A Joint Bayesian Framework for MR Brain Scan Tissue and Structure Segmentation Based on Distributed Markovian Agents - Computational Intelligence in Healthcare: Advanced Methodologies - page 77

as well. It cannot be performed based only on intensity distributions and requires
the introduction of apriori knowledge. Most of the proposed approaches share
two main characteristics. First, tissue and subcortical structure segmentations
are considered as two successive tasks and treated relatively independently al-
though they are clearly linked: a structure is composed of a specific tissue, and
knowledge about structure locations provides valuable information about local
intensity distributions. Second, tissue models are estimated globally through the
entire volume and then suffer from imperfections at a local level. Alternative local
procedures exist but are either used as a preprocessing step [1] or use redundant
information to ensure consistency of local models [2]. Recently, good results have
been reported using an innovative local and cooperative approach [3], [4]. The
approach is implemented using a multi-agent framework. It performs tissue and
subcortical structure segmentation by distributing through the volume a set of
local agents that compute local Markov Random Field (MRF) models which bet-
ter reflect local intensity distributions. Local MRF models are used alternatively
for tissue and structure segmentations and agents cooperate with other agents in
their neighborhood for model refinement. Although satisfying in practice, these
tissue and structure MRF's do not correspond to a valid joint probabilistic model
and are not compatible in that sense. As a consequence, important issues such
as convergence or other theoretical properties of the resulting local procedure
cannot be addressed. In addition, in [4], cooperation mechanisms between local
agents are somewhat arbitrary and independent of the MRF models themselves.
In this paper, we aim at filling in the gap between an ecient distributed system
of agents and a joint modeling accounting for their cooperative processing in a
formal manner. Markov models with the concept of conditional independence,
whereby each variable is related locally (conditionally) to only a few other vari-
ables, are good candidates to complement the symbolic level of the agent-based
cooperations with the numerical level inherent to the targeted applications.
Following these considerations, we propose a fully Bayesian framework in
which we define a joint model that links local tissue and structure segmenta-
tions but also the model parameters. It follows that both types of cooperations,
between tissues and structures and between local models, are deduced from the
joint model and optimal in that sense. Our model, originally introduced in [5]
and described in details in this chapter, has the following main features: 1)
cooperative segmentation of both tissues and structures is encoded via a joint
probabilistic model specified through conditional MRF models which capture
the relations between tissues and structures. This model specifications also inte-
grate external apriori knowledge in a natural way; 2) intensity nonuniformity
is handled by using a specific parameterization of tissue intensity distributions
which induces local estimations on subvolumes of the entire volume; 3) global
consistency between local estimations is automatically ensured by using a MRF
spatial prior for the intensity distributions parameters. Estimation within our
framework is defined as a maximum a posteriori (MAP) estimation problem and
is carried out by adopting an instance of the Expectation Maximization (EM) al-
gorithm [6]. We show that such a setting can adapt well to our conditional models