An Intrinsic Framework for Analysis of Facial Surfaces

A statistical analysis of shapes of facial surfaces can play an important role in biometric authentication and other face-related applications. The main difficulty in developing such an analysis comes from the lack of a canonical system to represent and compare all facial surfaces. This paper suggests a specific, yet natural, coordinate system on facial surfaces, that enables comparisons of their shapes. Here a facial surface is represented as an indexed collection of closed curves, called facial curves, that are level curves of a surface distance function from the tip of the nose. Defining the space of all such representations of face, this paper studies its differential geometry and endows it with a Riemannian metric. It presents numerical techniques for computing geodesic paths between facial surfaces in that space. This Riemannian framework is then used to: (i) compute distances between faces to quantify differences in their shapes, (ii) find optimal deformations between faces, and (iii) define and compute average of a given set of faces. Experimental results generated using laser-scanned faces are presented to demonstrate these ideas.