Diffuse-reflectance model for smooth dielectric surfaces

Abstract

A reflectance model that accurately predicts diffuse reflection from smooth inhomogeneous dielectric surfaces as a function of both viewing angle and angle of incidence is proposed. Utilizing results of radiative-transfer theory for subsurface multiple scattering, this new model precisely accounts for how incident light and the distribution of subsurface scattered light are influenced by Fresnel attenuation and Snell refraction at a smooth air–dielectric surface boundary. Whereas similar assumptions about subsurface scattering and Fresnel attenuation have been made in previous research on diffuse-reflectance modeling, the proposed model combines these assumptions in a different way and yields a more accurate expression for diffuse reflection that is shown to account for a number of empirical observations not predicted by existing models. What is particularly new about this diffuse-reflectance model is the resulting significant dependence on the viewing angle with respect to the surface normal. This dependence on the viewing angle explains distinctive properties of the behavior of diffuse reflection from smooth dielectric objects, properties not accounted for by existing diffuse-reflection models. Among these properties are prominent diffuse-reflection maxima effects occurring on objects when incident point-source illumination is greater than 50° relative to viewing, including the range from 90° to 180°, where the light source is behind the object with respect to viewing. For this range of incident illumination there is significant deviation from Lambertian behavior over a large portion of most smooth dielectric object surfaces, which makes it important for the computer vision community to be aware of such effects during incorporation of reflectance models into implementation of algorithms such as shape-from-shading. A number of experimental results are presented that verify the proposed diffuse-reflectance model.