Image Processing Reference
In-Depth Information
Let the function
F
(
x
) = 1 − (1 −
e
)
x
(6.7)
with
F
(0) = 1,
F
(1) =
e
.
Substituting Equation 6.7 in Equation 6.5, the membership function is
written as
(
)
μ
()
t
=−−
11
(
e cREF gm t
)
(, ())
if
gt
≤
B
B
(
)
()
t
11
(
e cREF gm t
)
(, ()
)
if
gt
μ
=−−
>
O
O
If
c
(
x
) = 1 −
x
for all
x
∈ [0, 1] and
REF
(
A
,
B
) = 1−|
x
−
y
| and
e
= 0.5, then
μ
()
t
=− −
105
.
g mt
( )
if
gt
≤
B
B
(6.8)
μ
()
t
=− −
105
.
g mt
( )
if
gt
>
O
O
Intuitionistic fuzzy set is constructed as
{
}
(
)
α
1
/
β
Ax
=
, (),
μ
x
1
−
μ
()|
x xX
∈
IFS
A
A
The membership value = μ(
g
,
T
)
α
and the non-membership value = 1 − μ(
g
,
T
)
1/β
.
The optimal threshold is selected using Yager's intuitionistic fuzzy
entropy:
1
−
∑
L
1
IFEt
MM
hg g
()
=
() (),
π
π
( )
g
=− −
1
μ
( )
g
ν
( )
g
A
A
A
A
A
×
g
=
0
So,
1
−
∑
L
1
(
)
1
/
β
α
IFEt
MM
hg
()
=
() () ()
μ
g
−
μ
g
(6.9)
A
t
t
×
g
=
0
For each threshold grey level,
t
, intuitionistic fuzzy entropy is computed and
the grey level corresponding to the minimum entropy is selected as the opti-
mal threshold.
α = 4/3 and β = 5/4 are used as the constant values.
With α
> 6 or β
> 6, the results are not accurate, and with α
= β
= 1, it
b e c o m e s f u z z y.
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