Fast facial shape recovery from a single image with general, unknown lighting by using tensor representation

In this paper, we propose a fast 3-D facial shape recovery algorithm from a single image with general, unknown lighting. In order to derive the algorithm, we formulate a nonlinear least-square problem with two parameter vectors which are related to personal identity and light conditions. We then combine the spherical harmonics for the surface normals of a human face with tensor algebra and show that in a certain condition, the dimensionality of the least-square problem can be further reduced to one-tenth of the regular subspace-based model by using tensor decomposition (N-mode SVD), which greatly speeds up the computations. In order to enhance the shape recovery performance, we have incorporated prior information in updating the parameters. In the experiment, the proposed algorithm takes less than 0.4 s to reconstruct a face and shows a significant performance improvement over other reported schemes.