Information Technology Reference
In-Depth Information
current voxel x is located inside the contour C(x) within the local image X
x
.
According to Eq.
5.5
, when a voxel, located at position y, is classified as belonging
to the object, i.e. R(x) = 1, then a point x in its vicinity has a high probability of
being marked as the object (i.e. L(y) ? 1) and is less likely to be considered as the
background (L(y) ? -1).
Maximising the posterior distribution in Eq.
5.4
is equivalent to minimising its
negative logarithm, and thus the energy function can be presented as:
E ¼
Z
H
0
ð
u
ð
x
ÞÞ
X
f
Z
2
½log P
ð
I
ð
y
Þj
y
2
X
i
\
X
x
Þ
X
i
\
X
x
i¼1
ð
5
:
7
Þ
þ
log P
ð
L
ð
y
Þj
y
2
X
i
\
X
x
Þ
dy
M
i
ð
u
ð
y
ÞÞg
dx
þ
l
Z
jr
H
ð
u
ð
x
ÞÞj
dx
where M
1
(/(y)) = H(/) and M
2
(/(y)) = 1-H(/), and H
0
(
) denotes the derivative
of Heaviside function:
(
H
ð
/
Þ
¼
0
;
if /
0
1
;
if / [ 0
and the associated Euler-Lagrange equation can be then obtained as:
þ
log
p
1
p
2
þ
v
Z
L
ð
x
Þ
k
r
ð
x
;
y
Þ
dy
r
/
jr
/
j
o
/
ot
¼ d
ð
/
Þ
l div
p
1
¼
Z
X
1
\
X
x
exp
ð
ð
l
1
ð
x
Þ
I
ð
y
ÞÞ
2
2r
1
ð
x
Þ
1
2p
p
dy
r
1
!
ð
5
:
8
Þ
Z
exp
ð
l
2
ð
x
Þ
I
ð
y
ÞÞ
2
2r
2
ð
x
Þ
1
2p
p
2
¼
p
dy
r
2
X
2
\
X
x
where p
1
and p
2
denote the probability density distribution of the object and
background, respectively.
5.3.2 Slice-by-Slice Correction
The segmentation results obtained from the first stage are rather accurate. How-
ever, due to the complexity of medical images and associated artefacts, these may
contain outliers, such as kissing non-arterial vessels and other fragments (e.g. as
shown in Fig.
5.5
a). In order to further improve segmentation performance, we
Search WWH ::
Custom Search