Crowd Analysis Based On Linear Dynamical Systems

It's obvious that the behavior analysis of crowd scenes presents challenging tasks in computer vision.It has been intensively studied by numerous authors.This paper presents a novel method to identify five specific crowd behaviors(bottlenecks,fountainheads,lanes,rings,and blocking)in videos.The American psychologist Gibson first proposed the concept of optical flow in the 1940s.By calculating the correlation of pixel points between two consecutive frames,the best matching of pixels is constructed,and the optical flow field is established.The optical flow describes the visual stimulus provided to animals moving through the world,which is the displacement information of all the pixels on the imaging projected by the moving object within a certain time.The preparation work is extracting the optical flow field of the video.Time summa-tion of the optical flow field depicts the density map of the scene.Time integration of the optical flow field provides particle trajectories.Clustering the accumulation points are used to locate regions of interest(ROI)in the video scene.The behavior classification is provided by linear approximation theorem of the dynamical system through the Jacobian matrix.The eigenvalue condition for each particle in ROI determines the dynamic stabil-ity of particles.Each type of the eigenvalue condition corresponds to one of the five crowd behaviors.The eigenvalues are both negative implying bottlenecks.The eigenvalues are both negative implying bottlenecks.The eigenvalues are both positives implying foun-tainheads.At least one eigenvalue is zero implying lanes.The eigenvalues are opposite signs implying blocking.the eigenvalues are complex conjugates implying rings.The empirical evaluation,tested on over 60 crowd and traffic scenes,demonstrates superiorities on identifying crowd behaviors.