In this paper we demonstrate robust estimation of the model parameters of a fully-linear data-driven BRDF model from a reflectance map under known natural lighting. To regularize the estimation of the model parameters, we leverage the reflectance similarities within a material class. We approximate the space of homogeneous BRDFs using a Gaussian mixture model, and assign a material class to each Gaussian in the mixture model. We formulate the estimation of the model parameters as a non-linear maximum a-posteriori optimization, and introduce a linear approximation that estimates a solution per material class from which the best solution is selected. We demonstrate the efficacy and robustness of our method using the MERL BRDF database under a variety of natural lighting conditions, and we provide a proof-of-concept real-world experiment.