Automatic Analysis of Facial Expressions Based on Deep Covariance Trajectories

In this paper, we propose a new approach for facial expression recognition. The solution is based on the idea of encoding local and global Deep Convolutional Neural Network (DCNN) features extracted from still images, in compact local and global covariance descriptors. The space geometry of the covariance matrices is that of Symmetric Positive Definite (SPD) matrices. By performing the classification of static facial expressions using a valid Gaussian kernel on the SPD manifold and Support Vector Machine (SVM), we show that the covariance descriptors computed on DCNN features are more effective than the standard classification with fully connected layers and softmax. Besides, we propose a completely new and original solution to model the temporal dynamic of facial expressions as deep trajectories on the SPD manifold. As an extension of the classification pipeline of covariance descriptors, we apply SVM with valid positive definite kernels derived from global alignment for deep covariance trajectories classification. By conducting extensive experiments on the Oulu-CASIA, CK+, and SFEW datasets, we show that both the proposed static and dynamic approaches achieve state-of-the-art performance for facial expression recognition outperforming most recent approaches.