基于反S数学模型的地图目标分形无标度区自动确定  

Automatic Determination of Fractal Non-scale Interval of Map Objects Based on Inverse ‘S’ Mathematical Model

作　　者：蔡金华[1] 龙毅[1] 毋河海[1] 陈丹[1] 

机构地区：[1]武汉大学资源与环境科学学院,武汉市珞喻路129号430079

出　　处：《武汉大学学报（信息科学版）》2004年第3期249-253,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目 ( 4 99710 68)

摘　　要：在观测尺度r的取值范围足够大时 ,地图目标的Richardson曲线往往呈反S形态。根据这一特点 ,采用反S数学模型———带导数的三次多项式模型拟合Richardson曲线 ,并根据该模型推导出分形无标度区间的计算公式 ,提出了一种自动确定地图目标分形无标度区的新方法 。When the range of observed scale is wide enough the Richardson curve of a map object always has a shape like an inverse ‘S’. Considering this fractal character of map objects, this paper proposes a new method for determining the fractal non-scale interval of a map object. This new method substitutes an inverse ‘S’ mathematical model-Cubic Polynomial Model with Derivative for the original Richardson curve of a map object, and then establishes the mathematical formula for determining the non-scale interval on the basis of this mathematical model. Finally we tested the validity of the new method by some typical experiments, and the results of the experiments show that this method can work well.

关 键 词：反S数学模型 分维 分形 地图目标 

分 类 号：P208[天文地球—地图制图学与地理信息工程] P283.7[天文地球—测绘科学与技术]