Survey of Research on Representation and Reasoning Models of Spatial Directional Relations

doi:10.19678/j.issn.1000-3428.0064822

Abstract

Abstract:

As indispensable components of spatial relations, spatial directional relations are widely used in many fields such as urban intelligent traffic control, environmental resource detection, and disaster prevention and reduction. Spatial directional relations represent a significant and challenging issue in fields such as geographic information systems, spatial database, artificial intelligence, and pattern recognition.This study conducts a comprehensive analysis and comparison of existing spatial directional relationship expression and inference models.First, the research progress on current models for directional relations between objects in two-dimensional space are introduced in detail in terms of single and group target objects.In addition, the characteristics, advantages, and disadvantages of the current models for directional relations in three-dimensional space are analyzed from point to block.The study expounds the current research status of models that use uncertainty directional relations from the two aspects of extended models based on those that use precision objects for directional relations and models based on uncertainty set theory for uncertain objects. The study then discusses the advantages, drawbacks, and applicable fields for each type of model.Finally, the shortcomings of current research are explained, and the future research directions of spatial orientation relations are prospected in terms of automatic reasoning technology, joint representation of spatial relations, and group target objects.

Key words: directional relations, spatial relations, spatial database, group target object, uncertain set theory

摘要：

空间方向关系作为空间关系不可缺少的组成部分，广泛应用于城市智能交通管控、环境资源检测、防灾减灾等诸多任务，日益成为地理信息系统、空间数据库、人工智能、模式识别等领域研究的热点。综合分析和梳理现有空间方向关系表达与推理模型，针对二维空间对象，从单目标对象、群组目标对象等方面详细介绍目前二维空间方向关系表达与推理模型的研究进展，依据描述对象的不同进行分类，对每类模型的特性及适用范围进行定性分析比较。针对三维空间对象，从点到区域依次分析当前三维空间方向关系表达与推理模型的特点、优势和不足。针对不确定性对象，从确定性空间方向关系模型的扩展模型、基于不确定性集合理论模型2个方面阐述不确定性方向关系模型的研究现状，并对每类模型的优缺点、适用范围等进行分析总结。最后阐明当前工作存在的不足，并从自动推理技术、空间关系的联合表达以及群组目标对象等方面对空间方向关系的未来研究方向进行展望。

关键词: 方向关系, 空间关系, 空间数据库, 群组目标对象, 不确定性集合理论

Xingxing DONG, Jixun GAO, Xiaotong WANG, Song LI. Survey of Research on Representation and Reasoning Models of Spatial Directional Relations[J]. Computer Engineering, 2023, 49(9): 1-15.

董星星, 高继勋, 王晓桐, 李松. 空间方向关系表达与推理模型研究综述[J]. 计算机工程, 2023, 49(9): 1-15.

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Figures/Tables 15

Fig.1 Cone model

Fig.2 Error situations of the cone model

Fig.3 Projection-based direction model for point objects

Fig.4 Double cross model

Fig.5 Direction relation matrix model

Fig.6 Voronoi region and Voronoi diagram of point set target

Fig.7 Polygon and its Voronoi diagram

Fig.8 Voronoi diagram model

Fig.9 Convex hull model

Fig.10 3DR27 model

Fig.11 Legend of the direction relation between wide border regions

Fig.12 Direction relations between fuzzy objects

References 87

1	王淼, 王晓桐, 李松, 等. 二维基本矩形主方向关系的原关系推理. 西安交通大学学报, 2020, 54 (4): 133- 143. URL
	WANG M, WANG X T, LI S, et al. Reasoning with the original relations of the basic 2D rectangular cardinal direction relation. Journal of Xi'an Jiaotong University, 2020, 54 (4): 133- 143. URL
2	张韵, 彭建东, 王晶晶, 等. 基于地学信息图谱的江汉平原土地利用时空变化分析. 水土保持研究, 2020, 27 (4): 85- 92. URL
	ZHANG Y, PENG J D, WANG J J, et al. Analysis onspatial and temporal change of land use in Jianghan plain based on geo-information atlas. Research of Soil and Water Conservation, 2020, 27 (4): 85- 92. URL
3	王彦坤, 樊红, 王伟玺, 等. 地标空间方向的位置描述定位模型. 测绘科学, 2020, 45 (9): 18- 24. URL
	WANG Y K, FAN H, WANG W X, et al. A positioning localities model about landmark locality description based on spatial direction relationship. Science of Surveying and Mapping, 2020, 45 (9): 18- 24. URL
4	邓兴升, 黄小鹏. 线性参照系与大地坐标系的相互转换. 测绘工程, 2019, 28 (1): 9- 13. URL
	DENG X S, HUANG X P. Coordinates transforming between linear referencing system and geodetic system. Engineering of Surveying and Mapping, 2019, 28 (1): 9- 13. URL
5	LIANG H, LÜ K L, SUN Y S, et al. Semantic driven 3D scene construction based on spatial relationship and case-base[C]//Proceedings of the 7th International Conference on Virtual Reality. Washington D. C., USA: IEEE Press, 2021: 54-61.
6	KORSTANJE J. Coordinate systems and projections. Berkeley, USA: Apress, 2022: 27- 49.
7	RML A, CCA B, AEM B. Decisions, uncertainty and spatial information. Spatial Statistics, 2022, 50, 100619. doi: 10.1016/j.spasta.2022.100619
8	白梅, 苌仕涵, 王习特. 基于位置的路网Skyline查询处理研究. 计算机工程, 2022, 48 (1): 127- 134. URL
	BAI M, CHANG S H, WANG X T. Research on locatin based Skyline queries processing in road network. Computer Engineering, 2022, 48 (1): 127- 134. URL
9	郭亮亮, 靳燕, 杨博, 等. 一种基于两级缓存的高效时序数据库系统. 测试技术学报, 2022, 36 (2): 147- 152. doi: 10.3969/j.issn.1671-7449.2022.02.010
	GUO L L, JIN Y, YANG B, et al. A high-efficiency time series database system based on two-level cache. Journal of Test and Measurement Technology, 2022, 36 (2): 147- 152. doi: 10.3969/j.issn.1671-7449.2022.02.010
10	HAAR R. Computational models of spatial relations[D]. College Park, USA: University of Maryland, 1976.
11	FRANK A U. Qualitative spatial reasoning: cardinal directions as an example. International Journal of Geographical Information Systems, 1996, 10 (3): 269- 290. doi: 10.1080/02693799608902079
12	FREKSA C. Using orientation information for qualitative spatial reasoning[C]//Proceedings of International Conference on Theories and Methods of Spatial-Temporal Reasoning in Geographic Space. Berlin, Germany: Springer, 1992: 162-178.
13	ZIMMERMANN K. Enhancing qualitative spatial reasoning: combining orientation and distance[C]//Proceedings of International Conference on Spatial Information Theory. Berlin, Germany: Springer, 1993: 69-76.
14	丹晓飞. 一种面向点对象的空间方位关系的栅格表达[D]. 武汉: 湖北大学, 2021.
	DAN X F. A raster expression of spatial orientation relations for point object[D]. Wuhan: Hubei University, 2021. (in Chinese)
15	WANG J B, DUAN Z J, HAN X X, et al. Top/bottomk score estimation of spatial database based on bounded main memory. Journal of Tsinghua University(Natural Science Edition), 2022, 27 (2): 223- 234.
16	PAPADIAS D, SELLIS T. Qualitative representation of spatial knowledge in two-dimensional space. The VLDB Journal, 1994, 3 (4): 479- 516. doi: 10.1007/BF01231605
17	GOYAL R K. Similarity assessment for cardinal directions between extended spatial objects[D]. Orono, USA: The University of Maine, 2000.
18	GOYAL R K, EGENHOFER M J. Consistent queries over cardinal directions across different levels of detail[C]//Proceedings of the 11th International Workshop on Database and Expert Systems Applications. Washington D. C., USA: IEEE Press, 2002: 876-880.
19	GOYAL R K, EGENHOFER M J. Similarity of cardinal directions[C]//Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases. New York, USA: ACM Press, 2001: 36-58.
20	曹菡, 陈军, 杜道生. 空间目标方向关系的定性扩展描述. 测绘学报, 2001, 30 (2): 162- 167. doi: 10.3321/j.issn:1001-1595.2001.02.011
	CAO H, CHEN J, DU D S. Qualitative extended description of spatial target orientation relationship. Journal of Surveying and Mapping, 2001, 30 (2): 162- 167. doi: 10.3321/j.issn:1001-1595.2001.02.011
21	SKIADOPOULOS S, KOUBARAKIS M. Composing cardinal directions relations[C]//Proceedings of the 7th International Symposium on Spatial and Temporal Databases. Berlin, Germany: Springer, 2001: 299-317.
22	万静, 齐坡. 基于矩阵模型的方向关系表示与推理. 计算机工程与设计, 2014, 35 (10): 3590- 3650. doi: 10.16208/j.issn1000-7024.2014.10.001
	WAN J, QI P. Representation and reasoning of direction relationship based on matrix model. Computer Engineering and Design, 2014, 35 (10): 3590- 3650. doi: 10.16208/j.issn1000-7024.2014.10.001
23	张海军, 陈映辉. 基于类图像处理与向量化的大数据脚本攻击智能检测. 计算机工程, 2020, 46 (3): 129-137, 143. doi: 10.19678/j.issn.1000-3428.0053360
	ZHANG H J, CHEN Y H. Intelligent detection for bigdata scripting attack based on image processing inspired method and vectorization. Computer Engineering, 2020, 46 (3): 129-137, 143. doi: 10.19678/j.issn.1000-3428.0053360
24	YI H. A secure blockchain system for Internet of vehicles based on 6G-enabled network in box. Computer Communications, 2022, 186, 45- 50. doi: 10.1016/j.comcom.2022.01.007
25	LI J H. Research on fuzzy retrieval method of blockchain information based on B+Tree index structure. Berlin, Germany: Springer, 2022.
26	张啸剑, 徐雅鑫, 孟小峰. 基于本地化差分隐私的空间数据近似k-近邻查询. 计算机研究与发展, 2022, 59 (7): 1610- 1624. URL
	ZHANG X J, XU Y X, MENG X F. Approximate k-nearest neighbor queries of spatial data under local differential privacy. Journal of Computer Research and Development, 2022, 59 (7): 1610- 1624. URL
27	刘志丹, 林维鑫, 伍楷舜. 一种面向大规模空间文本数据的空间结构匹配算法. 计算机学报, 2022, 45 (6): 1261- 1275. URL
	LIU Z D, LIN W X, WU K S. A spatial structure matching algorithm for large spatial-textual datasets. Chinese Journal of Computers, 2022, 45 (6): 1261- 1275. URL
28	贾萍, 杨杰, 诸云强, 等. 地理空间模型输入数据自动匹配方法研究. 测绘与空间地理信息, 2022, 45 (5): 26- 31. URL
	JIA P, YANG J, ZHU Y Q, et al. Research on the automatic matching method of input data for geospatial models. Geomatics & Spatial Information Technology, 2022, 45 (5): 26- 31. URL
29	陈思宇, 张嘎. 基于空间分布的边坡位移测量数据质量评估方法研究. 岩土工程学报, 2022, 44 (5): 845- 850. URL
	CHEN S Y, ZHANG G. Quality evaluation for measured data of slope displacement based on its spatial distribution. Chinese Journal of Geotechnical Engineering, 2022, 44 (5): 845- 850. URL
30	康顺, 李佳田, 瞿珊珊. 凹边形地标参照的主方向关系推理方法. 武汉大学学报(信息科学版), 2018, 43 (1): 24- 30. URL
	KANG S, LI J T, QU S S. Reasoning method of principal direction relationship of concave landmark reference. Geomatics and Information Science of Wuhan University, 2018, 43 (1): 24- 30. URL
31	李朋朋, 刘纪平, 闫浩文, 等. 基于方向关系矩阵的空间方向相似性计算改进模型. 测绘科学技术学报, 2018, 35 (2): 216- 220. URL
	LI P P, LIU J P, YAN H W, et al. An improved model for calculating the similarity of spatial direction based on direction relation matrix. Journal of Geomatics Science and Technology, 2018, 35 (2): 216- 220. URL
32	MAITI S, SUBRAMANYAM R B V. Mining behavioural patterns from spatial data. Engineering Science and Technology, 2019, 22 (2): 618- 628.
33	宗琴, 刘艳霞, 张慧丽. 一种基于复合表达模型的方向相似性算法. 测绘科学技术学报, 2020, 37 (1): 90- 95. URL
	ZONG Q, LIU Y X, ZHANG H L. A directional similarity algorithm based on composite representation model. Journal of Geomatics Science and Technology, 2020, 37 (1): 90- 95. URL
34	王云阁, 郭黎, 李豪, 等. 一种基于改进TDD模型的空间场景相似性度量方法. 测绘科学技术学报, 2021, 38 (3): 309- 315. URL
	WANG Y G, GUO L, LI H, et al. A method for measuring space scene similarity based on improved TDD model. Journal of Geomatics Science and Technology, 2021, 38 (3): 309- 315. URL
35	龚希, 谢忠, 周林, 等. 空间方向相似性二元组模型度量方法. 测绘学报, 2021, 50 (12): 1705- 1716. URL
	GONG X, XIE Z, ZHOU L, et al. A two-tuple modelbased spatial direction similarity measurement method. Acta Geodaetica et Cartographica Sinica, 2021, 50 (12): 1705- 1716. URL
36	CHENG M M, SUN Q, KANG S L, et al. Direction relation matrix model considering the location characteristics. Journal of Physics Series, 2022, (1): 012060.
37	LI S, SONG S, HAO X H, et al. Directional nearest neighbor query method for specified geographical direction space based on Voronoi diagram. High Technology Letters, 2022, 28 (2): 122- 133.
38	YU B, CHEN N. Transit Voronoi diagrams in multimode public transport networks. Computers, Environment and Urban Systems, 2022, 96, 101849. doi: 10.1016/j.compenvurbsys.2022.101849
39	闫浩文, 郭仁忠. 基于Voronoi图的空间方向关系形式化描述. 武汉大学学报(信息科学版), 2003, 28 (4): 468-471, 479. URL
	YAN H W, GUO R Z. A formal description model of directional relationships based on Voronoi diagram. Geomatics and Information Science of Wuhan University, 2003, 28 (4): 468-471, 479. URL
40	FIGURSKA M, DAWIDOWICZ A, ZYSK E. Voronoi diagrams for senior-friendly cities. International Journal of Environmental Research and Public Health, 2022, 19 (12): 7447. doi: 10.3390/ijerph19127447
41	杨强. 基于Delaunay三角剖分的二维交互建模研究. 物探化探计算技术, 2021, 43 (2): 256- 260. URL
	YANG Q. Study of two-dimensional interactive modeling based on Delaunay triangulation. Computing Techniques for Geophysical and Geochemical Exploration, 2021, 43 (2): 256- 260. URL
42	禄小敏, 闫浩文, 王中辉. 群组目标空间方向关系研究进展. 地理信息世界, 2018, 25 (1): 28- 31. URL
	LU X M, YAN H W, WANG Z H. The modeling of spatial direction relations between object groups. Geomatics World, 2018, 25 (1): 28- 31. URL
43	李艳波. 自适应邻域形态学理论及其FPGA实现[D]. 西安: 西安电子科技大学, 2019.
	LI Y B. Adaptive neighborhood morphology theory and its FPGA implementation[D]. Xi'an: Xidian University, 2019. (in Chinese)
44	张立峰. 基于凸壳的点群目标空间方向关系研究. 甘肃联合大学学报(自然科学版), 2009, 23 (5): 39- 41. URL
	ZHANG L F. Research on directional relationships of grouped point object based on convex hull. Journal of Gansu Lianhe University (Natural Science Edition), 2009, 23 (5): 39- 41. URL
45	王中辉, 闫浩文. 基于Voronoi方向图模型的群组目标空间方向关系计算. 武汉大学学报(信息科学版), 2013, 38 (5): 584- 588. URL
	WANG Z H, YAN H W. Computation of direction relations between object groups based on direction Voronoi diagram model. Geomatics and Information Science of Wuhan University, 2013, 38 (5): 584- 588. URL
46	禄小敏, 闫浩文, 王中辉. 群组目标空间方向关系建模. 地球信息科学学报, 2018, 20 (6): 721- 729. URL
	LU X M, YAN H W, WANG Z H. The modeling of spatial direction relationship between object groups. Journal of Geo-Information Science, 2018, 20 (6): 721- 729. URL
47	陈超, 王中辉, 马品. 面状群(组)目标空间方向关系的形式化描述与计算. 测绘与空间地理信息, 2021, 44 (9): 17- 21. URL
	CHEN C, WANG Z H, MA P. Formal description and computation of the spatial direction relationships between polygonal object groups. Geomatics & Spatial Information Technology, 2021, 44 (9): 17- 21. URL
48	王玉竹, 闫浩文. 一种改进的群组目标空间方向关系计算模型. 测绘科学, 2022, 47 (4): 169- 174. URL
	WANG Y Z, YAN H W. An improved computational model on spatial direction between object groups. Science of Surveying and Mapping, 2022, 47 (4): 169- 174. URL
49	WANG K H, GUAN X L. 3D reconstruction and rendering models in urban architectural design using Kalman filter correction algorithm. Wireless Communications and Mobile Computing, 2022, 22 (1): 1- 11.
50	LUNDGREN A V A, DOS SANTOS M A O, BEZERRA B L D, et al. Systematic review of computer vision semantic analysis in socially assistive robotics. Artificial Intelligence, 2022, 3 (1): 229- 249.
51	YIN F, LI C, WANG H B, et al. Automatic tracking of weak acoustic targets within jamming environment by using image processing methods. Applied Sciences, 2022, 12 (13): 6698.
52	刘庆, 杨宇航, 陈侃侃. 测绘地理信息系统的架构与功能. 电子测试, 2022, 36 (6): 72- 74. URL
	LIU Q, YANG Y H, CHEN K K. Architecture and function of surveying and mapping geographic information system. Electronic Test, 2022, 36 (6): 72- 74. URL
53	PACHECO J, ESCRIG M T, TOLEDO F. Representing and reasoning on three-dimensional qualitative orientation point objects[C]//Proceedings of International Conference on Artificial Intelligence. Berlin, Germany: Springer, 2001: 298-305.
54	刘新, 刘文宝. 3D-GIS中方向关系描述及其推理. 测绘科学, 2007, 32 (3): 23-25, 192. URL
	LIU X, LIU W B. Direction relation description and its qualitative reasoning in 3-dimensional GIS. Science of Surveying and Mapping, 2007, 32 (3): 23-25, 192. URL
55	王淼, 郝忠孝. 三维空间方向关系的定性描述与推理. 计算机工程, 2009, 35 (15): 22- 25. URL
	WANG M, HAO Z X. Qualitative representation and reasoning on direction relation of three-dimension space. Computer Engineering, 2009, 35 (15): 22- 25. URL
56	张丽平, 李松, 王红. 3D对象动态方位邻接关系及双向关联表示. 计算机工程与应用, 2009, 45 (29): 68- 71. URL
	ZHANG L P, LI S, WANG H. Dynamic direction adjacent relations and bidirectional association representation of 3D objects. Computer Engineering and Applications, 2009, 45 (29): 68- 71. URL
57	王淼, 黄治国, 李松. 基于代数理论的三维主方向关系的反关系推理. 计算机应用, 2014, 34 (4): 1144- 1148. URL
	WANG M, HUANG Z G, LI S. Inverse reasoning of 3D cardinal direction relations based on block algebra. Journal of Computer Applications, 2014, 34 (4): 1144- 1148. URL
58	顾卫杰, 刘永山. 双投影矩阵模型的方向关系组合推理研究. 测绘科学技术学报, 2014, 31 (5): 538-542, 546. URL
	GU W J, LIU Y S. Research on directional relation combinational reasoning of double projections matrix model. Journal of Geomatics Science and Technology, 2014, 31 (5): 538-542, 546. URL
59	赵硕, 张丽平. 3DR39模型及双向关联表示. 科技通报, 2011, 27 (3): 412-415, 420. URL
	ZHAO S, ZHANG L P. 3DR39 model and the bidirectional association representation. Bulletin of Science and Technology, 2011, 27 (3): 412-415, 420. URL
60	郝晓红, 张丽平, 赵龄强, 等. 3DR39-3d方位关系模型与反方位关系. 计算机工程, 2014, 40 (7): 258- 262. URL
	HAO X H, ZHANG L P, ZHAO L Q, et al. 3DR39-3d orientation relation model and reverse orientation relation. Computer Engineering, 2014, 40 (7): 258- 262. URL
61	齐新军, 宗明魁. 3DR34关系模型表示与分析. 煤炭技术, 2011, 30 (3): 210- 212. URL
	QI X J, ZONG M K. Representation and analysis of 3DR34 relation model. Coal Technology, 2011, 30 (3): 210- 212. URL
62	李占宣, 何云斌, 李松. 增强型3DR34关系模型表示与分析. 计算机工程与应用, 2012, 48 (19): 131- 134. URL
	LI Z X, HE Y B, LI S. Representation and analysis of enhanced 3DR34 relation model. Computer Engineering and Applications, 2012, 48 (19): 131- 134. URL
63	郝晓红, 张丽平, 李松. 三维空间中3DR44方向关系表示模型. 计算机工程, 2011, 37 (1): 75-77, 80. URL
	HAO X H, ZHANG L P, LI S. 3DR44 direction relation representation model in three dimensional space. Computer Engineering, 2011, 37 (1): 75-77, 80. URL
64	郝晓红, 李松, 张丽平. 3DR44-4d方位关系表示模型. 计算机工程, 2012, 38 (3): 57- 59. URL
	HAO X H, LI S, ZHANG L P. Representation model of 3DR44-4d orientation relation. Computer Engineering, 2012, 38 (3): 57- 59. URL
65	赵泽茹. 基于3DR50方向关系模型查询算法[D]. 河北, 秦皇岛: 燕山大学, 2017.
	ZHAO Z R. Query algorithm based on 3DR50 direction relational model[D]. Qinhuangdao, Hebei: Yanshan University, 2017. (in Chinese)
66	郝晓红, 李松, 郝忠孝. 复杂3D空间中的3DR46模型的表示与推理. 计算机科学与探索, 2020, 14 (12): 2004- 2013. URL
	HAO X H, LI S, HAO Z X. Representation and reasoning for model of 3DR46 in complex 3D space. Journal of Frontiers of Computer Science and Technology, 2020, 14 (12): 2004- 2013. URL
67	王建, 闫丹凤, 宋巍, 等. 考虑三维空间关系的海洋科学数据本体构建及推理研究. 测绘地理信息, 2022, 47 (1): 69- 73. URL
	WANG J, YAN D F, SONG W, et al. Construction and reasoning of marine science data ontology considering 3D spatial relations. Journal of Geomatics, 2022, 47 (1): 69- 73. URL
68	王生生, 王创峰, 谷方明. OPRA方向关系网络的时空推理. 吉林大学学报(工学版), 2017, 47 (4): 1238- 1243. URL
	WANG S S, WANG C F, GU F M. Spatio-temporal reasoning for OPRA direction relation network. Journal of Jilin University (Engineering and Technology Edition), 2017, 47 (4): 1238- 1243. URL
69	CHEN H, VASARDANI M, WINTER S, et al. A graph database model for knowledge extracted from place descriptions. ISPRS International Journal of Geo-Information, 2018, 7 (6): 221.
70	ZHOU S A, ZHANG J G, ZHANG Q Y, et al. Uncertainty theory-based structural reliability analysis and design optimization under epistemic uncertainty. Applied Sciences, 2022, 12 (6): 2846.
71	COHN A G, GOTTS N M. The 'egg-yolk' representation of regions with indeterminate boundaries. London, UK: CRC Press, 2020: 171- 187.
72	虞强源, 刘大有, 刘亚彬. 一种不确定区域的扩展蛋黄模型. 电子学报, 2004, 32 (4): 610- 615. URL
	YU Q Y, LIU D Y, LIU Y B. An extended egg-yolk model between indeterminate regions. Acta Electronica Sinica, 2004, 32 (4): 610- 615. URL
73	蔡剑红, 李德仁. 多尺度下的不确定性空间方向锥形模型研究. 武汉大学学报(信息科学版), 2007, 32 (8): 735- 739. URL
	CAI J H, LI D R. Research on cone-shaped models of cardinal direction relations considering positional uncertainty of multiple spatial-scale data. Geomatics and Information Science of Wuhan University, 2007, 32 (8): 735- 739. URL
74	陈娟, 刘大有, 贾海洋. 不确定区域间定性方向关系模型. 吉林大学学报(工学版), 2013, 43 (1): 111- 116. URL
	CHEN J, LIU D Y, JIA H Y. Modelling qualitative direction relations between indeterminate regions. Journal of Jilin University (Engineering and Technology Edition), 2013, 43 (1): 111- 116. URL
75	董轶群, 刘大有, 王芳, 等. 一种基于MBR的不确定区域间方向关系建模方法. 电子学报, 2011, 39 (2): 329- 335. URL
	DONG Y Q, LIU D Y, WANG F, et al. A MBR-based approach for modeling direction relations between uncertain regions. Acta Electronica Sinica, 2011, 39 (2): 329- 335. URL
76	孙伟, 欧阳继红, 马亭新, 等. 不确定区域间方向关系的相似性度量方法. 电子学报, 2014, 42 (3): 597- 601. URL
	SUN W, OUYANG J H, MA T X, et al. Similarity assessment of approximate direction relations. Acta Electronica Sinica, 2014, 42 (3): 597- 601. URL
77	XIANG J. A novel direction relation reasoning model based environmental protection GIS. Earth and Environmental Science, 2021, 702 (1): 012047.
78	杜世宏, 王桥, 魏斌, 等. 空间方向关系粗糙推理. 测绘学报, 2003, 32 (4): 334- 338. URL
	DU S H, WANG Q, WEI B, et al. Spatial orientational relations rough reasoning. Acta Geodaetica et Cartographic Sinica, 2003, 32 (4): 334- 338. URL
79	杜世宏, 王桥, 杨一鹏, 等. 空间方向关系模糊描述. 计算机辅助设计与图形学学报, 2005, 17 (8): 1744- 1751. URL
	DU S H, WANG Q, YANG Y P, et al. Fuzzy description of spatial direction relations. Journal of Computer Aided Design & Computer Graphics, 2005, 17 (8): 1744- 1751. URL
80	吴冰娇, 王中辉, 杨飞. 用于多尺度道路网匹配的语义相似性计算模型. 测绘科学, 2022, 47 (3): 166- 173. URL
	WU B J, WANG Z H, YANG F. A semantic similarity computational model for multi-scale road network matching. Science of Surveying and Mapping, 2022, 47 (3): 166- 173. URL
81	SCHWEITZER S A, COWEN E A. A method for analysis of spatial uncertainty in image based surface velocimetry. Frontiers in Water, 2022, 4, 744278.
82	李松, 郝忠孝. 多范畴的Vague区域关系表示与分析. 高技术通讯, 2010, 20 (3): 253- 258. URL
	LI S, HAO Z X. Representation and analyse of multi-category relations of Vague regions. Chinese High Technology Letters, 2010, 20 (3): 253- 258. URL
83	郭继发. 高阶模糊地理对象的方向关系研究. 武汉大学学报(信息科学版), 2011, 36 (12): 1414-1417, 1422. URL
	GUO J F. Direction relation between high order fuzzy geographical objects. Geomatics and Information Science of Wuhan University, 2011, 36 (12): 1414-1417, 1422. URL
84	陈迪, 朱欣焰, 周春辉, 等. 基于自适应采样粒度模型的空间方向关系模糊描述方法. 测绘学报, 2013, 42 (3): 359- 366. URL
	CHEN D, ZHU X Y, ZHOU C H, et al. A fuzzy description method for directional relationship based on adaptive sampling granularity model. Acta Geodaetica et Cartographica Sinica, 2013, 42 (3): 359- 366. URL
85	关胜况, 胡圣武. 基于粗集的面实体方向关系的研究. 地理空间信息, 2015, 13 (2): 98-100, 13. URL
	GUAN S K, HU S W. Research on direction relationship of area based on the rough set. Geospatial Information, 2015, 13 (2): 98-100, 13. URL
86	董轶群, 徐文星, 刘建东, 等. 不确定边界区域间方向关系建模方法. 北京邮电大学学报, 2016, 39 (1): 18- 23. URL
	DONG Y Q, XU W X, LIU J D, et al. Approach to modeling direction relations between regions with uncertain boundaries. Journal of Beijing University of Posts and Telecommunications, 2016, 39 (1): 18- 23. URL
87	毛政元, 范琳娜, 李霖. 二维空间中距离不确定性的测度方法研究[J/OL]. 武汉大学学报(信息科学版): 1-13. [2022-04-13]. https://doi:10.13203/j.whugis20220131.
	MAO Z Y, FAN L N, LI L. Methodological researchon measuring distance uncertainty in two-dimensional space [J/OL]. Geomatics and Information Science of Wuhan University: 1-13[2022-04-13]. https://doi:10.13203/j.whugis20220131. (in Chinese)

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