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In examining the history of computer application, we discover that early computer systems were developed primarily for applications related to scientific computation, as in weather prediction, aerospace applications, and nuclear physics applications. At this stage, the computer system served as a big calculator to perform, in the main, manipulation of numbers. Then it was found that computer systems could also be used for business applications, information storage and retrieval, word processing, and report generation. The history of computer application is summarized in Table I. The complexity of pictures makes picture processing much more difficult than number and alphanumerical processing. Therefore, new techniques, new algorithms, and above all, new pictorial knowledge, [1] are needed to overcome the limitatins of existing computer systems. New frontiers in designing computer systems are the ways to handle the representation,[2,3] classification, manipulation, processing, storage, and retrieval of pictures. Especially, the ways to deal with similarity measures and the meaning of the word "approximate" and the phrase "approximate reasoning" are an important and an indispensable part of an intelligent pictorial information system. [4,5] The main objective of this paper is to investigate the mathematical foundation for the effective organization and efficient retrieval of pictures in similarity-directed pictorial databases, [6] based on similarity retrieval techniques [7] and fuzzy languages [8]. The main advantage of this approach is that similar pictures are stored logically close to each other by using quantitative similarity measures. Thus, for answering queries, the amount of picture data needed to be searched can be reduced and the retrieval time can be improved. In addition, in a pictorial database, very often it is desired to find pictures (or feature vectors, histograms, etc.) that are most similar to or most dissimilar [9] to a test picture (or feature vector). Using similarity measures, one can not only store similar pictures logically or physically close to each other in order to improve retrieval or updating efficiency, one can also use such similarity measures to answer fuzzy queries involving nonexact retrieval conditions. In this paper, similarity directed pictorial databases involving geometric figures, chromosome images, [10] leukocyte images, cardiomyopathy images, and satellite images [11] are presented as illustrative examples.
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