将高斯点云重新定义为几何体，实现更精准的三维重建。
Geometry-Grounded Gaussian Splatting
- 把高斯点视为随机固体，从理论上建立几何表示基础。
- 在公开数据集上实现当前最优的三维形状重建效果。
- 适合需要高精度几何重建的科研与工业应用。
高斯点绘（Gaussian Splatting, GS）在新视角合成中展现出卓越的质量与效率，但由高斯原型提取形状仍是开放问题。由于几何参数化不足和近似误差，现有重建方法普遍存在多视角不一致且对噪声点敏感的问题。本文通过严格的理论推导，证明高斯原型是特定类型的随机固体。该理论框架为几何约束的高斯点绘提供了原理性基础，使高斯原型可直接作为显式几何表示。利用随机固体的体素特性，本方法高效生成高质量深度图，实现细粒度几何提取。实验表明，在公开数据集上，本方法在所有基于高斯点绘的方法中取得了最佳的形状重建性能。
原文摘要 · Abstract (English)
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.
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