  We propose a flexible prior model for the parameters of binary Markov random
fields (MRF) defined on rectangular lattices and with maximal cliques defined
from a template maximal clique. The prior model allows higher-order
interactions to be included. We also define a reversible jump Markov chain
Monte Carlo (RJMCMC) algorithm to sample from the associated posterior
distribution. The number of possible parameters for an MRF with for instance k
x l maximal cliques becomes high even for small values of k and l. To get a
flexible model which may adapt to the structure of a particular observed image
we do not put any absolute restrictions on the parametrisation. Instead we
define a parametric form for the MRF where the parameters have interpretation
as potentials for the various clique configurations, and limit the effective
number of parameters by assigning apriori discrete probabilities for events
where groups of parameter values are equal. To run our RJMCMC algorithm we have
to cope with the computationally intractable normalising constant of MRFs. For
this we adopt a previously defined approximation for binary MRFs, but we also
briefly discuss other alternatives. We demonstrate the flexibility of our prior
formulation with simulated and real data examples.
