Markov Random Fields Regularization
MPM CRITERION (Maximum Posterior Marginal)
We use Markovian modelling to regularize the classified image by introducing
contextual information. The MPM criterion minimizes the number of misclassified
pixels. It is thus better adapted to classification-segmentation purpose
than MAP (Maximum A Posteriori) criterion when it is possible to compute
it.
X is the random field relating to the observed image.
L is the random field relating to the labeled image.
X beeing known we look for L that maximizes the following probability:
MPM approach consists in maximizing the marginal posterior probabilities.
DATA TERM 1
We consider U=[uij] to be the likelihood. So
the probability is defined as follows:
where ujs is the degree of membership of pixel s to cluster j.
DATA TERM 2
We consider the data attachment to be Gaussian. The parameters (mean
and variance of each classe) are estimated using the classification obtained
with the modified fuzzy Cmeans algorithm:
where 
is the variance of cluster i.
is the mean of cluster i.
A PRIORI MODEL
The a priori model is the Potts model.
RESULTS
We run experiments on SPOT5 simulated images provided by CNES (French
Space Agency). The resolution is 5 meters.
(a) et (c): Segmented images with data
attachment 1.
(b) et (d): Segmented images with data attachment 2.
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Last
modified: Tue May 5 12:10:48 MET DST 1998