Biomedical Engineering Reference
In-Depth Information
To resolve the boundary-leaking problem, Kichenassamy et al. [43] and Yezzi
et al. [23] introduced a pull-back term (
·∇
c
φ ) due to the edge strength; here
1
1+ |∇G σ ·I ( x,y ) |
c ( x, y )=
. It is an additional force term based on the color feature.
To provide an additional attraction force when the front was in the vicinity of an
edge, Siddiqui et al. [44] introduced an extra term 2 div x
φ according to
area minimization. It is an additional force term based on the shape feature.
In the case of tagged MR, new features can also be introduced along the same
lines. The high clarity of tag lines makes segmentation more difficult than with an
untagged image. According to human response, texture is the most distinguishable
feature (Figure 8a). In this example, the tag lines are in the vertical direction; hence
we design an additional term B based on texture feature BPV [45]:
y
y + N 1
2
BPV( x, y )= N
M ) 2 ,
( I ( x, i )
y− N 1
2
y + N 1
2
N
M
=
|
I ( x, i )
I ( x, y ) |
.
(38)
y− N 1
2
Here, the distance is measured by the standard deviation. BPV( x, y ) is the BPV
value of point ( x, y ), 1
N− 1
2
N− 1
2
, m and n are the height
and width of the image, and N is the width of the window, which is approximately
7 or 9 according to the width of the tag lines. I ( x, y ) is the intensity value of
the block center. The reasoning of the above equation is as follows. When the
intensity value of some point is quite distinct compared to points that are on the
same line and whose center is located at the point, the BPV value of this point is
smaller, and vice versa. Now, the speed function has been augmented to
x
m ,
y
n
+ µ div x
y
φ
K I ( εk + F A + F I )+ β
c
·∇
φ
F
=
+ γ (BPV) ,
|∇ φ |
(39)
where K I is the A item, used to control the balance between the original speed
term and the additional speed term. Larger K I will speed up the decrease in value
of the speed term. The coefficients β , µ , and γ are constants, which should be
defined according to the contribution of their corresponding part. In Eq. (39), such
image features as curvature, shape, and texture information have been combined
into the speed term. An experiment based on this augmented speed item is carried
out in the following section.
 
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