Relaxed Rigidity with Ray-based Grouping for Dynamic Gaussian Splatting

The reconstruction of dynamic 3D scenes using 3D GaussianSplatting has shown significant promise. A key challenge, however, re-mains in modeling realistic motion, as most methods fail to align the mo-tion of Gaussians with real-world physical dynamics. This misalignmentis particularly problematic for monocular video datasets, where failingto maintain coherent motion undermines local geometric structure, ulti-mately leading to degraded reconstruction quality. Consequently, manystate-of-the-art approaches rely heavily on external priors, such as opti-cal flow or 2D tracks, to enforce temporal coherence. In this work, wepropose a novel method to explicitly preserve the local geometric struc-ture of Gaussians across time in 4D scenes. Our core idea is to introducea view-space ray grouping strategy that clusters Gaussians intersectedby the same ray, considering only those whose α-blending weights ex-ceed a threshold. We then apply constraints to these groups to maintaina consistent spatial distribution, effectively preserving their local geom-etry. This approach enforces a more locally coherent motion model byensuring that local geometry remains stable over time, eliminating thereliance on external guidance. We demonstrate the efficacy of our methodby integrating it into two distinct baseline models. Extensive experimentson challenging monocular datasets show that our approach significantlyoutperforms existing methods, achieving superior temporal consistencyand reconstruction quality.