A study on evaluation of natural shape lines using fractal theory and fuzzy systems theory

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1. Feature extraction of natural shape linesIf we want to make a wide range map while gathering a large number of residential maps and scaling down them directly, the obtained map will not be easy to see. Therefore, some kinds or simplification methods are required. Especially, when complicated natural shape lines like the coast lines and the lake lines are scaled down, it is necessary to simplify them while at the same time they still must be easy to see.In this study, we first proposed a method to divide the natural shape lines into three parts with features such as "linear", "intricate" and "man-made" by using fractal analysis. Then we developed the scale-down and simplification methods according to natural shape line features mentioned above.2. Development of scale-down and simplification methods for natural shape linesWe constructed fuzzy rules which evaluate the "easy-to-see" property of the map obtained by scaling down and simplifying the "intricate" natural shape lines. The ant … More ecedent part variables of the rules are (1) fractal dimension value of the obtained map, (2) the value of reduced scale and (3) the maximum ratio of direction between two adjacent points. These variables are divided into three parts with fuzzy labels such as "small", "medium" and "large". The consequent part variable is the evaluation value of the "easy-to-see" property and is divided seven fuzzy labels. Hence, we developed the method to determine the parameters or the simplification algorithms (Opheim algorithm and Reuman-Witkam algorithm) by using the fuzzy evaluation rules.Even though the "linear" natural shape lines are scaled down and simplified, the evaluation of the "easy-to-see" property scarcely changes. Therefore, the parameters of the simplification algorithms are to be fixed at the standard values. To the "man-made" shape lines the simplification is not to be applied.Finally, we could develop the scale-down and simplification method for the natural shape lines while the obtained map is easy to see. Less