3D Gaussian Splatting has garnered extensive attention and application in real-time neural rendering. Concurrently, concerns have been raised about the limitations of this technology in aspects such as point cloud storage, performance , and robustness in sparse viewpoints , leading to various improvements. However, there has been a notable lack of attention to the projection errors introduced by the local affine approximation inherent in the splatting itself, and the consequential impact of these errors on the quality of photo-realistic rendering. This paper addresses the projection error function of 3D Gaussian Splatting, commencing with the residual error from the first-order Taylor expansion of the projection function $\phi$. The analysis establishes a correlation between the error and the Gaussian mean position. Subsequently, leveraging function optimization theory, this paper analyzes the function's minima to provide an optimal projection strategy for Gaussian Splatting referred to Optimal Gaussian Splatting. Experimental validation further confirms that this projection methodology reduces artifacts, resulting in a more convincingly realistic rendering.

翻译：三维高斯喷射（3D Gaussian Splatting）在实时神经渲染领域获得了广泛关注与应用。与此同时，该技术在点云存储、渲染性能及稀疏视角鲁棒性等方面的局限性引发了学界关注，催生了诸多改进方案。然而，当前研究普遍忽视了高斯喷射本身固有的局部仿射近似所引入的投影误差，以及这些误差对逼真渲染质量的潜在影响。本文针对三维高斯喷射的投影误差函数展开研究，从投影函数φ的一阶泰勒展开残差入手，建立了误差与高斯均值位置之间的关联性。进而基于函数优化理论，通过分析该函数的极值特性，提出了一种面向高斯喷射的最优投影策略——最优高斯喷射（Optimal Gaussian Splatting）。实验验证表明，该投影方法能有效减少伪影，获得更具真实感的渲染结果。