Linear approximation of Bidirectional Reflectance Distribution Functions

Various empirical and theoretical models of the surface reflectance have been introduced so far. Most of these models are based on functions with non-linear parameters and therefore faces some computational difficulties involved in non-linear optimization processes. In this paper, we introduce a new approach for approximating Bidirectional Reflectance Distribution Functions (BRDF) by employing response surface methodology. The proposed model employs principal component transformations of the explanatory variables which are essentially functions of incoming and outgoing light directions. The resulting model is linear and can be used to represent both isotropic and anisotropic reflectance for diffuse and glossy materials. Considering some widely used reflection models including the Ward model, the Ashikhmin–Shirley model and the Lafortune model, we demonstrate empirically that satisfactory approximations can be made by means of the proposed general, simple and computationally efficient linear model.