Visual perception-based quantitative calculation of 3D spatial similarity relations

doi:10.11947/j.AGCS.2026.20250096

Abstract

Abstract:

Spatial similarity relations are a fundamental theory for multi-scale representation of spatial data. The evolution of basic spatial data from 2D to 3D has presented new challenges for research on spatial similarity relations. In this study, the concept of 3D spatial similarity relations is proposed, and a quantitative calculation method for 3D spatial similarity relations based on visual perception is further proposed to address the limitation of scale effect. First, building upon spatial similarity relationships in multi-scale maps, we define 3D spatial similarity relationships and summarize the challenges encountered in extending from 2D to 3D. Then, by comprehensively considering the attributes of 3D spatial data, the rendering mechanisms of 3D models, and the principles of human visual perception, an in-depth analysis of the visual perception processes, mechanisms, and characteristics of 3D spatial similarity relations is conducted. Following this, a reverse calculation strategy informed by visual perception is introduced, which converts complex calculations in 3D space into equivalent operations within 2D screen space, thereby enabling the quantitative measurement of 3D spatial similarity relations. Experimental results and practical applications demonstrate that the proposed method enables scale-adaptive quantitative calculations of 3D spatial similarity relations and offers valuable support for level of detail (LOD) construction and continuous visualization of 3D building scenes.

Key words: spatial similarity relation, visual perception, multi-scale representation, cartographic generalization, 3D GIS

CLC Number:

P208

Biao HE, Haojia LIN, Renzhong GUO, Xi KUAI, Ding MA, Chen ZHANG. Visual perception-based quantitative calculation of 3D spatial similarity relations[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(1): 138-153.

Figures/Tables 14

Fig. 1

Tab. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Tab. 2

Fig. 9

Fig. 10

Tab. 3

Fig. 11

References 25

[1]	艾廷华, 张翔. 地理信息科学中尺度概念的诠释与表达[J]. 测绘学报, 2022, 51(7): 1640-1652. DOI: . doi: 10.11947/j.AGCS.2022.20220143
	AI Tinghua, ZHANG Xiang. An interpretation and representation of scale concept in geo-information sciences[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(7): 1640-1652. DOI: . doi: 10.11947/j.AGCS.2022.20220143
[2]	褚天舒, 闫浩文, 禄小敏. 面向地图综合的道路网相似度计算模型[J]. 测绘科学, 2022, 47(1): 181-187.
	CHU Tianshu, YAN Haowen, LU Xiaomin. A similarity calculation model of road network for map generalization[J]. Science of Surveying and Mapping, 2022, 47(1): 181-187.
[3]	高晓蓉. 顾及几何和语义相似的居民地自动综合方法[J]. 测绘学报, 2025, 54(7): 1346. DOI: . doi: 10.11947/j.AGCS.2025.20230384
	GAO Xiaorong. Automated settlement generalization methods considering geometric and semantic similarity[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(7): 1346. DOI: . doi: 10.11947/j.AGCS.2025.20230384
[4]	李兆兴, 翟京生, 武芳. 线要素综合的形状相似性评价方法[J]. 武汉大学学报(信息科学版), 2019, 44(12): 1859-1864.
	LI Zhaoxing, ZHAI Jingsheng, WU Fang. A shape similarity assessment method for linear feature generalization[J]. Geomatics and Information Science of Wuhan University, 2019, 44(12): 1859-1864.
[5]	刘鹏程, 罗静, 艾廷华, 等. 基于线要素综合的形状相似性评价模型[J]. 武汉大学学报(信息科学版), 2012, 37(1): 114-117.
	LIU Pengcheng, LUO Jing, AI Tinghua, et al. Evaluation model for similarity based on curve generalization[J]. Geomatics and Information Science of Wuhan University, 2012, 37(1): 114-117.
[6]	禄小敏. 顾及权重信息的地图点群目标自动综合方法[J]. 测绘学报, 2024, 53(2): 398-398. DOI: . doi: 10.11947/j.AGCS.2024.20230010
	LU Xiaomin. Point cluster generalization approaches taking into account the weights of the points[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(2): 398-398. DOI: . doi: 10.11947/j.AGCS.2024.20230010
[7]	郭仁忠. 空间分析[M]. 2版. 北京: 高等教育出版社, 2001.
	GUO Renzhong. Spacial analysis[M]. 2nd ed. Beijing: Higher Education Press, 2001.
[8]	DU Shihong, QIN Qimin, WANG Qiao, et al. Evaluating structural and topological consistency of complex regions with broad boundaries in multi-resolution spatial databases[J]. Information Sciences, 2008, 178(1): 52-68.
[9]	FORMICA A, POURABBAS E, RAFANELLI M. Constraint relaxation of the polygon-polyline topological relation for geographic pictorial query languages[J]. Computer Science and Information Systems, 2013, 10(3): 1053-1075.
[10]	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.
	AN Xiaoya, SUN Qun, XIAO Qiang, et al. A multi-level shape description method and its application in geometric similarity measurement of multi-scale spatial data[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(4): 495-501.
[11]	陈占龙, 徐永洋, 谢忠. 矢量面状要素几何相似性度量方法探讨[J]. 测绘科学, 2016, 41(5): 105-110.
	CHEN Zhanlong, XU Yongyang, XIE Zhong. Discussion on geometrical similarity measurement of vector planar elements[J]. Science of Surveying and Mapping, 2016, 41(5): 105-110.
[12]	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 Tao, DU Qingyun, MAO Haichen. Spatial similarity assessment model and its application in line groups[J]. Geomatics and Information Science of Wuhan University, 2012, 37(8): 992-995.
[13]	孟妮娜, 艾廷华, 周校东. 制图综合中空间关系相似度的集成表达[J]. 华中师范大学学报(自然科学版), 2009, 43(4): 693-697.
	MENG Nina, AI Tinghua, ZHOU Xiaodong. Integrated expression of spatial relations similarity for cartographic generalization[J]. Journal of Central China Normal University (Natural Sciences), 2009, 43(4): 693-697.
[14]	王荣, 闫浩文, 禄小敏. Douglas-Peucker算法全自动化的多尺度空间相似关系方法[J]. 地球信息科学学报, 2021, 23(10): 1767-1777.
	WANG Rong, YAN Haowen, LU Xiaomin. Automation of the Douglas-Peucker algorithm based on spatial similarity relations[J]. Journal of Geo-information Science, 2021, 23(10): 1767-1777.
[15]	宗琴, 姜树辉, 彭荃. 多尺度矢量地图数据库中模糊相似关系的图谱构建[J]. 测绘科学, 2020, 45(3): 117-121.
	ZONG Qin, JIANG Shuhui, PENG Quan. Mapping of fuzzy similarity relation in multi-scale vector map database[J]. Science of Surveying and Mapping, 2020, 45(3): 117-121.
[16]	YAN Haowen. Fundamental theories of spatial similarity relations in multi-scale map spaces[J]. Chinese Geographical Science, 2010, 20(1): 18-22.
[17]	闫浩文. 空间相似关系[M]. 北京: 科学出版社, 2022.
	YAN Haowen. Spatial similarity relation[M]. Beijing: Science Press, 2022.
[18]	闫浩文. 空间相似关系的理论体系与潜在研究方向[J]. 测绘学报, 2023, 52(11): 1962-1973. DOI: . doi: 10.11947/j.AGCS.2023.20220695
	YAN Haowen. Theoretical system and potential research issues of spatial similarity relations[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(11): 1962-1973. DOI: . doi: 10.11947/j.AGCS.2023.20220695
[19]	HOLT A. Spatial similarity and GIS: the grouping of spatial kinds[C]//Proceedings of the 7th Annual Colloquium of the Spatial Information Research Center. Dunedin: CiteSeer, 1999: 241-250.
[20]	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): 42-48.
	YAN Haowen, CHU Yandong. On the fundamental issues of spatial similarity relations in multi-scale maps[J]. Geography and Geoinformation Science, 2009, 25(4): 42-48.
[21]	林浩嘉, 郭仁忠, 贺彪, 等. 视觉感知导向的实景三维建筑场景LOD自适应可视化[J]. 测绘学报, 2025, 54(6): 1054-1070. DOI: . doi: 10.11947/j.AGCS.2025.20240347
	LIN Haojia, GUO Renzhong, HE Biao, et al. Visual-perception-oriented LOD adaptive visualization for realistic 3D building scenes[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(6): 1054-1070. DOI: . doi: 10.11947/j.AGCS.2025.20240347
[22]	林浩嘉. 视觉感知驱动的三维建筑表面模型自动综合与可视化[J]. 测绘学报, 2025, 54(4): 773. DOI: . doi: 10.11947/j.AGCS.2025.20230512
	LIN Haojia. Automatic generalization and visualization of 3D building surface models driven by visual perception[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(4): 773. DOI: . doi: 10.11947/j.AGCS.2025.20230512
[23]	AKENINE-MOLLER T, HAINES E, HOFFMAN N. Real-time rendering, fourth edition[M]. Boca Raton: AK Peters/CRC Press, 2018.
[24]	KANDEL E R, SCHWARTZ J H, JESSELL T. Principles of neural science[M]. 5th ed. New York: McGraw-hill, 2013.
[25]	KASCHKE M, DONNERHACKE K H, RILL M S. Optical devices in ophthalmology and optometry: technology, design principles and clinical applications[M]. Weinheim: Wiley, 2014.

类型	二维矢量数据	三维空间数据
数据性质	对世界的抽象描述	对世界的真实描述
表现形式	二维平面	三维场景
组成要素	二维平面中的点、线、面	三维空间中的点、线、面、体
信息构成	几何、空间关系、语义	几何、空间关系、语义、纹理
尺度表达	分尺度离散切换	连续尺度平滑过渡

目标	模型	TN	VN	TR/像素	PR	GE	TE
单体目标S	S₀	4084	3147	2048×1024	10.572 3	0	0
	S₁	2041	2003	1024×512	21.144 5	15.135 6	2.000 0
	S₂	1020	1335	512×256	42.289 1	30.271 2	4.000 0
	S₃	780	1094	256×128	84.578 2	60.542 5	8.000 0
	S₄	596	911	128×64	169.156 3	121.085 0	16.000 0
群组目标G₀	A₀	5400	16 200	2048×2048	10.460 6	0	0
	B₀	6972	20 916	2048×2048	9.494 8	0	0
	C₀	3406	10 218	2048×1024	9.154 8	0	0
群组目标G₁	A₁	2699	8097	1024×1024	20.932 3	20.040 1	2.001 1
	B₁	3485	10 455	1024×1024	18.995 5	20.029 7	2.000 6
	C₁	1703	5109	1024×512	18.309 6	14.180 4	2.000 0
群组目标G₂	A₂	1473	4419	512×512	41.890 1	40.080 2	4.004 6
	B₂	1751	5253	512×512	38.012 6	40.059 5	4.003 5
	C₂	1022	3066	512×256	36.624 4	28.360 8	4.000 6
群组目标G₃	A₃	1285	3855	256×256	84.714 8	80.160 5	8.098 5
	B₃	1534	4602	256×256	76.690 4	80.119 0	8.077 1
	C₃	827	2481	256×128	73.463 3	56.721 6	8.024 6
群组目标G₄	A₄	905	2715	128×128	170.046 7	160.321 0	16.255 9
	B₄	1095	3285	128×128	154.351 5	160.238 0	16.256 4
	C₄	621	1863	128×64	147.692 3	113.443 1	16.132 8

视点	量化参数	单体目标S					群组目标G
视点	量化参数	S₀	S₁	S₂	S₃	S₄	G₀	G₁	G₂	G₃	G₄
V₁	SGE	0	1.634 6	3.269 3	6.538 6	13.077 2	0	2.164 3	4.328 7	8.657 3	17.314 7
	STE	0	2.283 6	4.567 2	9.134 4	18.268 9	0	2.260 7	4.524 1	9.149 2	18.365 0
	VGE	0	0	1.269 3	4.538 6	11.077 2	0	0.164 3	2.3287	6.657 3	15.314 7
	VTE	0	1.283 6	3.567 2	8.134 4	17.268 9	0	1.260 7	3.524 1	8.149 2	17.365 0
	PVE	0	0.001 2	0.004 5	0.011 7	0.026 2	0	0.001 3	0.005 4	0.013 7	0.030 3
	SIM	1	0.998 8	0.995 5	0.988 3	0.973 8	1	0.998 7	0.994 6	0.986 3	0.969 7
V₂	SGE	0	0.710 7	1.421 4	2.842 9	5.685 7	0	0.941 0	1.882 0	3.764 1	7.528 1
	STE	0	0.992 9	1.985 7	3.971 5	7.943 0	0	0.982 9	1.967 0	3.977 9	7.984 8
	VGE	0	0	0	0.842 9	3.685 7	0	0	0	1.764 1	5.528 1
	VTE	0	0	0.985 7	2.971 5	6.943 0	0	0	0.967 0	2.977 9	6.984 8
	PVE	0	0	0.000 9	0.003 5	0.009 8	0	0	0.000 9	0.004 4	0.011 6
	SIM	1	1	0.999 1	0.996 5	0.990 2	1	1	0.999 1	0.995 6	0.988 4
V₃	SGE	0	0.355 4	0.710 7	1.421 4	2.842 9	0	0.470 5	0.941 0	1.882 0	3.764 1
	STE	0	0.496 4	0.992 9	1.985 7	3.971 5	0	0.491 5	0.983 5	1.989 0	3.992 4
	VGE	0	0	0	0	0.842 9	0	0	0	0	1.764 1
	VTE	0	0	0	0.985 7	2.971 5	0	0	0	0.989 0	2.992 4
	PVE	0	0	0	0.000 9	0.003 5	0	0	0	0.000 9	0.004 4
	SIM	1	1	1	0.999 1	0.996 5	1	1	1	0.999 1	0.995 6
V₄	SGE	0	0.177 7	0.355 4	0.710 7	1.421 4	0	0.235 3	0.470 5	0.941 0	1.882 0
	STE	0	0.248 2	0.496 4	0.992 9	1.985 7	0	0.245 7	0.491 8	0.994 5	1.996 2
	VGE	0	0	0	0	0	0	0	0	0	0
	VTE	0	0	0	0	0.985 7	0	0	0	0	0.996 2
	PVE	0	0	0	0	0.000 9	0	0	0	0	0.000 9
	SIM	1	1	1	1	0.999 1	1	1	1	1	0.999 1
V₅	SGE	0	0.088 8	0.177 7	0.355 4	0.710 7	0	0.117 6	0.235 3	0.470 5	0.941 0
	STE	0	0.124 1	0.248 2	0.496 4	0.992 9	0	0.122 9	0.245 9	0.497 2	0.998 1
	VGE	0	0	0	0	0	0	0	0	0	0
	VTE	0	0	0	0	0	0	0	0	0	0
	PVE	0	0	0	0	0	0	0	0	0	0
	SIM	1	1	1	1	1	1	1	1	1	1