目标组方向关系定量计算与定性描述模型

王中辉, 李馨涵

王中辉, 李馨涵. 目标组方向关系定量计算与定性描述模型[J]. 武汉大学学报 ( 信息科学版), 2024, 49(12): 2290-2300. DOI: 10.13203/j.whugis20230320
引用本文: 王中辉, 李馨涵. 目标组方向关系定量计算与定性描述模型[J]. 武汉大学学报 ( 信息科学版), 2024, 49(12): 2290-2300. DOI: 10.13203/j.whugis20230320
WANG Zhonghui, LI Xinhan. A Model for Quantitatively Calculating and Qualitatively Describing Direction Relationships Between Object Groups[J]. Geomatics and Information Science of Wuhan University, 2024, 49(12): 2290-2300. DOI: 10.13203/j.whugis20230320
Citation: WANG Zhonghui, LI Xinhan. A Model for Quantitatively Calculating and Qualitatively Describing Direction Relationships Between Object Groups[J]. Geomatics and Information Science of Wuhan University, 2024, 49(12): 2290-2300. DOI: 10.13203/j.whugis20230320

目标组方向关系定量计算与定性描述模型

基金项目: 

国家自然科学基金 41861060

国家自然科学基金 41561090

中央引导地方科技发展资金 YDZX20216200001803

兰州交通大学优秀平台 201806

详细信息
    作者简介:

    王中辉,博士,教授,主要从事空间关系、地图综合研究。1449041349@qq.com

A Model for Quantitatively Calculating and Qualitatively Describing Direction Relationships Between Object Groups

  • 摘要:

    目标组方向关系建模是空间关系理论研究的重要内容之一,但现有模型未能对目标组方向关系进行合理的分类,且忽略了目标组的分布形态和构成要素的分布密集度对方向关系的影响,导致方向关系判定出现偏差。提出一种目标组方向关系的定量计算与定性描述模型,首先,借助Delaunay三角剖分构建两目标组之间的邻近区域;其次,通过预处理邻近区域三角形,区分不同类型的目标组方向关系;然后,将目标组定量方向关系分解为邻近区域三角形的顶点和边之间的定量方向关系(即局部定量方向关系)进行计算;最后,将局部定量方向关系转换融合为目标组定性方向关系。实验结果表明,该模型具有较好的适用性和可行性,能够有效克服现有模型存在的缺陷,提高目标组方向关系判定的准确性。

    Abstract:
    Objectives 

    The modeling of direction relationships between object groups is one of the important research topics in the theory of spatial relationships. However, existing models fail to reasonably classify the direction relationships between object groups, and ignore the impacts of distribution shapes of object groups and distribution density of their sub-objects on direction relationships, making it difficult to accurately determine direction relationships.

    Methods 

    To solve the problem, this paper classified the direction relationships between object groups into three categories in the light of different visual cognitive outcomes of object groups; and it was found that the adjacent regions between object groups can reflect the impacts of distribution shapes of object groups and distribution density of their sub-objects on direction relationships. Based on this, a model for quantitatively calculating and qualitatively describing direction relationships between object groups was proposed. First, Delaunay triangulation is used to construct the adjacent region between object groups; then, different types of direction relationships are distinguished by preprocessing the triangles in the adjacent region; after that, the quantitative direction relationships between object groups are separated into the ones between the vertices and the edges of the triangles (i.e. the local quantitative direction relationships) for calculation. Finally, local quantitative direction relationships are transformed and integrated into the qualitative direction relationships between object groups.

    Results 

    Experimental results show that:(1) The proposed model can reasonably classify the direction relationships between object groups, and accurately distinguish and describe the direction relationships in some complex situations. (2) It can fully consider the impacts of distribution shapes of object groups and distribution density of their sub-objects on direction relationships, and effectively determine the direction relationships between different geometric types of object groups in map space.

    Conclusions 

    The proposed model has good applicability and feasibility, which can overcome the disadvantages of existing models, and improve the accuracy of determining the direction relationships between object groups.

  • http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20230320
  • 图  1   目标组方向关系的分类

    Figure  1.   Classification of the Direction Relationships Between Object Groups

    图  2   目标组的分布形态对方向关系的影响

    Figure  2.   Impact of Distribution Shape of Object Group on Direction Relationships

    图  3   目标组构成要素的分布密集度对方向关系的影响

    Figure  3.   Impact of Distribution Density of the Sub-objects of Object Group on Direction Relationships

    图  4   邻近区域的构建过程

    Figure  4.   Process for Constructing the Adjacent Region

    图  5   八方向系统

    Figure  5.   Eight-Direction System

    图  6   邻近区域三角形的预处理

    Figure  6.   Preprocess of Triangles in Adjacent Region

    图  7   目标组邻近区域三角形的分类

    Figure  7.   Classification of Triangles in Adjacent Region Between Object Groups

    图  8   三角形的顶点与边之间的定量方向关系计算

    Figure  8.   Calculation of Quantitative Direction Relationship Between the Vertex and Edge of Triangle

    图  9   目标组邻近区域三角形

    Figure  9.   Adjacent Region Triangles Between Object Groups

    图  10   整体与整体之间方向关系的判定

    Figure  10.   Determination of Direction Relationships Between Whole and Whole

    图  11   整体与部分之间方向关系的判定

    Figure  11.   Determination of Direction Relationships Between Whole and Parts

    图  12   部分与部分之间方向关系的判定

    Figure  12.   Determination of Direction Relationships Between Parts and Parts

    图  15   本文模型的地图数据实验

    Figure  15.   Map Data Experiments for the Proposed Model

    表  1   图9所示邻近区域三角形的顶点和边之间的定量方向关系及其权重

    Table  1   Quantitative Direction Relationship and Its Weight Between the Vertex and Edge of Adjacent Region Triangle Shown in Fig. 9

    三角形编号定量方向关系/(°)局部定性方向关系权重三角形编号定量方向关系/(°)局部定性方向关系权重
    124NE0.786-1204SW0.90
    243NE0.516-2-1252S0.57
    3-1-134NE0.816-2-2298SE0.62
    3-1-2352E0.557294SE1.01
    3-269N0.808-1335SE1.39
    4-1156NW1.358-2295SE1.49
    4-2111N1.199347E0.87
    5249S0.52
    下载: 导出CSV

    表  2   八方向系统中定量方向和主方向之间的映射关系

    Table  2   Mapping Relationships Between Quantitative Directions and Cardinal Directions in the Eight-Direction System

    定量方向区间/(°)主方向定量方向区间/(°)主方向
    (67.5, 112.5]N(247.5, 292.5]S
    (112.5, 157.5]NW(292.5, 337.5]SE
    (157.5, 202.5]W(337.5, 360]∪[0, 22.5]E
    (202.5, 247.5]SW(22.5, 67.5]NE
    下载: 导出CSV

    表  3   表1所示局部定性方向关系的融合结果

    Table  3   Fusion Results of the Local Qualitative DirectionRelationships Shown in Tab.1

    主方向权重主方向权重
    N1.99S1.09
    NE2.10SW0.90
    E1.42NW1.35
    SE4.51
    下载: 导出CSV

    表  4   空间认知实验调查表

    Table  4   Questionnaire for the Spatial Cognitive Test

    本文模型方向Voronoi图模型方向关系矩阵模型
    实验案例认可不确定不认可实验案例认可不确定不认可实验案例认可不确定不认可
    图10(a)83215图10(b)83215图10(c)14383
    图10(d)86311图10(e)86311图10(f)8686
    图10(g)79120图10(h)79120图10(i)19279
    图11(a)9019图11(b)8290图11(c)9019
    图11(d)63235图11(e)9289图11(f)26272
    图11(g)72325图11(h)11386图11(i)9883
    图12(a)70327图12(b)5392图12(c)22375
    图12(d)59932图12(e)61678图12(f)191665
    图12(g)53839图12(h)22870图12(i)17875
    下载: 导出CSV

    表  5   空间认知实验统计结果

    Table  5   Statistical Results of Spatial Cognitive Test

    模型nX¯σX¯的95%置信区间
    本文模型972.7812.02[64.93,80.63]
    方向Voronoi图模型934.3334.53[11.77,56.89]
    方向关系矩阵模型924.8923.66[9.43,40.35]
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-08-29
  • 网络出版日期:  2024-02-25
  • 刊出日期:  2024-12-04

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