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.
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. Effective use of support vector machines (SVMs) in classification necessitates the appropriate choice of a kernel. Designing problem specific kernels involves the definition of a similarity measure, with the condition that kernels are positive semi-definite (PSD). An alternative approach which places no such restrictions on the similarity measure is to construct a set of inputs and let each example be represented by its similarity to all the examples in this set and then apply a conventional SVM to this transformed data. Dynamic time warping (DTW) is a well established distance measure for time series but has been of limited use in SVMs since it is not obvious how it can be used to derive a PSD kernel. The feasibility of the similarity based approach for DTW is investigated by applying the method to a large set of time-series classification problems. 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. We study the problem of classifying actions of human subjects using depth movies generated by Kinect or other depth sensors. Representing human body as dynamical skeletons, we study the evolution of their (skeletons’) shapes as trajectories on Kendall’s shape manifold. The action data is typically corrupted by large variability in execution rates within and across subjects and, thus, causing major problems in statistical analyses. To address that issue, we adopt a recently-developed framework of [1] , [2] to this problem domain. Here, the variable execution rates correspond to re-parameterizations of trajectories, and one uses a parameterization-invariant metric for aligning, comparing, averaging, and modeling trajectories. This is based on a combination of transported square-root vector fields (TSRVFs) of trajectories and the standard Euclidean norm, that allows computational efficiency. We develop a comprehensive suite of computational tools for this application domain: smoothing and denoising skeleton trajectories using median filtering, up- and down-sampling actions in time domain, simultaneous temporal-registration of multiple actions, and extracting invertible Euclidean representations of actions. Due to invertibility these Euclidean representations allow both discriminative and generative models for statistical analysis. For instance, they can be used in a SVM-based classification of original actions, as demonstrated here using MSR Action-3D, MSR Daily Activity and 3D Action Pairs datasets. Using only the skelet al information, we achieve state-of-the-art classification results on these datasets.