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Fig. 3.
Implementation using a two agent-layer architecture and a shared space for
communication
Also, the observed variations of appearance in tissues and structures reflect the
spatial dependency of the tissue model parameters to be computed. Figure 2
then illustrates the hierarchical organization of the variables under considera-
tion and its adequation with the agent hierarchy at a symbolic level. In the
following section, we show that this hierarchical decomposition can be expressed
in terms of a coherent systems of probability distributions for which inference
can be carried out. Regarding implementation, we adopt subsequently the two
agent-layer architecture, as illustrated in Figure 3, where tissue and structure
agents cooperate through shared information including tissue intensity models,
anatomical atlas, tissue and structure segmentations.
3 Hierarchical Analysis Using the EM Algorithm
Hierarchical modeling is, in essence, based on the simple fact from probability
that the joint distribution of a collection of random variables can be decom-
posed into a series of conditional models. That is, if
Y
,
Z
,
θ
are random vari-
ables, then we write the joint distribution in terms of a factorization such as
p
(
y
,
z
,θ
)=
p
(
y
θ
)
p
(
θ
). The strength of hierarchical approaches is that
they are based on the specification of coherently linked system of conditional
models. The key elements of such models can be considered in three stages, the
data stage, process stage and parameter stage. In each stage, complicated depen-
dence structure is mitigated by conditioning. For example, the data stage can
incorporate measurement errors as well as multiple datasets. The process and
parameter stages can allow spatial interactions as well as the direct inclusion of
scientific knowledge. These modeling capabilities are especially relevant to tackle
the task of MRI brain scan segmentation. In image segmentation problems, the
|
z
,θ
)
p
(
z
|
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