Identifying Behaviors in Crowd Scenes Using Stability Analysis for Dynamical Systems

A method is proposed for identifying five crowd behaviors (bottlenecks, fountainheads, lanes, arches, and blocking) in visual scenes. In the algorithm, a scene is overlaid by a grid of particles initializing a dynamical system defined by the optical flow. Time integration of the dynamical system provides particle trajectories that represent the motion in the scene; these trajectories are used to locate regions of interest in the scene. Linear approximation of the dynamical system provides behavior classification through the Jacobian matrix; the eigenvalues determine the dynamic stability of points in the flow and each type of stability corresponds to one of the five crowd behaviors. The eigenvalues are only considered in the regions of interest, consistent with the linear approximation and the implicated behaviors. The algorithm is repeated over sequential clips of a video in order to record changes in eigenvalues, which may imply changes in behavior. The method was tested on over 60 crowd and traffic videos.