Clustering of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 157

where uu
ik

* () denotes the intuitionistic (conventional) fuzzy membership
matrix of the i ith data in k ith class.
Substituting Equation 7.22 in the conventional FCM method, the modified
cluster centre is written as

ik

∑
∑

n

*

ux

ik i

*

v =

i = 1

( 7. 2 3)

k

n

*

u

ik

i = 1

Using this equation, the cluster centre is updated and simultaneously the
membership matrix is updated.
At each iteration, the cluster centre and the membership matrix are updated
and the algorithm stops when the difference of the updated membership
matrix and the previous matrix is less than ε, that is,

* new

*

prev

max UU

ik

− < ε

ik

ik

ε is a user-defined value and is selected as ε = 0.03.
Thus, the criterion function in conventional FCM is modified using intu-
itionistic fuzzy set.
In the clustering algorithm, three features are considered, namely, pixel
grey value, pixel mean and standard deviation. A small square window of
size 3 × 3 is used throughout the image to calculate the mean and the standard
deviation. Regarding the selection of α in Equation 7.21, with α ≤ 0.5, images
are binary thresholded, and with α > 0.5, clustered images are obtained. But
better results are obtained with α = 0.85.

E x a mple 7.4

An example is shown on CT scan images of the brain to show the efficacy of
the algorithm. Figure 7.6 shows the tumour/clot in the brain. Along with the
intuitionistic fuzzy method, conventional FCM algorithm is also shown.

The intuitionistic fuzzy clustering method clusters the tumour from the
image clearly.

7.7 Kernel-Based Intuitionistic Fuzzy Clustering
In intuitionistic fuzzy c means (IFCM) clustering, all the regions are not clus-
tered clearly and it is not robust to noise. To overcome the drawback of intu-
itionistic fuzzy clustering and make it more robust, the objective function