Representations for Recognition Under Variable Illumination

Due to illumination variability, the same object can appear dramatically different even when viewed in fixed pose. Consequently, an object recognition system must employ a representation that is either invariant to, or models this variability. This chapter presents an appearance-based method for modeling this variability. In particular, we prove that the set of n-pixel monochrome images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a convex polyhedral cone in Rn and that the dimension of this illumination cone equals the number of distinct surface normals. For a non-convex object with a more general reflectance function, the set of images is also a convex cone. Geometric properties of these cones for monochrome and color cameras are considered. Here, present a method for constructing a cone representation from a small number of images when the surface is continuous, possibly non-convex, and Lambertian; this accounts for both attached and cast shadows. For a collection of objects, each object is represented by a cone, and recognition is performed through nearest neighbor classification by measuring the minimal distance of an image to each cone. We demonstrate the utility of this approach to the problem of face recognition (a class of non-convex and non-Lambertian objects with similar geometry). The method is tested on a database of 660 images of 10 faces, and the results exceed those of popular existing methods.