A Model for Quantitatively Calculating and Qualitatively Describing Direction Relationships Between Object Groups
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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:ObjectivesThe 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.
MethodsTo 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.
ResultsExperimental 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.
ConclusionsThe 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.
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http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20230320
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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 1 24 NE 0.78 6-1 204 SW 0.90 2 43 NE 0.51 6-2-1 252 S 0.57 3-1-1 34 NE 0.81 6-2-2 298 SE 0.62 3-1-2 352 E 0.55 7 294 SE 1.01 3-2 69 N 0.80 8-1 335 SE 1.39 4-1 156 NW 1.35 8-2 295 SE 1.49 4-2 111 N 1.19 9 347 E 0.87 5 249 S 0.52 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 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 N 1.99 S 1.09 NE 2.10 SW 0.90 E 1.42 NW 1.35 SE 4.51 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) 83 2 15 图10(b) 83 2 15 图10(c) 14 3 83 图10(d) 86 3 11 图10(e) 86 3 11 图10(f) 8 6 86 图10(g) 79 1 20 图10(h) 79 1 20 图10(i) 19 2 79 图11(a) 90 1 9 图11(b) 8 2 90 图11(c) 90 1 9 图11(d) 63 2 35 图11(e) 9 2 89 图11(f) 26 2 72 图11(g) 72 3 25 图11(h) 11 3 86 图11(i) 9 8 83 图12(a) 70 3 27 图12(b) 5 3 92 图12(c) 22 3 75 图12(d) 59 9 32 图12(e) 6 16 78 图12(f) 19 16 65 图12(g) 53 8 39 图12(h) 22 8 70 图12(i) 17 8 75 表 5 空间认知实验统计结果
Table 5 Statistical Results of Spatial Cognitive Test
模型 n 的95%置信区间 本文模型 9 72.78 12.02 [64.93,80.63] 方向Voronoi图模型 9 34.33 34.53 [11.77,56.89] 方向关系矩阵模型 9 24.89 23.66 [9.43,40.35] -
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