Statistically-based reflection model for rough surfaces

Modeling light reflection from rough surfaces is an essential problem in computer graphics, computational vision, and multispectral imaging. Existing methods commonly separate the total reflection into diffuse and specular components, but this leads to the nonphysical arbitrariness in choosing the relative weights for the two components. There also lacks a sufficient model for the self-shadowing effect, which is important for rough surfaces. To eliminate these drawbacks, we propose a new reflection model entirely using physical parameters. The surfaces are assumed homogeneous, isotropic. and microscopically smooth, and their height probability densities are assumed Gaussian. Thus we derive the one-bounce reflection through Fresnel coefficient, self-shadowing factor, and probability function for surface orientation. The shadowing factor is calculated analytically from the statistical properties of a rough surface, including the height probability density and correlation function, and it agrees well with numerical simulation. Since all involved parameters in this model are physical, it can be easily verified with measurement. Besides, as a single term, this model generates a sharp specular highlight when a surface is smooth and shows diffuse behavior when the surface is rough. This advantage will be shown through rendered images.