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Having obtained an initial segmentation, the texture model
parameters can be estimated from the larger patches that result from
this initialization step. This segmentation result is then
iteratively refined in the next stage using a Markovian prior
for the labels field, where in each iteration the texture model parameters are
reestimated for each patch.
More specifically, the estimated parametric models of the individual textures
are employed to construct an energy function. This energy
function is used in a simulated annealing algorithm to obtain maximum aposteriori (MAP) estimates of the
label field. The label field estimation is iteratively performed
until the algorithm converges. The optimal estimate of the label field at site s is given by:
where f is the label and d is the data field. The energy U_{s}(df) is evaluated at each site s using
the following procedure:
 Let W(s) be some window centered at s. Let F^{d}(s) be
the magnitude of the DFT of the observed image,
evaluated in that window.
 Using the texture model parameters that correspond to the current label f of the site, we
synthesize the texture, and evaluate the magnitude of the synthesized field DFT, F^{f}(s),
in the same window W(s).
 The conditional energy is then given by:
Note that by adopting our estimate of the conditional energy,phase
errors due to possible translation discrepancies are eliminated. Let
C be the set of cliques corresponding to some neighborhood
system. Here the field is assumed to be a first order Markov random
field. The regularization energy at site s is then defined
using a Potts model:
Figure:
Unsupervised segmentation of a satelite image. From top to the
bottom : Original image; Sea; Urban region.

Figure:
Unsupervised segmentation of a medical image. From top to the
bottom : Original image; Final segmentation result.

Next: Conclusions and future work
Up: Indexing and segmentation of
Previous: Distance measure for textures
Radu Stoica
19990521