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1.5.4

## Summary of MAP-MRF Approach

The procedure of the MAP-MRF approach for solving computer vision problems is summarized in the following:

1. Pose a vision problem as one of labeling in categories LP1-LP4 and choose an appropriate MRF representation f.
2. Derive the posterior energy to define the MAP solution to a problem.
3. Find the MAP solution.
The process of deriving the posterior energy is summarized as the following four steps:
1. Define a neighborhood system on and the set of cliques for .
2. Define the prior clique potentials to give .
3. Derive the likelihood energy .
4. Add and to yield the the posterior energy .
The prior model depends on the type of the scene ( e.g. the type of surfaces) we expect. In vision, it is often one of the Gibbs models introduced in Section 1.3. The likelihood model depends on physical considerations such as the sensor process (transformations, noise, etc. ). It is often assumed to be Gaussian. The parameters in both models need be specified for the definitions of the models to be complete. The specifications can be something of arts when done manually and it is desirable that it is done automatically.

In the subsequent chapters, we are concerned with the following issues:

1. Choosing an appropriate representation for the MRF labeling.
2. Deriving the a posteriori distribution of the MRF as the criterion function of the labeling solution. It mainly concerns the specification of the forms of the prior and the likelihood distributions. The involved parameters may or may not be specified at this stage.
3. Estimating involved parameters in the prior and the likelihood distributions. The estimation is also based on some criterion, very often, maximum likelihood.   In the unsupervised case, it is performed together with MAP labeling.
4. Searching for the MRF configuration to maximize the posterior distribution. This is mainly algorithmic. The main issues are the quality (globalness) of the solution and the efficiency.