Clustering Dynamic Textures with the Hierarchical EM Algorithm for Modeling Video

Dynamic texture (DT) is a probabilistic generative model, defined over space and time, that represents a video as the output of a linear dynamical system (LDS). The DT model has been applied to a wide variety of computer vision problems, such as motion segmentation, motion classification, and video registration. In this paper, we derive a new algorithm for clustering DT models that is based on the hierarchical EM algorithm. The proposed clustering algorithm is capable of both clustering DTs and learning novel DT cluster centers that are representative of the cluster members in a manner that is consistent with the underlying generative probabilistic model of the DT. We also derive an efficient recursive algorithm for sensitivity analysis of the discrete-time Kalman smoothing filter, which is used as the basis for computing expectations in the E-step of the HEM algorithm. Finally, we demonstrate the efficacy of the clustering algorithm on several applications in motion analysis, including hierarchical motion clustering, semantic motion annotation, and learning bag-of-systems (BoS) codebooks for dynamic texture recognition.