Chapter 14: General MRF Models
Charles A. Bouman · Society for Industrial and Applied Mathematics eBooks · 2022
In the previous chapter, we showed how state sequence estimation of HMMs can be used to label samples in a 1-D signal. In 2-D, this same approach corresponds to image segmentation, that is, the labeling of pixels into discrete classes. However, in order to formalize this approach to image segmentation, we will first need to generalize the concept of a Markov chain to two or more dimensions. As with the case of AR models, this generalization is not so straightforward because it implies the need for noncausal prediction, which results in loopy dependencies in the model. Generally, these loopy dependencies make closed-form calculation of the PMF impossible due to the intractable form of the so-called partition function, or normalizing constant, of the distribution.