Tangent Fisher Vector on Matrix Manifolds for Action Recognition

In this paper, we address the problem of representing and recognizing human actions from videos on matrix manifolds. For this purpose, we propose a new vector representation method, named tangent Fisher vector, to describe video sequences in the Fisher kernel framework. We first extract dense curved spatio-temporal cuboids from each video sequence. Compared with the traditional 'straight cuboids', the dense curved spatio-temporal cuboids contain much more local motion information. Each cuboid is then described using a linear dynamical system (LDS) to simultaneously capture the local appearance and dynamics. Furthermore, a simple yet efficient algorithm is proposed to learn the LDS parameters and approximate the observability matrix at the same time. Each video sequence is thus represented by a set of LDSs. Considering that each LDS can be viewed as a point in a Grassmann manifold, we propose to learn an intrinsic GMM on the manifold to cluster the LDS points. Finally a tangent Fisher vector is computed by first accumulating all the tangent vectors in each Gaussian component, and then concatenating the normalized results across all the Gaussian components. A kernel is defined to measure the similarity between tangent Fisher vectors for classification and recognition of a video sequence. This approach is evaluated on the state-of-the-art human action benchmark datasets. The recognition performance is competitive when compared with current state-of-the-art results.