Non-Lambertian Model-based Facial Shape Recovery from Single Image Under Unknown General Illumination

Through depth perception, humans have the ability to determine distances based on a single 2D image projected on their retina, where shape-from-shading (SFS) provides a mean to mimic such a phenomenon. The goal of this paper is to recover 3D facial shape from a single image of unknown general illumination, while relaxing the non-realistic assumption of Lambert Ian reflectance. Prior shape, albedo and reflectance models from real data, which are metric in nature, are incorporated into the shape recovery framework. Adopting a frequency-space based representation of the image irradiance equation, we propose an appearance model, termed as Harmonic Projection Images, which accounts explicitly for different human skin types as well as complex illumination conditions. Assuming skin reflectance obeys Torrance-Sparrow model, we prove analytically that it can be represented by at most 5th order harmonic basis whose closed form is provided. The recovery framework is a non-iterative approach which incorporates regression-like algorithm in the minimization process. Our experiments on synthetic and real images illustrate the robustness of our appearance model vis-a-vis illumination variation.