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Simulation is often used to verify statistical models. In this
case, simulation is used to generate synthetic images by drawing
random samples from the model distribution using stochastic
sampling methods. Here, the Gibbs sampler proposed by Geman and
Geman [12] is employed. Many different experiments have
been carried out to compare the FGM model and the GHMRF model.
Figure 1 shows two examples, in which the number of
intensity levels was set equal to the number of classes and the
Gaussian emission distributions have the same standard deviation
for all classes. For the GHMRF model, a homogeneous and isotropic
MRF model is employed to generate the prior distribution with
clique potential
.
The two rows
in Figure 1 correspond, respectively, to simulations
with 3 and 5 classes. The first column is the sample drawn from
the FGM model while the other three columns show samples drawn
from the GHMRF model with different standard deviations.
Apparently, the FGM model generates meaningless noise images
whereas the GHMRF model generates images with controllable spatial
structures  the smaller the standard deviation, the clearer the
spatial structures.
Figure 1:
Image simulation by the FGM model and the GHMRF model.
The first row shows the 3class case. (a) FGM model; (b)(d) GHMRF
mode with standard deviation 0.23, 0.4, 0.5, respectively. The
second row shows the 5class case. (e) FGM model; (f)(h) GHMRF
model with standard deviation 0.3, 0.47, 0.55,
respectively.

Next: MRFMAP Classification
Up: Segmentation of Brain MR
Previous: Hidden Markov Random Field
Yongyue Zhang
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