Representing BRDF by wavelet transformation of pair-copula constructions

Bidirectional Reflectance Distribution Functions (BRDFs) are well-known functions in computer graphics, and these special functions represent the surface reflectance of materials. BRDFs can be viewed as multivariate probability density function (pdf) of incoming photons leaving in a particular outgoing direction. However, constructing a multivariate probability distribution for modeling a given BRDF is difficult. A family of distributions, namely Copula distributions have been used to approximate BRDF. In this work, we employ the Pair-Copula constructions to represent the measured BRDF densities. As the measured BRDF densities have large storage needs, we use Wavelet transforms for a compact BRDF representation. We also compare the proposed BRDF representation with a number of well-known BRDF models, and show that our compact BRDF representation provides good approximation to measured BRDF data.