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 ϕ. 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.
3D高斯散射在实时神经渲染中获得了广泛的关注和应用。同时，也有人对这项技术在点云存储、性能以及在稀疏视点下的鲁棒性等方面的局限性提出了担忧，这导致了各种改进。然而，对于散射本身固有的局部仿射近似引入的投影错误及这些错误对于照片级真实渲染质量的影响，缺乏足够的关注。本文讨论了3D高斯散射的投影误差函数，从投影函数ϕ的一阶泰勒展开的残差误差开始。分析建立了误差与高斯平均位置之间的相关性。随后，利用函数优化理论，本文分析了函数的最小值，以提供一个称为最优高斯散射的高斯散射的最优投影策略。实验验证进一步确认了这种投影方法减少了伪影，结果是更加令人信服的真实渲染。