Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this study, the authors tackle the problem of categorising human actions by devising bag of words (BoWs) models based on covariance matrices of spatiotemporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of symmetric positive definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, the authors propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison with several state-of-the-art methods.
Human action recognition has been addressed extensively in the computer vision community from various perspectives. Some methods rely on global descriptors; two examples are the methods proposed by Ali and Shah @cite_44 and Razzaghi al @cite_47 . @cite_44 , a set of optical flow based kinematic features is extracted. Kinematic models are computed by applying principal component analysis on the volumes of kinematic features. Razzaghi al @cite_47 represent human motion by spatio-temporal volume and propose a new affine invariant descriptor based on a function of spherical harmonics. A downside of global representations is their reliance on localisation of the region of interest, and hence they are sensitive to viewpoint change, noise, and occlusion @cite_49 .
@cite_44 @cite_47 @cite_49
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We propose a set of kinematic features that are derived from the optical flow for human action recognition in videos. The set of kinematic features includes divergence, vorticity, symmetric and antisymmetric flow fields, second and third principal invariants of flow gradient and rate of strain tensor, and third principal invariant of rate of rotation tensor. Each kinematic feature, when computed from the optical flow of a sequence of images, gives rise to a spatiotemporal pattern. It is then assumed that the representative dynamics of the optical flow are captured by these spatiotemporal patterns in the form of dominant kinematic trends or kinematic modes. These kinematic modes are computed by performing principal component analysis (PCA) on the spatiotemporal volumes of the kinematic features. For classification, we propose the use of multiple instance learning (MIL) in which each action video is represented by a bag of kinematic modes. Each video is then embedded into a kinematic-mode-based feature space and the coordinates of the video in that space are used for classification using the nearest neighbor algorithm. The qualitative and quantitative results are reported on the benchmark data sets. The aim of this paper is to introduce a new descriptor for the spatio-temporal volume (STV). Human motion is completely represented by STV (action volume) which is constructed over successive frames by stacking human silhouettes in consecutive frames. Action volume comprehensively contains spatial and temporal information about an action. The main contribution of this paper is to propose a new affine invariant action volume descriptor based on a function of spherical harmonic coefficients. This means, it is invariant under rotation, non-uniform scaling and translation. In the 3D shape analysis literature, there have been a few attempts to use coefficients of spherical harmonics to describe a 3D shape. However, those descriptors are not affine invariant and they are only rotation invariant. In addition, the proposed approach employs a parametric form of spherical harmonics that handles genus zero surfaces regardless of whether they are stellar or not. Another contribution of this paper is the way that action volume is constructed. We applied the proposed descriptor to the KTH, Weizmann, IXMAS and Robust datasets and compared the performance of our algorithm to competing methods available in the literature. The results of our experiments show that our method has a comparable performance to the most successful and recent existing algorithms. We propose a new action and gesture recognition method based on spatio-temporal covariance descriptors and a weighted Riemannian locality preserving projection approach that takes into account the curved space formed by the descriptors. The weighted projection is then exploited during boosting to create a final multiclass classification algorithm that employs the most useful spatio-temporal regions. We also show how the descriptors can be computed quickly through the use of integral video representations. Experiments on the UCF sport, CK+ facial expression and Cambridge hand gesture datasets indicate superior performance of the proposed method compared to several recent state-of-the-art techniques. The proposed method is robust and does not require additional processing of the videos, such as foreground detection, interest-point detection or tracking.