How can i prove that a simple MRF of some interest in image processing and analysis is the Ising model, whose energy function is: $U(X)=a|X|+b_{1}|(X \ominus B_{1})|+b_{2}|(X \ominus B_{2})|$
when we know that the Ιsing model is given by: $U(X)=\sum_{i}\sum_{j}[aX(i,j)+b_{1}X(i,j)X(i-1,j)+b_{2}X(i,j)X(i,j-1)]$
for Gibbs Distributon: $Pr(X)=\frac{1}{Z}e^{-\frac{1}{T}U(X)}$
where $B_{1}=[(0,0),(1,0)]$ and $B_{2}=[(0,0),(0,1)]$ are structuring elements with 2-pixel horizontally and vertically. X=X(i,j) (with values 0,1) is a random binary image, coming from a Markov-Gibbs model with zero threshold conditions