Trajectory analysis in natural images using mixtures of vector fields

This work introduces a new approach to modeling object trajectories in image sequences. Trajectories performed by natural objects (e.g., people, animals) typically depend on the position of each object in the scene and can change in an unpredictable way. Despite this diversity, there is often a small number of typical motion patterns based on which it is possible to explain all the observed trajectories. To achieve this goal, we model each of these motion patterns using a motion field and allow objects to switch between fields in a space-varying, possible probabilistic, way. Our approach provides a space-dependent motion model which can be estimated using an expectation-maximization (EM) algorithm. Experiments with both synthetic and real data are presented to illustrate the ability of the proposed approach in modeling different motion patterns.