Symmetry-Preserving 4D Gaussian Splatting and Mapping for Motion-Aware Dynamic Scene Reconstruction

This paper introduces a novel and efficient approach for Gaussian Splatting in dynamic scenes that leverages symmetry principles for enhanced computational efficiency and visual fidelity. First, we diverge from conventional methods that process static and dynamic regions uniformly by implementing an adaptive separation mechanism. This approach exploits the inherent symmetry-breaking properties between static and dynamic Gaussian points, utilizing motion differentials to identify and isolate dynamic elements. This symmetry-aware partitioning allows for the application of specialized processing techniques to each region type, with static regions benefiting from their temporal symmetry while dynamic regions receive targeted deformation modeling. Second, through this fine-grained partitioning of static and dynamic components guided by symmetry analysis, we achieve more judicious allocation of computational resources. The symmetric treatment of spatially coherent static regions and the focused processing of symmetry-breaking dynamic elements substantially reduce memory requirements and training time while preserving reconstruction quality. This optimization effectively conserves valuable computational resources without compromising visual fidelity. Third, we introduce a sophisticated deformation modeling framework that learns the transformational characteristics of grids composed of multiple Gaussian points. By incorporating radial basis function principles, which inherently preserve local rotational and translational symmetries, our method efficiently encodes complex motion information of dynamic Gaussian points. This symmetry-preserving deformation approach not only enables high-fidelity reconstruction of dynamic regions but also significantly improves the rendering of continuously evolving shadow interactions by maintaining physical consistency. The result is a marked reduction in visual distortion and rendering outputs that demonstrate exceptional correspondence to ground truth imagery across diverse dynamic scenes.