Beyond the Lambertian assumption: A generative model for Apparent BRDF fields of faces using anti-symmetric tensor splines

Human faces are neither exactly Lambertian nor entirely convex and hence most models in literature which make the Lambertian assumption, fall short when dealing with specularities and cast shadows. In this paper, we present a novel anti-symmetric tensor spline (a spline for tensor-valued functions) based method for the estimation of the Apparent BRDF (ABRDF) field for human faces that seamlessly accounts for specularities and cast shadows. Furthermore, unlike other methods, it does not require any 3D information to build the model and can work with as few as 9 images. In order to validate the accuracy of our anti-symmetric tensor spline model, we present a novel approximation of the ABRDF using a continuous mixture of single-lobed spherical functions. We demonstrate the effectiveness of our anti-symmetric tensor-spline model in comparison to other popular models in the literature, by presenting extensive results for face relighting and face recognition using the Extended Yale B database.