Near Sets: Theory and Applications

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Henry, Christopher James
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The focus of this research is on a tolerance space-based approach to image analysis and correspondence. The problem considered in this thesis is one of extracting perceptually relevant information from groups of objects based on their descriptions. Object descriptions are represented by feature vectors containing probe function values in a manner similar to feature extraction in pattern classification theory. The motivation behind this work is the synthesizing of human perception of nearness for improvement of image processing systems. In these systems, the desired output is similar to the output of a human performing the same task. Thus, it is important to have systems that accurately model human perception. Near set theory provides a framework for measuring the similarity of objects based on features that describe them in much the same way that humans perceive the similarity of objects. In this thesis, near set theory is presented and advanced, and work is presented toward a near set approach to performing content-based image retrieval. Furthermore, results are given based on these new techniques and future work is presented. The contributions of this thesis are: the introduction of a nearness measure to determine the degree that near sets resemble each other; a systematic approach to finding tolerance classes, together with proofs demonstrating that the proposed approach will find all tolerance classes on a set of objects; an approach to applying near set theory to images; the application of near set theory to the problem of content-based image retrieval; demonstration that near set theory is well suited to solving problems in which the outcome is similar to that of human perception; two other near set measures, one based on Hausdorff distance, the other based on Hamming distance.
description, near sets, tolerance near sets, tolerance space, perception, probe functions, feature values, nearness measure, content-based image retrieval (CBIR)