Context-dependent Detection of Unusual Events in Videos by Geometric Analysis of Video Trajectories. Longin Jan Latecki ( firstname.lastname@example.org ) Computer and Information Science s Temple University, Philadelphia Nilesh Ghubade and Xiangdong Wen ( email@example.com ). Agenda. Introduction
Context-dependent Detection of Unusual Events in VideosbyGeometric Analysis of Video Trajectories
Longin Jan Latecki
Computer and Information Sciences
Temple University, Philadelphia
Nilesh Ghubade and Xiangdong Wen
Motion trajectory Video trajectory
Consider a video in which an object (a set of pixels) is moving on a uniformbackground. The object is visible in all framesand it is moving with a constant speed on a linear trajectory.Then the video trajectory in the feature space is a straight line.
If n objects are moving with constant speeds on a linear trajectory,then the trajectory is a straight line in the feature space.
Consider a video in which an object (a set ofpixels) is moving on a uniform background.
Then the trajectoryvectors are containedin the plane.
If n objects are moving, then the dimension of the trajectory is at most 2n.
If a new object suddenly appears in the movie, the dimension of the trajectory increases at least by 1 and at most by 3.
Using singular value decomposition, based on:
C. Rao, A. Yilmaz, and M.Shah.View-Invariant Representation and Recognition of actions.Int. J. of Computer Vision 50, 2002.
M. Seitz and C. R. Dyer.View-invariant analysis of cyclic motion.
Int. J. of Computer Vision 16, 1997.
We compute err in a window of 11 consecutive frames in our experiments.
Frames with decreasing relevance
Discrete Curve Evolution P=P0, ..., PmPi+1 is obtained from Pi by deleting the vertices of Pi that have minimal relevance measure K(v, Pi) = K(u,v,w) = |d(u,v)+d(v,w)-d(u,w)|
err for seciurity1 video
We divide the video polygonal curve P into parts T_i. For videos with 25 fps:T_i contains 25 frames.
We apply discrete curve evolution to each T_iuntil three points remain: a, b, c.Curveness measure of T_i:
C(T_i,P) = |d(a, b) + d(b, c) - d(a, c)|
b is the most relevant frame in T_i
and the first vertex of T_i+1
2D projection by PCA of video trajectory for security7
Rustam waving his hand.
Keyframes = 1 378 52 142 253 235 148 31 155 167
Keyframes = 1 378 253 220 161 109 50 155 149 270
2 persons entering-exiting in a hall.
Keyframes = 1 300 35 240 221 215 265 241 278 280
Keyframes = 1 300 37 265 241 240 235 278 280 282
Histogram of lena
Image after segmentation – we get a outline of her face, hat etc
Original Image of Lena