1.5.4

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

- Pose a vision problem as one of labeling in categories LP1-LP4
and choose an appropriate MRF representation
**f**. - Derive the posterior energy to define the MAP solution to a problem.
- Find the MAP solution.

- Define a neighborhood system on and the set of cliques for .
- Define the prior clique potentials to give .
- Derive the likelihood energy .
- Add and to yield the the posterior energy .

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

- Choosing an appropriate representation for the MRF labeling.
- 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. - 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.
- 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.