A Fractal Description and Multi-scale Expression Method of Fourier Information Metrics

XIAO Tianyuan; LIU Pengcheng; AI Tinghua; LI Jingzhong

doi:10.13203/j.whugis20180336

Volume 45 Issue 1

Jan. 2020

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Geomatics and Information Science of Wuhan University > 2020 > 45(1): 119-125. > DOI: 10.13203/j.whugis20180336

XIAO Tianyuan, LIU Pengcheng, AI Tinghua, LI Jingzhong. A Fractal Description and Multi-scale Expression Method of Fourier Information Metrics[J]. Geomatics and Information Science of Wuhan University, 2020, 45(1): 119-125. DOI: 10.13203/j.whugis20180336

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A Fractal Description and Multi-scale Expression Method of Fourier Information Metrics

1.
Key Laboratory for Geographical Process Analysis & Simulation, Central China Normal University, Wuhan 430079, China
2.
School of Urban and Environmental Science, Central China Normal University, Wuhan 430079, China
3.
School of Resource and Environmental Sciences, Wuhan University, Wuhan 430079, China

Funds:

The National Natural Science Foundation of China 41531180

The National Natural Science Foundation of China 41671448

the National Key Research and Development Program of China 2017YFB0503500

Independent Research Project of the Central Universities CCNU18CG010

Digital Mapping and Land Information Application Engineering Open Research Fund Project of Key Laboratory of the Ministry of Natural Resources ZRZYBWD201909

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Author Bio:
XIAO Tianyuan, master, specializes in map generalization and multi-scale representation. E-mail: 963664361@qq.com
Corresponding author:
LIU Pengcheng, PhD, associate professor. E-mail: liupc@mail.ccnu.edu.cn
Received Date: December 05, 2018
Published Date: January 04, 2020

Graphical Abstract

Abstract

Abstract

This paper presents a new method for describing the complexity of geographic line elements. Firstly, the Fourier series is used to transform the geographic line elements from the spatial domain to the frequency domain for analysis. Fourier expansions are performed on different geographic line elements to obtain different Fourier descriptors, then we use the method of setting the area threshold to control the deviation of the geographic elements before and after the Fourier expansion to a certain extent, so that the curve reduced by the Fourier descriptor can replace the original geographic line elements. Secondly, based on Shannon's information entropy theory, the amount of information of the fitted curve after Fourier expansion is calculated. Then, by combining the frequency domain with the fractal theory, the data of the amount of information is further processed based on the Head-tail data break and Koch's Two-Eighth Law, and the concept of the distribution index p is proposed. Finally, the distribution index and the square root model are combined, and the approximate expression of the distribution index of the map at different scales is obtained by the least squares method. We select the contour data of a region to conduct experiments, and experiment results show that the distribution index has a good expression effect on the complexity of geographic line elements at different scales, and can be applied to multi-scale expression of line elements.
- geographic line elements,
- Fourier series,
- amount of information,
- fractal,
- multi-scale representation

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References (18)

References

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A Fractal Description and Multi-scale Expression Method of Fourier Information Metrics

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