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degrees of locality, mimicking a multi resolution approach and refining from
coarse partitions of the entire volume to finer ones.
Also considering more general weights w , to deal with possible conflicts be-
tween tissue and structure labels, is possible in our framework and would be
an interesting refinement. Eventually, our choice of prior for the intensity dis-
tribution parameters was guided by the need to define appropriate conditional
specifications p ( θ c |
θ k ( ν )
N ( c ) )in(10)thatleadtoavalidMarkovmodelforthe θ k 's.
Nevertheless, incompatible conditional specifications can still be used for infer-
ence, eg. in a Gibbs sampler or ICM algorithm with some valid justification (see
[30] or the discussion in [31]). In applications, one may found that having a
joint distribution is less important than incorporating information from other
variables such as typical interactions. In that sense, conditional modeling allows
enormous flexibility in dealing with practical problems. However, it is not clear
when incompatibility of conditional distributions is an issue in practice and the
theoretical properties of the procedures in this case are largely unknown and
should be investigated.
In terms of algorithmic eciency, our agent-based approach enables us to
by-pass computationally intensive implementations usually inherent to MRF
models. It results in very competitive computational times unusual for such
structured models.
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