Presentación de Vicomtech sobre seguimiento de objetos realizada durante las jornadas HOIP 2010 organizadas por la Unidad de Sistemas de Información e Interacción TECNALIA.
Más información en http://www.tecnalia.com/es/ict-european-software-institute/index.htm
3. 1.- Introduction
Object tracking in video-surveillance applications
Estimate properties of the imaged objects
Propagate knowledge through time
Multiple object tracking is a challenge
W
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H L
H
(x0,y0) (x0,y0)
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
4. 2.- Bayesian filtering
Model the problem as a propagation of random variables
through time
Each property is represented by a random variable
The set of properties define the object at time t: state vector
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
5. 2.- Bayesian filtering
Infererence: estimate the values of the state vector (reality)
based on a sequence of observations (images) applying
uncertainty models
Observation model: how the object is expected to appear in
images
• Observation equation: p(zk|xk)
Dynamic model: what type of motion the object is expected to
show?
• Dynamic equation: p(xk|xk-1)
Find posterior distribution p(xk|z1:k) and obtain a point-estimate
p(xk|z1:k) -> xk
• Mean, robust-mean, mode, median, etc.
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
6. 2.- Bayesian filtering
K-1 K K+1 TIME
p(zk|xk): Observation model
zk-1 zk zk+1 MEASUREMENTS
(VISIBLE)
STATES
xk-1 xk xk+1 (HIDDEN)
p(xk|xk-1): Dynamic model
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
7. 2.- Bayesian filtering
Bayes’ rule
Combine observation and prediction models
Observation Prior
Under some assumptions, one can obtain the optimal solution to
this problem
• Kalman filter if distributions are Gaussians and models are
linear
However, typical video-surveillance problems are highly non-linear
and/or non-Gaussian
• Sub-optimal solutions need to be computed
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
8. 3.- Particle filters
Particle filters
Sequential Monte Carlo (SMC) method, aka
• Condensation algorithm, bootstrap filter, survival of the fittest…
It is a technique for implementing a recursive Bayesian
filter by representing the posterior density as a set of
samples or particles
WEIGHTED UNWEIGHTED
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
9. 3.- Particle filters
Understanding particles
Each particle represents a hypothesis of the state-vector
The set of particles represents the “reliability” of each region of the
space
The combination of particles lead to the best estimate
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
11. Marcos Nieto, Carlos Cuevas and Luis Salgado, “Measurement-based Reclustering for
Multiple Object Tracking with Particle Filters,” in IEEE Proc. International Conference on
Image Processing (ICIP2009).
3.- Particle filters / Human tracking
ELLIPTICAL MODEL
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
12. Marcos Nieto, Carlos Cuevas and Luis Salgado, “Measurement-based Reclustering for
Multiple Object Tracking with Particle Filters,” in IEEE Proc. International Conference on
Image Processing (ICIP2009).
3.- Particle filters / Human tracking
Observation model
Ratio between inside pixels and ellipse area
Ratio between inside and total pixels
Compactness around center of the ellipse
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
13. Marcos Nieto, Carlos Cuevas and Luis Salgado, “Measurement-based Reclustering for
Multiple Object Tracking with Particle Filters,” in IEEE Proc. International Conference on
Image Processing (ICIP2009).
3.- Particle filters / Human tracking
Multiple objects
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
14. Carlos R. del Blanco, Fernando Jaureguizar and Narciso García, “Visual Tracking of
Multiple Interacting Objects Through Rao-Blackwellized Data Association Particle
Filtering,” in IEEE Proc. International Conference on Image Processing (ICIP2010).
3.- Particle filters / Human tracking
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
15. R. Mohedano, N. García, “Robust Multi-Camera 3D Tracking from Mono-Camera 2D
Tracking using Bayesian Association”, IEEE Trans. Consumer Electronics, vol. 56, no. 1,
pp. 1-8, Feb. 2010.
3.- Particle filters / Human tracking
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
16. 4.- MCMC
Approximation with unweighted particles
Markov Chain Monte Carlo (MCMC)
Metropolis-Hastings algorithm to generate a Markov Chain that
approximates to the posterior
Metropolis-Hastings allows
obtaining samples for an
arbitrary distribution by making
a chain which accepts or
rejects samples
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
17. 4.- MCMC
Approximation with unweighted particles
MCMC methods improve the results obtained by importance
sampling strategies for high dimensional spaces
MCMC is therefore recommended to be used when the dimensions
of the problem increase
Metropolis-Hastings is the most typically used generic sampling
algorithm for MCMC
Other alternatives
• Slice sampler
• Gibbs sampler
• Levenberg-Marquardt
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
21. 4.- MCMC / Vehicle tracking
Inferring 3D volume from 2D observations
There is a projective ambiguity that can not be solved analytically
There are 3D infinite
volumes that project onto
the same 2D shape
But only one is the right
one!
MCMC-based approach
• Combination of projective geometry constraints
• Temporal coherence
• Prior knowledge about vehicle configurations
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)
25. 5.- Conclusions
Object tracking can be modelled as an probabilistic
inference problem
Uncertainty is mathematically handled
Potentially any problem can be tackled like this!
Particle filters are a popular tool to solve non-linear and
analytically intractable inference problems
Importance sampling algorithms (CONDENSATION)
MCMC methods represents a step forward solving high-
dimensional problems
Optimization technique could be applied to reduce the
computational complexity and allow real-time performance
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Marcos Nieto (mnieto@vicomtech.org) Hands-on Image Processing 2010 (HOIP’10)