Biomedical Engineering Reference
In-Depth Information
the average of all
U
variances
σ
ind
Y u,c,i
2
.
x
VO
c,i
denotes the mean
x
coordinate of
(
x, y
), and is taken to be
x
pop
c,i
is taken to be
y
pop
c,i
p
VO
c,i
, and
y
VO
c,i
. The principal axes
, and are set to
X
pop
c,i
and
Y
pop
c,i
of
p
VO
c,i
(
x, y
) are
X
VO
c,i
and
Y
VO
c,i
, respectively. The
distributions
p
VO
c,i
(
x, y
) were meant to represent the spatial distribution of selec-
tions made by an average individual user. Therefore, the variability of
p
VO
c,i
(
x, y
)
was set to the average variability of the individual distributions
p
ind
u,c,i
(
x, y
) rather
than that of the population distribution
p
pop
c,i
(
x, y
), which would contain more
variability than found in any one user because
p
pop
c,i
(
x, y
) is constructed from the
pooled selections of all observers.
When using virtual operator VO
i
to initialize our 2D segmentation algorithm
for a particular TRUS prostate image
i
, the coordinates of control point
c
, i.e.,
(
x
c,i
,y
c,i
), are generated from the corresponding distributions
p
VO
(
x, y
). Be-
c,i
cause
x
and
y
are principal axes,
p
VO
c,i
(
x, y
) is separable, and can be written as
p
VO
c,i
(
x, y
)=
p
VO
c,i
(
x
)
p
VO
c,i
(
y
), where
p
VO
c,i
(
x
) is a univariate Gaussian distribu-
and a variance of
σ
V
Xc,i
2
, and
p
VO
tion with a mean of
x
VO
c,i
(
y
) has a mean of
c,i
and a variance of
σ
V
Y c,i
2
.
x
c,i
y
VO
c,i
is generated from
p
VO
c,i
(
x
) using any stan-
dard algorithm for random number generation. Similarly,
y
c,i
is generated from
p
VO
c,i
(
y
). This method of using VO
i
as well as the method for constructing VO
i
assumes that there are no correlations in the selection of control points.
3.3. Example of Virtual Operator Construction
We have constructed 15 virtual operators, one for each of 15 mid-gland 2D
TRUS images extracted from the 3D images described in Section 2.3.1. To form
the virtual operators, five trained operators (i.e.,
U
=5) each selected all four
control points in each of the 15 images in one session. Each session was repeated
10 times (i.e.,
R
=10) to yield a total population of 50 selections for each control
point
c
in image
i
. The sessions were separated by 3 days each, and the images
were presented in random order at each session in order to minimize the effects of
memory. The outputs of the four steps involved in constructing a virtual operator
are illustrated in Figures 7 through 9. Figure 7a illustrates the output of the first
step. The Figure shows a typical image of the prostate with the population of 50
selections per control point superimposed on the image. The output of the second
step is four population distributions,
p
pop
c,i
(
x, y
), describing the selections for each
control point
c
(
c
=1
,
2
,
3
,
4). The spatial extent of each
p
pop
c,i
(
x, y
) is depicted
by an ellipse in Figure 7b; the original selections are omitted for clarity. Figures
7c-f show closeups of all four distributions
p
pop
c,i
(
x, y
), and include the original
selections. The ellipse for control point
c
is centered at (
x
pop
c,i
,
y
pop
c,i
). The direction
of the semi-major axis of the ellipse is specified by
X
pop
c,i
, and the length of the
semi-major axis is two times
σ
pop
Xc,i
. The length of the semi-minor axis (
Y
pop
) is
c,i
two times
σ
pop
Y c,i
. Hence, the ellipse includes 95% of the samples along each axis.
