# Deformable Beta Splatting

arXiv: https://arxiv.org/abs/2501.18630 · HTML: https://mlsanity.com/paper/2501.18630/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 64 references that are in the map.
- First posted on arXiv 27 Jan 2025.

## Builds on (most cited first, 30 of 44)

- [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: 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)
- [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)
- [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)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Gaussian Grouping: Segment and Edit Anything in 3D Scenes](https://mlsanity.com/paper/2312.00732/) (2023)
- [Feature 3DGS: Supercharging 3D Gaussian Splatting to Enable Distilled Feature Fields](https://mlsanity.com/paper/2312.03203/) (2023)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [GaussianDreamer: Fast Generation from Text to 3D Gaussians by Bridging 2D and 3D Diffusion Models](https://mlsanity.com/paper/2310.08529/) (2023)
- [LucidDreamer: Domain-free Generation of 3D Gaussian Splatting Scenes](https://mlsanity.com/paper/2311.13384/) (2023)
- [Language Embedded 3D Gaussians for Open-Vocabulary Scene Understanding](https://mlsanity.com/paper/2311.18482/) (2023)
- [VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality](https://mlsanity.com/paper/2401.16663/) (2024)
- [DeRF: Decomposed Radiance Fields](https://mlsanity.com/paper/2011.12490/) (2020)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [Compact 3D Scene Representation via Self-Organizing Gaussian Grids](https://mlsanity.com/paper/2312.13299/) (2023)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS](https://mlsanity.com/paper/2403.13806/) (2024)
- [Motion-aware 3D Gaussian Splatting for Efficient Dynamic Scene Reconstruction](https://mlsanity.com/paper/2403.11447/) (2024)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration](https://mlsanity.com/paper/2403.11056/) (2024)

## Built on by (most cited first, 30 of 38)

- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere](https://mlsanity.com/paper/2512.14180/) (2025)
- [3DGabSplat: 3D Gabor Splatting for Frequency-adaptive Radiance Field Rendering](https://mlsanity.com/paper/2508.05343/) (2025)
- [AdaGaR: Adaptive Gabor Representation for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2601.00796/) (2026)
- [Radiance Meshes for Volumetric Reconstruction](https://mlsanity.com/paper/2512.04076/) (2025)
- [SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction](https://mlsanity.com/paper/2506.19139/) (2025)
- [Splat Feature Solver](https://mlsanity.com/paper/2508.12216/) (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)
- [Consistent Instance Field for Dynamic Scene Understanding](https://mlsanity.com/paper/2512.14126/) (2025)
- [ContraGS: Codebook-Condensed and Trainable Gaussian Splatting for Fast, Memory-Efficient Reconstruction](https://mlsanity.com/paper/2509.03775/) (2025)
- [Universal Beta Splatting](https://mlsanity.com/paper/2510.03312/) (2025)
- [Nexels: Neurally-Textured Surfels for Real-Time Novel View Synthesis with Sparse Geometries](https://mlsanity.com/paper/2512.13796/) (2025)
- [Neural Harmonic Textures for High-Quality Primitive Based Neural Reconstruction](https://mlsanity.com/paper/2604.01204/) (2026)
- [Confidence-Based Mesh Extraction from 3D Gaussians](https://mlsanity.com/paper/2603.24725/) (2026)
- [Power Foam: Unifying Real-Time Differentiable Ray Tracing and Rasterization](https://mlsanity.com/paper/2604.24994/) (2026)
- [Radiant Triangle Soup with Soft Connectivity Forces for 3D Reconstruction and Novel View Synthesis](https://mlsanity.com/paper/2505.23642/) (2025)
- [NanoGS: Training-Free Gaussian Splat Simplification](https://mlsanity.com/paper/2603.16103/) (2026)
- [Depth Peeling for High-Fidelity Gaussian-Enhanced Surfel Rendering](https://mlsanity.com/paper/2605.25345/) (2026)
- [A Bag of Tricks for Efficient Implicit Neural Point Clouds](https://mlsanity.com/paper/2508.19140/) (2025)
- [Fourier Splatting: Generalized Fourier encoded primitives for scalable radiance fields](https://mlsanity.com/paper/2603.19834/) (2026)
- [Hybrid Latents: Geometry-Appearance-Aware Surfel Splatting](https://mlsanity.com/paper/2604.14928/) (2026)
- [Beyond Spherical Harmonics: Rethinking Appearance Models for Radiance Reconstruction](https://mlsanity.com/paper/2606.09794/) (2026)
- [The Architecture of Trust: A Framework for AI-Augmented Real Estate Valuation in the Era of Structured Data](https://mlsanity.com/paper/2508.02765/) (2025)
- [IDU: Incremental Dynamic Update of Existing 3D Virtual Environments with New Imagery Data](https://mlsanity.com/paper/2508.17579/) (2025)
- [Iterative Motion Compensation for Canonical 3D Reconstruction from UAV Plant Images Captured in Windy Conditions](https://mlsanity.com/paper/2510.15491/) (2025)
- [A Step to Decouple Optimization in 3DGS](https://mlsanity.com/paper/2601.16736/) (2026)
- [Augmented Radiance Field: A General Framework for Enhanced Gaussian Splatting](https://mlsanity.com/paper/2602.19916/) (2026)
- [From ex(p) to poly: Gaussian Splatting with Polynomial Kernels](https://mlsanity.com/paper/2603.18707/) (2026)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) has advanced radiance field reconstruction by enabling real-time rendering. However, its reliance on Gaussian kernels for geometry and low-order Spherical Harmonics (SH) for color encoding limits its ability to capture complex geometries and diverse colors. We introduce Deformable Beta Splatting (DBS), a deformable and compact approach that enhances both geometry and color representation. DBS replaces Gaussian kernels with deformable Beta Kernels, which offer bounded support and adaptive frequency control to capture fine geometric details with higher fidelity while achieving better memory efficiency. In addition, we extended the Beta Kernel to color encoding, which facilitates improved representation of diffuse and specular components, yielding superior results compared to SH-based methods. Furthermore, Unlike prior densification techniques that depend on Gaussian properties, we mathematically prove that adjusting regularized opacity alone ensures distribution-preserved Markov chain Monte Carlo (MCMC), independent of the splatting kernel type. Experimental results demonstrate that DBS achieves state-of-the-art visual quality while utilizing only 45% of the parameters and rendering 1.5x faster than 3DGS-MCMC, highlighting the superior performance of DBS for real-time radiance field rendering. Interactive demonstrations and source code are available on our project website: https://rongliu-leo.github.io/beta-splatting/.