Belief Networks in Computer
Vision Applications
Alex Yakushev
CMPS 290C final project
Winter 2006
Kalman Filters
Predicted position =
(Previous Position)*
(Motion model )
+ Noise
True position =
observed position
+ Noise
Extrapolate object
position by taking
a weighted average
of the two.
Only depends on
current observation
and previous state
Kalman Filter as a Belief
Network
Motion model
P x k∣ x k − 1 ~ N x k ;
Prediction covariance
x k− 1 , P k − 1
Model Noise
xk
xk+1
zk
zk+1
State model
Observation noise
P z k∣x k ~ N Hx k ; Z k , R
T
Q
Kalman Filters
Becomes a simple update rule
K k= Pk H T H Pk H T R
xk = x k K k zk − H k xk
Pk= I − K k H Pk
−1
x k 1= x k
T
P k 1= P k
Q
Something completely different
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Are old fashioned Bayesian networks of any
use?
What if the object we are trying to track does
not have a constant velocity or acceleration?
Sherrah and Gong have designed a BN to
track hand and face movements.
Something completely different
(Sherrah, Gong)
Results (Sherrah, Gong)
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For their setup they had 70% of frames classified
correctly without any contextual knowledge
This improved to 78% with a Kalman filter
87% with their method...
...but Assumptions are unreasonable:
1. the subject is oriented roughly towards the camera
for most of the time
2. the subject is wearing long sleeves
3. reasonably good color segmentation of the head
and hands is possible, and
4. the head and hands are the larges moving skin
color clusters in the image
“Dynamic Bayesian Network”
State variables st belong to a set of S discrete symbols.
(Pavlovic, Rehg, Cham, Murphy)
Dynamic Bayesian Network
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Two hidden variables (xt, st)
If x0 is Gaussian then x1 is a mixture of S
Gaussians, x2 is a mixture of S2 Gaussians...
No “simple” update rule
Exact inference is expensive
(Pavlovic, Rehg, Cham,
Conclusions
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As usual, increase in expressive power costs
computation time
People create custom networks, and either
give a solution for the specific structure, or
use approximate inference
No silver bullet, good results possible with
both simple and complex network structures
Using a simpler structure (Markov Network)
may work for many applications
References
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Jamie Sherrah, Shaogang Gong, Tracking Discontinuous Motion
Using Bayesian Inference, Lecture Notes in Computer Science,
Volume 1843, Jan 2000, Pages 150 – 166
V. Pavlović, J. M. Rehg, T. J. Cham, and K. P. Murphy, A dynamic
Bayesian network approach to figure tracking using learned
dynamic models, in International Conference on Computer Vision,
Corfu, Greece, September 1999.
Murphy, K., Dynamic Bayesian Networks: Representation,
Inference and Learning. PhD thesis, UC Berkeley, Computer
Science Division (2002)
Hai Tao, Object Tracking and Kalman Filtering, CMPE264 Lecture
notes,
http://www.soe.ucsc.edu/classes/cmpe264/Winter06/Lec15.pdf