Flexible trajectory modeling using a mixture of parametric motion fields for video surveillance

Many approaches to trajectory analysis tasks (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, this type of models is not suitable for handling space-dependent dynamics, that are more naturally captured by non-linear models. As is well known, these are more difficult to identify. 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 non-linear dynamical models. The proposed model is applied to human trajectory modeling, a central task in video surveillance.