Abstract-Facial expression analysis is one of the important components for effective human-computer interaction. However, to develop robust and generalizable models for expression analysis one needs to break the dependence of the models on the choice of the coordinate frame of the camera i.e. expression models should generalize across facial poses. To perform this systematically, one needs to understand the space of observed images subject to projective transformations. However, since the projective shape-space is cumbersome to work with, we address this problem by deriving models for expressions on the afÀne shape-space as an approximation to the projective shape-space by using a Riemannian interpretation of deformations that facial expressions cause on different parts of the face. We use landmark conÀgurations to represent facial deformations and exploit the fact that the afÀne shape-space can be studied using the Grassmann manifold. This representation enables us to perform various expression analysis and recognition algorithms without the need for the normalization as a preprocessing step. We extend some of the available approaches for expression analysis to the Grassmann manifold and experimentally show promising results, paving the way for a more general theory of view-invariant expression analysis.
For example, Taheri et al. REF used landmark configurations of the face to represent facial deformations on the Grassmann manifold G(2, n).
Towards view-invariant expression analysis using analytic shape manifolds
Face and Gesture 2011
Face and Gesture 2011
Computer Science Mathematics