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

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.