## Markov networks and conditional random fields

So far, we have covered directed acyclic graphs in the area of probabilistic graph models, including every aspect of representation, inference, and learning. When the graphs are undirected, they are known as **Markov networks** (**MN**) or **Markov random **
**field** (**MRF**). We will discuss some aspects of Markov networks in this section covering areas of representation, inference, and learning, as before. Markov networks or MRF are very popular in various areas of computer vision such as segmentation, de-noising, stereo, recognition, and so on. For further reading, see (*References* [10]).

### Representation

Even though a Markov network, like Bayesian networks, has undirected edges, it still has local interactions and distributions. We will first discuss the concept of parameterization, which is a way to capture these interactions, and then the independencies in MN.

#### Parameterization

The affinities between the variables in MN are captured through three alternative parameterization...