Fourier-based multi-scale representation and progressive transmission of cartographic curves on the internet
Fourier-based multi-scale representation and progressive transmission of cartographic curves on the internet
复制标题
基于傅立叶的多尺度表示和地图曲线在互联网上的渐进传输
DOI：
10.1080/15230406.2015.1088799
复制
发表时间：
2016-11-01
影响因子：
2.5
通讯作者：
Ai, Tinghua
中科院分区：
文献类型：
--
作者：
Liu, Pengcheng;Li, Xingong;Ai, Tinghua
长期以来，从同一空间数据源自动生成多尺度表示一直是地图综合领域的研究热点。本文基于傅立叶变换技术，提出了一种在Internet上实现地图曲线渐进变换的连续、多尺度表示模型。在我们的方法中，所有的曲线，无论是封闭的或开放的，被描绘为周期函数，进一步表示为傅里叶级数。研究了不同类型曲线的傅里叶级数的收敛程度，并根据原始曲线与重构曲线之间的相似性推导了截断频率。利用信息论和地图学中的根式定律，建立了地图比例尺与傅立叶频率之间的关系。基于所提出的多尺度模型，我们还介绍了渐进传输方法的原理和实现。我们的方法进行评估，从地形图的轮廓。结果表明，该模型是一种有效的地图曲线多尺度表达方法。
Automatic generation of multi-scale representations from the same spatial data source has been the research focus in map generalization for a long time. Based on the Fourier technique, this paper proposes a continuous, multi-scale representation model for progressive transformation of cartographic curves on the Internet. In our method, all the curves, whether closed or open, are depicted as periodical functions which are further expressed as Fourier series. The convergence degrees of the Fourier series are explored for different kinds of curves, and truncating frequencies are derived based on the similarity between the original and reconstructed curves. Using information theory and the Radical Law in cartography, the relationship between map scales and Fourier frequencies is established. Based on the proposed multi-scale model, we also introduce the principles and implementation of a progressive transmission method. Our method is evaluated using the contours from a topographic map. The results show that our model is a valid approach to multi-scale representation of cartographic curves.