Statistical Analysis of Bidirectional Reflectance Distribution Functions

Bidirectional Reflectance Distribution Functions (BRDFs) are commonly employed in Computer Graphics and Computer Vision to model opaque materials. On the one hand, a BRDF is a complex 4D function of both light and view directions, which should ensure reciprocity and energy conservation laws. On the other hand, when computing radiance reaching the eye from a surface point, the view direction is held fixed. In this respect, we are only interested in a 2D BRDF slice that acts as a filter on the local environment lighting. The goal of our work is to understand the statistical properties of such a filter as a function of viewing elevation. To this end, we have conducted a study of measured BRDFs where we have computed statistical moments for each viewing angle. We show that some moments are correlated together across dimensions and orders, while some others are close to zero and may safely be discarded. Our study opens the way to novel applications such as moment-based manipulation of measured BRDFs, material estimation and image-based material editing. It also puts empirical and physically-based material models in a new perspective, by revealing their effect as view-dependent filters.