Shape-based description of the facial surface

The mathematics used to describe surfaces, differential geometry, has been known for some time, but its power for the description of biological surfaces is only just being appreciated. The description of the facial surface presented uses the surface type primitives of Besl and Jain. These are defined by the surface curvatures. The Gaussian curvature is an intrinsic property, unchanging with the way the surface is embedded in 3D space whereas the mean curvature is an extrinsic property. These surface curvatures are independent of each other and both are needed to describe the surface unambiguously.