A Joint Bayesian Framework for MR Brain Scan Tissue and Structure Segmentation Based on Distributed Markovian Agents - Computational Intelligence in Healthcare: Advanced Methodologies - page 90

derivations by setting the m c 's to zero and η cc | − 1 where to |N ( c ) |N ( c ) | is the

( c ). This means that the distribution p ( μ c | μ k N ( c ) )is number of subvolumes in N

a Gaussian centered at c ∈N ( c ) μ c /

and therefore that all neighbors c of
c act with the same weight. The precision parameters λ 0 k
c

|N ( c ) |

is set to N c λ g where
λ g is a rough precision estimation for class k obtained for instance using some
standard EM algorithm run globally on the entire volume and N c is the number
of voxels in c that accounts for the effect of the sample size on precisions. The
α c 's were set to |N ( c ) | and b c to |N ( c ) | /λ g so that the mean of the corresponding

Gamma distribution is λ g and the shape parameter α c

somewhat accounts for

the contribution of the |N ( c ) | neighbors. Then, the size of subvolumes is set

to 20 20 voxels. The subvolume size is a mildly sensitive parameter. In

practice, subvolume sizes from 20

× 20 ×

× × × ×

30 give similar good
results on high resolution images (1 mm 3 ). On low resolution images, a size of
25

20 20 to 30 30

× ×

25 may be preferred.
Evaluation was then performed following the two main aspects of our model.
The first aspect is the partitioning of the global clustering task into a set of local
clustering tasks using local MRF models. The advantage of our approach is that,
in addition, a way to ensure consistency between all these local models is dictated
by the model itself. The second aspect is the cooperative setting which is relevant
when two global clustering tasks are considered simultaneously. It follows that
we first assessed the performance of our model considering the local aspect only.
We compared (Section 6.1) the results obtained with our method, restricted to
tissue segmentation only, with other recent or state-of-the-art methods for tissue
segmentation. We then illustrate more of the modeling ability of our approach
by showing results for the joint tissue and structure segmentation (Section 6.2).
As in [19], [20], [21], for a quantitative evaluation, we used the Dice similarity
metric [22] measuring the overlap between a segmentation result and the gold
standard.

25

6.1 A Local Method for Segmenting Tissues

We first carried out tissue segmentation only (FBM-T) and compare the results
with LOCUS-T [4], FAST [23] from FSL and SPM5 [19] on both BrainWeb
[24] phantoms (Table 1) and real 3T brain scans (Figure 4). Our method shows

Table 1. FBM-T. Mean Dice metric and mean computational time (M.C.T) values
on BrainWeb over 8 experiments for different values of noise (3%, 5%, 7%, 9%) and
nonuniformity (20%, 40% )