LagrangeGS: Non-Conservative Lagrangian System on Dynamic 3D Gaussian Splatting

2026-08-23

AI Summary

该研究通过构建非保守拉格朗日系统LagrangeGS解决3D高斯点云动态场景重建中的物理不一致、不可逆及长期外推几何崩溃问题。

Abstract

Dynamic 3D Gaussian Splatting (3DGS) achieves photorealistic reconstruction of time-varying scenes, and recent physics-aware extensions improve extrapolation by explicitly predicting velocity fields. However, these extensions merely fit vector fields to visual deformations without satisfying Lagrangian mechanics, leading to three major issues: (i) physically inconsistent trajectories, (ii) lack of time-reversibility, and (iii) geometric collapse during long-term extrapolation. In this paper, we propose LagrangeGS, which formulates dynamic 3DGS as a non-conservative Lagrangian system. While this Lagrangian formulation fundamentally solves (i), a direct application of general LNNs to dynamic 3DGS requires a large velocity-Hessian inversion for millions of Gaussian particles. To overcome this computational bottleneck, we approximate the velocity-Hessian as an identity matrix, decoupling particle dynamics for computational tractability. For (ii), we restrict the non-conservative forces to be explicitly time independent, enabling consistent backward integration. Finally, to address (iii), we introduce local rigid alignment that regularizes particle trajectories. Extensive evaluations on dynamic scene benchmarks demonstrate that LagrangeGS enables stable long-term extrapolation, consistent time reversal, and counterfactual physics-based editing without retraining.

Problem

• Dynamic 3D Gaussian Splatting
• Lagrangian Mechanics
• Time-Reversibility
• Geometric Collapse
• Long-Term Extrapolation

Innovation

• non-conservative Lagrangian system
• dynamic 3D Gaussian Splatting
• velocity-Hessian approximation
• time-reversibility
• local rigid alignment