Global optimization for estimating a BRDF with multiple specular lobes

This paper presents a global minimization framework for estimating analytical BRDF model parameters using the techniques of convex programming and branch and bound. 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 and nonlinear. We consider the Cook-Torrance model, 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 method using the extensive high-precision measurements from the MERL BRDF database.