Fast and Accurate Gaussian Process Modelling of Real-World Materials

Our goal in this article is to propose a fast and easy to implement BRDF modeling method that provides both accurate and compact representations for all types of BRDF, i.e., isotropic or anisotropic. To achieve this objective, we use a Bayesian regression method with a Gaussian process prior which allows obtaining compact BRDF representations in a purely analytical way. For this purpose, we use a generalzed distance covariance kernel which is much better suited to BRDF features than the usual Gaussian kernel. To speed up the processing, we adapt this method to the specificities of BRDFs through an appropriate input data structure and distribution of observations so as to drastically reduce the problem dimensionality through an efficient factorization method. In this way, all calculations at both fitting and rendering steps are reduced to basic matrix products and the computation of a BRDF representation with our modeling method takes only a few seconds. Furthermore, rather than using a systematic approach as in state-of-the-art methods, the size and complexity of the BRDF representation can be adapted to the application requirements as regards the fitting accuracy and rendering constraints. Besides, our BRDF representation can be easily converted to spherical harmonics expansions, which allows easier integration in usual rendering algorithms. We also propose importance sampling methods derived from our BRDF modeling method that leads to fast and easy implementations. Experimental applications of our method to various types of isotropic and anisotropic BRDFs show that state-of-the-art methods can be outperformed in most cases by using a small set of observations for the regression.