Model Identification

Identification of a generic MGRF model in Eq. (6.2.5) involves recovering a characteristic neighbourhood $\mathcal{N}$ and estimating the potential vector $\mathbf{V}^\mathsf{T}$, from image signal statistics $\mathbf{F}{({g})}$ given by an image ${g}$.

There is a chicken-and-egg problem in the identification; On the one hand, the potentials $\mathbf{V}^\mathsf{T}$ need to be known to compute the partial energy in Eq. (6.2.3) for selecting clique families into the characteristic neighbourhood. But, on the other hand, the potentials $\mathbf{V}^\mathsf{T}$ require an explicit interaction structure $\mathcal{N}$ before can be computed. An analytic first approximation of potentials is proposed to work around the problem. The idea is to first compute an approximation of potentials for recovering the characteristic neighbourhood, and then to refine the potentials using a more accurate method (e.g., stochastic approximation) based on the estimated neighbourhood. Model identification of a generic MGRF model has three main steps,

1. Compute the analytic first approximation of potentials
2. Recover the characteristic neighbourhood $\mathcal{N}$.
3. Potential refinement via stochastic approximation.