一种地图点群空间分布特征的局部分维分析方法

以分数维为分析指标的分形几何理论,为地图点群目标的空间复杂性分析提供了一种定量方法。但是研究表明,地图点群目标的分形性质往往表现出局部的非均匀特性,因此主要以研究对象整体分维估值为主的分维分析方法难以描述这种变化。本文在分维扩展方法的基础上,提出了一种基于滑动窗口的局部分维分析方法--元分维模型,并通过实践证明该方法可以有效地揭示地图点群空间分布特征的差异,从而为地图点群目标的空间分布特征分析提供了一个新的思路。

A Method of Local Fractal Dimension Analysis on Spatial Distribution Characteristics of Cartographic Point Group

As a main factor of fractal geometry,fractal dimension is used to quantificationally analyze the spatial distribution characteristics of the cartographic point group.But it is proved in practice that the cartographic point group usually shows nonuniformity of local fractal characteristics.This paper puts forward a Meta Fractal Dimension Model(abbreviated as MFDM) based on the extended analysis that can be applied to describe the change of local shape of map objects.The MFDM,which makes the fractal method an expansion,shows good analytical ability for spatial distribution characteristics of the cartographic point group,thus is more effective than the traditional fractal methods: on the one hand,the experimental results reveal the spatial distribution characteristics and their change status of these internal points in a certain scope that is called neighboring radium or side length r;on the other hand,the distribution histogram and profile curve of MFD,which in the meantime thinks about macro-scope and micro-scope analysis,can further detect the internal spatial distribution pattern of these original points.So the method of the MFDM can be adopted to analyze point groups on the medium-or small-scale maps and to discover the distribution disciplines of the geographical objects.But there are also some aspects to be noticeable in applying this method: the original point group must reach a certain number;there must be a reasonable fractal scale and a non-scaling interval;and the size of the sliding window should rely on the research content and purpose.