Global optimization for estimating a multiple-lobe analytical BRDF

We present a global minimization framework for estimating the parameters of multiple-lobe analytical BRDF model using the techniques of convex programming and branch and bound. When an analytical BRDF is used to model a natural or artificial surface, reflections can often be represented accurately with multiple non-Lambertian lobes. A BRDF model with multiple lobes can be highly nonlinear and poses a challenge in data fitting for parameter estimation. Traditional local minimization suffers from local minima and requires a large number of initial conditions and supervision for successful results especially when a model is highly complex. We consider the Cook-Torrance model with multiple specular lobes, a parametric model with the Gaussian-like Beckmann distributions for specular reflectances. Instead of optimizing the multiple parameters simultaneously, we search over all possible surface roughness values based on a branch-and-bound algorithm, and reduce the estimation problem to convex minimization with known fixed surface roughness. Our algorithm guarantees globally optimal solutions. Experiments have been carried out for isotropic surfaces to validate the presented method using the extensive high-precision measurements from the MERL BRDF database.