| Summary: | 博士 === 義守大學 === 資訊工程學系博士班 === 97 === It is known that a weighted order statistic filter (WOSF) generates a linearly separable Boolean function and 2 different WOSF may generate the same Boolean function. Therefore a natural question “how to characterize WOSF which correspond the same Boolean function” arises.
In this thesis, we induce the characterization of maximal margin classification of SVM to represent a class of WOSF. In this method, one merely utilizes a normal vector and bias to represent all WOS filters with same output but different weight vectors and threshold values. Also, we construct equivalent classes for WOSF based on the maximal margin classification of SVM. Two types of equivalent classes are proposed. The first one is called BF equivalent class. The parameters representing the hyperplane are adopted as the representative of the class, which is unique. The second class is the global equivalent class which is derived by additional sign change and permutation on the components of the BF class representatives. Therefore we can efficiently characterize all of the WOSF through only few representatives of equivalent classes and save computation cost when searching for various WOSF.
Besides, we search the weight vectors of order 2 to order 6 by the operation of computer, and collect the minimum weight vectors based on the criterion of WOSF with the same outputs. Also, we characterize three properties of global equivalent classes by the process of constructing equivalent classes. These properties can assist us to compute the numbers of global equivalent classes.
However, each element of global class corresponds to one group of outputs, these outputs can be obtained by the position shift of components of original outputs vectors, and not need to perform the additional mathematical computation or machine learning. Therefore, we propose three translated formulas to find these outputs. For each translated formula, we give explicative proof to prove the accuracy of translated formulas.
Finally, in this thesis, we introduce the elementary principle of digital image processing, and give some examples to illustrate the application of WOSF in digital image filtering.
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