Biomedical Engineering Reference
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of triangular shaped distribution with correctly tuned parameters satisfies this new
perception. The new perception is based on the observation that relatively low
contrast and relatively high contrast are both noticeably inferior to the resultant
image; conversely, the optimum contrast is favorable. The reason is that relatively
low contrast will obscure the pertinent features image which is significant in appli-
cation; contrarily, relatively high contrast will produce over-enhanced contrast and
lead to the saturated intensity artifacts.
(C) The Detail Preservation Score (DPS) Function
Firstly, we define the input of DPS which is the Average Structural Different
(ASD) as follows:
x
if
,
j
− µ
x
(
y
if
,
j
− µ
y
)
(3.12)
d
(
X
,
Y
)
=
N
1
MN
1 if
d
(
x
if
,
j
,
y
if
,
j
) ≥
0
0 if
d
(
x
if
,
j
,
y
if
,
j
) ≤
0
(3.13)
ASD
(
X
,
Y
) =
s
(
x
if
,
j
,
y
if
,
j
)
if
=
0
The Detail Preservation Score (DPS) is designed as a function that output a
numerical score which can be used to gauge the performance of the detail pres-
ervation ability of the histogram equalization corresponds to the simultaneous
discrepancy of pixel-mean intensity between the input image and the histogram
equalized image. The function is designed so that the simultaneous pixel-mean
intensity change is the function domain,
U
and
V
are the parameters, and the
bound values between 0 and 1 are the function range. The detail of the function is
discussed as follows:
3.3.1.2 Optimal Solution of the Aggregated Multiple Objectives
Function
Solving the multiple objectives optimization amount to searching an optimal
n-dimensional variables vector,
x
= {
x
1
...
x
n
}
which is known as the 'optimiza-
tion parameters' that fulfil all imposed constraints and at the same time optimizes
all the conflicting performance criteria or objectives, represented by a m-dimen-
sional vector objective function
if
(
x
) =
[
5
]. In the context of multi-
ple objectives histogram equalization, there is only one optimization parameter
(n
=
1), which is the decomposition point of bi-modal histogram equalization, and
there are 3 objectives (
m
=
3) which are the maximum contrast, minimum bright-
ness mean-shift and minimum detail loss. As mentioned, minimizing the mean-
shift or detail loss is conflicting with maximizing the enhanced contrast; therefore,
we need to find an optimal feasible (or Pareto optimal) decomposition point that
can satisfy the three objectives simultaneously; the set of all Pareto optimal solu-
tion is called the efficient frontier.
if
1
...
if
m
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