Image Processing Reference
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pattern classification procedure. A set of rules may be used for image feature extraction
(e.g., in image segmentation) as well as for classifying them (e.g., for image recognition)
into the set of relevant image descriptors.
While in the past fuzzy rule-based systems have been applied mainly to control prob-
lems (Sugeno, 1985; Lee, 1990), recently they have been also used in pattern recognition
tasks (Nozaki, Ishibuchi, and Tanaka, 1996; Klir and Yuan, 1995; Grabisch, 1996; Grabisch
and Nicolas, 1994; Ishibuchi and Nakashima, 1999b,a; Grabisch and Dispot, 1992; Ishibuchi,
Nozaki, and Tanaka, 1992; Tarnawski and Cichosz, 2008; Tarnawski, Fraczek, Krecicki, and
Jelen, 2008b; Tarnawski, Fraczek, Jelen, Krecicki, and Zalesska-Krecicka, 2008a). A fuzzy
rule base consists of a set of fuzzy If-Then rules which together with an inference engine,
a fuzzifier, and a defuzzifier, form a fuzzy rule-based system. The role of the fuzzifier is to
map inputs related to crisp image features to fuzzy subsets by applying appropriate mem-
bership functions. In rule-based systems, inference (reasoning) is understood as the final
unique assignment of an object under consideration to a specified class. For fuzzy classifi-
cation systems, this assessment corresponds to a defuzzification process, also called fuzzy
reasoning, which chooses the class with the highest membership degree. One might ask the
question: what are the advantages of fuzzy rules over crisp rules for image understanding
problems? In image understanding tasks the antecedents and the consequents of an If-Then
rule are often represented in the form of fuzzy rules. The reason for this is that in real
images it is usual to have noisy or imprecise information. Image objects attributes such
as “rather dark” , “well contrasted”, “highly patterned” or the spatial relationships be-
tween image objects described as “close to”, defy a precise definition, and are hence better
modelled by fuzzy sets.
In this chapter we show how fuzzy rule-based systems can be successfully employed in
medical image undertanding tasks. We first provide an introductory section which covers
the fundamentals of fuzzy rule-based classification systems. The following sections are fo-
cussed on several approaches of problem-oriented methodologies for fuzzy rules generation.
We group them into two parts where the first is concerned with weighted fuzzy rule-based
system which allow additional adjustment through weighted input patterns, and the second
comprises fuzzy clustering and learning by examples. In the first strategy the antecedent
part of the rules is initialized manually, while for the second membership functions reflecting
the input training data distribution are obtained by fuzzy clustering. In both approaches
the consequent part is determined from the given training patterns, but in two completely
different ways. The approach based on weighted fuzzy rule-base systems requires the full
training data set, i.e. input and output of every element in the training set. Therefore, this
approach represents a supervised generation of fuzzy rule bases. In the second approach,
we perform automatic labelling of input patterns with class labels. Also, in some cases we
require the system to propose the optimal number of classes of input feature space. There-
fore, this leads to an unsupervised generation of rules. Both methods are task-dependent
and the choice one of these depends on the form of the training data used for rule gener-
ation. The topic chapter provides an overview on the current trends in fuzzy-rule based
systems with a special emphasis on medical image understanding. Original methods de-
veloped by the authors serve as examples related to computer aided diagnosis in medical
imaging, in particular breast cancer diagnosis from digitised images of fine needle aspirates,
and from thermograms, and for diagnosis of precancerous and cancerous lesions by contact
Experimental results confirm the e cacy of the presented fuzzy rule base
Fundamentals of fuzzy rule-based classification system
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