# Gaussian Splatting with Discretized SDF for Relightable Assets

arXiv: https://arxiv.org/abs/2507.15629 · HTML: https://mlsanity.com/paper/2507.15629/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 45 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (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)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Reconstruction](https://mlsanity.com/paper/2212.05231/) (2022)
- [GaussianShader: 3D Gaussian Splatting with Shading Functions for Reflective Surfaces](https://mlsanity.com/paper/2311.17977/) (2023)
- [GS-IR: 3D Gaussian Splatting for Inverse Rendering](https://mlsanity.com/paper/2311.16473/) (2023)
- [Neural-PIL: Neural Pre-Integrated Lighting for Reflectance Decomposition](https://mlsanity.com/paper/2110.14373/) (2021)
- [Neural Reflectance Fields for Appearance Acquisition](https://mlsanity.com/paper/2008.03824/) (2020)
- [Modeling Indirect Illumination for Inverse Rendering](https://mlsanity.com/paper/2204.06837/) (2022)
- [TensoIR: Tensorial Inverse Rendering](https://mlsanity.com/paper/2304.12461/) (2023)
- [NeRO: Neural Geometry and BRDF Reconstruction of Reflective Objects from Multiview Images](https://mlsanity.com/paper/2305.17398/) (2023)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Relightable 3D Gaussians: Realistic Point Cloud Relighting with BRDF Decomposition and Ray Tracing](https://mlsanity.com/paper/2311.16043/) (2023)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [IRON: Inverse Rendering by Optimizing Neural SDFs and Materials from Photometric Images](https://mlsanity.com/paper/2204.02232/) (2022)
- [GIR: 3D Gaussian Inverse Rendering for Relightable Scene Factorization](https://mlsanity.com/paper/2312.05133/) (2023)
- [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)
- [NeILF++: Inter-Reflectable Light Fields for Geometry and Material Estimation](https://mlsanity.com/paper/2303.17147/) (2023)
- [PermutoSDF: Fast Multi-View Reconstruction with Implicit Surfaces using Permutohedral Lattices](https://mlsanity.com/paper/2211.12562/) (2022)
- [Critical Regularizations for Neural Surface Reconstruction in the Wild](https://mlsanity.com/paper/2206.03087/) (2022)

## Built on by (most cited first, 13 of 13)

- [Benchmarking PhD-Level Coding in 3D Geometric Computer Vision](https://mlsanity.com/paper/2603.30038/) (2026)
- [SurfPhase: 3D Interfacial Dynamics in Two-Phase Flows from Sparse Videos](https://mlsanity.com/paper/2602.11154/) (2026)
- [DySurface: Consistent 4D Surface Reconstruction via Bridging Explicit Gaussians and Implicit Functions](https://mlsanity.com/paper/2605.10360/) (2026)
- [F-RNG: Feed-Forward Relightable Neural Gaussians](https://mlsanity.com/paper/2605.25975/) (2026)
- [Geometry Gaussians: Decoupling Appearance and Geometry in Gaussian Splatting](https://mlsanity.com/paper/2606.05124/) (2026)
- [DreamLifting: A Plug-in Module Lifting MV Diffusion Models for 3D Asset Generation](https://mlsanity.com/paper/2509.07435/) (2025)
- [HybridSplat: Fast Reflection-baked Gaussian Tracing using Hybrid Splatting](https://mlsanity.com/paper/2512.08334/) (2025)
- [High-fidelity Multi-view Normal Integration with Scale-encoded Neural Surface Representation](https://mlsanity.com/paper/2603.20337/) (2026)
- [Relightable Gaussian Splatting for Virtual Production Using Image-Based Illumination](https://mlsanity.com/paper/2605.09024/) (2026)
- [Gaussian-Voxel Duet: A Dual-Scaffolding Hybrid Representation for Fast and Accurate Monocular Surface Reconstruction](https://mlsanity.com/paper/2605.26616/) (2026)
- [TRON: Tracing Rays to Orchestrate a Neural Renderer for 3D Gaussian Reconstructions](https://mlsanity.com/paper/2606.11314/) (2026)
- [MooMIns -- Monocular 3D Reconstruction and Object Pose Estimation from Multiple Instances](https://mlsanity.com/paper/2606.14389/) (2026)
- [Casual Flash Lighting for Gaussian Splat Inverse Rendering](https://mlsanity.com/paper/2610.06035/) (2026)

## Abstract (arXiv)

3D Gaussian splatting (3DGS) has shown its detailed expressive ability and highly efficient rendering speed in the novel view synthesis (NVS) task. The application to inverse rendering still faces several challenges, as the discrete nature of Gaussian primitives makes it difficult to apply geometry constraints. Recent works introduce the signed distance field (SDF) as an extra continuous representation to regularize the geometry defined by Gaussian primitives. It improves the decomposition quality, at the cost of increasing memory usage and complicating training. Unlike these works, we introduce a discretized SDF to represent the continuous SDF in a discrete manner by encoding it within each Gaussian using a sampled value. This approach allows us to link the SDF with the Gaussian opacity through an SDF-to-opacity transformation, enabling rendering the SDF via splatting and avoiding the computational cost of ray marching.The key challenge is to regularize the discrete samples to be consistent with the underlying SDF, as the discrete representation can hardly apply the gradient-based constraints (eg Eikonal loss). For this, we project Gaussians onto the zero-level set of SDF and enforce alignment with the surface from splatting, namely a projection-based consistency loss. Thanks to the discretized SDF, our method achieves higher relighting quality, while requiring no extra memory beyond GS and avoiding complex manually designed optimization. The experiments reveal that our method outperforms existing Gaussian-based inverse rendering methods. Our code is available at https://github.com/NK-CS-ZZL/DiscretizedSDF.