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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