Biomedical Engineering Reference
In-Depth Information
The optimal solution is obtained via optimization of aggregated three performance
criteria functions using weighted-sum approach [
6
]. Three criteria are summed up
into a single objective function and each criterion is given a coefficient, to define the
relative importance of each criterion in the aggregated objective function as formu-
lated as followings:
N
F
(
x
) =
c
i
fi
i
(
x
)
(3.14)
i
=
1
WHERE F
I
= {
NBPS
,
NOCS
,
NDPS
}
Correctly tuned coefficients are essential to provide correct relative correlation
between the measurements in
RBD
,
RCD
and
ASD
to the corresponding scores
in
NBPS
,
NOCS
and
NDPS
respectively. These coefficients settings do not have
standard rules of setting, it depends on the applications and the quality of the input
images [
7
]. The added value of histogram equalization is that this technique stand-
ardizes the intensity distribution of the image luminance. Therefore, invariably, the
parameters setting MBOBHE depends heavily on the applications. In the context
of hand bone segmentation application, these coefficients are set to have equal
importance. The optimization is then solved by evolutionary algorithm [
8
]. In next
chapter of result and analysis, the performance of MBOBHE in the context of
BAA using TW3 method will be justified via qualitative analysis by benchmark-
ing the MBOBHE to existing types of HE methods such as GHE, BBHE, DSIHE,
MMBEBHE, RMSHE and RSIHE.
3.3.1.3 Histogram Decomposition
The computed Pareto solution is used as a decomposing point to decompose the
histogram into two sub-images: a lower sub-image and upper sub-image repre-
sented by
X
L
and
X
U
respectively based on the decomposing point, this process
can be described using the mathematical Eq. (
3.15
).
(3.15)
X
=
X
L
∪
X
U
where
X
L
= {
X
(
i
,
j
)|
X
(
i
,
j
) ≤
X
S
,
∀
X
(
i
,
j
) ∈
X
}
X
U
= {
X
(
i
,
j
)|
X
(
i
,
j
) >
X
S
,
∀
X
(
i
,
j
) ∈
X
}
In other words, the lower sub-image
X
L
is constituted of
{
X
0
,
X
1
,
...
,
X
S
}
and
the upper sub-image
X
U
is constituted of
{
X
S
+
1
,
X
S
+
2
,
X
S
+
3
,
...
,
X
L
−
1
}
. Suppose
n
L
and
n
k
U
represent the number of pixels with gray level
X
k
in
X
L
and
X
U
respec-
tively,
n
L
denotes the total number of pixels in sub-image
X
L
, as expressed in
Eq. (
3.16
);
n
L
denotes the total number of pixels in sub-image,
X
U
, as expressed
in Eq. (
3.17
). The probability density function (PDF) of sub image
X
L
is defined
as in Eq. (
3.18
) and the
PDF
of sub-image
X
U
is defined as in Eq. (
3.19
)
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