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

Understanding the anisotropic reflectance of complex Earth surfaces from satellite imagery is crucial for numerous applications. Neural radiance fields (NeRF) have become popular as a machine learning technique capable of deducing the bidirectional reflectance distribution function (BRDF) of a scene from multiple images. However, prior research has largely concentrated on applying NeRF to close-range imagery, estimating basic Microfacet BRDF models, which fall short for many Earth surfaces. Moreover, high-quality NeRFs generally require several images captured simultaneously, a rare occurrence in satellite imaging. To address these limitations, we propose BRDF-NeRF, developed to explicitly estimate the Rahman-Pinty-Verstraete (RPV) model, a semi-empirical BRDF model commonly employed in remote sensing. We assess our approach using two datasets: (1) Djibouti, captured in a single epoch at varying viewing angles with a fixed Sun position, and (2) Lanzhou, captured over multiple epochs with different viewing angles and Sun positions. Our results, based on only three to four satellite images for training, demonstrate that BRDF-NeRF can effectively synthesize novel views from directions far removed from the training data and produce high-quality digital surface models (DSMs).