Low-dimensional representations of shaded surfaces under varying illumination

The aim of this paper is to find the best representation for the appearance of surfaces with Lambertian reflectance under varying illumination. Previous work using principal component analysis (PCA) found the best sub-space to represent all images of an object under a varying point light source. We extend this to images from any illumination distribution. Specifically we calculate the bases for all configurations of a point plus ambient light source and two point light sources, as well as from a database of captured real world illumination. We also reformulate the optimization criterion used in PCA. The resulting basis, we believe has higher representability and is better for analyzing images of shaded objects. The different bases are compared on a database of images to test the representability.