Biomedical Engineering Reference
In-Depth Information
speed function is vital for final results. The speed function is designed to con-
trol the movement of the curve. In different problems, the key is to determine
the appropriate stopping criteria for the evolution. In a segmentation case, the
segmentation precision depends on when and where the evolving curved surface
stops, and the stopping criteria of the evolving surface also depends on the speed
term
F
. So the construction of
F
is critical. However, when segmenting the
medical images with the classical speed function, especially when there are blurry
boundaries and a strong tag line, the propagating front may not capture the true
boundary, by either leaking through it, or stopping at the non-boundary area.
In this section, two improvements to augment the speed function are intro-
duced to handle the tagged MRI. A relaxation factor is first introduced, followed
by image content items.
4.1. Relaxation Factor
In [9], the construction of a speed term is described as
F
=
F
A
+
F
G
, where
F
A
is a constant. It does not depend on the geometry of the front, but its sign
determines the direction of front movement.
F
G
depends on the geometry of the
front. In [9], a negative speed term is constructed as in Eq. (29), and then the speed
term is constructed as:
F
=
F
A
+
F
I
, where
F
I
is defined as
F
A
M
1
−
−
F
I
(
x, y
)=
M
2
{|∇
G
σ
·
I
(
x, y
)
|−
M
2
}
.
(29)
The expression
G
σ
·
I
(
x, y
) denotes the image convolved with a Gaussian smooth-
ing filter whose characteristic width is
σ
.
M
1
and
M
2
are the maximum and min-
imum values of the magnitude of image gradient
|∇
G
σ
·
I
(
x, y
)
|
. So the speed
term
F
tends to zero when the image gradient is large.
However, in practice, the gradient values on the object boundary seldom reach
the maximum value (
M
1
). In other words, the evolvement cannot stop at the object
boundary. Especially for MR images in which the boundaries are blurry, results
are even worse. To solve this problem, a
relaxation factor δ
is introduced to relax
the bounding of
M
1
−
M
2
:
r
=
|∇
G
σ
·
I
(
x, y
)
|−
M
2
,
(30)
M
1
−
M
2
−
δ
where
δ
∈
[0
,M
1
−
M
2
]. We trim
r
to 1:
r
if
r<
1
r
=
,
1
if
r
≥
1
and the reconstructed negative speed term will be
F
I
(
x, y
)=
−
r
·
F
A
.
