System theoretic approaches to action recognition model the dynamics of a scene with linear dynamical systems (LDSs) and perform classification using metrics on the space of LDSs, e.g. Binet-Cauchy kernels. However, such approaches are only applicable to time series data living in a Euclidean space, e.g. joint trajectories extracted from motion capture data or feature point trajectories extracted from video. Much of the success of recent object recognition techniques relies on the use of more complex feature descriptors, such as SIFT descriptors or HOG descriptors, which are essentially histograms. Since histograms live in a non-Euclidean space, we can no longer model their temporal evolution with LDSs, nor can we classify them using a metric for LDSs. In this paper, we propose to represent each frame of a video using a histogram of oriented optical flow (HOOF) and to recognize human actions by classifying HOOF time-series. For this purpose, we propose a generalization of the Binet-Cauchy kernels to nonlinear dynamical systems (NLDS) whose output lives in a non-Euclidean space, e.g. the space of histograms. This can be achieved by using kernels defined on the original non-Euclidean space, leading to a well-defined metric for NLDSs. We use these kernels for the classification of actions in video sequences using (HOOF) as the output of the NLDS. We evaluate our approach to recognition of human actions in several scenarios and achieve encouraging results.

In this paper, we consider the problem of categorizing videos of dynamic textures under varying view-point. We propose to model each video with a collection of Linear Dynamics Systems (LDSs) describing the dynamics of spatiotemporal video patches. This bag of systems (BoS) representation is analogous to the bag of features (BoF) representation, except that we use LDSs as feature descriptors. This poses several technical challenges to the BoF framework. Most notably, LDSs do not live in a Euclidean space, hence novel methods for clustering LDSs and computing codewords of LDSs need to be developed. Our framework makes use of nonlinear dimensionality reduction and clustering techniques combined with the Martin distance for LDSs for tackling these issues. Our experiments show that our BoS approach can be used for recognizing dynamic textures in challenging scenarios, which could not be handled by existing dynamic texture recognition methods.