Biomedical Engineering Reference
In-Depth Information
The term ( ν ) for each point x is replaced by the function ν i ( x ) so the velocity
function is defined as
F i ( x )= ν i ( x )
·
k ( x ) ,
i =1 ,
···
,K,
(15)
where
1 f i = i ( x ) ,
1
ν i ( x )=
(16)
otherwise .
If the pixel x belongs to the front of the class i = i ( x ) associated with the level
set function φ i , the front will expand; otherwise, it will contract. Now, we write
Eq. (7) in the general form using the derivative δ α ( · ) of the smeared version of the
Heaviside function H α ( · ) [39], as follows:
∂φ i ( x, t )
∂t
= δ α ( φ i ( x, t ))(
·
k ( x )
ν i ( x ))
φ i ( x, t )
.
(17)
The function δ α ( · ) selects the narrow band (NB) points around the front. Solution
of the PDEs such as 7) requires numerical processing at each point of the image or
volume, which is a time-consuming process. Since we are interested only in the
changes of the front, then the solution is important at the points around the front.
Such NB points are selected in Eq. (17) thanks to the smeared delta function δ α ( · ).
Note that the width of the NB around the moving front is determined by the value
of the parameter α . In practice, α is usually taken equal to 1.5, so the that the
NB is 3 pixels wide. Points outside the NB are assigned large positive or large
negative values in order to be excluded from the computation phase. This highly
improves the speed of the numerical process.
4.2.9. Experimental results
Having obtained the skull-stripped MRI slices, the segmentation algorithm is
to be applied to all the datasets to isolate the white matter. Applying the automatic
seed initialization directly may result in misclassifying some pixels that share the
graylevel range of the brain. This may lead to segmentation of the eye as the brain,
for example. Therefore, gray levels only are not sufficient for good segmentation.
To solve this problem, the previously discussed level set segmentation with
the stochastic ExpectationMaximization algorithm for initialization has been used,
and it has shown promising results. The results with the algorithm are shown in
Figure 7. A 3D evolution of the (WM) surface is shown in Figure 8.
4.3. White Matter Parcellation
Whitematter parcellation aims at dividing thewhitematter into inner and outer
compartments. Various studies have developed techniques to divide the white mat-
ter into radiating, bridging, and sagittal compartments so as to use these compart-
ments for further analysis of different brain disorders [18, 16]. The methodology
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