Image Enhancement - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 95

Based on the fuzzy set, the membership degree of the IF image is com-
puted from Chaira's IF generator as

−
+−

1 μ () g

(5.15)

IFS A

μ () g =− 1

A

λ

1 ( e 1 ) () μ g

A

with λ > 0.
Using Chaira's fuzzy negation, φ( x ) = (1 − x )/1 + ( e λ − 1) x , λ > 0, the non-
membership degree of the IF image is computed as

= (

)

IFS IFS

ν (;) g λ ϕμ λ ( ;) g

A A

or

IFS

−
+−

1 μ () g

(5.16)

IFS

ν () g =

A

λ + 1

IFS

1 ( e 1 ) () μ g

λ in Equation 5.16 in the denominator is changed to λ + 1, implying that
1

1
+−

λ IFS IFS λ μ . With the change in λ,

the non-membership degree, ν IFS ( , will change but will still follow
the condition ν

( e 1 ) () μ g

is changed to 1

1
+− ( e

+

1 ) () g

A A

IFS

() 1

IFS

()

g ≤− μ g . This is done to obtain a better contrast-

A A

enhanced image. So,

⎛ ⎞

11 1
1

−− −
+−

μ () g

A

⎜ ⎟

λ

( e 1 ) () μ

μ

g

⎝ ⎠

A

IFS

ν (;) g λ =

A

⎛ ⎞

1 − ( g )

λ + 1 A

1 +−− ( e 1 1 )

⎜ ⎟

1 (

λ

1 ) ()

+− e μ g

⎝ ⎠

A

1 ()

−
+− +−

μ g

(5.17)

A

=

1 (

λ

1 ) () (

λ + 1

1 ) ()

λ

e μ g e μ g e

A A

1 ()

− μ g

A

=

1 + ( e

21 λ +

− 1 ) () μ g

A

The hesitation degree is computed as

(5.18)

IFS IFS IFS

π (;) g λ =− 1 μ ( ;) (;) g λ − ν g λ

A A A

To obtain the optimum value of λ, the IF entropy is used.
The IF entropy is calculated as

N N

1

∑ ∑

() ()

1 − π g

IE A () = π ge

Aij

⋅

IFSij

N

j = 1 i = 1