Biomedical Engineering Reference
In-Depth Information
Chapter 11
Co-Volume Level Set Method in Subjective
Surface Based Medical Image Segmentation
Karol Mikula,
1
Alessandro Sarti,
2
and Fiorella Sgallari
3
11.1 Introduction
It is well known that the so-called
level set equation
[42, 43, 54, 55]
∇
u
|∇
u
|
u
t
=|∇
u
|∇ ·
(11.1)
for curvature-driven motion as well as its nontrivial generalizations are well
suited to image processing applications and they are often used nowadays. In
this chapter we deal with a specific equation of mean curvature flow type [48-50],
namely,
∇
u
g
(
|∇
G
σ
∗
I
0
u
t
=
2
+|∇
u
|
2
|
)
ε
(11.2)
ε
∇·
,
2
+|∇
u
|
2
where
u
(
t
,
x
) is an unknown (segmentation) function defined in
Q
T
≡
[0
,
T
]
×
.
⊂
IR
d
is a bounded domain with a Lipschitz continuous boundary
∂
,
[0
,
T
] is a time interval,
I
0
is a given image, and
ε>
0 is a parameter. The
equation is accompanied with zero Dirichlet boundary conditions and initial
1
Department of Mathematics, Slovak University of Technology, Radlinsk eho 11, 813 68
Bratislava, Slovakia, E-mail:
mikula@vox.svf.stuba.sk
2
DEIS,
University
of
Bologna,
Via
Risorgimento
2,
40136
Bologna,
Italy,
E-mail:
asarti@deis.unibo.it
3
Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40127
Bologna, Italy, E-mail:
sgallari@dm.unibo.it
583
