The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.
3D高斯平滑（3DGS）最近因结合了基于原始和体积3D表示的优势，从而提高了3D场景渲染的质量和效率而受到欢迎。然而，3DGS并非无别名，其在不同分辨率下的渲染可能会产生严重的模糊或锯齿。这是因为3DGS将每个像素视为一个孤立的单点而不是一个区域，导致对像素足迹变化的不敏感。因此，这种离散的采样方案不可避免地导致了别名问题，这是由于受限的采样带宽。在本文中，我们推导出一种解决这一问题的分析解。更具体地说，我们使用条件逻辑函数作为一维高斯信号的累积分布函数（CDF）的解析近似，并通过减去CDF来计算高斯积分。然后，我们在二维像素着色中引入这种近似，并提出分析平滑，它在2D像素窗口区域内解析近似高斯积分，以更好地捕捉每个像素的强度响应。此外，我们使用像素窗口积分区域的近似响应参与体渲染的透射计算，使分析平滑对不同分辨率下像素足迹的变化敏感。在各种数据集上的实验验证了我们的方法具有更好的抗锯齿能力，提供了更多细节和更好的保真度。