引用本文: 刘鹏程, 艾廷华, 毕旭. 傅立叶级数支持下的等高线多尺度表达模型[J]. 武汉大学学报 ( 信息科学版), 2013, 38(2): 221-224.
LIU Pengcheng, AI Tinghua, BI Xu. Multi-scale Representation Model for Contour Based on Fourier Series[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2): 221-224.
 Citation: LIU Pengcheng, AI Tinghua, BI Xu. Multi-scale Representation Model for Contour Based on Fourier Series[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2): 221-224.

## Multi-scale Representation Model for Contour Based on Fourier Series

• 摘要: 基于傅立叶级数提取等高线的特征向量,并提出了一种等高线多尺度表达的数据模型。对开等高线采用以首尾点连线作镜像处理的方式将其拓展成闭合曲线,进而将闭合曲线描述成弧长的周期函数,并将其表示为傅立叶级数。以一定阶次的傅立叶级数展开曲线与原始曲线形成的缝隙面积为依据,计算当前展开曲线的比例尺,建立傅立叶级数展开项数与等高线比例尺的对应关系。不同于传统的通过对曲线上点和弯曲的取舍来实现尺度变化的方法,通过控制傅立叶特征向量的长度来实现不同尺度的等高线表达。

Abstract: Automatically building of multi-scale representation model based on the same data source has been the focus in the field of map generalization.This paper extracts characteristic vector of contour based on Fourier series,and provides a model of multi-scale representation of contour.Open contours are mirrored into close contours according to the line including the start and end point,then the close contours are expressed into periodical functions about the length of arc and further Fourier series.Building the matching relationship between Fourier series expanding items and contour map scales based on the crack which formed due to the original curve and the current expanding curve.The model based on Fourier series provided in this paper is a method of reconstructing the curve through adjusting the length of characteristic vector instead of selecting the points and bent on the curve in the traditional methods and can be carried out.It is a progressive scale contour representation.

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