next up previous
Next: MRF-MAP Estimation Up: Segmentation of Brain MR Previous: Model Simulation and Image

   
MRF-MAP Classification

The image classification problem we consider involves assigning to each pixel a class label taking a value from the set $\mathcal L$. The pixels are indexed by a two-dimensional rectangular lattice $\mathcal S$ and each pixel is characterized by an intensity value yi from the set $\mathcal D$. A labelling of $\mathcal S$ will be denoted by x, where $x_i, i \in \mathcal S$ is the corresponding class label of pixel i. We write x* for the true but unknown labelling configuration and $\hat{\mathbf x}$ for an estimate of x*, both of which are interpreted as particular realizations of a random field X, which is an MRF with a specified distribution P(x). The observable image itself is denoted by y, which is a realization of a GHMRF as described in Section 2. The problem of classification is to recover x*, given the observed image y.

 

Yongyue Zhang
2000-05-11