Rough-Fuzzy Clustering Algorithm for Segmentation of Brain MR Images - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 31

Section 2.5.2 for the data sets I-20497761, I-20497763, and I-20497777 (Fig. 2.4) . The

TABLE 2.7 Performance of Random and Discriminant Analysis Based Initialization

Method
DataSet Algorithms Initialization DBIndex DunnIndex Index Time(ms)

I-204 HCM Random 0.23 1.58 9.86 8297
97761 Proposed 0.15 2.64 12.44 4080
FCM Random 0.19 1.63 12.73 40943
Proposed 0.12 2.69 13.35 38625
RCM Random 0.19 1.66 10.90 9074
Proposed 0.14 2.79 12.13 6670
RFCM Random 0.15 2.07 11.89 19679
Proposed 0.11 2.98 13.57 16532
I-204 HCM Random 0.26 1.37 10.16 3287
97763 Proposed 0.16 2.03 13.18 3262
FCM Random 0.21 1.54 10.57 46157
Proposed 0.15 2.24 13.79 45966
RCM Random 0.21 1.60 10.84 10166
Proposed 0.14 2.39 13.80 6770
RFCM Random 0.17 1.89 11.49 19448
Proposed 0.10 2.38 14.27 15457
I-204 HCM Random 0.33 1.52 6.79 4322
97777

β

Proposed 0.16 2.38 8.94 3825
FCM Random 0.28 1.67 7.33 42284
Proposed 0.15 2.54 10.02 40827
RCM Random 0.27 1.71 7.47 8353
Proposed 0.13 2.79 9.89 7512
RFCM Random 0.19 1.98 8.13 18968
Proposed 0.11 2.83 11.04 16930

FIGURE 2.4 Examples of some brain MR images: I-20497761, I-20497763, I-20497777

discriminant analysis based initialization method is found to improve the performance in
terms of DB index, Dunn index, and β index as well as reduce the time requirement of all
c-means algorithms. It is also observed that HCM with this initialization method performs
similar to RFCM with random initialization, although it is expected that RFCM is superior
to HCM in partitioning the objects. While in random initialization, the c-means algorithms
get stuck in local optimums, the discriminant analysis based initialization method enables
the algorithms to converge to an optimum or near optimum solutions. In effect, the exe-
cution time required for different c-means algorithms is lesser in this scheme compared to
random initialization.

2.6.3 Comparative Performance Analysis

Table 2.8 compares the performance of different c-means algorithms on some brain MR
images with respect to DB, Dunn, and β index. The segmented versions of different c-