# SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction

arXiv: https://arxiv.org/abs/2506.19139 · HTML: https://mlsanity.com/paper/2506.19139/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 55 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Builds on (most cited first, 30 of 39)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [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)
- [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)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [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)
- [Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenes](https://mlsanity.com/paper/2404.10772/) (2024)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [Relightable 3D Gaussians: Realistic Point Cloud Relighting with BRDF Decomposition and Ray Tracing](https://mlsanity.com/paper/2311.16043/) (2023)
- [3D Gaussian Ray Tracing: Fast Tracing of Particle Scenes](https://mlsanity.com/paper/2407.07090/) (2024)
- [Reducing the Memory Footprint of 3D Gaussian Splatting](https://mlsanity.com/paper/2406.17074/) (2024)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [StopThePop: Sorted Gaussian Splatting for View-Consistent Real-time Rendering](https://mlsanity.com/paper/2402.00525/) (2024)
- [GSDF: 3DGS Meets SDF for Improved Rendering and Reconstruction](https://mlsanity.com/paper/2403.16964/) (2024)
- [3DGSR: Implicit Surface Reconstruction with 3D Gaussian Splatting](https://mlsanity.com/paper/2404.00409/) (2024)
- [Tetra-NeRF: Representing Neural Radiance Fields Using Tetrahedra](https://mlsanity.com/paper/2304.09987/) (2023)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis](https://mlsanity.com/paper/2402.12377/) (2024)
- [On the Error Analysis of 3D Gaussian Splatting and an Optimal Projection Strategy](https://mlsanity.com/paper/2402.00752/) (2024)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media](https://mlsanity.com/paper/2405.15425/) (2024)

## Built on by (most cited first, 7 of 7)

- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [Reconstructing 4D Spatial Intelligence: A Survey](https://mlsanity.com/paper/2507.21045/) (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)
- [FlowObject: Flow Steering for Bridging Generative Priors and Reconstruction Fidelity](https://mlsanity.com/paper/2606.19019/) (2026)
- [Manifold-GS: Certified Hybrid Assets via Varifold-Conservative Gaussian Splatting](https://mlsanity.com/paper/2608.00214/) (2026)
- [Efficient Confidence-Aware Densification for 3DGS](https://mlsanity.com/paper/2610.13541/) (2026)

## Abstract (arXiv)

Recent advances in 3D Gaussian representations have significantly improved the quality and efficiency of image-based scene reconstruction. Their explicit nature facilitates real-time rendering and fast optimization, yet extracting accurate surfaces - particularly in large-scale, unbounded environments - remains a difficult task. Many existing methods rely on approximate depth estimates and global sorting heuristics, which can introduce artifacts and limit the fidelity of the reconstructed mesh. In this paper, we present Sorted Opacity Fields (SOF), a method designed to recover detailed surfaces from 3D Gaussians with both speed and precision. Our approach improves upon prior work by introducing hierarchical resorting and a robust formulation of Gaussian depth, which better aligns with the level-set. To enhance mesh quality, we incorporate a level-set regularizer operating on the opacity field and introduce losses that encourage geometrically-consistent primitive shapes. In addition, we develop a parallelized Marching Tetrahedra algorithm tailored to our opacity formulation, reducing meshing time by up to an order of magnitude. As demonstrated by our quantitative evaluation, SOF achieves higher reconstruction accuracy while cutting total processing time by more than a factor of three. These results mark a step forward in turning efficient Gaussian-based rendering into equally efficient geometry extraction.