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Fuzzy Logic Applied to Biomedical Image Analysis
Abstract
Ever since Zadeh established the basis of fuzzy logic in his famous article Fuzzy Sets (Zadeh, 1965), an increasing number of research areas have used his technique to solve and model problems and apply it, mainly, to control systems. This proliferation is largely due to the good results in classifying the ambiguous information that is typical of complex systems. Success in this field has been so overwhelming that it can be found in many industrial developments of the last decade: control of the Sendai train (Yasunobu & Miyamoto, 1985), control of air-conditioning systems, washing machines, auto-focus in cameras, industrial robots, etc. (Shaw, 1998) Fuzzy logic has also been applied to computerized image analysis (Bezdek & Keller & Krishnapuram & Pal, 1999) because of its particular virtues: high noise insensitivity and the ability to easily handle multidimensional information (Sutton & Bezdek & Cahoon, 1999), features that are present in most digital images analyses. In fuzzy logic, the techniques that have been most often applied to image analysis have been fuzzy clustering algorithms, ever since Bezdek proposed them in the seventies (Bezdek, 1973). This technique has evolved continuously towards correcting the problems of the initial algorithms and obtaining a better classification: techniques for a better initialization of these algorithms, and algorithms that would allow the evaluation of the solution by means of validity functions. Also, the classification mechanism was improved by modifying the membership function of the algorithm, allowing it to present an adaptative behaviour; recently, kernel functions were applied to the calculation of memberships. (Zhong & Wei & Jian, 2003) At the present moment, applications of fuzzy logic are found in nearly all Computer Sciences fields, it constitutes one of the most promising branches of Artificial Intelligence both from a theoretic and commercial point of view. A proof of this evolution is the development of intelligent systems based on fuzzy logic. This article presents several fuzzy clustering algorithms applied to medical images analysis. We also include the results of a study that uses biomedical images to illustrate the mentioned concepts and techniques.
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