基于遥感图像的城市形态分维计算网格法的实现

英文篇名：Realization of the Box-Counting Method for Calculating the Fractal Dimension of the Urban Form Based on the Remote Sensing Image
中文刊名：北京大学学报(自然科学版)
英文刊名：Acta Scientiarum Naturalium Universitatis Pekinensis
作者：葛美玲 ; 蔺启忠
英文作者：GE Meiling 1) ; 2) ; 4)LIN Qizhong 3)(1)Institute of Geographical Sciences and Natural Resources Research ; CAS ; Beijing ; 100101 ; 2)Graduate University of Chinese Academy of Scienses ; Beijing ; 100039 ; 3)Institute of Remote Sensing Applications ; CAS ; Beijing ; 100101)
中文关键词：分维数 ; 网格法 ; 城市形态 ; 北京 ; 遥感 ; GIS ; Matlab
英文关键词：fractal dimension ; box-counting method ; urban form ; Beijing ; remote sensing ; GIS ; Matlab
出版日期：2007-07-20
机构：中国科学院地理科学与资源研究所,中国科学院遥感应用研究所北京,100101中国科学院研究生院,北京,100039,北京,100101
年：2007
期：04
出版单位：北京大学学报(自然科学版)

摘要

在城市的分形研究中,常会计算其分维数,用分维数刻画城市的分形特征。作者以计算北京城市形态的分维数为例,介绍2种用网格法计算分维的方法:矢量法和栅格法。矢量法是在ArcView平台下通过叠加分析完成的,栅格法则是在Matlab环境下编程实现的。文章还将从实现过程、适用程度和计算结果3个方面对这2种方法作比较,得到的结论为矢量法和栅格法各有长短,各有适用场合。在具体的应用中,应根据实际情况选择合适的方法。
In the research of fractal cities,the fractal dimension is very important.It is used to describe the fractal character of the city.The authors design two ways to calculate the fractal dimension by the box-counting method through an example of Beijing,which are called the vector method and the grid method respectively.The former calculates the fractal dimension through an intersecting analysis in ArcView;and the latter is carried out by programming in Matlab.They are compared from three aspects:the calculating process,the limits in use and the results.As a result,they get the conclusion that there are merits and faults on both methods and they should be chosen to use properly in practical situation.

引文

[1]Mandelbrot BB著,陈守吉,凌复华译.大自然的分形几何学.上海:上海远东出版社,1998.
    [2]陈,陈凌.分形几何学.北京:地震出版社,1998.
    [3]Batty M,Longley P A.Fractal Cities:AGeometry of Form and Function.London:Academic Press,Harcourt Brace&Company,Publishers,1994.
    [4]陈彦光.分形城市与城市规划.规划研究,2005,29(2):33-51.
    [5]Benguigui L.When and where is a city fractal?.Environment and Planning B,2000,27:507-519.
    [6]De Keersmaecker M-L,Frankhauser P,Thomas I.Using fractal dimensions for characterizing intra-urban diversity:the example of Brussels.Geographical Analysis,2003,35(4):310-328.
    [7]冯健.杭州城市形态和土地利用结构的时空演化.地理学报,2003,58(3):343-353.
    [8]姜世国.基于北京遥感图像和GIS的分形城市形态研究:理论、方法和实践.北京:北京大学,2004.
    [9]姜世国,周一星.北京城市形态的分形集聚特征及其实践意义.地理研究,2006,25(1):204-212.
    [10]陈彦光,刘明华.城市结构和形态的分形模型与分维测算.信阳师范学院学报(自然科学版),1998,11(3):269-272.
    [11]White R,Engelen G.Cellular automata and fractal urban form:a cellular modeling approachtothe evolution of urban land-use patterns.Environment and Planning A,1993,25(8):1175-1199.
    [12]陈彦光.豫北地区城镇体系的分形研究.长春:东北师范大学地理系,1995.
    [13]刘继生,陈彦光.城镇体系空间结构的分形维数及其测算方法.地理研究,1999,18(2):171-178.
    [14]叶俊,陈秉钊.分形理论在城市研究中的应用.城市规划汇刊,2001(4):38-42.
    [15]Batty M.Cities as Fractals:Simulating Growth and Form//Crilly AJ,Earmshaw R A,Jones H.Fractals and Chaos.NewYork:Springer-Verlag,1991,43-69.
    [16]赵英时,等.遥感应用分析原理与方法.北京:科学出版社,2003.
    [17]彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法.中国矿业大学学报,2004,33(1):19-24.
    [18]罗宏宇,陈彦光.城市土地利用形态的分维刻画方法探讨.东北师大学报自然科学版,2002,34(4):107-113.