Image Enhancement - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 97

(a) (b) (c)

FIGURE 5.6
(a) CT scan brain (CT-2) image, (b) IF enhancement by Chaira (method III) and (c) the IF
method by Chaira (method IV). (Modified from Chaira, T., Construction of intuitionistic fuzzy
contrast enhanced medical images, in Proc. of IEEE International Conference on Human Computer
Interaction , IIT Kharagpur, India, 2012; Chaira, T., J. Intell. Fuzzy Syst. , 2013.)

Method V : Vlachos and Sergiadis [18] suggested hesitancy histogram equal-
ization for image enhancement. As has been described earlier, an IF image
is written as

{ }

Ax

IFS

= , (), () μν x x xX ∈

A A

where μ A ( x ) and v A ( x ) are the membership and non-membership functions in
the interval [0, 1], respectively.
Using the concept of the fuzzy histogram, an IF histogram is constructed
using an IF number. A symmetrical triangular F -number is used to construct
the fuzzy histogram and is represented as

⎛ xg

p

− ⎞

μ F x () max, = 01 −

⎜ ⎟

⎝ ⎠

where p is a real number that controls the shape of the F -number. Using the
IF generator, the IF membership function is written as

λ − 1

⎛ ⎞

⎛ − ⎞

xg
p

μ () =− − 11 01 max, −

g x

⎜ ⎟

⎜ ⎟

⎝ ⎠

⎝ ⎠

and the non-membership function is written as

λλ ( − 1 )

⎛ ⎞

⎛ − ⎞

xg
p

ν () =− − 1 max, 0 1

g x

⎜ ⎟

⎜ ⎟

⎝ ⎠

⎝ ⎠