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：三维高斯泼溅（3D Gaussian Splatting）在实时神经渲染领域受到广泛关注和应用。与此同时，该技术在点云存储、性能以及稀疏视角下的鲁棒性等方面的局限性引发了担忧，并催生了多种改进方案。然而，现有研究普遍忽视了泼溅过程中局部仿射近似引入的投影误差，以及这些误差对逼真渲染质量的潜在影响。本文针对三维高斯泼溅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误差入手，建立误差与高斯均值位置之间的关联。进而，基于函数优化理论，通过分析函数的极值点，提出一种针对高斯泼溅的最优投影策略，称为最优高斯泼溅（Optimal Gaussian Splatting）。实验验证进一步表明，该投影方法能有效减少伪影，从而提升渲染结果的真实感。