Representations for recognition under variable illumination

Due to illumination variability, the same object can appear dramatically di fferent 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 mod eling this variability. In particular, we prove that the set of n-pixel mon ochrome images of a convex object with a Lambertian reflectance function, i lluminated by an arbitrary number of point light sources at infinity, forms a convex polyhedral cone in R-n and that the dimension of this illuminatio n cone equals the number of distinct surface normals. For a non-convex obje ct with a more general reflectance function, the set of images is also a co nvex cone. Geometric properties of these cones for monochrome and color cam eras are considered. Here, present a method for constructing a cone represe ntation from a small number of images when the surface is continuous, possi bly non-convex, and Lambertian; this accounts for both attached and cast sh adows. For a collection of objects, each object is represented by a cone, a nd recognition is performed through nearest neighbor classification by meas uring the minimal distance of an image to each cone. We demonstrate the uti lity of this approach to the problem of face recognition (a class of non-co nvex and non-Lambertian objects with similar geometry). The method is teste d on a database of 660 images of 10 faces, and the results exceed those of popular existing methods.