  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.
