Image Processing Reference
In-Depth Information
Then using Equation 6.19, the membership function becomes
(6.20)
e
xy
1
−−
||
μ
() .
x
=
0 582
⋅
(
−
1
)
The value 0.582 is computed from 1/(exp(1) −1) = 0.582.
For a certain threshold '
t
' that separates the object and background regions,
the membership function of the object region is written using Equation 6.20
as
1
−−
|
am
|
μ
Aij
() .
a
=
0 582
(
e
−
1
),
if
at
≤
,
forthe object
ij
O
ij
Likewise, the membership function μ
A
(
a
ij
) of the background region is writ-
ten as
forthe background
(6.21)
1
−−
|
am
|
μ
Aij
() .
a
=
0 582
(
e
−
1
),
if
at
>
,
ij
B
ij
with
m
O
(
t
) and
m
B
(
t
) are computed using Equation 6.6, respectively.
The Sugeno-type intuitionistic fuzzy generator is used to find the non-
membership function in an intuitionistic fuzzy domain that is written as
1
−
+⋅
μ
λμ
()
()
,
x
A
ν
()
x
=
λ
>
0
1
x
A
For thresholding the images, the image is initially filtered with a Gaussian
filter of size 3 × 3. The filtered image is divided into several windows (1/4)*
the image size. With smaller window size, the threshold picks very small
particles, which results in poor extraction and performance of the image.
The membership values are calculated for each window, and the non-
membership values are also computed using Sugeno-type intuitionistic
fuzzy generator. The hesitation degree is calculated using the membership
and non-membership values. The value of λ in the construction of an intu-
itionistic fuzzy set is taken as λ
= 0.8. For each threshold, fuzzy divergence
between an ideal and actual thresholded images is calculated. The diver-
gence measure between the ideal and actual thresholded images is com-
puted using Equation 6.18 as
∑
∑
22
()
1
1
()
⎣
μ
a
−
−
μ
a
DAB
(,)
=
−
(
−
μ
( )
a
⋅
e
Aij
−
μ
(
a
)
⋅
e
A ij
IFS
A
ij
Aij
i
j
μ
() ()
a
+
π
a
−
1
+− −
22
(
μ
(
a
)
−
π
(
a
))
⋅
e
Aij Aij
Aij
A
ij
a a
e
Aij Aij
1
−
μ
() ()
−
π
⎦
−
(()
μ
a
+
π
(
a
))
⋅
(6.22)
Aij
A
i
j
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