Clustering of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 163

where X N , Y N and Z N are the CIE tristimulus values with reference to the
white point ( D 65 ).
The colour clustering algorithm, suggested by Chaira [5,6] using intuition-
istic fuzzy set theory, is used to segment human cell images that use CIELab
colour space. This method clusters the nucleus and cytoplasm of pathologi-
cal RBC or WBC in the blood cell image. Other colour spaces such as RGB
and HSV are also used. But CIELab colour space gives better results as it is a
perceptually dependent colour model.
Initially, Sugeno-type intuitionistic fuzzy complement is used to construct
an intuitionistic fuzzy set. Thus, with the help of Sugeno fuzzy generator,
IFS becomes

⎧ ⎫

⎪
⎪

( 1 −

+⋅

μ
λμ

( )) x

⎪
⎪

IFS A

Ax = , (), μ x

x xX

∈

λ A

( 1 ( ))

A

with hesitation degree

( 1 −

+⋅

μ
λμ

( )) x

A

π () x =− − 1 μ () x ( 7. 2 5 )

A A

( 1 ( )) x

A

Six features for each data point are taken - 3 for L , a and b values of each
colour pixel and 3 for the mean of L , a and b values of the neighbourhood of
the pixel. For each pixel, the mean or the average values of L , a and b are cal-
culated in the 3 × 3 window neighbourhood. This is moved throughout the
image to find the average for each pixel neighbourhood, which is similar to
the conventional FCM clustering. The value 'λ' in Equation 7.25 plays a signif-
icant role in intuitionistic fuzzy clustering. When the value of λ is increased
gradually from 2, the clustered image is degraded, that is, the regions are
not properly clustered. With the value of λ = 1, the cluster seems to be better.

Performance evaluation : In order to verify the performance of segmentation
methods, ground truth or manually segmented images are constructed. It
is similar to that of monochrome image performance computation. The mis-
classification error of the clustered images is calculated as [14]

1 1 2 2 3 3 4 4

Error =− ∩+∩+∩+∩
++

RRRRRRRR
RRR

ET GT ET GT ET GT ET GT

1

1 2 3 4

+ R

GT GT GT GT

wher RRR R
ET

1

,

2

,

3

and

4

are the regions in the experimental segmented/

ET ET ET

clustered image
RRR

1 2 3 4

, , and are the different regions in the ground truth
segmented/clustered image

R

GT GT GT GT