# Effective Rank Analysis and Regularization for Enhanced 3D Gaussian Splatting

arXiv: https://arxiv.org/abs/2406.11672 · HTML: https://mlsanity.com/paper/2406.11672/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [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)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [GaussianShader: 3D Gaussian Splatting with Shading Functions for Reflective Surfaces](https://mlsanity.com/paper/2311.17977/) (2023)
- [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)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [GIR: 3D Gaussian Inverse Rendering for Relightable Scene Factorization](https://mlsanity.com/paper/2312.05133/) (2023)
- [Neural 3D Reconstruction in the Wild](https://mlsanity.com/paper/2205.12955/) (2022)
- [NSML: Meet the MLaaS platform with a real-world case study](https://mlsanity.com/paper/1810.09957/) (2018)
- [Adaptive Shells for Efficient Neural Radiance Field Rendering](https://mlsanity.com/paper/2311.10091/) (2023)
- [Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis](https://mlsanity.com/paper/2402.12377/) (2024)

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

- [Textured Gaussians for Enhanced 3D Scene Appearance Modeling](https://mlsanity.com/paper/2411.18625/) (2024)
- [4D Gaussian Splatting in the Wild with Uncertainty-Aware Regularization](https://mlsanity.com/paper/2411.08879/) (2024)
- [RobustSplat: Decoupling Densification and Dynamics for Transient-Free 3DGS](https://mlsanity.com/paper/2506.02751/) (2025)
- [OmniSplat: Taming Feed-Forward 3D Gaussian Splatting for Omnidirectional Images with Editable Capabilities](https://mlsanity.com/paper/2412.16604/) (2024)
- [Aquatic-GS: A Hybrid 3D Representation for Underwater Scenes](https://mlsanity.com/paper/2411.00239/) (2024)
- [Vision Pretraining for Dense Spatial Perception](https://mlsanity.com/paper/2607.05247/) (2026)
- [GaussFusion: Improving 3D Reconstruction in the Wild with A Geometry-Informed Video Generator](https://mlsanity.com/paper/2603.25053/) (2026)
- [DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions](https://mlsanity.com/paper/2501.12369/) (2025)
- [Low-Frequency First: Eliminating Floating Artifacts in 3D Gaussian Splatting](https://mlsanity.com/paper/2508.02493/) (2025)
- [Terra: Explorable Native 3D World Model with Point Latents](https://mlsanity.com/paper/2510.14977/) (2025)
- [Robust and High-Fidelity 3D Gaussian Splatting: Fusing Pose Priors and Geometry Constraints for Texture-Deficient Outdoor Scenes](https://mlsanity.com/paper/2511.06765/) (2025)
- [EGGS: Exchangeable 2D/3D Gaussian Splatting for Geometry-Appearance Balanced Novel View Synthesis](https://mlsanity.com/paper/2512.02932/) (2025)
- [Drop-In Perceptual Optimization for 3D Gaussian Splatting](https://mlsanity.com/paper/2603.23297/) (2026)
- [Spatiotemporal Degradation-Aware 3D Gaussian Splatting for Realistic Underwater Scene Reconstruction](https://mlsanity.com/paper/2604.23551/) (2026)
- [GeoSplat: A Deep Dive into Geometry-Constrained Gaussian Splatting](https://mlsanity.com/paper/2509.05075/) (2025)
- [Fix False Transparency by Noise Guided Splatting](https://mlsanity.com/paper/2510.15736/) (2025)
- [3D Skew Gaussian Splatting with Any Camera Trajectory Visualization Engine](https://mlsanity.com/paper/2605.18334/) (2026)
- [A Mixed-Primitive-based Gaussian Splatting Method for Surface Reconstruction](https://mlsanity.com/paper/2507.11321/) (2025)
- [ARGS: Advanced Regularization on Aligning Gaussians over the Surface](https://mlsanity.com/paper/2508.21344/) (2025)
- [Analysis of Converged 3D Gaussian Splatting Solutions: Density Effects and Prediction Limit](https://mlsanity.com/paper/2602.08909/) (2026)
- [Catalyst4D: High-Fidelity 3D-to-4D Scene Editing via Dynamic Propagation](https://mlsanity.com/paper/2603.12766/) (2026)
- [Relaxed Rigidity with Ray-based Grouping for Dynamic Gaussian Splatting](https://mlsanity.com/paper/2603.24994/) (2026)
- [Wispy to Voluminous: Prior-free Multi-view Capture of Strand-level Facial Hair](https://mlsanity.com/paper/2606.08041/) (2026)
- [RankVR: Low-Rank Structure Perception and Value Recalibration for Robust Composed Image Retrieval](https://mlsanity.com/paper/2606.11689/) (2026)
- [Improving Sparse-View 3DGS Generalization via Flat Minima Optimization](https://mlsanity.com/paper/2607.00885/) (2026)
- [Dynamic Inverse Rendering for Enhanced Material-Lighting Decomposition](https://mlsanity.com/paper/2607.09329/) (2026)
- [HyperGS: Fast and Generalizable Gaussian Video Representation](https://mlsanity.com/paper/2607.11500/) (2026)
- [G2ARD-GS: Geometry-Guided Anchor-Regularized Gaussian Splatting Distillation](https://mlsanity.com/paper/2608.05704/) (2026)
- [KISS-GS: 3D Gaussian Splatting Compression Kept Simple](https://mlsanity.com/paper/2608.26948/) (2026)
- [AD-GS: Anatomical Density-guided 3D Gaussian Splatting for Sparse-View Dental CBCT Reconstruction](https://mlsanity.com/paper/2610.14963/) (2026)

## Abstract (arXiv)

3D reconstruction from multi-view images is one of the fundamental challenges in computer vision and graphics. Recently, 3D Gaussian Splatting (3DGS) has emerged as a promising technique capable of real-time rendering with high-quality 3D reconstruction. This method utilizes 3D Gaussian representation and tile-based splatting techniques, bypassing the expensive neural field querying. Despite its potential, 3DGS encounters challenges such as needle-like artifacts, suboptimal geometries, and inaccurate normals caused by the Gaussians converging into anisotropic shapes with one dominant variance. We propose using the effective rank analysis to examine the shape statistics of 3D Gaussian primitives, and identify the Gaussians indeed converge into needle-like shapes with the effective rank 1. To address this, we introduce the effective rank as a regularization, which constrains the structure of the Gaussians. Our new regularization method enhances normal and geometry reconstruction while reducing needle-like artifacts. The approach can be integrated as an add-on module to other 3DGS variants, improving their quality without compromising visual fidelity. The project page is available at https://junhahyung.github.io/erankgs.github.io.