For instance, robots could better adapt their grip and handling methods for various materials, improving efficiency and safety in dynamic environments.

Despite its strengths, Spring-Gaus does have limitations, primarily its current confinement to elastic object modeling, thus excluding materials that exhibit plastic deformation. Future iterations will aim to overcome this by extending the model to capture a broader spectrum of material behaviors, including plasticity.

Conclusion

Spring-Gaus represents a significant stride forward in the quest to accurately model, reconstruct, and simulate elastic objects from visual observations. By integrating 3D Gaussians with a physics-based simulation, this framework not only achieves high fidelity in appearance and geometry but also unlocks a new field of possibility in understanding and interacting with the physical world through digital means. As we continue to refine and expand upon this foundation, the potential applications across computer vision, robotics, and interactive media are both exciting and boundless.