Image Enhancement - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 94

ν ≤− 1 . This is done to obtain a better contrast-enhanced image.

The modified non-membership function is given as

IFS

() g μ

IFS

() g

A A

( 1 + λμ ) )

()

( g

A

1 −

IFS

−
++

1 μ

λμ

() g +⋅

+ ++
+⋅

1 λμ g

IFS IFS A

ν () ( g = φ μ ( )) g = =

A A

( λ 11

1

)( λ μ

λμ

) ()
()

g

IFS

1 ( 1 ) () g

A

1

(5.14)

g

A

1 − μ () g

A

=

2

13 +⋅⋅ λμ () g + λ μ () () g + μ g

A A A

IFS IFS

The hesitation degree is calculated as π 1 ( ) ( ) .

λ is calculated using the IF entropy. The IF entropy is calculated as

=− − μ g ν g

mn A A

N N

1

∑ ∑

() ()

1 − π g

IE A () = π ge

Aij

⋅

Aij

N

j = 1 i = 1

The optimum value of λ is calculated as

λ = max( (;)) IE A λ

opt

λ

Among all the entropic values for different values of λ, the λ value that corre-
sponds to the maximum entropy is selected. With this λ value, the member-
ship and the hesitation degrees are calculated.
Then fuzzy hedge is applied on the IF image which is given as

= ( () .

) 125

IFS IFS

μ () g μ g

new A

Contrast stretching is applied on the intuitionistic image using the INT
operator.
The intensifier operation is written as

2

2 ⋅ ⎣ μ

new

() g ⎦ if 0 < μ

new

() . g ≤ 05

IFS IFS

enh

μ () g =

2

⎣

new

⎦

new

121 −− μ () g if 05 . ≤ μ IFS ( ) g ≤ 1

IFS

where μ enh is the enhanced IF image.

5.4.4 Contrast Enhancement by Chaira (Method IV)

This method is suggested by Chaira [7] using Chaira's IF generator. The
image is fuzzified with the membership function μ A ( g ) using Equation 5.1.