# Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set

arXiv: https://arxiv.org/abs/2410.14189 · HTML: https://mlsanity.com/paper/2410.14189/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 79 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 30 of 64)

- [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)
- [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)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [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)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [SparseNeRF: Distilling Depth Ranking for Few-shot Novel View Synthesis](https://mlsanity.com/paper/2303.16196/) (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)
- [NICER-SLAM: Neural Implicit Scene Encoding for RGB SLAM](https://mlsanity.com/paper/2302.03594/) (2023)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [DN-Splatter: Depth and Normal Priors for Gaussian Splatting and Meshing](https://mlsanity.com/paper/2403.17822/) (2024)
- [NeuRIS: Neural Reconstruction of Indoor Scenes Using Normal Priors](https://mlsanity.com/paper/2206.13597/) (2022)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)

## Built on by (most cited first, 30 of 49)

- [You See it, You Got it: Learning 3D Creation on Pose-Free Videos at Scale](https://mlsanity.com/paper/2412.06699/) (2024)
- [DiffGS: Functional Gaussian Splatting Diffusion](https://mlsanity.com/paper/2410.19657/) (2024)
- [Binocular-Guided 3D Gaussian Splatting with View Consistency for Sparse View Synthesis](https://mlsanity.com/paper/2410.18822/) (2024)
- [MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction](https://mlsanity.com/paper/2506.24096/) (2025)
- [Zero-Shot Scene Reconstruction from Single Images with Deep Prior Assembly](https://mlsanity.com/paper/2410.15971/) (2024)
- [FatesGS: Fast and Accurate Sparse-View Surface Reconstruction using Gaussian Splatting with Depth-Feature Consistency](https://mlsanity.com/paper/2501.04628/) (2025)
- [MaterialRefGS: Reflective Gaussian Splatting with Multi-view Consistent Material Inference](https://mlsanity.com/paper/2510.11387/) (2025)
- [MAtCha Gaussians: Atlas of Charts for High-Quality Geometry and Photorealism From Sparse Views](https://mlsanity.com/paper/2412.06767/) (2024)
- [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)
- [MonoInstance: Enhancing Monocular Priors via Multi-view Instance Alignment for Neural Rendering and Reconstruction](https://mlsanity.com/paper/2503.18363/) (2025)
- [GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting](https://mlsanity.com/paper/2503.19458/) (2025)
- [Gaussian Splatting with Discretized SDF for Relightable Assets](https://mlsanity.com/paper/2507.15629/) (2025)
- [NeRFPrior: Learning Neural Radiance Field as a Prior for Indoor Scene Reconstruction](https://mlsanity.com/paper/2503.18361/) (2025)
- [MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step](https://mlsanity.com/paper/2411.01208/) (2024)
- [MonoGSDF: Exploring Monocular Geometric Cues for Gaussian Splatting-Guided Implicit Surface Reconstruction](https://mlsanity.com/paper/2411.16898/) (2024)
- [GLS: Geometry-aware 3D Language Gaussian Splatting](https://mlsanity.com/paper/2411.18066/) (2024)
- [SparseRecon: Neural Implicit Surface Reconstruction from Sparse Views with Feature and Depth Consistencies](https://mlsanity.com/paper/2508.00366/) (2025)
- [VTGaussian-SLAM: RGBD SLAM for Large Scale Scenes with Splatting View-Tied 3D Gaussians](https://mlsanity.com/paper/2506.02741/) (2025)
- [GSurf: Learning Signed Distance Fields from Splatting Opaque Gaussians for High-quality 3D Reconstruction](https://mlsanity.com/paper/2411.15723/) (2024)
- [DGNS: Deformable Gaussian Splatting and Dynamic Neural Surface for Monocular Dynamic 3D Reconstruction](https://mlsanity.com/paper/2412.03910/) (2024)
- [Repurposing 2D Diffusion Models with Gaussian Atlas for 3D Generation](https://mlsanity.com/paper/2503.15877/) (2025)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [GAP: Gaussianize Any Point Clouds with Text Guidance](https://mlsanity.com/paper/2508.05631/) (2025)
- [VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment](https://mlsanity.com/paper/2510.11473/) (2025)
- [2D Triangle Splatting for Direct Differentiable Mesh Training](https://mlsanity.com/paper/2506.18575/) (2025)
- [Car-GS: Addressing Reflective and Transparent Surface Challenges in 3D Car Reconstruction](https://mlsanity.com/paper/2501.11020/) (2025)
- [UrbanGS: A Scalable and Efficient Architecture for Geometrically Accurate Large-Scene Reconstruction](https://mlsanity.com/paper/2602.02089/) (2026)
- [Speeding Up the Learning of 3D Gaussians with Much Shorter Gaussian Lists](https://mlsanity.com/paper/2603.09277/) (2026)
- [From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians](https://mlsanity.com/paper/2604.07337/) (2026)

## Abstract (arXiv)

It is vital to infer a signed distance function (SDF) in multi-view based surface reconstruction. 3D Gaussian splatting (3DGS) provides a novel perspective for volume rendering, and shows advantages in rendering efficiency and quality. Although 3DGS provides a promising neural rendering option, it is still hard to infer SDFs for surface reconstruction with 3DGS due to the discreteness, the sparseness, and the off-surface drift of 3D Gaussians. To resolve these issues, we propose a method that seamlessly merge 3DGS with the learning of neural SDFs. Our key idea is to more effectively constrain the SDF inference with the multi-view consistency. To this end, we dynamically align 3D Gaussians on the zero-level set of the neural SDF using neural pulling, and then render the aligned 3D Gaussians through the differentiable rasterization. Meanwhile, we update the neural SDF by pulling neighboring space to the pulled 3D Gaussians, which progressively refine the signed distance field near the surface. With both differentiable pulling and splatting, we jointly optimize 3D Gaussians and the neural SDF with both RGB and geometry constraints, which recovers more accurate, smooth, and complete surfaces with more geometry details. Our numerical and visual comparisons show our superiority over the state-of-the-art results on the widely used benchmarks.