## Abstract

We present a reliable and accurate global optimization framework for estimating parameters of isotropic analytical bidirectional reflectance distribution function (BRDF) models. This approach is based on a branch and bound strategy with linear programming and interval analysis. Conventional local optimization is often very inefficient for BRDF estimation since its fitting quality is highly dependent on initial guesses due to the nonlinearity of analytical BRDF models. The algorithm presented in this paper employs ${L}_{1}$-norm error minimization to estimate BRDF parameters in a globally optimal way and interval arithmetic to derive our feasibility problem and lower bounding function. Our method is developed for the Cook–Torrance model but with several normal distribution functions such as the Beckmann, Berry, and GGX functions. Experiments have been carried out to validate the presented method using 100 isotropic materials from the MERL BRDF database, and our experimental results demonstrate that the ${L}_{1}$-norm minimization provides a more accurate and reliable solution than the ${L}_{2}$-norm minimization.

© 2016 Optical Society of America

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