Hemisphere Harmonics Basis: A Universal Approach to Remote Sensing BRDF Approximation

Bidirectional reflectance distribution function (BRDF) is an important quantity in remote sensing, describing the variations of reflectance factors with viewing geometries. Current empirical or semi-empirical BRDF models are often constrained to limited types of landcovers due to the assumptions regarding surface cavity distribution. In this article, a universal approach to remote sensing BRDF approximation based on the HemiSphere Harmonics (HSH) basis function is proposed. We derived the HSH, which matches the BRDF definition domain, as basis functions of an infinite series to achieve high-precision BRDF representation. Besides, the proposed approach is universal across various landcovers since HSH basis functions are complete and orthogonal, enabling to approximate arbitrary BRDF data. To our knowledge, it is the first time to utilize the basis function for the BRDF approximation in remote sensing. The proposed approach was validated on both the satellite dataset with 16 landcovers and the UAV dataset with six landcovers. The results demonstrate that the proposed approach outperforms the current BRDF models and show universality across different landcovers, spectral bands, and platforms.