We present a technique to generate an illumination subspace for arbitrary 3D faces based on the statistics of measured illuminations under variable lighting conditions from many subjects. A bilinear model based on the higher-order singular value decomposition is used to create a compact illumination subspace given arbitrary shape parameters from a parametric 3D face model. Using a fitting procedure based on minimizing the distance of the input image to the dynamically changing illumination subspace, we reconstruct a shape-specific illumination subspace from a single photograph. We use the reconstructed illumination subspace in various face recognition experiments with variable lighting conditions and obtain accuracies which are very competitive with previous methods that require specific training sessions or multiple images of the subject.