# On the Error Analysis of 3D Gaussian Splatting and an Optimal Projection Strategy

arXiv: https://arxiv.org/abs/2402.00752 · HTML: https://mlsanity.com/paper/2402.00752/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 30 of 33)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [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)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [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)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [GaussianEditor: Swift and Controllable 3D Editing with Gaussian Splatting](https://mlsanity.com/paper/2311.14521/) (2023)
- [FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularization](https://mlsanity.com/paper/2303.07418/) (2023)
- [Compressed 3D Gaussian Splatting for Accelerated Novel View Synthesis](https://mlsanity.com/paper/2401.02436/) (2023)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [Segment Any 3D Gaussians](https://mlsanity.com/paper/2312.00860/) (2023)

## Built on by (most cited first, 30 of 39)

- [FlashGS: Efficient 3D Gaussian Splatting for Large-scale and High-resolution Rendering](https://mlsanity.com/paper/2408.07967/) (2024)
- [3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting](https://mlsanity.com/paper/2412.12507/) (2024)
- [Efficient Perspective-Correct 3D Gaussian Splatting Using Hybrid Transparency](https://mlsanity.com/paper/2410.08129/) (2024)
- [Radiant Foam: Real-Time Differentiable Ray Tracing](https://mlsanity.com/paper/2502.01157/) (2025)
- [HAHA: Highly Articulated Gaussian Human Avatars with Textured Mesh Prior](https://mlsanity.com/paper/2404.01053/) (2024)
- [Fisheye-GS: Lightweight and Extensible Gaussian Splatting Module for Fisheye Cameras](https://mlsanity.com/paper/2409.04751/) (2024)
- [ODGS: 3D Scene Reconstruction from Omnidirectional Images with 3D Gaussian Splattings](https://mlsanity.com/paper/2410.20686/) (2024)
- [Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?](https://mlsanity.com/paper/2502.19318/) (2025)
- [AtomGS: Atomizing Gaussian Splatting for High-Fidelity Radiance Field](https://mlsanity.com/paper/2405.12369/) (2024)
- [VRSplat: Fast and Robust Gaussian Splatting for Virtual Reality](https://mlsanity.com/paper/2505.10144/) (2025)
- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [TransparentGS: Fast Inverse Rendering of Transparent Objects with Gaussians](https://mlsanity.com/paper/2504.18768/) (2025)
- [LiDAR-GS:Real-time LiDAR Re-Simulation using Gaussian Splatting](https://mlsanity.com/paper/2410.05111/) (2024)
- [Gaussian Splatting for Efficient Satellite Image Photogrammetry](https://mlsanity.com/paper/2412.13047/) (2024)
- [GlossyGS: Inverse Rendering of Glossy Objects with 3D Gaussian Splatting](https://mlsanity.com/paper/2410.13349/) (2024)
- [AAA-Gaussians: Anti-Aliased and Artifact-Free 3D Gaussian Rendering](https://mlsanity.com/paper/2504.12811/) (2025)
- [OmniSplat: Taming Feed-Forward 3D Gaussian Splatting for Omnidirectional Images with Editable Capabilities](https://mlsanity.com/paper/2412.16604/) (2024)
- [FIORD: A Fisheye Indoor-Outdoor Dataset with LIDAR Ground Truth for 3D Scene Reconstruction and Benchmarking](https://mlsanity.com/paper/2504.01732/) (2025)
- [SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction](https://mlsanity.com/paper/2506.19139/) (2025)
- [CompGS++: Compressed Gaussian Splatting for Static and Dynamic Scene Representation](https://mlsanity.com/paper/2504.13022/) (2025)
- [ErpGS: Equirectangular Image Rendering enhanced with 3D Gaussian Regularization](https://mlsanity.com/paper/2505.19883/) (2025)
- [Industrial-Grade Sensor Simulation via Gaussian Splatting: A Modular Framework for Scalable Editing and Full-Stack Validation](https://mlsanity.com/paper/2503.11731/) (2025)
- [You Need a Transition Plane: Bridging Continuous Panoramic 3D Reconstruction with Perspective Gaussian Splatting](https://mlsanity.com/paper/2504.09062/) (2025)
- [SVAD: From Single Image to 3D Avatar via Synthetic Data Generation with Video Diffusion and Data Augmentation](https://mlsanity.com/paper/2505.05475/) (2025)
- [OB3D: A New Dataset for Benchmarking Omnidirectional 3D Reconstruction Using Blender](https://mlsanity.com/paper/2505.20126/) (2025)
- [GS-Verse: Mesh-based Gaussian Splatting for Physics-aware Interaction in Virtual Reality](https://mlsanity.com/paper/2510.11878/) (2025)
- [DC4GS: Directional Consistency-Driven Adaptive Density Control for 3D Gaussian Splatting](https://mlsanity.com/paper/2510.26921/) (2025)
- [Spectral-GS: Taming 3D Gaussian Splatting with Spectral Entropy](https://mlsanity.com/paper/2409.12771/) (2024)
- [LighthouseGS: Indoor Structure-aware 3D Gaussian Splatting for Panorama-Style Mobile Captures](https://mlsanity.com/paper/2507.06109/) (2025)
- [Refining Gaussian Splatting: A Volumetric Densification Approach](https://mlsanity.com/paper/2508.05187/) (2025)

## Abstract (arXiv)

3D Gaussian Splatting has garnered extensive attention and application in real-time neural rendering. Concurrently, concerns have been raised about the limitations of this technology in aspects such as point cloud storage, performance, and robustness in sparse viewpoints, leading to various improvements. However, there has been a notable lack of attention to the fundamental problem of projection errors introduced by the local affine approximation inherent in the splatting itself, and the consequential impact of these errors on the quality of photo-realistic rendering. This paper addresses the projection error function of 3D Gaussian Splatting, commencing with the residual error from the first-order Taylor expansion of the projection function. The analysis establishes a correlation between the error and the Gaussian mean position. Subsequently, leveraging function optimization theory, this paper analyzes the function's minima to provide an optimal projection strategy for Gaussian Splatting referred to Optimal Gaussian Splatting, which can accommodate a variety of camera models. Experimental validation further confirms that this projection methodology reduces artifacts, resulting in a more convincingly realistic rendering.