Non-stationary "shape activities"

The changing configuration of a group of moving landmarks can be modeled as a moving and deforming shape. The landmarks defining the shape could be moving objects(people/vehicles/robots) or rigid components of an articulated shape like the human body. In past work, the term "shape activity" has been used to denote a particular stochastic model for shape deformation. Dynamical models have been proposed for characterizing stationary shape activities (assume constant mean shape). In this work we define stochastic dynamic models for non-stationary shape activities and show that the stationary shape activity model follows as a special case of this. Most activities performed by a group of moving landmarks (here, objects) are not stationary and hence this more general model is needed. We also define a piecewise stationary model with non-stationary transitions which can be used to segment out and track a sequence of activities. Noisy observations coming from these models can be tracked using a particle filter. We discuss applications of our framework to abnormal activity detection, tracking and activity sequence segmentation.