Volumetrically Consistent 3D Gaussian Rasterization

TL;DR

This work targets the physical inaccuracies of 3D Gaussian Splatting (3DGS) by replacing its screen-space splatting with volumetric, analytic integration of 3D Gaussians inside a rasterizer. By deriving exact transmittance along camera rays and using alpha values $\alpha_i$ computed from the integrated density $\overline{T}_i$, the method closely follows the volume rendering equation $C(r)$ and $T(a,b)$, delivering more accurate opacity and improved view synthesis and tomography. The approach serves as a drop-in replacement for 3DGS's alpha computation, yielding higher-quality opaque surfaces, competitive runtimes, and applicability to tomography with fewer primitives. Empirically, it improves SSIM and LPIPS on standard view-synthesis benchmarks and matches or surpasses state-of-the-art tomography performance, while preserving the speed advantages of rasterization. The work further proposes practical implementation choices, including a density reparameterization and targeted densification strategies, to stabilize optimization and extend applicability to compact primitives and optimized tile sizes.

Abstract

Recently, 3D Gaussian Splatting (3DGS) has enabled photorealistic view synthesis at high inference speeds. However, its splatting-based rendering model makes several approximations to the rendering equation, reducing physical accuracy. We show that the core approximations in splatting are unnecessary, even within a rasterizer; We instead volumetrically integrate 3D Gaussians directly to compute the transmittance across them analytically. We use this analytic transmittance to derive more physically-accurate alpha values than 3DGS, which can directly be used within their framework. The result is a method that more closely follows the volume rendering equation (similar to ray-tracing) while enjoying the speed benefits of rasterization. Our method represents opaque surfaces with higher accuracy and fewer points than 3DGS. This enables it to outperform 3DGS for view synthesis (measured in SSIM and LPIPS). Being volumetrically consistent also enables our method to work out of the box for tomography. We match the state-of-the-art 3DGS-based tomography method with fewer points. Our code is publicly available at: https://github.com/chinmay0301ucsd/Vol3DGS

Figures (10)

• Figure 1: Volumetrically consistent $\alpha$ Computation Top row: 3D Gaussians that are not grey contribute to the pixel along the camera ray. Next, 1D Gaussian densities along the ray are used to compute $\alpha_i$ values required for color computation. 3DGS's splatting approximates the volume rendering equation and sets $\alpha_i = G_i(x_i)$, that is the maximum density of the Gaussian long the ray. Our approach instead performs volumetrically consistent $\alpha$ computation by accumulating the density along the ray $\alpha_i = 1 - \exp\left(- \int G_i(x)dx\right)$ in accordance with the volume rendering equation, which we derive in \ref{['sec:method']}. Both methods compute the final pixel color via $\alpha$ blending using their respective $\alpha$ values.
• Figure 2: Opacity as a function of density and scale.Top row: 1D cross sections of renderings for our method (solid) and 3DGS (dotted). Our method represents opaque objects better by two mechanisms: 1) increasing the scale along the camera ray (a); 2) increasing the volume density (b); both increase the flat region where $\alpha=1$. Since 3DGS splats 3D Gaussians onto the image plane as 2D Gaussians, irrespective of the scale (a) or the opacity (b), the cross-sections are all Gaussian with $\alpha=1$ possible only at the center. Bottom row: We optimize the parameters of a single 3D Gaussian to fit a circle using 3DGS and our method. As we saw in the top row (a) and (b), regardless of scale or opacity, 3DGS can only render a 2D Gaussian in image-space, resulting in a blurry fit of the opaque object. On the other hand, our method adjusts density and scale to produce a more opaque rendering.
• Figure 3: Fitting piecewise constant shapes with equal numbers of 3D Gaussians. (Please zoom in.) Our method, by increasing the volume density $\kappa$ can make rendered 3D Gaussians close to opaque (b), which is a closer match to the ground truth (a), with LPIPS $0.005$ (lower is better). 3DGS splats 3D Gaussians onto the screen as 2D Gaussians, which are only fully opaque at their center; this leads to artifacts especially near edges (see inset in second row) and much worse LPIPS $0.027$.
• Figure 4: Qualitative Results on View Synthesis We qualitatively show the strengths of our approach on several scenes from real datasets. Each row from top to bottom are for the scenes flowers, room, trains,playroom, counter and stump. Our method has less blurry regions compared to 3DGS in flowers. Our ability to represent opaque regions accurately shows up prominently in room. Our method is able to better capture fine details in the tiles in playroom. In counter 3DGS misses details on the floor that our method is able to capture. Finally, in stump, we are able to capture sharper details in the grass that 3DGS misses.
• Figure 5: Tomography visual results: For our method (top row) and the splatting-based SOTA $R^{2}$-Gaussian (zha2024r), we show slices of the reconstructed 3D density along the axial plane, perpendicular to the frontal views used during training. Each column corresponds to one of the distinct scenes from the datasets in zha2024r. Both methods produce visually similar reconstructions, with an average 2D PSNR of 29.94 (ours) and 30.06 (3DGS) for the displayed images.