Expression-invariant three-dimensional face recognition

One of the hardest problems in face recognition is dealing with facial expressions. Finding an expression-invariant representation of the face could be a remedy for this problem. We suggest treating faces as deformable surfaces in the context of Riemannian geometry, and propose to approximate facial expressions as isometries of the facial surface. This way, we can define geometric invariants of a given face under different expressions. One such invariant is constructed by isometrically embedding the facial surface structure into a low-dimensional flat space. Based on this approach, we built an accurate three-dimensional face recognition system that is able to distinguish between identical twins under various facial expressions. In this chapter we show how under the near-isometric model assumption, the difficult problem of face recognition in the presence of facial expressions can be solved in a relatively simple way.