# PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting

arXiv: https://arxiv.org/abs/2104.00674 · HTML: https://mlsanity.com/paper/2104.00674/

## Key facts

- Cited by 335 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 1 Apr 2021.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [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)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [Deferred Neural Rendering: Image Synthesis using Neural Textures](https://mlsanity.com/paper/1904.12356/) (2019)
- [Inverse Rendering for Complex Indoor Scenes: Shape, Spatially-Varying Lighting and SVBRDF from a Single Image](https://mlsanity.com/paper/1905.02722/) (2019)
- [Neural Reflectance Fields for Appearance Acquisition](https://mlsanity.com/paper/2008.03824/) (2020)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Neural Rerendering in the Wild](https://mlsanity.com/paper/1904.04290/) (2019)
- [Deep Reflectance Volumes: Relightable Reconstructions from Multi-View Photometric Images](https://mlsanity.com/paper/2007.09892/) (2020)
- [Deep 3D Capture: Geometry and Reflectance from Sparse Multi-View Images](https://mlsanity.com/paper/2003.12642/) (2020)
- [Inverse Path Tracing for Joint Material and Lighting Estimation](https://mlsanity.com/paper/1903.07145/) (2019)
- [Crowdsampling the Plenoptic Function](https://mlsanity.com/paper/2007.15194/) (2020)
- [Intrinsic3D: High-Quality 3D Reconstruction by Joint Appearance and Geometry Optimization with Spatially-Varying Lighting](https://mlsanity.com/paper/1708.01670/) (2017)
- [Seeing the World in a Bag of Chips](https://mlsanity.com/paper/2001.04642/) (2020)
- [Learning Implicit Surface Light Fields](https://mlsanity.com/paper/2003.12406/) (2020)
- [Radiometric Scene Decomposition: Scene Reflectance, Illumination, and Geometry from RGB-D Images](https://mlsanity.com/paper/1604.01354/) (2016)

## Built on by (most cited first, 30 of 335)

- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [SV3D: Novel Multi-view Synthesis and 3D Generation from a Single Image using Latent Video Diffusion](https://mlsanity.com/paper/2403.12008/) (2024)
- [GS-IR: 3D Gaussian Splatting for Inverse Rendering](https://mlsanity.com/paper/2311.16473/) (2023)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [Neural-PIL: Neural Pre-Integrated Lighting for Reflectance Decomposition](https://mlsanity.com/paper/2110.14373/) (2021)
- [Modeling Indirect Illumination for Inverse Rendering](https://mlsanity.com/paper/2204.06837/) (2022)
- [TensoIR: Tensorial Inverse Rendering](https://mlsanity.com/paper/2304.12461/) (2023)
- [Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising](https://mlsanity.com/paper/2206.03380/) (2022)
- [NeRO: Neural Geometry and BRDF Reconstruction of Reflective Objects from Multiview Images](https://mlsanity.com/paper/2305.17398/) (2023)
- [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)
- [NeRFactor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination](https://mlsanity.com/paper/2106.01970/) (2021)
- [Relightable Gaussian Codec Avatars](https://mlsanity.com/paper/2312.03704/) (2023)
- [F2-NeRF: Fast Neural Radiance Field Training with Free Camera Trajectories](https://mlsanity.com/paper/2303.15951/) (2023)
- [IRON: Inverse Rendering by Optimizing Neural SDFs and Materials from Photometric Images](https://mlsanity.com/paper/2204.02232/) (2022)
- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)
- [NeILF: Neural Incident Light Field for Physically-based Material Estimation](https://mlsanity.com/paper/2203.07182/) (2022)
- [Neural Gaffer: Relighting Any Object via Diffusion](https://mlsanity.com/paper/2406.07520/) (2024)
- [Neural Fields meet Explicit Geometric Representation for Inverse Rendering of Urban Scenes](https://mlsanity.com/paper/2304.03266/) (2023)
- [SAMURAI: Shape And Material from Unconstrained Real-world Arbitrary Image collections](https://mlsanity.com/paper/2205.15768/) (2022)
- [GIR: 3D Gaussian Inverse Rendering for Relightable Scene Factorization](https://mlsanity.com/paper/2312.05133/) (2023)
- [TANGO: Text-driven Photorealistic and Robust 3D Stylization via Lighting Decomposition](https://mlsanity.com/paper/2210.11277/) (2022)
- [Fully Explicit Dynamic Gaussian Splatting](https://mlsanity.com/paper/2410.15629/) (2024)
- [NerfAcc: A General NeRF Acceleration Toolbox](https://mlsanity.com/paper/2210.04847/) (2022)

## Abstract (arXiv)

We present PhySG, an end-to-end inverse rendering pipeline that includes a fully differentiable renderer and can reconstruct geometry, materials, and illumination from scratch from a set of RGB input images. Our framework represents specular BRDFs and environmental illumination using mixtures of spherical Gaussians, and represents geometry as a signed distance function parameterized as a Multi-Layer Perceptron. The use of spherical Gaussians allows us to efficiently solve for approximate light transport, and our method works on scenes with challenging non-Lambertian reflectance captured under natural, static illumination. We demonstrate, with both synthetic and real data, that our reconstructions not only enable rendering of novel viewpoints, but also physics-based appearance editing of materials and illumination.