WHAT IS THE SET OF IMAGES OF AN OBJECT UNDER ALL POSSIBLE ILLUMINATION CONDITIONS

The appearance of an object depends on both the viewpoint from which i t is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then - in theory - the objects can always be distinguishe d or recognized. The question arises: What is the set of images of an object under all lighting conditions and pose? In this paper, we consi der only the set of images of an object under variable illumination, i ncluding multiple, extended light sources and shadows. We prove that t he set of n-pixel images of a convex object with a Lambertian reflecta nce function, illuminated by an arbitrary number of point light source s at infinity, forms a convex polyhedral cone in IRn and that the dime nsion of this illumination cone equals the number of distinct surface normals. Furthermore, the illumination cone can be constructed from as few as three images. In addition, the set of n-pixel images of an obj ect of any shape and with a more general reflectance function, seen un der all possible illumination conditions, still forms a convex cone in IRn. Extensions of these results to color images are presented. These results immediately suggest certain approaches to object recognition. Throughout, we present results demonstrating the illumination cone re presentation.