# Volumetric Surfaces: Representing Fuzzy Geometries with Layered Meshes

arXiv: https://arxiv.org/abs/2409.02482 · HTML: https://mlsanity.com/paper/2409.02482/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 67 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 30 of 46)

- [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)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [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)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [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)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (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)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (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)
- [Neural Point-Based Graphics](https://mlsanity.com/paper/1906.08240/) (2019)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [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)
- [MERF: Memory-Efficient Radiance Fields for Real-time View Synthesis in Unbounded Scenes](https://mlsanity.com/paper/2302.12249/) (2023)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [RaDe-GS: Rasterizing Depth in Gaussian Splatting](https://mlsanity.com/paper/2406.01467/) (2024)
- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)

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

- [DiffSoup: Direct Differentiable Rasterization of Triangle Soup for Extreme Radiance Field Simplification](https://mlsanity.com/paper/2603.27151/) (2026)
- [LegacyAvatars: Volumetric Face Avatars For Traditional Graphics Pipelines](https://mlsanity.com/paper/2601.12285/) (2026)
- [Meshtryoshka: Differentiable Rendering of Real-World Scenes via Mesh Rasterization](https://mlsanity.com/paper/2606.28622/) (2026)
- [Inverse Rendering for Modeling with Line Primitives](https://mlsanity.com/paper/2609.00625/) (2026)
- [ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction](https://mlsanity.com/paper/2609.06723/) (2026)

## Abstract (arXiv)

High-quality view synthesis relies on volume rendering, splatting, or surface rendering. While surface rendering is typically the fastest, it struggles to accurately model fuzzy geometry like hair. In turn, alpha-blending techniques excel at representing fuzzy materials but require an unbounded number of samples per ray (P1). Further overheads are induced by empty space skipping in volume rendering (P2) and sorting input primitives in splatting (P3). We present a novel representation for real-time view synthesis where the (P1) number of sampling locations is small and bounded, (P2) sampling locations are efficiently found via rasterization, and (P3) rendering is sorting-free. We achieve this by representing objects as semi-transparent multi-layer meshes rendered in a fixed order. First, we model surface layers as signed distance function (SDF) shells with optimal spacing learned during training. Then, we bake them as meshes and fit UV textures. Unlike single-surface methods, our multi-layer representation effectively models fuzzy objects. In contrast to volume and splatting-based methods, our approach enables real-time rendering on low-power laptops and smartphones.