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

1.自然形状线的特征提取如果要制作大范围的地图，同时采集大量的居民点地图并直接按比例缩小，得到的地图将不容易看到。因此，需要一些种类或简化的方法。特别是在对海岸线、湖岸线等复杂的自然形状线进行缩小时，需要对其进行简化，同时又要容易看到，本研究首次提出了一种利用分形分析将自然形状线划分为线性、复杂和人造三部分的方法。在此基础上，根据上述自然形状线的特点，提出了相应的缩小和简化方法。自然形状线缩小和简化方法的发展我们构建了模糊规则，用来评估通过缩小和简化复杂的自然形状线而获得的地图的“易见性”。蚂蚁…规则中较多的部分变量是(1)得到的地图的分维值，(2)缩比的值，(3)相邻两点之间的最大方向比。这些变量被分成三个部分，带有模糊的标签，如“小”、“中”和“大”。其结果部分变量为易见属性的评价值，并被划分为7个模糊标签。因此，我们提出了一种利用模糊评判规则来确定参数或简化算法(Opheim算法和Reuman-Witkam算法)的方法，即使对自然线形线条进行了缩小和简化，但对其易视性的评价几乎没有变化。因此，简化算法的参数将固定在标准值。对于“人造”的轮廓线，不再进行简化，最终可以在得到的地图直观的情况下，对自然轮廓线进行缩小和简化。较少

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