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In this paper we explore the use of complex numbers as means of representing angular statistics for surface normal data. Our aim is to use the representation to construct a statistical model that can be used to describe the variations in fields of surface normals. We focus on the problem of representing facial shape. The fields of surface normals used to train the model are furnished by range images. We compare the complex representation with one based on angles, and demonstrate the advantages of the new method. Once trained, we illustrate how the model can be fitted to brightness images by searching for the set of parameters that both satisfy Lambert’s law and minimize the integrability error.

Estimation of Facial Angular Information Using a Complex-Number-Based Statistical Model