# Geometry Field Splatting with Gaussian Surfels

arXiv: https://arxiv.org/abs/2411.17067 · HTML: https://mlsanity.com/paper/2411.17067/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 75 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 30 of 50)

- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [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)
- [MVSNet: Depth Inference for Unstructured Multi-view Stereo](https://mlsanity.com/paper/1804.02505/) (2018)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [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)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networks](https://mlsanity.com/paper/1911.10127/) (2019)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Cascade Cost Volume for High-Resolution Multi-View Stereo and Stereo Matching](https://mlsanity.com/paper/1912.06378/) (2019)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [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)
- [Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction](https://mlsanity.com/paper/2205.15848/) (2022)
- [PatchmatchNet: Learned Multi-View Patchmatch Stereo](https://mlsanity.com/paper/2012.01411/) (2020)
- [SparseNeuS: Fast Generalizable Neural Surface Reconstruction from Sparse Views](https://mlsanity.com/paper/2206.05737/) (2022)
- [NeRO: Neural Geometry and BRDF Reconstruction of Reflective Objects from Multiview Images](https://mlsanity.com/paper/2305.17398/) (2023)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [RGBleftrightarrowX: Image decomposition and synthesis using material- and lighting-aware diffusion models](https://mlsanity.com/paper/2405.00666/) (2024)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [TransMVSNet: Global Context-aware Multi-view Stereo Network with Transformers](https://mlsanity.com/paper/2111.14600/) (2021)
- [RaDe-GS: Rasterizing Depth in Gaussian Splatting](https://mlsanity.com/paper/2406.01467/) (2024)

## Built on by (most cited first, 13 of 13)

- [When Gaussian Meets Surfel: Ultra-fast High-fidelity Radiance Field Rendering](https://mlsanity.com/paper/2504.17545/) (2025)
- [Reconstructing 4D Spatial Intelligence: A Survey](https://mlsanity.com/paper/2507.21045/) (2025)
- [SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction](https://mlsanity.com/paper/2506.19139/) (2025)
- [HaloGS: Loose Coupling of Compact Geometry and Gaussian Splats for 3D Scenes](https://mlsanity.com/paper/2505.20267/) (2025)
- [MS-GS: Multi-Appearance Sparse-View 3D Gaussian Splatting in the Wild](https://mlsanity.com/paper/2509.15548/) (2025)
- [Geometry-Grounded Gaussian Splatting](https://mlsanity.com/paper/2601.17835/) (2026)
- [Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity for Efficient Relighting and Geometry Reconstruction](https://mlsanity.com/paper/2509.18497/) (2025)
- [From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians](https://mlsanity.com/paper/2604.07337/) (2026)
- [Confidence-Based Mesh Extraction from 3D Gaussians](https://mlsanity.com/paper/2603.24725/) (2026)
- [A Mixed-Primitive-based Gaussian Splatting Method for Surface Reconstruction](https://mlsanity.com/paper/2507.11321/) (2025)
- [DriveSplat: Unified Neural Gaussian Reconstruction for Dynamic Driving Scenes](https://mlsanity.com/paper/2508.15376/) (2025)
- [GVGS: Gaussian Visibility-Aware Multi-View Geometry for Accurate Surface Reconstruction](https://mlsanity.com/paper/2601.20331/) (2026)
- [Shell-Supervised Gaussian Splatting for Urban Real-to-Sim Reconstruction](https://mlsanity.com/paper/2606.30014/) (2026)

## Abstract (arXiv)

Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent work for stochastic opaque surfaces, which can then be converted to volume densities. We adapt Gaussian kernels or surfels to splat the geometry field rather than the volume, enabling precise reconstruction of opaque solids. Our first contribution is to derive an efficient and almost exact differentiable rendering algorithm for geometry fields parameterized by Gaussian surfels, while removing current approximations involving Taylor series and no self-attenuation. Next, we address the discontinuous loss landscape when surfels cluster near geometry, showing how to guarantee that the rendered color is a continuous function of the colors of the kernels, irrespective of ordering. Finally, we use latent representations with spherical harmonics encoded reflection vectors rather than spherical harmonics encoded colors to better address specular surfaces. We demonstrate significant improvement in the quality of reconstructed 3D surfaces on widely-used datasets.