Scale-related evolution of BRDFs

In computer graphics, objects are often modeled as polygonal meshes with flat facets, the reflection of light from facets is described by the so-called bi-directional reflectance distribution function (BRDF). Along with the intrinsic optical properties of the material, it captures the effects due to surface microstructure, i.e. shape features smaller than the facet size and therefore not representable by the mesh model). If the typical facet size changes, some structures may switch from the "responsibility domain" of BRDFs to that of the geometric model, or vice versa. Therefore, for sufficiently complex surfaces, BRDFs are inherently scale-dependent. If one measures a BRDF at one scale, and applies at another, it must be adjusted ("evolved") according to the specific surface structure. In this report, we derive explicit BRDF evolution equations and discuss their implications.