摘要
相较于传统删减顶点的线要素综合方法,基于傅里叶变换的线要素综合更能保留曲线的全局特征,但现有的傅里叶综合方法无法自动减少和控制点数,更多适用于曲线的平滑及多尺度表达。因此本文提出一种利用离散傅里叶变换进行线要素综合的方法。对曲线进行离散傅里叶变换,获得有限项傅里叶描述子;根据期望的压缩比对傅里叶描述子进行截断;根据截断后的描述子项进行离散傅里叶逆变换获得化简曲线。本文提出的这种傅里叶方法能够减少化简后曲线顶点数,适用于地图综合领域。本文通过四组实验验证了算法的可行性,展示其如下优点:(1)能够在相应尺度上对线性地物进行平滑、渐进的化简和表达(2)在现有傅里叶变换法的基础上能够保留曲线原顶点;(3)以顶点数作为综合过程参数,能够自动减少曲线顶点数;(4)相较于传统节点压缩方法,更注重整体形态的化简,在综合过程中能更好地保留曲线的整体特征;(5)在转换尺度较大的综合过程中,相较于传统节点压缩方法所保留的几何精度更高。
Compared with traditional polyline generalization methods via deleting vertices, the line generalization based on Fourier transform can better retain the global characteristics of the polyline. However,the existing Fourier-based methods are more suitable for curve smoothing and multi-scale representation, and are not able to automatically control the targeting number of points on polylines. Therefore, a polyline generalization method using discrete Fourier transform is proposed in this paper. The discrete Fourier transform is first performed on the polyline to obtain a Fourier descriptor with finite terms. The Fourier descriptor then is truncated according to the desired compression ratio. Finally, the simplified polyline is obtained by inverse discrete Fourier transform based on the truncated descriptor. In this paper, a Fourier method which can reduce the number of vertex points of the simplified curve is proposed, which can be applied to the field of map generalization. In this paper, the feasibility of the proposed algorithm is verified by four groups of experiments,and its advantages are shown as follows:(1) it can simplify and express linear features smoothly and gradually on the corresponding scale;(2) it can retain the original vertices of the curve on the basis of the existing Fourier transform method;(3) the number of vertex points is taken as the generalization parameter, and the number of vertex points of the curve can be automatically reduced;(4) compared with the traditional node compression method, it pays more attention to the simplification of the overall shape, and can better retain the overall characteristics of the curve in generalization;(5) in the generalization process with large conversion scale, the geometric accuracy retained in this study is higher than that of the traditional node compression method.
作者
何山
闫浩文
李蓬勃
HE Shan;YAN Haowen;LI Pengbo(School of Surveying and Geographic Information System,Lanzhou Jiaotong University,Lanzhou 730070,China;National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring,Lanzhou 730070,China;Gansu Provincial Engineering Laboratory for National Geographic State Monitoring,Lanzhou 730070,China)
出处
《地球信息科学学报》
CSCD
北大核心
2022年第12期2309-2321,共13页
Journal of Geo-information Science
基金
国家自然科学基金项目(41930101)
青年科学基金项目(41801395)。
关键词
离散傅里叶变换
线要素
地图综合
频率域
节点压缩
曲线化简
多尺度表达
小波变换
Discrete Fourier Transform(DFT)
polyline
cartographic generalization
frequency domain
node compression
curve simplification
multiscale representation
wavelet transform
