Automatic Analysis of Facial Expressions Based on Deep Covariance Trajectories

In this paper, we propose a new approach for facial expression recognition using deep covariance descriptors. 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 conducting the classification of static facial expressions using Support Vector Machine (SVM) with a valid Gaussian kernel on the SPD manifold, we show that deep covariance descriptors 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 performing 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 many recent approaches.Comment: A preliminary version of this work appeared in "Otberdout N, Kacem A, Daoudi M, Ballihi L, Berretti S. Deep Covariance Descriptors for Facial Expression Recognition, in British Machine Vision Conference 2018, BMVC 2018, Northumbria University, Newcastle, UK, September 3-6, 2018. ; 2018 :159." arXiv admin note: substantial text overlap with arXiv:1805.0386

Building Deep Networks on Grassmann Manifolds

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches.Comment: AAAI'18 pape