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

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).