The application of tensor representation and HoSVD for detecting 3D-facial shape recovery

This paper proposes a fast 3D-facial shape recovery algorithm from a single image with general, Unknown lighting. To derive the algorithm , we formulate a nonlinear least-square problem with two-parameter vectors related to personal identity and light conditions. We then combine the spherical harmonics for the surface normal of a human face with tensor algebra and show that in a particular 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 speeds up the computations. To enhance the shape recovery performance, we have incorporated prior information in updating the parameters. The proposed algorithm takes less than 0.4 s to reconstruct a face in the experiment and shows a significant performance improvement over other reported scheme.