Image Enhancement - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 100

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.