Biomedical Engineering Reference
In-Depth Information
piecewise constant functions and finding a partition of Ω such that
f
in Ω
i
equals
a constant, and Ω=
i
Ω
i
C
. Based on Eq. (16), Chan and Vese proposed the
following minimization problem for a two-phase segmentation:
µ
Ω
dxdy
+
v
Ω
min
C,c
o
,c
b
δ
(
φ
)
|∇
φ
|
H
(
φ
)
dxdy
+
λ
o
inside
(
C
)
|
c
o
|
2
H
(
φ
)
dxdy
f
−
(17)
H
(
φ
))
dxdy
.
+
λ
b
outside
(
C
)
|
c
b
|
2
(1
−
f
−
Here
φ
is the level set function, and
H
(
φ
) is the Heaviside function:
1
,
φ
≥
0
,
H
(
φ
)=
(18)
0
,
φ<
0
.
Finding a minimum of (17) is done by introducing an artificial time variable, and
moving
φ
in the steepest descent direction to steady state:
div
∇
,
φ
c
o
)
2
+(
f
c
b
)
2
−
φ
t
=
δ
ε
(
φ
)
−
(
f
−
−
v
+
µ
·
(19)
|∇
φ
|
subject to
φ
(
x
,
0) =
φ
0
(
x
). Here
δ
ε
is a globally positive approximation to the
δ
function (see [58]). The recovered image is a piecewise constant approximation
to
f
0
. We use Chan-Vese model in the application for cortex segmentation below.
Generally, the above deformable models implemented by means of the level
set method suffer from a slower speed of convergence than parametric deformable
models due to their computational complexity. However, they can automatically
handle topology changes and allow for multiple simultaneous boundary estima-
tions, which is the case with most medical imaging.
In the following sections we present our work on medical image segmentation
in three different applications, including tongue segmentation within color images
used in computerized tongue diagnosis, cerebral cortex segmentation in MR im-
ages, and cardiac valve segmentation in echocardiographic sequences. We apply
different deformable models for each.
3.
TONGUE BODY EXTRACTION BASED ON A COLOR GVF SNAKE
3.1. Introduction
Tongue diagnosis is one of the most important approaches to retrieving signif-
icant physiological information on the human body employed in the famous four
diagnostic processes of Traditional Chinese Medicine (TCM): inspection, listen-
ing and smelling, inquiry, and palpation. TCM doctors have long used information
about the color, luster, shape, and movement of a patient's tongue to determine his
disease and body condition [67]. However, the clinical competence of traditional
