Local spherical harmonics for facial shape and albedo estimation

In this paper, we present a novel facial albedo and 3D shape recovery method with a local spherical harmonic illumination model. From a face in an image, the proposed method can produce a high-quality 3D shape and albedo using a novel parameterization of local illuminations. Because a facial shape is partially convex, a single spherical harmonics is generally used for the illumination of a face within a constrained illumination environment. However, when a facial image is captured in an unconstrained scene, the illumination is inappropriately estimated due to the presence of shadow and specular reflections. To address this issue, we propose a novel local spherical harmonic illumination model for representing the illumination of a face. Unlike the existing parameterization of local illumination, our local spherical harmonic illumination model utilizes a smooth weight function for the seamless representation of natural illumination. Therefore, the albedo and shape information in an image can be precisely estimated using the first-order spherical harmonics. For accurate estimation of albedo, we also utilize facial albedo statistics to prevent the estimated albedo from becoming biased toward input image. Furthermore, we developed an accurate and reliable 3D shape reconstruction method from a normal map based on tetrahedron-based deformation. Comparing to the Laplacian deformation based method, our method is applicable to any mesh regardless of its structure. Through rigorous experiments, we demonstrate that the proposed local spherical harmonic illumination model is effective in estimating the complex illumination and can recover a high-quality facial albedo and 3D shape.