Expression-invariant representations for human faces

An essential question in many fields that deal with the nature of facial appearance is what are the invariants of the human face under various expressions. That is, can someone’s face have a unique description, that is independent of his or her facial expression. We previously suggested, without a proof, to treat facial expressions as isometries of deformable surfaces in the context of Riemannian geometry. Here we introduce, for the first time, an experiment that supports this claim. We also extend the model to handle topology-changing transformation, namely, expressions with open and closed mouth.