Image Processing Reference
In-Depth Information
A new membership function is computed using fuzzy
t
-conorm by Chaira,
which is algebraic in nature and is computed as
upper
lower
upper
lower
μ
()
g
+
μ
()
g
+ ⋅
λμ
()
g
⋅
μ
()
g
enh
g
μ
()
=
up
per
lower
(
1
+⋅
λμ
)
()
g
⋅
μ
()
g
+
1
This is obtained from
=
++
+
xy xy
xy
λ
*
(,)
Cxy
(
1
λ
)
+
1
μ
upper
(
g
) and μ
lower
(
g
) are the upper and lower membership functions of the
Type II fuzzy set, respectively.
λ
= im_avg
, where
im
_
avg
is the average of the image. The new image with
the new membership function so formed is the enhanced image.
To compute the value of α, fuzzy linguistic hedge 0 ≤ α
≤ 1 is used to gener-
ate the lower and upper membership functions from a type I fuzzy member-
ship function. Parameter α is usually determined heuristically to satisfy the
requirement 0 ≤ α ≤ 1. In this method, α
= 0.75 is used. The upper and lower
ranges of the Type II fuzzy membership function are calculated with α = 0.75
in Equation 5.18.
5.5.2 Enhancement Using Hamacher
t
-Conorm
A similar procedure as described earlier is followed using Hamacher
t
-conorm [11]. The new membership function is computed using Hamacher
t
-conorm as
upper
lower
upper
lower
μ
()
g
+
μ λμ μ
() (
g
+ −⋅
2
)
()
g
⋅
()
g
enh
g
μ
()
=
upper
lower
11λλμ
−−
(
)
⋅
( )
g
⋅
μ
( )
g
and λ
=
im
_
avg
, where
im
_
avg
is the average of the image. As in the previous
method, the upper and lower ranges of the Type II fuzzy membership func-
tion are calculated with α
= 0.8. The new image so formed is the enhanced
image [5].
Enhancement using other
t
-conorms may also be used using the same
procedure.
5.5.3 Enhancement Using Type II Fuzzy Set
This type of enhancement was suggested by Ensafi and Tizhoosh [8]. It consid-
ers Type II fuzzy set to enhance the images. The image is divided into several
windows, and for each window, the subimage is fuzzified using Equation 5.1.
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