Rough-Fuzzy Clustering Algorithm for Segmentation of Brain MR Images - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 24

TABLE 2.1 Performance of FCM and RFCM on

I-20497774
Value DBIndex DunnIndex β Index
of c FCMRFCM FCMRFCM FCM RFCM
2 0.51 0.21 2.30 6.17 2.15 2.19
3 0.25 0.17 1.11 1.62 3.55 3.74
4 0.16 0.15 1.50 1.64 9.08 9.68
5 0.39 0.17 0.10 0.64 10.45 10.82
6 0.20 0.19 0.66 1.10 16.93 17.14
7 0.23 0.27 0.98 0.12 21.63 22.73
8 0.34 0.27 0.09 0.31 25.82 26.38
9 0.32 0.28 0.12 0.13 31.75 32.65
10 0.30 0.24 0.08 0.12 38.04 39.31

with increase in the value of c. For a particular value of c, the performance of RFCM is
better than that of FCM.
Fig. 2.2 shows the scatter plots of the highest and second highest memberships of all the
objects in the data set of I-20497774 at first and final iterations respectively, considering
w = 0.95, m = 2.0, and c = 4. The diagonal line represents the zone where two highest

memberships of objects are equal. From Fig. 2.2, it is observed that though the average
difference between two highest memberships of the objects are very low at first iteration
(δ = 0.145), they become ultimately very high at the final iteration (δ = 0.652).

1

At 1st Iteration After 20th Iteration

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

Highest Membership Value Highest Membership Value

FIGURE 2.2 Scatter plots of two highest membership values of all objects in data set I-20497774

Table 2.2 compares the performance of different c-means algorithms on some brain MR
images with respect to DB, Dunn, and β index considering c = 4 (back-ground, gray
matter, white matter, and CSF). All the results reported in Table 2.2 confirm that the
RFCM algorithm produces pixel clusters more promising than do the conventional methods.
Some of the existing algorithms like PCM and FPCM have failed to produce multiple
clusters as they generate coincident clusters even when they have been initialized with the
final prototypes of FCM. Also, the values of DB, Dunn, and β index of RFCM are better
compared to other c-means algorithms.

2.5 Segmentation of Brain MR Images