Bidirectional Reflection Distribution Function of Thoroughly Pitted Surfaces

We derive the BRDF (Bidirectional Reflection Distribution Function) at the mega scale of opaque surfaces that are rough on the macro and micro scale. The roughness at the micro scale is modeled as a uniform, isotropically scattering, Lambertian surface. At the macro scale the roughness is modeled by way of a distribution of spherical concavities. These pits influence the BRDF via vignetting, cast shadow, interreflection and interposition, causing it to differ markedly from Lambertian. Pitted surfaces show strong backward scattering (so called “opposition effect”). When we assume that the macro scale can be resolved, the radiance histogram and the spatial structure of the textons of the textured surface (at the mega scale) can be calculated. This is the main advantage of the model over previous ones: One can do exact (numerical) calculations for a surface geometry that is physically realizable.

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