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.
One outstanding issue encountered when modeling the temporal evolution of the face as a trajectory is the temporal misalignment resulting from the different execution rate of the facial expression. This issue necessitates the use of an algorithm based generally on dynamic programming to align different trajectories. Several works including @cite_2 @cite_3 @cite_41 used DTW to align trajectories in a Riemannian manifold; however, this algorithm does not define a proper metric, which is indeed required in the classification phase to define a valid positive-definite kernel. As alternative solution, different works @cite_3 @cite_41 @cite_19 proposed to ignore this constraint by using a variant of SVM with an arbitrary kernel without any restrictions on the kernel function.
@cite_41 @cite_19 @cite_3 @cite_2
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In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the advantage to bring naturally a second desirable quantity when comparing shapes -- the spatial covariance -- in addition to the conventional affine-shape representation. We derive then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the manifold. Specifically, our approach involves three steps: 1) facial landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of rank 2, to build time-parameterized trajectories; 2) a temporal alignment is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; 3) finally, pairwise proximity function SVM (ppfSVM) is used to classify them, incorporating the latter (dis-)similarity measure into the kernel function. We show the effectiveness of the proposed approach on four publicly available benchmarks (CK+, MMI, Oulu-CASIA, and AFEW). The results of the proposed approach are comparable to or better than the state-of-the-art methods when involving only facial landmarks. In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes — the spatial covariance — in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skelet al data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks. Temporal misalignment and duration variation in video actions largely influence the performance of action recognition, but it is very difficult to specify effective temporal alignment on action sequences. To address this challenge, this paper proposes a novel discriminative learning-based temporal alignment method, called maximum margin temporal warping (MMTW), to align two action sequences and measure their matching score. Based on the latent structure SVM formulation, the proposed MMTW method is able to learn a phantom action template to represent an action class for maximum discrimination against other classes. The recognition of this action class is based on the associated learned alignment of the input action. Extensive experiments on five benchmark datasets have demonstrated that this MMTW model is able to significantly promote the accuracy and robustness of action recognition under temporal misalignment and variations. Research in the areas of 3-D face recognition and 3-D facial expression analysis has intensified in recent years. However, most research has been focused on 3-D static data analysis. In this paper, we investigate the facial analysis problem using dynamic 3-D face model sequences. One of the major obstacles for analyzing such data is the lack of correspondences of features due to the variable number of vertices across individual models or 3-D model sequences. In this paper, we present an effective approach for establishing vertex correspondences using a tracking-model-based approach for vertex registration, coarse-to-fine model adaptation, and vertex motion trajectory (called vertex flow) estimation. We propose to establish correspondences across frame models based on a 2-D intermediary, which is generated using conformal mapping and a generic model adaptation algorithm. Based on our newly created 3-D dynamic face database, we also propose to use a spatiotemporal hidden Markov model (ST-HMM) that incorporates 3-D surface feature characterization to learn the spatial and temporal information of faces. The advantage of using 3-D dynamic data for face recognition has been evaluated by comparing our approach to three conventional approaches: 2-D-video-based temporal HMM model, conventional 2-D-texture-based approach (e.g., Gabor-wavelet-based approach), and static 3-D-model-based approaches. To further evaluate the usefulness of vertex flow and the adapted model, we have also applied a spatial-temporal face model descriptor for facial expression classification based on dynamic 3-D model sequences.