分形分析中的无标度区确定问题

Determination of Fractal Scaleless Range

分形无标度区的求取是随机分形应用研究的前提和基础。介绍目前求解无标度区的几种方法并分析其优缺点 ,提出一种基于标准偏差的自适应方法。同时针对自然地形、遥感图像等特大尺度范围的情况 ,在该方法中引入遗传算法 ,应用遗传算法的快速寻优功能 ,加快标度区间的确定速度。将这些方法应用于地形分析中的分形参数提取实验 ,证明自适应方法能较为准确、可靠地提取分形参数 ;而加入遗传算法的改进方法 ,大大地缩短了无标度区间的搜索时间 。

After analyzing the advantage and disadvantage of these methods for fractal terrain analyses, the author proposes a more steady, reliable adaptive method to auto determine scaleless range.This method concentrates attention on obtaining the most wide fractal scaleless range in the condition of passing linear testing. Meanwhile, this method also concerns about the accuracy of fractal parameters and the detection of gross error. The procedure of this method is described in this paper later. In order to test this method's effect and efficiency, digital fractal terrain analyses using different methods are executed on some of typical landscape in China. The results of experiment are compared in detail. It has shown that the adaptive method can determine the scaleless range with higher reliability and higher accuracy. Moreover, in the case of that other methods can't determine scaleless range correctly, the method proposed in this paper can also obtain the scaless range correctly. Concerning about the problem of large scale fractal objects, such as remote sensing image, genetic algorithm is introduced into this method. The encoding mechanism, fitness function, genetic operator and control parameters of genetic algorithm in this method are discussed in detail. Experiments of fractal scaleless range determining using adaptive method with and without genetic algorithms show that adaptive method with genetic algorithms can reduce greatly the amounts of calculation.