In search of illumination invariants

We consider the problem of determining functions of an image of an object that are insensitive to illumination changes. We first show that for an object with Lambertian reflectance there are no discriminative functions that are invariant to illumination. This result leads as to adopt a probabilistic approach in which we analytically determine a probability distribution for the image gradient as a function of the surface's geometry and reflectance. Our distribution reveals that the direction of the image gradient is insensitive to changes in illumination direction. We verify this empirically by constructing a distribution for the image gradient from more than 20 million samples of gradients in a database of 1,280 images of 20 inanimate objects taken under varying lighting condition. Using this distribution we develop an illumination insensitive measure of image comparison and test it on the problem of face recognition.