Improving shape recovery by estimating properties of slightly-rough surfaces

We illustrate the use of the Beckmann formulation of the Kirchhoff theory for surface analysis problems in computer vision. The Beckmann model is a physical model that describes the reflectance of light from rough surfaces. Here, we use the modified form of the Beckmann model for slightly-rough surfaces using the modification of C.L. Vernold and J.E. Harvey (see Proc. SPIE, vol.3426, p.51-6, 1998). The parameters of the model are the surface roughness and the correlation length. We show how the surface roughness can be estimated using the specular reflectance properties. We also propose a technique for estimating the correlation length using pairs of surface images, subject to different illumination directions. With these parameters to hand, the Beckmann model may be used to perform photometric correction, and hence shape-from-shading may be applied to the corrected Lambertian image to recover improved shape. This model may also be used to re-illuminate the recovered surface. We present experiments to illustrate the utility of the method for each of these tasks.