Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration

3D Gaussian Splatting (3DGS) recently gained popularity 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 still produces severe blurring or jaggies when rendered at varying resolutions because the discrete sampling scheme used treats each pixel as an isolated single point, which is insensitive to changes in the footprints of pixels and is restricted in sampling bandwidth. In this paper, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) of the Gaussian signal and calculate the integral by subtracting the CDFs. We introduce this approximation to 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. Then, 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. Extensive experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.