The fuzzy rules to identify tissues followed by an ssFCM clustering were applied to 39 normal slices from 8 volunteers and 66 abnormal slices from 7 patients. These slices lie in a range from near the center of the ventricles in the axial plane, characterized by a distinct X-shaped csf area and a single symmetric region of white matter to slices near the top of the brain in the axial plane, where the ventricular area is completely absent. There were 6 normal slices and 4 slices with pathology used to develop the fuzzy rule structure. These 10 slices may be viewed as a set of training slices.
To approximate ground truth a set of supervised k nearest neighbor (kNN) segmentations were used [5]. These segmentations were created by multiple observers choosing training sets for each slice. Segmentations that resulted in visually good partitions of the data are used for comparison with our unsupervised approaches. The value k=7 was used.
| 1||c|| | 2c||Regular FCM | 2c||Hybrid System | ||
| Mean | Std. Dev. | Mean | Std. Dev. | |
| Classification Differences (33 normals) | 4080.3 | 1328.7 | 5076.9 | 1566.9 |
| Classification Differences (62 abnormals) | 2376.4 | 1144.7 | 2402.5 | 1327.2 |
| Execution Time (33 normals) | 23.1 | 7.2 | 4.8 | 2.0 |
| Execution Time (62 abnormals) | 21.4 | 9.8 | 3.7 | 1.3 |
| 1||c|| | 2c||Regular FCM | 2c||Hybrid System | ||
| Mean | Std. Dev. | Mean | Std. Dev. | |
| Classification Differences (6 normals) | 3986.5 | 846.5 | 3558.8 | 464.7 |
| Classification Differences (4 abnormals) | 2773.0 | 1039.1 | 2167.8 | 879.5 |
| Execution Time (6 normals) | 21.7 | 6.4 | 5.7 | 2.0 |
| Execution Time (4 abnormals) | 19.8 | 6.4 | 3.0 | 1.1 |
Tables I and II summarize the comparison between the hybrid system (fuzzy rules followed by ssFCM) and regular FCM vs. pseudo ground-truth (kNN) for normal and abnormal slices respectively. The time required is much less for the hybrid system. There are more classification differences from the kNN based ``ground truth'' for the hybrid system than FCM. To determine whether the differences were significant we applied a Wilcoxon's sum of ranks test [7]. The z values obtained are shown in Table III. A value z <= 1.64 indicates that there is a greater than 10% chance that the observed difference is likely to occur by chance and hence cannot be proven significant. So, the z values in Table III lead us to conclude there is no significant difference in the segmentation results.