Probabilistic expression analysis on manifolds

In this paper, we propose a probabilistic video-based facial expression recognition method on manifolds. The concept of the manifold of facial expression is based on the observation that the images of all possible facial deformations of an individual make a smooth manifold embedded in a high dimensional image space. An enhanced Lipschitz embedding is developed to embed the aligned face appearance in a low dimensional space while keeping the main structure of the manifold. In the embedded space, a complete expression sequence becomes a path on the expression manifold, emanating from a center that corresponds to the neutral expression. Each path consists of several clusters. A probabilistic model of transition between the clusters and paths is learned through training videos in the embedded space. The likelihood of one kind of facial expression is modeled as a mixture density with the clusters as mixture centers. The transition between different expressions is represented as the evolution of the posterior probability of the six basic paths. The experimental results demonstrate that the probabilistic approach can recognize expression transitions effectively. We also synthesize image sequences of changing expressions through the manifold model.