Auto-models

Auto-models [6] are the simplest MGRF models in texture analysis, which are defined over rather simple neighbourhood systems with ``contextual constraints on two labels'' [64]. The Gibbs energy function for an auto-model only involves first- and second-order cliques, having the following general form [25],

$$E({g})=\sum_{i \in \mathbf{R}}{\mathbf{\alpha}_i({g}_i) \cdot {g}_i}+ \sum_{(i,j) \in C}\beta_{ij} \cdot {{g}_i}{{g}_j}$$ (5.2.16)

where $\mathbf{\alpha}_i$ is an arbitrary functions, $\beta_{ij}$ specifies the interaction between sites $i$ and $j$, and $C$ is the set of all second order cliques. The model parameters to be estimated are $\{\mathbf{\alpha}_i({g}_i)\}$ and $\{\beta_{ij}\}$. Due to their simplicity, auto-models involve relatively low computational cost in model creation and identification.

There are several variations of auto-models, such as auto-binomial model [20] and auto-normal model [13,18], each of which assumes slightly different models of pair-wise pixel interaction.