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

arXiv: https://arxiv.org/abs/2403.11056 · HTML: https://mlsanity.com/paper/2403.11056/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 40 references that are in the map.
- First posted on arXiv 17 Mar 2024.

## Builds on (most cited first, 30 of 32)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [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)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [GaussianShader: 3D Gaussian Splatting with Shading Functions for Reflective Surfaces](https://mlsanity.com/paper/2311.17977/) (2023)
- [GS-IR: 3D Gaussian Splatting for Inverse Rendering](https://mlsanity.com/paper/2311.16473/) (2023)
- [GaussianAvatar: Towards Realistic Human Avatar Modeling from a Single Video via Animatable 3D Gaussians](https://mlsanity.com/paper/2312.02134/) (2023)
- [Deblur-NeRF: Neural Radiance Fields from Blurry Images](https://mlsanity.com/paper/2111.14292/) (2021)
- [GPS-Gaussian: Generalizable Pixel-wise 3D Gaussian Splatting for Real-time Human Novel View Synthesis](https://mlsanity.com/paper/2312.02155/) (2023)
- [Tri-MipRF: Tri-Mip Representation for Efficient Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2307.11335/) (2023)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [Relightable Gaussian Codec Avatars](https://mlsanity.com/paper/2312.03704/) (2023)
- [Drivable 3D Gaussian Avatars](https://mlsanity.com/paper/2311.08581/) (2023)
- [HDR-NeRF: High Dynamic Range Neural Radiance Fields](https://mlsanity.com/paper/2111.14451/) (2021)
- [GIR: 3D Gaussian Inverse Rendering for Relightable Scene Factorization](https://mlsanity.com/paper/2312.05133/) (2023)
- [NerfAcc: A General NeRF Acceleration Toolbox](https://mlsanity.com/paper/2210.04847/) (2022)

## Built on by (most cited first, 30 of 67)

- [TrajectoryCrafter: Redirecting Camera Trajectory for Monocular Videos via Diffusion Models](https://mlsanity.com/paper/2503.05638/) (2025)
- [3D Gaussian Splatting: Survey, Technologies, Challenges, and Opportunities](https://mlsanity.com/paper/2407.17418/) (2024)
- [3D-HGS: 3D Half-Gaussian Splatting](https://mlsanity.com/paper/2406.02720/) (2024)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [DashGaussian: Optimizing 3D Gaussian Splatting in 200 Seconds](https://mlsanity.com/paper/2503.18402/) (2025)
- [Rethinking End-to-End 2D to 3D Scene Segmentation in Gaussian Splatting](https://mlsanity.com/paper/2503.14029/) (2025)
- [Lighting Every Darkness with 3DGS: Fast Training and Real-Time Rendering for HDR View Synthesis](https://mlsanity.com/paper/2406.06216/) (2024)
- [Fisheye-GS: Lightweight and Extensible Gaussian Splatting Module for Fisheye Cameras](https://mlsanity.com/paper/2409.04751/) (2024)
- [StreetSurfGS: Scalable Urban Street Surface Reconstruction with Planar-based Gaussian Splatting](https://mlsanity.com/paper/2410.04354/) (2024)
- [A Survey on 3D Gaussian Splatting Applications: Segmentation, Editing, and Generation](https://mlsanity.com/paper/2508.09977/) (2025)
- [4D Gaussian Splatting: Modeling Dynamic Scenes with Native 4D Primitives](https://mlsanity.com/paper/2412.20720/) (2024)
- [NeRF Is a Valuable Assistant for 3D Gaussian Splatting](https://mlsanity.com/paper/2507.23374/) (2025)
- [NeuralGS: Bridging Neural Fields and 3D Gaussian Splatting for Compact 3D Representations](https://mlsanity.com/paper/2503.23162/) (2025)
- [Reconstruct, Inpaint, Test-Time Finetune: Dynamic Novel-view Synthesis from Monocular Videos](https://mlsanity.com/paper/2507.12646/) (2025)
- [AAA-Gaussians: Anti-Aliased and Artifact-Free 3D Gaussian Rendering](https://mlsanity.com/paper/2504.12811/) (2025)
- [SolidGS: Consolidating Gaussian Surfel Splatting for Sparse-View Surface Reconstruction](https://mlsanity.com/paper/2412.15400/) (2024)
- [ZeroGS: Training 3D Gaussian Splatting from Unposed Images](https://mlsanity.com/paper/2411.15779/) (2024)
- [3DGabSplat: 3D Gabor Splatting for Frequency-adaptive Radiance Field Rendering](https://mlsanity.com/paper/2508.05343/) (2025)
- [Mipmap-GS: Let Gaussians Deform with Scale-specific Mipmap for Anti-aliasing Rendering](https://mlsanity.com/paper/2408.06286/) (2024)
- [GLS: Geometry-aware 3D Language Gaussian Splatting](https://mlsanity.com/paper/2411.18066/) (2024)
- [GaussHDR: High Dynamic Range Gaussian Splatting via Learning Unified 3D and 2D Local Tone Mapping](https://mlsanity.com/paper/2503.10143/) (2025)
- [COS3D: Collaborative Open-Vocabulary 3D Segmentation](https://mlsanity.com/paper/2510.20238/) (2025)
- [AdaGaR: Adaptive Gabor Representation for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2601.00796/) (2026)
- [Gaussian Splashing: Direct Volumetric Rendering Underwater](https://mlsanity.com/paper/2411.19588/) (2024)
- [Anti-Aliased 2D Gaussian Splatting](https://mlsanity.com/paper/2506.11252/) (2025)
- [Can3Tok: Canonical 3D Tokenization and Latent Modeling of Scene-Level 3D Gaussians](https://mlsanity.com/paper/2508.01464/) (2025)
- [2DGH: 2D Gaussian-Hermite Splatting for High-quality Rendering and Better Geometry Features](https://mlsanity.com/paper/2408.16982/) (2024)
- [SpecGaussian with Latent Features: A High-quality Modeling of the View-dependent Appearance for 3D Gaussian Splatting](https://mlsanity.com/paper/2409.05868/) (2024)
- [Arbitrary-Scale 3D Gaussian Super-Resolution](https://mlsanity.com/paper/2508.16467/) (2025)
- [Holistic Large-Scale Scene Reconstruction via Mixed Gaussian Splatting](https://mlsanity.com/paper/2505.23280/) (2025)

## Abstract (arXiv)

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.