Surface Reflectance Characterization by Statistical Tools

Figure 1: A statistical definition of glossiness of surface reflectance, named variant index of glossiness rg ( fr(x,ωo)) (abbreviated as VIG), for the rendering purposes is studied and proposed in this paper to extend the Heckbert’s notation for diffuse, glossy, and specular BRDFs. The classification of surface reflectance functions as diffuse, spec-ular, and glossy has been introduced by Heckbert more than two decades ago. Many rendering algorithms are dependent on such a classification, as different kinds of light transport will be han-dled by specialized methods, for example, caustics require specular bounce or refraction. As the surface reflectance models are more and more rich and descriptive including those based on measured data, it has not been possible to keep such a characterization sim-ple. Each surface reflectance model is mostly handled separately, or alternatively, the rendering algorithm restricts itself to the use of some subset of reflectance models. We provide a general charac-terization for arbitrary surface reflectance representation by means of statistical tools. We demonstrate by rendered images using Ma-tusik’s BRDF data sets for two environment maps and two 3D ob-jects (sphere and Utah teapot) that there is even a visible percep-tual correspondence to the proposed surface reflectance character-ization, when we use monochromatic surface reflectance and the albedo is normalized for rendering images to equalize perceived brightness. The proposed characterization is intended to be used to optimize rendering algorithms