河系几何相似性的层次度量方法

doi:10.12082/dqxxkx.2021.210279

地球信息科学学报 ›› 2021, Vol. 23 ›› Issue (12): 2139-2150.doi: 10.12082/dqxxkx.2021.210279

• 地球信息科学理论与方法 • 上一篇下一篇

河系几何相似性的层次度量方法

杨飞¹^,²^,³(), 王中辉¹^,²^,³^,^*()

1.兰州交通大学测绘与地理信息学院,兰州 730070
2.地理国情监测技术应用国家地方联合工程研究中心,兰州 730070
3.甘肃省地理国情监测工程实验室,兰州 730070

收稿日期:2021-05-19 修回日期:2021-06-17 出版日期:2021-12-25 发布日期:2022-02-25
通讯作者: *王中辉（1978— ）,男,甘肃古浪人,副教授,主要从事地图综合、空间关系研究。E-mail: 1449041349@qq.com
作者简介:杨飞（1995— ）,男,安徽合肥人,硕士生,主要研究方向为空间相似、地图综合。E-mail: 1774947511@qq.com
基金资助:
国家自然科学基金项目(41930101);国家自然科学基金项目(41861060);国家自然科学基金项目(41561090);兰州交通大学优秀平台(201806);中央引导地方科技发展资金项目

River Systems Geometric Similarity Measurement Method under Hierarchical Analysis

YANG Fei¹^,²^,³(), WANG Zhonghui¹^,²^,³^,^*()

1. Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China
2. National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring, Lanzhou 730070, China
3. Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China

Received:2021-05-19 Revised:2021-06-17 Online:2021-12-25 Published:2022-02-25
Supported by:
National Natural Science Foundation of China(41930101);National Natural Science Foundation of China(41861060);National Natural Science Foundation of China(41561090);Lanzhou Jiaotong University Excellent Platform(201806);Local Science and Technology Development Fund Projects under the Guidance of Central Government

摘要/Abstract

摘要：

已有的线群目标几何相似性度量方法主要基于数理统计的思想,通过统计整体变化信息计算几何相似性,缺少对局域特征的表达,并不适用于具有高度分形特征的河系。为此,本文将河系几何特征划分为3层次的信息特征：单条河流的形状特征、局部区域的结构特征、全局范围的分布特征。首先,结合角链码法与Hausdorff距离计算单条河流的形状相似度;然后,根据 “二八定律”确定局部特征区域,通过坐标系转换计算M： N的河系局域结构相似度;最后综合整体描述子得到全局分布相似度,并在该基础上,构建差异指标进行河系多尺度相似性计算与综合质量评价。实验表明,该方法的计算结果优于均值指标法,能有效应用于制图综合的质量评价。

关键词: 层次分析, 河系几何特征, 几何相似性, Hausdorff距离, 夹角链码法, 二八定律, 分形维数, 制图综合质量评价

Abstract:

The existing line groups geometric similarity measurement methods are mainly based on mathematical statistics. Geometric similarity is calculated through the statistics of overall change information. These methods lack the expression of local features and they are not suitable for river systems with highly fractal features. River systems are the basic elements of maps, and they have obvious fractal features and complex structural features. When we calculate the geometric similarity of river systems, the difference of the overall characteristics before and after cartographic generalization should be included, and the change of the local characteristics should also be considered. To this end, this paper divides geometric characteristics of river system into three levels of information characteristics: The shape characteristics of a single river, the structural characteristics of local area, and the distribution characteristics of global scope. Firstly, Included Angle Chain and Hausdorff distance are combined to calculate the shape similarity of a single river. Then, the local characteristic regions are determined according to the "80/20 Principle". This method is extended to calculate the local structure similarity of M: N river system through coordinate conversion. Finally, the overall feature descriptor is integrated to obtain the global distribution similarity. On this basis, a difference index is constructed to perform similarity calculation and quality evaluation of generalization. The results show that the calculation result of this method is better than the mean index method, and this method can be effectively applied to quality evaluation of generalization. The details are as follows. Firstly, the proposed method makes up for the shortcoming that the mean index method could only measure the overall change information. The changes of global distribution characteristics and local structure characteristics before and after cartographic generalization are expressed in the proposed method. Secondly, the method in this paper is more sensitive than the mean index method, and the calculation results of geometric similarity are more in line with human psychological cognition. Thirdly, the difference index P reflects the degree of generalization, the irrationality of deletion and simplification before and after generalization are detected.

Key words: hierarchical analysis, geometric features of river systems, geometric similarity, Hausdorff distance, Included Angle Chain, 80/20 Principle, Fractal dimension, quality evaluation of cartography generalization

杨飞, 王中辉. 河系几何相似性的层次度量方法[J]. 地球信息科学学报, 2021, 23(12): 2139-2150.DOI:10.12082/dqxxkx.2021.210279

YANG Fei, WANG Zhonghui. River Systems Geometric Similarity Measurement Method under Hierarchical Analysis[J]. Journal of Geo-information Science, 2021, 23(12): 2139-2150.DOI:10.12082/dqxxkx.2021.210279

图/表 19

图1

图2

表1

误差 δ的可接受范围

比例尺	误差 $δ$ /m
1:5000	0.5
1:10 000	1
1:25 000	2.5
1:50 000	5
1:100 000	10
1:250 000	25
1:500 000	50
1:1 000 000	100

表1

图3

图4

图5

图6

图7

图8

表2

图9

图10

表3

表4

表5

图11

图12

图13

图14

参考文献 31

[1]	闫浩文, 褚衍东. 多尺度地图空间相似关系基本问题研究[J]. 地理与地理信息科学, 2009, 25(4):42-44,48.
	[ Yan H W, Chu Y D. On the fundamental issues of spatial similarity relations in multi-scale maps[J]. Geography and Geo-information Science, 2009, 25(4):42-44,48. ]
[2]	郭文月, 刘海砚, 孙群, 等. 顾及几何特征相似性的多源等高线匹配方法[J]. 测绘学报, 2019, 48(5):643-653.
	[ Guo W Y, Liu H Y, Sun Q, et al. A multisource contour matching method considering the similarity of geometric features[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(5):643-653. ]
[3]	唐炉亮, 李清泉, 杨必胜. 空间数据网络多分辨率传输的几何图形相似性度量[J]. 测绘学报, 2009, 38(4):336-340.
	[ Tang L L, Li Q Q, Yang B S. Shape similarity measuring for multi-resolution transmission of spatial datasets over the Internet[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(4):336-340. ]
[4]	周晓光, 汪红松, 吴志强. 引入二维交细分类型的地表覆盖矢量数据增量更新[J]. 测绘学报, 2017, 46(1):114-122.
	[ Zhou X G, Wang H S, Wu Z Q. An incremental updating method for land cover database using refined 2-dimensional intersection type[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(1):114-122.
[5]	安晓亚. 空间数据几何相似性度量理论方法与应用研究[D]. 郑州:信息工程大学, 2011.
	[ An X Y. Research on theory, methods and applications of geometry similarity measurement for spatial data[D]. Zhengzhou: Information Engineering University, 2011. ]
[6]	徐丰, 牛继强, 林昊, 等. 利用等距同构建立多尺度空间实体相似性度量模型[J]. 武汉大学学报·信息科学版, 2019, 44(9):1399-1406.
	[ Xu F, Niu J Q, Lin H, et al. Establishment of the similarity metric model of multi-scale spatial object using isometry[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9):1399-1406. ]
[7]	Chehreghan A, Ali Abbaspour R. An assessment of spatial similarity degree between polylines on multi-scale, multi-source maps[J]. Geocarto International, 2017, 32(5):471-487. doi: 10.1080/10106049.2016.1155659
[8]	安晓亚, 孙群, 肖强, 等. 一种形状多级描述方法及在多尺度空间数据几何相似性度量中的应用[J]. 测绘学报, 2011, 40(4):495-501,508.
	[ An X Y, Sun Q, Xiao Q A, et al. A shape multilevel description method and application in measuring geometry similarity of multi-scale spatial data[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(4):495-501,508. ]
[9]	孙金礼, 陈杰, 邓敏. 线状空间数据传输的几何相似性度量算法与实验分析[J]. 地球信息科学学报, 2011, 13(5):701-706. doi: 10.3724/SP.J.1047.2011.00701
	[ Sun J L, Chen J E, Deng M. The algorithms of geometry similarity measurement and experimental analysis for linear spatial data transmission[J]. Journal of Geo-information Science, 2011, 13(5):701-706. ]
[10]	程绵绵, 孙群, 李少梅, 等. 多尺度点群广义Hausdorff距离及在相似性度量中的应用[J]. 武汉大学学报·信息科学版, 2019, 44(6):885-891.
	[ Cheng M M, Sun Q, Li S M, et al. Generalized Hausdorff distance of multi-scale point group and its application in similarity measurement[J]. Geomatics and Information Science of Wuhan University, 2019, 44(6):885-891. ]
[11]	安晓亚, 刘平芝, 杨云, 等. 一种线状要素几何相似性度量方法及其应用[J]. 武汉大学学报·信息科学版, 2015, 40(9):1225-1229.
	[ An X Y, Liu P Z, Yang Y, et al. A geometric similarity measurement method and applications to linear feature[J]. Geomatics and Information Science of Wuhan University, 2015, 40(9):1225-1229. ]
[12]	Alt H, Godau M. Computing the Fréchet distance between two polygonal curves[J]. International Journal of Computational Geometry & Applications, 1995, 5(1n02):75-91.
[13]	Xu Y Y, Xie Z, Chen Z L, et al. Shape similarity measurement model for holed polygons based on position graphs and Fourier descriptors[J]. International Journal of Geographical Information Science, 2017, 31(2):253-279. doi: 10.1080/13658816.2016.1192637
[14]	刘涛, 杜清运, 毛海辰. 空间线群目标相似度计算模型研究[J]. 武汉大学学报·信息科学版, 2012, 37(8):992-995.
	[ Liu T, Du Q Y, Mao H C. Spatial similarity assessment model and its application in line groups[J]. Geomatics and Information Science of Wuhan University, 2012, 37(8):992-995. ]
[15]	Yan H W, Shen Y Z, Li J. Approach to calculating spatial similarity degrees of the same river basin networks on multi-scale maps[J]. Geocarto International, 2016, 31(7):765-782. doi: 10.1080/10106049.2015.1076063
[16]	Yi R S, Arredondo Á, Stansifer E, et al. Shapes of river networks[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2018, 474(2215):20180081. doi: 10.1098/rspa.2018.0081
[17]	艾廷华, 刘耀林, 黄亚锋. 河网汇水区域的层次化剖分与地图综合[J]. 测绘学报, 2007, 36(2):231-236,243.
	[ Ai T H, Liu Y L, Huang Y F. The hierarchical watershed partitioning and generalization of river network[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(2):231-236,243.
[18]	张青年. 逐层分解选取指标的河系简化方法[J]. 地理研究, 2007, 26(2):222-228.
	[ Zhang Q N. Drainage generalization by layered division of the number of retained rivers in river trees[J]. Geographical Research, 2007, 26(2):222-228. ]
[19]	赵宇, 陈雁秋. 曲线描述的一种方法:夹角链码[J]. 软件学报, 2004, 15(2):300-307.
	[ Zhao Y, Chen Y Q. Included angle chain: A method for curve representation[J]. Journal of Software, 2004, 15(2):300-307. ]
[20]	null. The 80/20 principle: The secret of achieving more with less[J]. Long Range Planning, 1997, 30(6):956.
[21]	Sarker S, Veremyev A, Boginski V, et al. Critical nodes in river networks[J]. Scientific Reports, 2019, 9:11178. doi: 10.1038/s41598-019-47292-4
[22]	窦明, 于璐, 毛豪林, 等. 基于分形理论的淮河水系形态结构特征分析[J]. 武汉大学学报(工学版), 2019, 52(4):303-310.
	[ Dou M, Yu L, Mao H L, et al. Analysis of characteristics of river system form structure in Huaihe River Basin based on fractal theory[J]. Engineering Journal of Wuhan University, 2019, 52(4):303-310. ]
[23]	Fac-Beneda J. Fractal structure of the Kashubian hydrographic system[J]. Journal of Hydrology, 2013, 488:48-54. doi: 10.1016/j.jhydrol.2013.02.033
[24]	Wang S W, Ji H, Li P, et al. Growth diffusion-limited aggregation for basin fractal river network evolution model[J]. AIP Advances, 2020, 10(7):075317. doi: 10.1063/5.0011624
[25]	郭忆, 毕硕本, 闫业超, 等. 拉林河流域水系分维研究[J]. 测绘科学, 2015, 40(4):63-66,140.
	[ Guo Y, Bi S B, Yan Y C, et al. Calculation of the fractal dimension in Lalin River based on GIS[J]. Science of Surveying and Mapping, 2015, 40(4):63-66,140. ]
[26]	高义, 苏奋振, 周成虎, 等. 基于分形的中国大陆海岸线尺度效应研究[J]. 地理学报, 2011, 66(3):331-339.
	[ Gao Y, Su F Z, Zhou C H, et al. Scale effects of China mainland coastline based on fractal theory[J]. Acta Geographica Sinica, 2011, 66(3):331-339. ]
[27]	赵彬彬, 邓敏, 刘慧敏, 等. 多尺度地图的水系面目标与线目标匹配方法与实验[J]. 地球信息科学学报, 2011, 13(3):361-366. doi: 10.3724/SP.J.1047.2011.00361
	[ Zhao B B, Deng M, Liu H M, et al. An approach to matching area objects and line objects of river system in multi-scale maps[J]. Journal of Geo-information Science, 2011, 13(3):361-366. ]
[28]	黄子叶, 王易初, 倪晋仁. 汉江流域河网分级特征研究[J]. 北京大学学报(自然科学版), 2021, 57(2):351-360.
	[ Huang Z Y, Wang Y C, Ni J R. Hierarchical characteristics of river network in Hanjiang basin[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2021, 57(2):351-360. ]
[29]	江岭, 高辰, 韩枭, 等. 面向多分辨率DEM的河网相似性测度与分析[J]. 地球信息科学学报, 2021, 23(4):576-583. doi: 10.12082/dqxxkx.2021.200234
	[ Jiang L, Gao C, Han X A, et al. Quantifying spatial similarities of dainage networks on multi-resolution DEMs[J]. Journal of Geo-information Science, 2021, 23(4):576-583. ]
[30]	Sparrow C, Mandelbrot B. The fractal geometry of nature[J]. Journal of the Royal Statistical Society Series A (General), 1984, 147(4):616 doi: 10.2307/2981858
[31]	郭文月, 刘海砚, 孙群, 等. 面向区域增量更新的等高线群混合相似性度量模型[J]. 地球信息科学学报, 2019, 21(2):147-156. doi: 10.12082/dqxxkx.2019.180298
	[ Guo W Y, Liu H Y, Sun Q, et al. A contour group mixed similarity measurement model for region incremental updating[J]. Journal of Geo-information Science, 2019, 21(2):147-156. ]

	分维数	河网发育系数	河频率	河网密度
分维数	1	2	3	4
河网发育系数	1/2	1	2	2.5
河频率	1/3	1/2	1	1.5
河网密度	1/4	1/2.5	1/1.5	1

问题编号	问题内容	候选答案
1	图9（b）与图9（a）的相似度更符合哪个范围	40%~100%
2	图9（c）与图9（a）的相似度更符合哪个范围	30%~90%
3	图9（d）与图9（a）的相似度更符合哪个范围	20%~80%
4	图9（e）与图9（a）的相似度更符合哪个范围	10%~70%
5	图9（f）与图9（a）的相似度更符合哪个范围	0%~60%

河系	分维数相似度	河网发育系数相似度	河频率相似度	河网密度相似度	全局分布特征相似度	局域结构特征相似度	SIM	P
a与b	0.812	0.786	0.573	0.628	0.743	0.916	0.778	0.189
a与c	0.642	0.489	0.410	0.389	0.528	0.782	0.579	0.325
a与d	0.524	0.252	0.278	0.248	0.361	0.695	0.428	0.481
a与e	0.336	0.201	0.188	0.127	0.240	0.651	0.322	0.631
a与f	0.102	0.126	0.064	0.072	0.097	0.606	0.199	0.840

河系	长度相似度	平均长度相似度	曲折度相似度	线群密度相似度	SIM
a与b	0.628	0.913	0.980	0.628	0.787
a与c	0.389	0.950	0.978	0.389	0.677
a与d	0.248	0.892	0.968	0.248	0.589
a与e	0.127	0.830	0.951	0.127	0.509
a与f	0.072	0.772	0.938	0.072	0.464

河系几何相似性的层次度量方法

River Systems Geometric Similarity Measurement Method under Hierarchical Analysis

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

图/表 19

参考文献 31

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	孙阳, 刘新, 苏亚聪, 徐爽, 纪兵, 张志杰. 基于夜间灯光数据估算安徽省县级尺度城镇化水平[J]. 地球信息科学学报, 2020, 22(9): 1837-1847.
[2]	谭人华, 王艳慧, 关鸿亮. 基于GIS与模糊层次分析法的景观视觉资源综合评价[J]. 地球信息科学学报, 2019, 21(5): 663-674.
[3]	郭文月, 刘海砚, 孙群, 余岸竹, 陈焕新. 面向区域增量更新的等高线群混合相似性度量模型[J]. 地球信息科学学报, 2019, 21(2): 147-156.
[4]	李想, 肖桂荣, 蔡圣准. 结合网络文本的模糊层次分析法评价水环境敏感性[J]. 地球信息科学学报, 2019, 21(12): 1832-1844.
[5]	张乾, 闫浩文, 张黎明, 何毅. 基于空间关系的海上应急救援力量调度模型[J]. 地球信息科学学报, 2018, 20(6): 772-780.
[6]	杨忍, 牟乃夏, 彭澎, 刘希亮, 张恒才, 陆锋. “海上丝绸之路”沿线重要港口竞争力评价[J]. 地球信息科学学报, 2018, 20(5): 623-631.
[7]	张乾, 辛晓洲, 张海龙, 李月, 李小军, 裔传祥. 基于遥感数据和多因子评价的中国地区建设光伏电站的适宜性分析[J]. 地球信息科学学报, 2018, 20(1): 119-127.
[8]	杨立娟, 徐涵秋, 唐菲, 付伟, 王美雅, 孙凤琴. 天津中心渔港岸线集约利用评价模型研究[J]. 地球信息科学学报, 2017, 19(3): 417-424.
[9]	廖颖, 王心源, 周俊明. 基于地理探测器的大熊猫生境适宜度评价模型及验证[J]. 地球信息科学学报, 2016, 18(6): 767-778.
[10]	段晓旗, 刘涛, 武丹. 基于层次分析法的多尺度点群目标相似度计算[J]. 地球信息科学学报, 2016, 18(10): 1312-1321.
[11]	冯桂香, 明冬萍. 分形定量选择遥感影像最佳空间分辨率的方法与实验[J]. 地球信息科学学报, 2015, 17(4): 478-485.
[12]	李晓萌, 马玥, 孙永华, 宫辉力, 李小. 基于格网的洪水灾害危险性评价分析——以巴基斯坦为例[J]. 地球信息科学学报, 2013, 15(2): 314-320.
[13]	黄丽, 周卫, 王芙蓉. 地理数据共享效应的评价方法与应用[J]. 地球信息科学学报, 2011, 13(5): 617-622.
[14]	孙金礼, 陈杰, 邓敏. 线状空间数据传输的几何相似性度量算法与实验分析[J]. 地球信息科学学报, 2011, 13(5): 701-706.
[15]	王亚欣, 鞠洪波, 张怀清, 江东, 庄大方. 东洞庭湖国家级自然保护区湿地资源评价[J]. 地球信息科学学报, 2011, 13(3): 323-331.