Biomedical Engineering Reference
In-Depth Information
User Input Received
U
(
x
,t
) changes
Initialize
ψ
(
x
,
0)
U
(
x
,
0)=0
I
(
x
)
U
(
x
,t
)=
U
(
x
,t
f
)
∀t>t
f
|
t
1
|
t
2
...
|
t
k
t
¨
t
f
Fig. 3 Within each interval [
t
m
,
t
m
+1
], the level set is automatically evolved (the plant in Fig.
4
).
Then, at each time
t
m
+1
, user input is provided (the controller in Fig.
4
) changing
c
and
accumulating as
U
ð
x
;
t
Þ
.At
t
f
, the user determines that
cð
x
;
t
Þ
is satisfactory and segmentation is
complete
His function is to provide intermittent input to change
c
. It is assumed that when the
user is shown a slice from a 3D medical image sequence, he can generate the correct
segmentation,
c
∗
(i.e., he knows the ground truth and given enough time could
outline the ideal segmentation result).
As in Fig.
3
, during the segmentation, the user gives a finite number of inputs at
times
t
i
for
i
1,...,
k
; the user directly changes
cð
x
;
t
Þ
with his input. Hence,
∈
we can write the function modeling user inputs
U
ð
x
;
t
Þ
as:
t
k
þ
Þcð
t
k
Þ
g
k
ð
x
Þ¼cð
x
;
x
;
(7)
X
k
i¼
1
g
k
ð
(8)
u
ð
x
;
t
Þ¼
x
Þdð
t
t
i
Þ
Z
t
U
ð
x
;
t
Þ¼
u
ð
x
; tÞ
d
t:
(9)
0
The goal for this HSC algorithm is to perform segmentation while minimizing
the amount of user input, i.e., minimizing the domain over which
U
ð
;
Þ
x
t
is actuated
and
jj
L
2
.
Within each time interval [
t
m
,
t
m
+1
],
m
jj
U
1 (refer to Fig.
3
)
during segmentation, it is assumed the user is satisfied with the performance of
the automatic algorithm (because no input is provided as guidance). It is important
to note that simply alternating between manual labeling and automatic segmenta-
tion does not produce desired behavior: user input could be overridden during the
automatic phase. Instead, it is desirable to incorporate user input into the system
dynamics. Then, (
4
) would take the form:
1,...,
k
∈
c
t
¼
G
Þ
|
{z
}
nominal
þ
ðc;
I
H
Þ
|
{z
}
control
ðc;
U
(10)
