PersistGS: Differentiable Physics for Object Permanence in 4D Gaussian Splatting
Authors: Adrian Ramlal, John S. Zelek
Organizations: University of Waterloo
Abstract
Dynamic 3D Gaussian Splatting (3DGS) methods reconstruct time-varying scenes from synchronized multi-camera video using photometric supervision. When a moving object becomes fully occluded from all training cameras, this supervision vanishes: the Gaussians representing it receive no gradient signal and degrade. Existing approaches to incomplete observations in neural reconstruction rely on learned generative priors that prioritize visual plausibility over physical correctness. We propose PersistGS, a method that restores object permanence during occlusion by coupling differentiable rigid body simulation with 3D Gaussian Splatting. Our approach decomposes the scene into per-object Gaussians and collision meshes, estimates friction and velocity from the observed pre-occlusion trajectory via differentiable simulation, and uses the resulting SE(3) trajectory to position object Gaussians throughout the occlusion period. Because the predicted trajectory satisfies the governing equations of rigid body dynamics, it faithfully captures contact events (bounces, friction-based deceleration, direction changes) that kinematic extrapolation cannot model. We introduce a centroid silhouette loss that isolates positional gradients from appearance noise, yielding 40% lower trajectory error than photometric supervision. We evaluate using cameras withheld from training that observe the object during its occlusion. Experiments on synthetic scenes show that PersistGS outperforms constant velocity extrapolation by +2.46dB PSNR and comes within 0.19dB of a ground-truth trajectory upper bound.
Reconstructing dynamic 3D scenes from multi-view videos is a foundational task for robotics, AR/VR, and digital twins. While 3D Gaussian Splatting (3DGS) provides state-of-the art scene representation, its dynamic adaptations (4DGS) face significant challenges. Early MLP-based deformation models excel at interpolating within training frames but fail at temporal extrapolation --- important feature for forecasting in predictive systems. To address this, physically grounded approaches have been proposed to enable robust future forecasting, while, concurrently, semantic 4DGS methods have been developed for scene analysis and language-driven prompting. However, there is currently no framework that unites both physical consistency and semantic understanding. In this paper, we propose the first, to the best of our knowledge, unified 4DGS approach that is both physically grounded and semantically aware. Furthermore, to optimize computational efficiency, we introduce a novel rigid-body constraint mechanism. Instead of predicting the physical dynamics for every Gaussian particle, our model predicts the motion of a single anchor Gaussian per semantic object, updating the remaining Gaussians via relative transformations. This architectural design significantly accelerates novel view synthesis compared to an unconstrained baseline, while enabling object-accurate extrapolation and intuitive semantic interaction. Our project page: https://be2rlab.github.io/r5dgs/.
3D Gaussian Splatting has become a de facto scene representation for novel view synthesis, yet robustly learning 3D Gaussian primitives from visual input remains challenging. Standard optimization relies on gradient-based updates, but a common issue is the gradient vanishing phenomenon: a pixel far from a Gaussian primitive often has diminishing gradient magnitudes to influence primitive attributes, resulting in suboptimal scene reconstruction. In this paper, we propose a method to address gradient vanishing with a piecewise truncated gradient formulation that improves the optimization stability and robustness to initializations. We show that our method consistently improves 3D Gaussian Splatting with random and COLMAP initializations while being generalizable across static and dynamic Gaussian Splatting. As a by-product, we also examine the limitations of current benchmarks for dynamic scenes, and introduce a novel dataset for benchmarking dynamic Gaussian Splatting using synthetic 3D scenes. We demonstrate the effectiveness of our method in both static and dynamic settings for the public benchmarks and our proposed dataset.
3D Gaussian Splatting (3DGS) provides an explicit and efficient scene representation, but its primitives lack inherent object-level identity, hindering downstream tasks such as open-vocabulary scene understanding. Existing methods typically address this by either distilling high-dimensional feature embeddings into Gaussians or by lifting 2D mask labels into 3D via heuristic refinement. However, feature-based approaches incur heavy storage and decoding overhead, while lifting-based pipelines remain vulnerable to label contamination: Gaussians necessary for appearance reconstruction often receive incorrect object labels during 2D-to-3D projection. We propose OP2GS, an object-aware Gaussian representation that augments each primitive with an explicit instance identity and a dedicated instance opacity σ∗ for object-mask rendering. The original opacity σ remains responsible for visual reconstruction, while σ∗ models whether a Gaussian should contribute to a particular object mask. This dual-opacity formulation decouples visual existence from instance occupancy: mislabeled Gaussians can remain available for image rendering while becoming transparent in the object-mask branch. To learn this representation, we introduce a random object loss that optimizes the 1D instance occupancy field using the standard transmittance-based visibility of 3DGS. Semantic descriptors are then attached at the object level through multi-view aggregation, eliminating per-Gaussian feature storage. Compared with feature-training approaches, OP2GS achieves competitive open-vocabulary performance while significantly reducing computational overhead. Compared with training-free pipelines, it leverages physically consistent occupancy learning to resolve visibility ambiguities.