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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
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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)|
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
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