Isometric Embedding of Facial Surfaces into S3

The problem of isometry-invariant representation and comparison of surfaces is of cardinal importance in pattern recognition applications dealing with deformable objects. Particularly, in threedimensional face recognition treating facial expressions as isometries of the facial surface allows to perform robust recognition insensitive to expressions. Isometry-invariant representation of surfaces can be constructed by isometrically embedding them into some convenient space, and carrying out the comparison in that space. Presented here is a discussion on isometric embedding into S, which appears to be superior over the previously used Euclidean space in sense of the representation accuracy.