Recovering facial shape and albedo using a statistical model of surface normal direction

This paper describes how facial shape can be modelled using a statistical model that captures variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map surface normals from the unit sphere to points on a local tangent plane. The variations in surface normal direction are captured using the covariance matrix for the projected point positions. This allows us to model variations in face shape using a standard point distribution model. We train the model on fields of surface normals extracted from range data and show how to fit the model to intensity data using constraints on the surface normal direction provided by Lambert´s law. We demonstrate that this process yields accurate facial shape recovery and allows an estimate of the albedo map to be made from single, real world face images.