Rough Surface Analysis using Kirchhoff Theory

In this paper we illustrate the use of the Beckmann-Kirchhoff model for analysing rough surface reflectance. The Beckmann-Kirchhoff model is a physical model that describes the reflectance of light from rough surfaces. The parameter of the model is the surface slope, or ratio of the surface roughness to the correlation length. We show how this parameter may be estimated using pairs of surface images, subject to different illumination directions. With the parameter to hand, the Beckmann-Kirchhoff model may be used to perform Lambertian reflectance correction, and hence shape-from-shading may be applied to the rough surfaces. The model may also be used for surface re-illumination. We present experiments to illustrate the utility of the method for each of these tasks.