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. 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. 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:

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