Image Processing Reference
1. Construction of the training data set.
2. Generation of suitable set of membership functions manually or from the training
3. Generation of fuzzy rules with learning technique from training data or from the
set of clusters obtained from a clustering algorithm.
4. Optimisation of fuzzy rule base to make the recognition system more practical
and to speed up the process of reasoning.
5. Deffuzification scheme to perform the crisp classification.
Two techniques for generation of fuzzy rules from numerical training data set were pre-
sented in this chapter. The first approach produces a rule base for a fuzzy classifier with
weighted training patterns. The weight of an input pattern can be viewed as the cost of
its misclassification. Fuzzy rules are then generated by considering the weights and the
compatibility of training patterns. In medical diagnosis of cancer, false negatives (diagnos-
ing people with cancer as healthy) could be penalized more than false positives (diagnosing
healthy individuals as having tumor). A labelled training set is required, i.e. input patterns
represented as the feature vector and outputs as the class label. The input membership
functions needed for the antecedent part of fuzzy rules are also defined in advance. Two ap-
plications related to computer aided diagnosis of breast cancer described that this weighted
fuzzy classifier is capable of providing a high classification accuracy. We also presented a
learning method that is based on incremental learning principles where for each generated
rules a special value called a grade of certainty is assigned. Proper adjustment of grades of
certainty has been shown to lead to improved classification performance and reduced overall
The second presented approach, based on clustering and learning by examples is “less
supervised” as we do not need the complete labelled training data set. Moreover, we can
ask the system for suggestions about the optimal number of classes, although it should be
noted that optimal does not always mean better classification. The clustering approach
generates an optimal feature space partition using a cluster validity measure. We used this
approach for computer-aided diagnosing in contact endoscopy imaging because of the huge
amount of input patterns often described in an intuitive way by the expert. Alas, the system
performance is very much dependent on the partition of the input and output domain and for
this reason the clustering results should be verified by the expert during the rule generation.
In this way the system is able to generate a set of membership functions which actually
reflects the real data distribution. Another problem usually present in image understanding
tasks is that a large number of fuzzy rules are generated due to a large number of training
samples. This can be partially solved by limiting the number of clusters with a clustering
procedure to receive a smaller set of fuzzy rules or by rule minimisation strategies.