ABSTRACT
Image understanding is a process representing the complex interaction between a computer vision system and one or more digital images. According to (Tsotos, 1987), given a goal or a reason for looking at a particular scene, image understanding system should produce descriptions of both the images and the world scenes that the images represent. In terms of medical imaging, image undertanding should lead to a successful interpretation of the images and ideally contribute to an accurate diagnosis. Recent research aimed at machine learning methods to develop strategies with the use of ad-hoc knowledge about the analysed images and their context. Among them, one of the most promising approaches to explain human image understanding is rule-based symbolic processing. Here, rules are extracted through learning from examples or directly from expert knowledge. Many image understanding applications involve tasks such as image segmentation and edge detection that extract significant information from an image which then often represents the input to a
may 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 membership 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 classification 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 between 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 focussed 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. Therefore, 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 generation. The book chapter provides an overview on the current trends in fuzzy-rule based systems with a special emphasis on medical image understanding. Original methods developed 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 laryngoscopy. Experimental results confirm the efficacy of the presented fuzzy rule base approaches.
