Irradiation orientation from obliquely viewed texture

We studied image texture due to the shading of corrugated (3D textured) surfaces, which are Lambertian on the micro scale. Our theory applies to physically canonical cases of isotropic Gaussian random surfaces, under collimated illumination. In this investigation we analyze effects of oblique viewing, extending our theory which applied to normal viewing conditions only [5]. The theory for normal views predicts the structure tensors from either the gradient or the Hessian of the image intensity and allows for inferences of the orientation of irradiation of the surface. Even for surfaces that are not at all Gaussian, the BRDF [10] far from Lambertian, with vignetting and multiple scattering present, such inferences of the orientation of irradiation were accurate up to a few degrees. In this paper we derive predictions for oblique viewing conditions, for which the inferences of the irradiation orientation will deviate from the veridical value in a systematic manner, depending on the viewing and illumination directions. Theoretical predictions are compared with empirical data, for rendered and for real rough surfaces, and found to be in good agreement. We discuss issues of scale selection and robustness.