Modeling and classifying human activities from trajectories using a class of space-varying parametric motion fields

Many approaches to trajectory analysis, such as clustering or classification, use probabilistic generative models, thus not requiring trajectory alignment/registration. Switched linear dynamical models (e.g., HMMs) have been used in this context, due to their ability to describe different motion regimes. However, these models are not suitable for handling space-dependent dynamics that are more naturally captured by nonlinear models. As is well known, these are more difficult to identify. In this paper, we propose a new way of modeling trajectories, based on a mixture of parametric motion vector fields that depend on a small number of parameters. Switching among these fields follows a probabilistic mechanism, characterized by a field of stochastic matrices. This approach allows representing a wide variety of trajectories and modeling space-dependent behaviors without using global nonlinear dynamical models. Experimental evaluation is conducted in both synthetic and real scenarios. The latter concerning with human trajectory modeling for activity classification, a central task in video surveillance.