元分维曲线滑动窗口尺寸自动判定方法与应用

基于地图目标在空间形态上存在的内部差异性和邻近趋同性,在其分形分析中引入了元分维模型的思想。该模型是对传统分形分析的方法扩展,在其建立过程中滑动窗口决定着空间单元的局部影响范围,因此该窗口尺寸成为元分维模型构建的重要参数之一。在前期基于地图目标元分维模型的研究中,滑动窗口大小主要通过人为判断选取,没有考虑地图目标本身的形态结构特点,缺乏科学的定量化指标判定原则,因此存在随意性和执行效率低等问题。本文以地图线目标的元分维模型,即元分维曲线为主要研究对象,通过对其分维扩展的尺度分析,在倒置的Logistic模型函数拟合的基础上提出了一种自动确定滑动窗口尺寸的定量方法,并将该方法应用到对长江河道形态特征的分析研究中,验证了其可行性和合理性。

An Automatic Method to Determine the Size of Sliding Window for Meta Fractal Dimension Curve and Its Application

Based on the characteristics of the interior change and vicinity convergent,the Meta Fractal Dimension(MFD) model adopted sliding window technology is applied to the extended fractal dimension research for map objects.During the establishment of MFD,the sliding window determines the neighborhood scope to restrict the segment from map object and the degree of adjacent overlap,thus it is one of the important parameters for MFD.In the present research,however,it is chosen artificially,not from the morphological characteristics of the map object,for which caused randomly and unsatisfied operating efficiency.Considering the extended fractal characteristic with scaling variety,and based on its simulating function using inversion logistic model,this paper proposed a method to determine the size of gliding box automatically for building MFD of map line object,viz.Meta Fractal Dimension Curve.Several experiments done indicate that this method is easy to operate and has a relatively high calculation precision and a logical spatial analysis.