一种利用反S数学模型自动确定地图目标分形无标度区的新方法

摘要

在观测尺度r的取值范围足够大时,地图目标的Richardson曲线往往呈现反S形态.根据这一特点,采用反S数学模型--带导数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,提出一种自动确定地图目标分形无标度区的新方法,最后通过实验验证本方法的可行性和有效性.%If the scaling range of observing is large enough, the Richardson curve of a map object always has an inverse ogee shape. Considering this fractal character of map objects, this paper analyzed why this phenomenon appeared in detail, and proposed a new method for determining the fractal non-scaling 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. On the base of the mathematical model, a mathematical formula for determining the non-scaling interval was established. Finally some typical experiments validated the great efficiency of the new method.