Applications of Fuzzy Rule-based Systems in Medical Image Understanding - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 121

The area and perimeter of the nuclei are expressed in image pixels. All the remaining
parameters, except for the nuclei density index, are shape parameters. All of them are scalar
quantities and take decimal values in the range 0-3. Variation analysis selected the four
best discriminative parameters for specified histology evaluations as: area, nuclei density
index, elongateness coe cient, and area to convex area ratio.
A training set, formed from half of the analysed CE images (about 10,000 cell nuclei), was
used in the classification phase based on cluster analysis. During this phase, three classes
of nuclei were found. The rule bank for nuclei classification was created using learning by
examples as described in Section 6.3.5. The second half of nuclei served as test set for the
system testing. For minimization of fuzzy rules we used Strategy 1 using soundness degree
defined by Eq. 6.34 for every generated rule. In this system, we define the following centroid
deffuzification formula to determine the output class for each input pattern:
C = P j=1

IF R j C R j
P j=1

(6.49)

IF R j

where N is the number of rules, C R j is the class number generated by rule R j (C R j =

µ R j (x (t) ) and µ R j (x (t) ) denotes the mem-
bership grade of t-th feature in the fuzzy regions that the j-th rule occupies.
Nuclei classification results using generated fuzzy rule base are shown in Fig. 6.9 in the
right column. The classification with clustering was linguistically described by patholo-
gist from abnormal (class 1) to normal nuclei (class 3). While classes 1 and 3 are easily
distinguishable, class 2 shall be considered as an intermediate nuclei category. Since it is
more similar to class 1 (pathological cases) than to class 3 (normal) it was considered as an
abnormal category. The number of nuclei belonging to class 1 on NE images was low (in
the range 0 to 3) and the area occupied by this type of nuclei was less than 1% of the total
nuclei area. Therefore, these nuclei were excluded from further analysis.
The last step was the verification of the hypothesis that amount of area occupied by
nuclei from every class is characteristic for each type of laryngeal lesion. The results of
variation analysis showed that the input parameters related to amount of area occupied
by every category of nuclei on analysed CE image originate from different distributions.
Mean values of area occupied by every category of nuclei in relation to specified histological
evaluations are presented in Fig. 6.6.
The most significant finding is a low number of nuclei of class 1 (most pathological) on
the NE images. This finding increases the diagnostic accuracy between malignant lesion
(SCC, SD) and precancerous or normal cases. Our results may also suggest that diagnosis
of carcinoma and severe dysplasia can definitely be made when the nuclei in class 1 (i.e.
highly pathological) cover more than 5% of the total nuclei area, and when nuclei in class
2 (i.e. moderately pathological) cover more that 40% of total nuclei area. Concluding, the
observations from our research have direct implications. Specifically, we have confirmed
that practical assessment of the nuclear morphometry for the diagnosis of laryngeal lesions
by contact endoscopy is possible and can be improved by fuzzy rule-based system. Another
advantage of contact endoscopy is that it can indicate appropriate tissue area for biopsy.
The method proposed herein may aid the clinician especially in the initial phase of the
learning curve as the valuable contribution.

= Π 4 t=1 0, 1, . . . , M ) and IF R j is defined as IF R j

6.5 Conclusions

In general, in order to define a fuzzy rule-based system for image understanding tasks after
pre-processing, feature selection and extraction the following steps have to be taken: