Image Processing Reference
In-Depth Information
The image is compared with an ideally thresholded image. Considering
B
to be an ideally thresholded image where all the object/background pixels
perfectly belong to their respective regions, the membership function of
object pixels, μ
B
(
g
) = 1, Equation 6.13 is rewritten as
⎛
⎞
2
1
μ
μ
()
()
g
g
2
∑
g
(6.14)
A
DAB
(,)
=
h g
( )
⎜
μ
( )ln
g
⋅
+
ν
()ln
g
2
+
ln
⎟
IFS
A
A
+
1
+
μ
()
g
⎝
⎠
A
A
Divergence is calculated for all the threshold grey levels. The optimal thresh-
old is the grey value corresponding to the minimum divergence value.
Chaira [7]
suggested a divergence-based method for medical image
thresholding. The membership function is obtained using Equation 6.10 as
()
−⋅
exp(
cg m
|
−
|)
,
if
g
≤
t
,
forthe object
ij
O
ij
μ
Aij
a
=
forthe background
exp(
−⋅
cg m
|
−
|),
if
ij
gt
>
,
ij
B
where
m
O
(
t
) and
m
B
(
t
) are computed using Equation 6.6
The constant '
c
' is
c
= 1/(
g
max
−
g
min
) as described earlier.
The non-membership function is computed using Sugeno-type intuitionistic
fuzzy generator [21].
Sugeno's intuitionistic fuzzy generator is written as
(
1
−
+
μ
λμ
( ))
x
Nx
(())
μ
=
( ))
,
λ
>
0
(6.15)
(
1
x
with hesitation degree
(
1
−
+⋅
μ
λμ
( ))
x
(6.16)
A
π
()
x
=− −
1
μ
()
x
A
A
(
1
( ))
x
A
Intuitionistic fuzzy divergence suggested by Chaira and Ray [4] in section 3
is used for finding the optimal threshold. A brief idea on the intuitionistic
fuzzy divergence measure is detailed below.
6.4.2.1 Intuitionistic Fuzzy Divergence Measure
The intuitionistic fuzzy divergence measure considers three parameters,
namely, the membership degree, the non-membership degree and the
hesitation degree (or intuitionistic fuzzy index).
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