Manifold of facial expression

We propose the concept of manifold of facial expression based on the observation that images of a subject´s facial expressions define a smooth manifold in the high dimensional image space. Such a manifold representation can provide a unified framework for facial expression analysis. We first apply active wavelet networks (AWN) on the image sequences for facial feature localization. To learn the structure of the manifold in the feature space derived by AWN, we investigated two types of embeddings from a high dimensional space to a low dimensional space: locally linear embedding (LLE) and Lipschitz embedding. Our experiments show that LLE is suitable for visualizing expression manifolds. After applying Lipschitz embedding, the expression manifold can be approximately considered as a super-spherical surface in the embedding space. For manifolds derived from different subjects, we propose a nonlinear alignment algorithm that keeps the semantic similarity of facial expression from different subjects on one generalized manifold. We also show that nonlinear alignment outperforms linear alignment in expression classification.