A comparison of Cartesian coordinate-based representations for building three-dimensional models of faces

We present an experimental analysis of three different ways of constructing three-dimensional statistical models of faces using Cartesian coordinates, namely, height, surface gradient and one based on Fourier domain basis functions. We test the ability of each of the models for dealing with information provided by shape-from-shading. Experiments show that the surface gradient based representation is more robust to noise than alternative Cartesian representations. Moreover, the method can be operated using a simple non-exhaustive parameter adjustment procedure and ensures that the recovered surface satisfies the image irradiance equation as a hard constraint.