Biomedical Engineering Reference
In-Depth Information
Figure 2.
Four-phase level set model illustration. There are four regions in the image, using
two level set functions. They can be represented by
H
(
φ
1
)
H
(
φ
2
)
,
(1
−
H
(
φ
1
))
H
(
φ
2
)
,
H
(
φ
1
)(1
−
H
(
φ
2
))
and
(1
−
H
(
φ
1
))(1
−
H
(
φ
2
))
.
A four-phase representation using characteristic functions of the level set is pre-
sented in Figure 2. Here, with the Gaussian distribution assumption, the dissimi-
larity measure
D
i
can be simplified as follows:
σ
w
+(
µ
w
−
µ
i
)
2
σ
i
µ
w
)
2
+(
µ
i
−
1
2
D
i
=
+
−
,
(13)
4
σ
i
4
σ
w
where
σ
i
is the variance of the region
R
i
and
σ
w
is the variance of a neighborhood
region.
For MR image brain tissue segmentation, scalped brain MR images consist
of three regions: gray matter (GM), white matter (WM), and cerebrospinal fluid
(CSF). They have very complex topology and shape. In [28, 27], the authors
applied a four-phase level set model to brain tissue segmentation. During the evo-
lution of the curve, one region will reduce its size and finally disappear. However,
as the intensity values of the real MR Images are not strictly composed of three
regions due to the partial volume effect and inherent tissue class-related intensity
variations [1], the four-region initialization may lead to erroneous results. We
propose to use a three-phase level set representation, whose region definitions are
as follows:
CSF:
φ
1
>
0
,
<
0
,
1
=
H
(
φ
1
)(1
−
H
(
φ
2
))
,
2
WM:
φ
1
<
0
,
<
0
,
2
=(1
−
H
(
φ
1
))(1
−
H
(
φ
2
))
,
.
2
GM:
φ
2
>
0
G
3
=
H
(
φ
2
)
