多尺度点群广义Hausdorff距离及在相似性度量中的应用
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摘要
多尺度点群相似度计算在制图综合过程控制及结果评价中具有重要作用。针对现有方法的不足,提出一种基于广义Hausdorff距离的多尺度点群相似度计算方法。在传统Hausdorff距离基础上,建立距离相似度计算公式;给出拓扑距离的定义及计算方法,建立基于拓扑Hausdorff距离的拓扑相似度计算公式;以点群最小外包圆为基础建立方向关系参考框架,给出方向距离定义,建立基于方向Hausdorff距离的方向相似度计算公式,并得出总相似度计算公式。通过多尺度点群相似度计算实验及综合结果评价实验,验证了所述方法的可行性和有效性。
Multi-scale point group similarity calculation plays an important role in process control and result evaluation of cartographic generalization. In view of the shortcomings of the existing methods, a multi-scale point group similarity calculation method based on generalized Hausdorff distance is proposed. On the basis of the traditional Hausdorff distance, the calculation formula of distance similarity is built. The definition and calculation method of topology distance is qiven, the calculation formula of topology similarity is built using the topological Hausdorff distance. The direction distance definition is also given, the direction relation reference frame is established based on the smallest enclosing disk of point group. The direction distance definition is provided and the calculation formula of direction similarity is established by using the direction Hausdorff distance. And the calculation formula of total similarity is obtained. By multi-scale point group similarity computation experiment and point group generalization evaluation experiment, the feasibility and effectiveness of the method are verified.
Multi-scale point group similarity calculation plays an important role in process control and result evaluation of cartographic generalization. In view of the shortcomings of the existing methods, a multi-scale point group similarity calculation method based on generalized Hausdorff distance is proposed. On the basis of the traditional Hausdorff distance, the calculation formula of distance similarity is built. The definition and calculation method of topology distance is qiven, the calculation formula of topology similarity is built using the topological Hausdorff distance. The direction distance definition is also given, the direction relation reference frame is established based on the smallest enclosing disk of point group. The direction distance definition is provided and the calculation formula of direction similarity is established by using the direction Hausdorff distance. And the calculation formula of total similarity is obtained. By multi-scale point group similarity computation experiment and point group generalization evaluation experiment, the feasibility and effectiveness of the method are verified.
引文
[1] Yan Haowen,Chu Yandong.On the Fundamental Issues of Spatial Similarity Relations in Multi-scale Maps[J].Geography and Geo-Information Science,2009,25(4):42-44(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):42-44)
[2] Duan Xiaoqi,Liu Tao,Wu Dan.Spatial Similarity Assessment of Point Clusters in Multi-scale Map Spaces Based on Analytic Hierarchy Process[J].Journal of Geo-Information Science,2016,18(10):1 312-1 321(段晓旗,刘涛,武丹.基于层次分析法的多尺度点群目标相似度计算[J].地球信息科学学报,2016,18(10):1 312-1 321)
[3] Duan Xiaoqi,Liu Tao,Wu Dan,et al.Blank Area’s Influence on the Similarity Characteristic Factors for Point Cluster [J].Science of Surveying and Mapping,2016,41(12):75-80(段晓旗,刘涛,武丹,等.空白区域对点群相似性特征因子的影响[J].测绘科学,2016,41(12):75-80)
[4] Liu Tao,Du Qingyun,Yan Haowen.Spatial Similarity Assessment of Point Clusters [J].Geomatics and Information Science of Wuhan University,2011,36(10):1 149-1 153(刘涛,杜清运,闫浩文.空间点群目标相似度计算[J].武汉大学学报·信息科学版,2011,36(10):1 149-1 153)
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[6] Yan Haowen,Jonathan L.Spatial Similarity Relations in Multi-scale Map Spaces[M].New York:Springer,2014
[7] Bruns H T,Egenhofer M J.Similarity of Spatial Scenes[J].The Symposium on Spatial Data Handling,1996,8:31-42
[8] Jiang Hao,Chu Yandong,Yan Haowen,et al.Study on Computation of Similarity Relationships of Multi-scale Point Objects[J].Geography and Geo-Information Science,2009,25(6):1-4(江浩,褚衍东,闫浩文,等.多尺度地理空间点群目标相似关系的计算研究[J].地理与地理信息科学,2009,25(6):1-4)
[9] Tang Tao.The Research of Similar Measurement Method Based on the Hausdorff Distance[D].Nanning:Guangxi University,2012(唐涛.基于Hausdorff距离的相似性度量方法研究[D].南宁:广西大学,2012)
[10] Cao Jingjing.The Calculation Theory of Hausdorff Distance and Its Application to the Matching of 2D Geometrical Objects[D].Dalian:Dalian University of Technology,2013(曹京京.Hausdorff距离的计算原理及其在二维匹配中的应用[D].大连:大连理工大学,2013)
[11] Deng Min,Niu Shulian,Li Zhilin.A Generalized Hausdorff Distance for Spatial Objects in GIS [J].Geomatics and Information Science of Wuhan University,2007,32(7):641-645(邓敏,钮沭联,李志林.GIS空间目标的广义Hausdorff距离模型[J].武汉大学学报·信息科学版,2007,32(7):641-645)
[12] Zhou Meili,He Peng.System Similarity Measurement Based on Characteristics Diversity [J].Journal of Machine Design,2005,22(s1):71-72(周美立,何鹏.基于特征差异的系统相似性度量方法[J].机械设计,2005,22(s1):71-72)
[13] Yasuda K,Yin Y.A Dissimilarity Measure for Solving the Cell Formation Problem in Cellular Manufacturing[J].Computers & Industrial Engineering,2001,39(1):1-17
[14] Zhou Peide.Computational Geometry Algorithm Design,Analysis and Applications(Fifth Edition)[M].5th ed.Beijing:Tsinghua University Press,2016(周培德.计算几何—算法设计、分析及应用[M].5版.北京:清华大学出版社,2016)
[15] Wang Guiping,Wang Yan,Ren Jiachen.Graph Algorithm Theory,Implementation and Application [M].Beijing:Peking University Press,2011(王桂平,王衍,任嘉辰.图论算法理论、实现及应用[M].北京:北京大学出版社,2011)
[16] Deng Min,Li Zhilin,Wu Jing.Theory and Method of Spatial Relations [M].Beijing:Science Press,2013(邓敏,李志林,吴静.空间关系理论与方法[M].北京:科学出版社,2013)
[17] Welzl E.Smallest Enclosing Disks (Balls and Ellipsoids)[J].New Results & New Trends in Computer Science,1991,555(1):359-370
[18] Berg M D.Computational Geometry:Algorithms and Applications[M].New York:Springer,2000
[19] Nielsen F,Nock R.A Fast Deterministic Smallest Enclosing Disk Approximation Algorithm[J].Information Processing Letters,2005,93(6):263-268
[20] Wang Wei,Wang Wenping,Wang Jiaye.An Algorithm for Finding the Smallest Circle Containing All Points in a Given Point Set [J].Journal of Software,2000,11(9):1 237-1 240(汪卫,王文平,汪嘉业.求一个包含点集所有点的最小圆的算法[J].软件学报,2000,11(9):1 237-1 240)
[2] Duan Xiaoqi,Liu Tao,Wu Dan.Spatial Similarity Assessment of Point Clusters in Multi-scale Map Spaces Based on Analytic Hierarchy Process[J].Journal of Geo-Information Science,2016,18(10):1 312-1 321(段晓旗,刘涛,武丹.基于层次分析法的多尺度点群目标相似度计算[J].地球信息科学学报,2016,18(10):1 312-1 321)
[3] Duan Xiaoqi,Liu Tao,Wu Dan,et al.Blank Area’s Influence on the Similarity Characteristic Factors for Point Cluster [J].Science of Surveying and Mapping,2016,41(12):75-80(段晓旗,刘涛,武丹,等.空白区域对点群相似性特征因子的影响[J].测绘科学,2016,41(12):75-80)
[4] Liu Tao,Du Qingyun,Yan Haowen.Spatial Similarity Assessment of Point Clusters [J].Geomatics and Information Science of Wuhan University,2011,36(10):1 149-1 153(刘涛,杜清运,闫浩文.空间点群目标相似度计算[J].武汉大学学报·信息科学版,2011,36(10):1 149-1 153)
[5] Yan Haowen.Theory of Spatial Similarity Relations and Its Applications in Automated Map Generalization[D].Waterloo:University of Waterloo,2014
[6] Yan Haowen,Jonathan L.Spatial Similarity Relations in Multi-scale Map Spaces[M].New York:Springer,2014
[7] Bruns H T,Egenhofer M J.Similarity of Spatial Scenes[J].The Symposium on Spatial Data Handling,1996,8:31-42
[8] Jiang Hao,Chu Yandong,Yan Haowen,et al.Study on Computation of Similarity Relationships of Multi-scale Point Objects[J].Geography and Geo-Information Science,2009,25(6):1-4(江浩,褚衍东,闫浩文,等.多尺度地理空间点群目标相似关系的计算研究[J].地理与地理信息科学,2009,25(6):1-4)
[9] Tang Tao.The Research of Similar Measurement Method Based on the Hausdorff Distance[D].Nanning:Guangxi University,2012(唐涛.基于Hausdorff距离的相似性度量方法研究[D].南宁:广西大学,2012)
[10] Cao Jingjing.The Calculation Theory of Hausdorff Distance and Its Application to the Matching of 2D Geometrical Objects[D].Dalian:Dalian University of Technology,2013(曹京京.Hausdorff距离的计算原理及其在二维匹配中的应用[D].大连:大连理工大学,2013)
[11] Deng Min,Niu Shulian,Li Zhilin.A Generalized Hausdorff Distance for Spatial Objects in GIS [J].Geomatics and Information Science of Wuhan University,2007,32(7):641-645(邓敏,钮沭联,李志林.GIS空间目标的广义Hausdorff距离模型[J].武汉大学学报·信息科学版,2007,32(7):641-645)
[12] Zhou Meili,He Peng.System Similarity Measurement Based on Characteristics Diversity [J].Journal of Machine Design,2005,22(s1):71-72(周美立,何鹏.基于特征差异的系统相似性度量方法[J].机械设计,2005,22(s1):71-72)
[13] Yasuda K,Yin Y.A Dissimilarity Measure for Solving the Cell Formation Problem in Cellular Manufacturing[J].Computers & Industrial Engineering,2001,39(1):1-17
[14] Zhou Peide.Computational Geometry Algorithm Design,Analysis and Applications(Fifth Edition)[M].5th ed.Beijing:Tsinghua University Press,2016(周培德.计算几何—算法设计、分析及应用[M].5版.北京:清华大学出版社,2016)
[15] Wang Guiping,Wang Yan,Ren Jiachen.Graph Algorithm Theory,Implementation and Application [M].Beijing:Peking University Press,2011(王桂平,王衍,任嘉辰.图论算法理论、实现及应用[M].北京:北京大学出版社,2011)
[16] Deng Min,Li Zhilin,Wu Jing.Theory and Method of Spatial Relations [M].Beijing:Science Press,2013(邓敏,李志林,吴静.空间关系理论与方法[M].北京:科学出版社,2013)
[17] Welzl E.Smallest Enclosing Disks (Balls and Ellipsoids)[J].New Results & New Trends in Computer Science,1991,555(1):359-370
[18] Berg M D.Computational Geometry:Algorithms and Applications[M].New York:Springer,2000
[19] Nielsen F,Nock R.A Fast Deterministic Smallest Enclosing Disk Approximation Algorithm[J].Information Processing Letters,2005,93(6):263-268
[20] Wang Wei,Wang Wenping,Wang Jiaye.An Algorithm for Finding the Smallest Circle Containing All Points in a Given Point Set [J].Journal of Software,2000,11(9):1 237-1 240(汪卫,王文平,汪嘉业.求一个包含点集所有点的最小圆的算法[J].软件学报,2000,11(9):1 237-1 240)
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