# Geometry-Grounded Gaussian Splatting

arXiv: https://arxiv.org/abs/2601.17835 · HTML: https://mlsanity.com/paper/2601.17835/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 24 of 24)

- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (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)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [RaDe-GS: Rasterizing Depth in Gaussian Splatting](https://mlsanity.com/paper/2406.01467/) (2024)
- [R3D3: Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras](https://mlsanity.com/paper/2308.14713/) (2023)
- [MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction](https://mlsanity.com/paper/2506.24096/) (2025)
- [Sparse Voxels Rasterization: Real-time High-fidelity Radiance Field Rendering](https://mlsanity.com/paper/2412.04459/) (2024)
- [ScatterNeRF: Seeing Through Fog with Physically-Based Inverse Neural Rendering](https://mlsanity.com/paper/2305.02103/) (2023)
- [Quadratic Gaussian Splatting: High Quality Surface Reconstruction with Second-order Geometric Primitives](https://mlsanity.com/paper/2411.16392/) (2024)
- [GeoSVR: Taming Sparse Voxels for Geometrically Accurate Surface Reconstruction](https://mlsanity.com/paper/2509.18090/) (2025)
- [Objects as volumes: A stochastic geometry view of opaque solids](https://mlsanity.com/paper/2312.15406/) (2023)
- [Geometry Field Splatting with Gaussian Surfels](https://mlsanity.com/paper/2411.17067/) (2024)

## Built on by (most cited first, 5 of 5)

- [From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians](https://mlsanity.com/paper/2604.07337/) (2026)
- [VG2GT: Voxel-Gaussian Splatting Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2606.01573/) (2026)
- [ReconPlusGen: Injecting Reconstruction Prior into Multi-view 3D Generation through Noise Inversion and Modulation](https://mlsanity.com/paper/2609.11129/) (2026)
- [CoMVS-GS: Collaborative Multi-View Stereo and 3D Gaussian Splatting for Surface Reconstruction](https://mlsanity.com/paper/2608.18413/) (2026)
- [Volume Rendering with Metric--Phase Fields for Thin Structures and Sign-Ambiguous Geometry](https://mlsanity.com/paper/2610.13088/) (2026)

## Abstract (arXiv)

Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation, existing shape reconstruction methods suffer from poor multi-view consistency and are sensitive to floaters. In this paper, we present a rigorous theoretical derivation that establishes Gaussian primitives as a specific type of stochastic solids. This theoretical framework provides a principled foundation for Geometry-Grounded Gaussian Splatting by enabling the direct treatment of Gaussian primitives as explicit geometric representations. Using the volumetric nature of stochastic solids, our method efficiently renders high-quality depth maps for fine-grained geometry extraction. Experiments show that our method achieves the best shape reconstruction results among all Gaussian Splatting-based methods on public datasets.