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Longin Jan Latecki ( [email protected] ) Computer and Information Science s

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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

- Introduction
- Mapping of video to a trajectory
- Relation: motion trajectory video trajectory
- Discrete curve evolution
- Polygon simplification
- Key frames
- Unusual events in surveillance videos
- Results

- Mapping the video sequence to a polyline in a multi-dimensional space.
- The automatic extraction of relevant frames from videos is based on polygon simplification by discrete curve evolution.

- Mapping of the image stream to a trajectory (polyline) in a feature space.
- Representing each frame as:

………

X-coord of

the Bin’s

centroid

Y-coord of

the Bin’s

centroid

Bin’s

Frequency

Count

Frame 0

Bin0

Bin n

Frame N

Bin n

- Red-Green-Blue (rgb) Bins
- Each frame as a 24-bit color image (8 bit per color intensity):
- Bin 0 = color intensities from 0-31
- Bin 1 = color intensities from 32-63
- Bin 8 = color intensities from 224-255

- Three attributes per bin: -
- Row of the bin’s centroid
- Column of the bin’s centroid
- Frequency count of the bin.

- (8 bins per color level * 3 attributes/bin)*3 color levels = 72 feature

- Each frame as a 24-bit color image (8 bit per color intensity):

Theoretical Results:

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.

MovingDotMovieWithAdditionalDot.avi

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.

MovingDotMovieWithAdditionalDot.avi

MovingDotMovie_Clockwise.avi

MovingDotMovieWithAdditionalDot.avi

Relevance Ranking

Frame Number

0

1

1

100

Frames with decreasing relevance

98

12

99

5

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)|

v

v

w

w

u

u

Security1

- Bins Matrix
- Distance Matrix

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

security7

err for

seciurity7

2D projection by PCA of video trajectory for security7

Mov3

Mov3:

Rustam waving his hand.

- Bins Matrix
Keyframes = 1 378 52 142 253 235 148 31 155 167

- Distance Matrix
Keyframes = 1 378 253 220 161 109 50 155 149 270

Hall_monitor

err for

hall_monitor

Hall Monitor:

2 persons entering-exiting in a hall.

- Bins Matrix
Keyframes = 1 300 35 240 221 215 265 241 278 280

- Distance Matrix
Keyframes = 1 300 37 265 241 240 235 278 280 282

CameraAtLightSignal.avi

Histogram of lena

Image after segmentation – we get a outline of her face, hat etc

Original Image of Lena

Thank you