ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimation (2506.05317v2)

Abstract: Neural rendering has made significant strides in 3D reconstruction and novel view synthesis. With the integration with physics, it opens up new applications. The inverse problem of estimating physics from visual data, however, still remains challenging, limiting its effectiveness for applications like physically accurate digital twin creation in robotics and XR. Existing methods that incorporate physics into neural rendering frameworks typically require dense multi-view videos as input, making them impractical for scalable, real-world use. When presented with sparse multi-view videos, the sequential optimization strategy used by existing approaches introduces significant error accumulation, e.g., poor initial 3D reconstruction leads to bad material parameter estimation in subsequent stages. Instead of sequential optimization, directly optimizing all parameters at the same time also fails due to the highly non-convex and often non-differentiable nature of the problem. We propose ProJo4D, a progressive joint optimization framework that gradually increases the set of jointly optimized parameters guided by their sensitivity, leading to fully joint optimization over geometry, appearance, physical state, and material property. Evaluations on PAC-NeRF and Spring-Gaus datasets show that ProJo4D outperforms prior work in 4D future state prediction, novel view rendering of future state, and material parameter estimation, demonstrating its effectiveness in physically grounded 4D scene understanding. For demos, please visit the project webpage: https://daniel03c1.github.io/ProJo4D/

• The paper’s primary contribution is a progressive joint optimization strategy that incrementally couples sensitive parameters for improved inverse physics estimation.
• Empirical results show significant enhancements in 4D future state prediction and geometric reconstruction, achieving Chamfer Distance scores as low as 0.5.
• The framework simplifies inverse problems in neural rendering and paves the way for scalable digital twins in robotics and XR using sparse data.

ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimation

The paper presents "ProJo4D," a novel framework designed to address the complex task of inverse physics estimation from sparse multi-view videos, particularly focusing on deformable objects. The primary innovation offered by ProJo4D is its use of a progressive joint optimization strategy to estimate a 4D representation alongside physical parameters, simplifying the challenge of error accumulation associated with sequential optimization approaches.

Summary of Contributions

ProJo4D differentiates itself by utilizing a progressive optimization framework, which incrementally increases the number of parameters optimized together based on their sensitivity and influence. This approach contrasts sharply with the dominant paradigm of sequential optimization seen in existing methods—such as Spring-Gaus and GIC—which exhibit limitations under sparse multi-view conditions. By progressively coupling parameters during the optimization process, ProJo4D mitigates error propagation, leading to more accurate geometric reconstruction and better estimation of physical parameters like initial velocities and material properties.

Strong Numerical Outcomes

Empirical results highlight the superior performance of ProJo4D compared to current state-of-the-art algorithms. Evaluations on the PAC-NeRF and Spring-Gaus datasets demonstrate significant improvements in 4D future state prediction, novel view rendering of future states, and material parameter estimation. For instance, in Chamfer Distance evaluations—a direct measure of geometric estimation accuracy—ProJo4D achieved mean scores as low as 0.5 in dense captures and significantly reduced errors in sparse scenarios. Such numerical validation underscores the broad applicability and robustness of the progressive joint optimization approach.

Theoretical and Practical Implications

ProJo4D addresses core issues in the domain of neural rendering fused with physics-based modeling. Theoretically, the framework introduces a paradigm shift towards achieving holistic optimization over geometry, appearance, physical state, and material properties simultaneously, thereby reducing the need for complex architectural changes or heuristics typically required in existing methods. Practically, this research opens up new avenues for creating physically accurate digital twins in robotics and XR from less dense and more accessible datasets, enhancing the ability to deploy these systems broadly in real-world scenarios.

Speculation on Future Developments

The progressive joint optimization strategy showcased in ProJo4D may inspire broader applications across AI-driven modeling tasks, beyond deformable object estimation. Future developments could explore extending similar frameworks to diverse domains where inverse problems persist under sparse data constraints, such as medical imaging or dynamic environmental mapping. Additionally, integrating ProJo4D with lighter differentiable physics models or neural network-based simulators could yield computational efficiencies, reducing the resource overhead currently incumbent in real-world deployment.

By refining the process of parameter estimation in low-data environments, ProJo4D signifies a step towards more scalable and physically robust AI systems. The contributions made by this research provide a fertile ground for further exploration and application, potentially transforming the landscape of intelligent systems capable of complex physical reasoning.