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Probabilistic methods in image processing
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- Bayesian framework, Markov Random Fields
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- Random variables: pixels
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- Local interaction
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- Correlated noise ?
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- No geometric constraints
Markov Object Processes
Notations :
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- Image space: T
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- Object space: U (object parameters)
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- Objet support: R(u)
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- Configuration:
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- Configurations space:
is a measurable space, with measure ,
corresponding
to a uniform Poisson process.
Poisson process :
n(x) = number of objects of the configuration x.
Markov Object Process :
Markov Object Process simulation
Simulation using a Markov Chain : find a Markov chain Xt such that
MCMC methods
RJMCMC algorithm
Description:
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- general scheme
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- every transition can be defined: at each step,
a transition from the current state x to a new state y is proposed
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- the transition is accepted with a probability
depending on an acceptance ratio which depends on the law f
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- Challenge: define ``good'' transitions
We consider a proposal density q(.,.) which can be easily simulated.
At step t, Xt=x :
- 1.
- simulate y with density q(.,.)
- 2.
- compute:
- 3.
- with probability
,
set Xt+1=y, otherwise Xt+1=x
Next: Road network extraction
Up: Roads Extraction using a
Previous: Roads Extraction using a
Radu Stoica
2000-04-17