Image Processing Reference
In-Depth Information
average grey levels of the object and background regions,
m
O
(
t
) and
m
B
(
t
), are
computed using Equation 6.6.
Replacing
m
in Equation 6.11 by
m
O
and
m
B
, the membership function for
the object and background regions becomes
()
−⋅
exp(
cg m
|
−
|),
if
g
≤
t
,
forthe object
ij
O
ij
(6.12)
μ
Aij
g
=
exp(
−⋅
cg m
|
−
|),
if
ij
gt
>
,
forthe background
ij
B
where
t
is any chosen threshold
g
ij
is the (
i
,
j
)th pixel in image
A
The constant '
c
' is chosen to ensure that the membership of the grey level
corresponds to the range [0, 1] and is calculated as
c
= 1/(
g
max
−
g
min
), where
g
min
and
g
max
are the minimum and maximum values of the grey level in the
image, respectively.
Based on the fuzzy set, the membership and non-membership functions
in an intuitionistic fuzzy domain are constructed as follows:
Membership value,
μ
IFS
gT
(, )
=
λμ
( ,)
gT
λ
Non-membership value,
ν
IFS
gT
(,)( (, ))
=−
1
μ
gT
where
g
is the grey level of the image
T
is a certain threshold
λ
∈ [0, 1], and in this method, λ
= 0.2 is selected
From the intuitionistic fuzzy discrimination measure derived from the cross
e nt r o py,
DABI AB I BA
IFS
(,)
=
( ,) (, )
+
IFS
IFS
⎛
⎜
⎞
⎟
μ
()
x
ν
(
x
)
∑
Ai
A
i
I AB
(,)
=
μ
( )ln
x
⋅
+
ν
()ln
x
IFS
A
i
Ai
(
1/
)(()
μ
x
+
μ
(
x
))
(
1/
)(()
ν
x
+
ν
(
x
))
Ai Bi
Ai Bi
i
In the image, the intuitionistic fuzzy discrimination information is
⎛
⎞
()
() ()
2
μ
g
2
ν
()
g
∑
A
A
DAB
(,)
=
h g
( )
μ
( )ln
g
⋅
+
ν
()ln
g
⋅
⎜
⎟
IFS
A
A
μ
g
+
μ
g
ν
(
g
)
+
ν
( )
g
⎝
⎠
A
B
A
B
(6.13)
⎛
⎞
()
() ()
2
μ
g
2 (()
() ()
ν
g
∑
B
B
+
hg
() ()ln
μ
g
⋅
+
ν
()ln
g
⋅
⎜
⎟
B
B
μ
g
+
μ
g
ν
g
+
ν
g
⎝
⎠
B
A
A
B
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