# Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis

arXiv: https://arxiv.org/abs/2402.12377 · HTML: https://mlsanity.com/paper/2402.12377/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 69 references that are in the map.
- First posted on arXiv 19 Feb 2024.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [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)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [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)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [Deferred Neural Rendering: Image Synthesis using Neural Textures](https://mlsanity.com/paper/1904.12356/) (2019)
- [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)
- [Point-Based Neural Rendering with Per-View Optimization](https://mlsanity.com/paper/2109.02369/) (2021)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [Stable View Synthesis](https://mlsanity.com/paper/2011.07233/) (2020)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)
- [Adaptive Shells for Efficient Neural Radiance Field Rendering](https://mlsanity.com/paper/2311.10091/) (2023)
- [SMERF: Streamable Memory Efficient Radiance Fields for Real-Time Large-Scene Exploration](https://mlsanity.com/paper/2312.07541/) (2023)
- [NeRFMeshing: Distilling Neural Radiance Fields into Geometrically-Accurate 3D Meshes](https://mlsanity.com/paper/2303.09431/) (2023)

## Built on by (most cited first, 30 of 41)

- [Octree-GS: Towards Consistent Real-time Rendering with LOD-Structured 3D Gaussians](https://mlsanity.com/paper/2403.17898/) (2024)
- [RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS](https://mlsanity.com/paper/2403.13806/) (2024)
- [RaDe-GS: Rasterizing Depth in Gaussian Splatting](https://mlsanity.com/paper/2406.01467/) (2024)
- [GSDF: 3DGS Meets SDF for Improved Rendering and Reconstruction](https://mlsanity.com/paper/2403.16964/) (2024)
- [3D Gaussian Splatting: Survey, Technologies, Challenges, and Opportunities](https://mlsanity.com/paper/2407.17418/) (2024)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction](https://mlsanity.com/paper/2506.24096/) (2025)
- [Efficient Perspective-Correct 3D Gaussian Splatting Using Hybrid Transparency](https://mlsanity.com/paper/2410.08129/) (2024)
- [Sparse Voxels Rasterization: Real-time High-fidelity Radiance Field Rendering](https://mlsanity.com/paper/2412.04459/) (2024)
- [Radiant Foam: Real-Time Differentiable Ray Tracing](https://mlsanity.com/paper/2502.01157/) (2025)
- [Effective Rank Analysis and Regularization for Enhanced 3D Gaussian Splatting](https://mlsanity.com/paper/2406.11672/) (2024)
- [VR-Splatting: Foveated Radiance Field Rendering via 3D Gaussian Splatting and Neural Points](https://mlsanity.com/paper/2410.17932/) (2024)
- [Gaussian Frosting: Editable Complex Radiance Fields with Real-Time Rendering](https://mlsanity.com/paper/2403.14554/) (2024)
- [Geometry Field Splatting with Gaussian Surfels](https://mlsanity.com/paper/2411.17067/) (2024)
- [Volumetrically Consistent 3D Gaussian Rasterization](https://mlsanity.com/paper/2412.03378/) (2024)
- [SqueezeMe: Mobile-Ready Distillation of Gaussian Full-Body Avatars](https://mlsanity.com/paper/2412.15171/) (2024)
- [INPC: Implicit Neural Point Clouds for Radiance Field Rendering](https://mlsanity.com/paper/2403.16862/) (2024)
- [Aquatic-GS: A Hybrid 3D Representation for Underwater Scenes](https://mlsanity.com/paper/2411.00239/) (2024)
- [Radiance Meshes for Volumetric Reconstruction](https://mlsanity.com/paper/2512.04076/) (2025)
- [GSurf: Learning Signed Distance Fields from Splatting Opaque Gaussians for High-quality 3D Reconstruction](https://mlsanity.com/paper/2411.15723/) (2024)
- [SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction](https://mlsanity.com/paper/2506.19139/) (2025)
- [MeshSplat: Generalizable Sparse-View Surface Reconstruction via Gaussian Splatting](https://mlsanity.com/paper/2508.17811/) (2025)
- [Volumetric Surfaces: Representing Fuzzy Geometries with Layered Meshes](https://mlsanity.com/paper/2409.02482/) (2024)
- [Learning Efficient Fuse-and-Refine for Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2503.14698/) (2025)
- [Multiview Geometric Regularization of Gaussian Splatting for Accurate Radiance Fields](https://mlsanity.com/paper/2506.13508/) (2025)
- [Triangle Splatting+: Differentiable Rendering with Opaque Triangles](https://mlsanity.com/paper/2509.25122/) (2025)
- [Radiance Surfaces: Optimizing Surface Representations with a 5D Radiance Field Loss](https://mlsanity.com/paper/2501.18627/) (2025)
- [Nexels: Neurally-Textured Surfels for Real-Time Novel View Synthesis with Sparse Geometries](https://mlsanity.com/paper/2512.13796/) (2025)
- [From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians](https://mlsanity.com/paper/2604.07337/) (2026)
- [Oblique-MERF: Revisiting and Improving MERF for Oblique Photography](https://mlsanity.com/paper/2404.09531/) (2024)

## Abstract (arXiv)

While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric density field (e.g. NeRF) excel at reconstructing fine geometric detail. However, density fields often represent geometry in a "fuzzy" manner, which hinders exact localization of the surface. In this work, we modify density fields to encourage them to converge towards surfaces, without compromising their ability to reconstruct thin structures. First, we employ a discrete opacity grid representation instead of a continuous density field, which allows opacity values to discontinuously transition from zero to one at the surface. Second, we anti-alias by casting multiple rays per pixel, which allows occlusion boundaries and subpixel structures to be modelled without using semi-transparent voxels. Third, we minimize the binary entropy of the opacity values, which facilitates the extraction of surface geometry by encouraging opacity values to binarize towards the end of training. Lastly, we develop a fusion-based meshing strategy followed by mesh simplification and appearance model fitting. The compact meshes produced by our model can be rendered in real-time on mobile devices and achieve significantly higher view synthesis quality compared to existing mesh-based approaches.