# BRDF-NeRF: Neural Radiance Fields with Optical Satellite Images and BRDF Modelling

arXiv: https://arxiv.org/abs/2409.12014 · HTML: https://mlsanity.com/paper/2409.12014/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 63 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Builds on (most cited first, 24 of 24)

- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [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)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [Dense Depth Priors for Neural Radiance Fields from Sparse Input Views](https://mlsanity.com/paper/2112.03288/) (2021)
- [Neural Reflectance Fields for Appearance Acquisition](https://mlsanity.com/paper/2008.03824/) (2020)
- [NerfingMVS: Guided Optimization of Neural Radiance Fields for Indoor Multi-view Stereo](https://mlsanity.com/paper/2109.01129/) (2021)
- [SinNeRF: Training Neural Radiance Fields on Complex Scenes from a Single Image](https://mlsanity.com/paper/2204.00928/) (2022)
- [PS-NeRF: Neural Inverse Rendering for Multi-view Photometric Stereo](https://mlsanity.com/paper/2207.11406/) (2022)
- [Sat-NeRF: Learning Multi-View Satellite Photogrammetry With Transient Objects and Shadow Modeling Using RPC Cameras](https://mlsanity.com/paper/2203.08896/) (2022)
- [Semantic Stereo for Incidental Satellite Images](https://mlsanity.com/paper/1811.08739/) (2018)
- [Shadow Neural Radiance Fields for Multi-view Satellite Photogrammetry](https://mlsanity.com/paper/2104.09877/) (2021)
- [S3-NeRF: Neural Reflectance Field from Shading and Shadow under a Single Viewpoint](https://mlsanity.com/paper/2210.08936/) (2022)
- [Neural Reflectance for Shape Recovery with Shadow Handling](https://mlsanity.com/paper/2203.12909/) (2022)
- [SparseSat-NeRF: Dense Depth Supervised Neural Radiance Fields for Sparse Satellite Images](https://mlsanity.com/paper/2309.00277/) (2023)
- [SAT-NGP : Unleashing Neural Graphics Primitives for Fast Relightable Transient-Free 3D reconstruction from Satellite Imagery](https://mlsanity.com/paper/2403.18711/) (2024)
- [SUNDIAL: 3D Satellite Understanding through Direct, Ambient, and Complex Lighting Decomposition](https://mlsanity.com/paper/2312.16215/) (2023)
- [Incorporating Season and Solar Specificity into Renderings made by a NeRF Architecture using Satellite Images](https://mlsanity.com/paper/2308.01262/) (2023)
- [Radar Fields: An Extension of Radiance Fields to SAR](https://mlsanity.com/paper/2312.12961/) (2023)
- [Depth-Guided Robust and Fast Point Cloud Fusion NeRF for Sparse Input Views](https://mlsanity.com/paper/2403.02063/) (2024)
- [DeepSim-Nets: Deep Similarity Networks for Stereo Image Matching](https://mlsanity.com/paper/2304.08056/) (2023)
- [An evaluation of Deep Learning based stereo dense matching dataset shift from aerial images and a large scale stereo dataset](https://mlsanity.com/paper/2402.12522/) (2024)

## Built on by (most cited first, 2 of 2)

- [Tile and Slide : A New Framework for Scaling NeRF from Local to Global 3D Earth Observation](https://mlsanity.com/paper/2507.01631/) (2025)
- [Methods for evaluating the resolution of 3D data derived from satellite images](https://mlsanity.com/paper/2506.11876/) (2025)

## Abstract (arXiv)

Neural radiance fields (NeRF) have gained prominence as a machine learning technique for representing 3D scenes and estimating the bidirectional reflectance distribution function (BRDF) from multiple images. However, most existing research has focused on close-range imagery, typically modeling scene surfaces with simplified Microfacet BRDF models, which are often inadequate for representing complex Earth surfaces. Furthermore, NeRF approaches generally require large sets of simultaneously captured images for high-quality surface depth reconstruction - a condition rarely met in satellite imaging. To overcome these challenges, we introduce BRDF-NeRF, which incorporates the physically-based semi-empirical Rahman-Pinty-Verstraete (RPV) BRDF model, known to better capture the reflectance properties of natural surfaces. Additionally, we propose guided volumetric sampling and depth supervision to enable radiance field modeling with a minimal number of views. Our method is evaluated on two satellite datasets: (1) Djibouti, captured at varying viewing angles within a single epoch with a fixed Sun position, and (2) Lanzhou, captured across multiple epochs with different Sun positions and viewing angles. Using only three to four satellite images for training, BRDF-NeRF successfully synthesizes novel views from unseen angles and generates high-quality digital surface models (DSMs).