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Next: MRF-MAP Classification Up: Segmentation of Brain MR Previous: Hidden Markov Random Field

Model Simulation and Image Synthesis

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 $V_c({\mathbf x})=-\delta(x_i-x_j)$. 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 3-class case. (a) FGM model; (b)-(d) GHMRF mode with standard deviation 0.23, 0.4, 0.5, respectively. The second row shows the 5-class case. (e) FGM model; (f)-(h) GHMRF model with standard deviation 0.3, 0.47, 0.55, respectively.
\begin{figure*}
\begin{center}
\begin{tabular}{cccc}
\psfig{file = fgm-3.ps, ...
...dth}\\ (e) & (f) & (g) & (h)
\\
\end{tabular}
\end{center}
\end{figure*}


next up previous
Next: MRF-MAP Classification Up: Segmentation of Brain MR Previous: Hidden Markov Random Field
Yongyue Zhang
2000-05-11