3D Gaussian splatting models, as a novel explicit 3D representation, have been applied in many domains recently, such as explicit geometric editing and geometry generation. Progress has been rapid. However, due to their mixed scales and cluttered shapes, 3D Gaussian splatting models can produce a blurred or needle-like effect near the surface. At the same time, 3D Gaussian splatting models tend to flatten large untextured regions, yielding a very sparse point cloud. These problems are caused by the non-uniform nature of 3D Gaussian splatting models, so in this paper, we propose a new 3D Gaussian splitting algorithm, which can produce a more uniform and surface-bounded 3D Gaussian splatting model. Our algorithm splits an $N$-dimensional Gaussian into two N-dimensional Gaussians. It ensures consistency of mathematical characteristics and similarity of appearance, allowing resulting 3D Gaussian splatting models to be more uniform and a better fit to the underlying surface, and thus more suitable for explicit editing, point cloud extraction and other tasks. Meanwhile, our 3D Gaussian splitting approach has a very simple closed-form solution, making it readily applicable to any 3D Gaussian model.

翻译：三维高斯溅射模型作为一种新型显式三维表示，近年来已被广泛应用于显式几何编辑和几何生成等领域，进展迅速。然而，由于三维高斯溅射模型尺度混杂且形状不规则，其在表面附近可能产生模糊或针状效应。同时，三维高斯溅射模型倾向于压平大面积无纹理区域，导致点云极其稀疏。这些问题源于三维高斯溅射模型的非均匀特性，为此本文提出一种新型三维高斯分裂算法，能够生成更均匀且更贴合表面的三维高斯溅射模型。本算法将$N$维高斯分布分裂为两个$N$维高斯分布，确保数学特征一致性与外观相似性，使生成的三维高斯溅射模型更均匀且更好贴合底层表面，从而更适用于显式编辑、点云提取等任务。同时，该三维高斯分裂方法具有极简的闭式解，可便捷应用于任意三维高斯模型。