# Volumetrically Consistent 3D Gaussian Rasterization

arXiv: https://arxiv.org/abs/2412.03378 · HTML: https://mlsanity.com/paper/2412.03378/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 30 of 35)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [MERF: Memory-Efficient Radiance Fields for Real-time View Synthesis in Unbounded Scenes](https://mlsanity.com/paper/2302.12249/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [3D Gaussian Ray Tracing: Fast Tracing of Particle Scenes](https://mlsanity.com/paper/2407.07090/) (2024)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [StopThePop: Sorted Gaussian Splatting for View-Consistent Real-time Rendering](https://mlsanity.com/paper/2402.00525/) (2024)
- [RaDe-GS: Rasterizing Depth in Gaussian Splatting](https://mlsanity.com/paper/2406.01467/) (2024)
- [NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2209.14540/) (2022)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [Adaptive Shells for Efficient Neural Radiance Field Rendering](https://mlsanity.com/paper/2311.10091/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [SMERF: Streamable Memory Efficient Radiance Fields for Real-Time Large-Scene Exploration](https://mlsanity.com/paper/2312.07541/) (2023)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis](https://mlsanity.com/paper/2402.12377/) (2024)
- [Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media](https://mlsanity.com/paper/2405.15425/) (2024)

## Built on by (most cited first, 12 of 12)

- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [3DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Cameras](https://mlsanity.com/paper/2505.24053/) (2025)
- [SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction](https://mlsanity.com/paper/2506.19139/) (2025)
- [Splat the Net: Radiance Fields with Splattable Neural Primitives](https://mlsanity.com/paper/2510.08491/) (2025)
- [ConeGS: Error-Guided Densification Using Pixel Cones for Improved Reconstruction With Fewer Primitives](https://mlsanity.com/paper/2511.06810/) (2025)
- [UGOD: Uncertainty-Guided Differentiable Opacity and Soft Dropout for Enhanced Sparse-View 3DGS](https://mlsanity.com/paper/2508.04968/) (2025)
- [Moment-Based 3D Gaussian Splatting: Resolving Volumetric Occlusion with Order-Independent Transmittance](https://mlsanity.com/paper/2512.11800/) (2025)
- [Radioactive 3D Gaussian Ray Tracing for Tomographic Reconstruction](https://mlsanity.com/paper/2602.01057/) (2026)
- [On the Skinning of Gaussian Avatars](https://mlsanity.com/paper/2509.11411/) (2025)
- [From Volume Rendering to 3D Gaussian Splatting: Theory and Applications](https://mlsanity.com/paper/2510.18101/) (2025)
- [The Impact and Outlook of 3D Gaussian Splatting](https://mlsanity.com/paper/2510.26694/) (2025)
- [Gaussian Splatting for Real-Time Scene Reconstruction: Methods, Systems, and Trade-offs](https://mlsanity.com/paper/2610.17513/) (2026)

## Abstract (arXiv)

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