Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation, existing shape reconstruction methods suffer from poor multi-view consistency and are sensitive to floaters. In this paper, we present a rigorous theoretical derivation that establishes Gaussian primitives as a specific type of stochastic solids. This theoretical framework provides a principled foundation for Geometry-Grounded Gaussian Splatting by enabling the direct treatment of Gaussian primitives as explicit geometric representations. Using the volumetric nature of stochastic solids, our method efficiently renders high-quality depth maps for fine-grained geometry extraction. Experiments show that our method achieves the best shape reconstruction results among all Gaussian Splatting-based methods on public datasets.

翻译：Gaussian Splatting (GS) 在新视角合成中已展现出卓越的质量与效率。然而，从高斯基元中提取几何形状仍是一个悬而未决的问题。由于几何参数化与近似方法的不足，现有的形状重建方法存在多视角一致性差且对悬浮伪影敏感的问题。本文通过严谨的理论推导，将高斯基元确立为一类特定的随机实体。该理论框架通过将高斯基元直接作为显式几何表征进行处理，为基于几何基础的Gaussian Splatting提供了原理性支撑。利用随机实体的体素化特性，我们的方法能够高效渲染高质量深度图，以实现细粒度几何提取。实验表明，在公开数据集上，我们的方法在所有基于Gaussian Splatting的方法中取得了最优的形状重建结果。