Two-image Comparison under Different Illumination Conditions

We present a new theory that shows that two images of the same object taken under two different light directions can be made virtually identical by filtering each image by a directional derivative filter. The direction and magnitude of the derivative is generally different for each image, and depends on illumination directions used. The method requires the object surface to be of uniform Lambertian reflectance and a shallow relief, and the light directions used to be sufficiently inclined from the surface macro-normal. For a specific case when the surface consists of spherical patches, the two images can be made identical, for any two light directions used provided that none of them is perpendicular to the viewing axis. We provide some simple experiments which illustrate the validity of this theory.