基于方向关系矩阵的空间方向相似性计算改进模型
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摘要
空间方向关系作为空间关系的一个重要分支,其相似性研究已成为地理信息科学领域的热点问题。对于Goyal提出的基于方向关系矩阵计算空间方向相似性模型进行以下两个方面改进:首先通过方向关系的反转运算计算对象目标与参考目标的最小投影矩阵在包含或相交情况下的空间方向关系,扩展了方向关系矩阵的使用范围;其次利用运筹学中解决平衡运输问题的伏格尔法计算两个多元素方向关系矩阵之间的方向距离,克服了由平衡运输表中元素位置变化而引起方向距离变化的局限。通过实例证明该方法计算简单,得到的方向距离更优,相似性更加准确。
Spatial direction relation is an important branch of spatial relations,the research of its similarity has become a hot issue in the field of geographic information science. The following two aspects are improved for the spatial direction similarity model based on the direction relation matrix proposed by Goyal. Firstly,the spatial direction relation of the object and the reference object's minimum projection matrix is calculated using the reversal operation of the direction relation in the case of inclusion or intersection,which extends the using range of the direction relation matrix. Secondly,the direction distance between two multi-element direction relation matrices is calculated using the Vogel method,which is used to solve the balance transportation problem in operational research to overcome the limitation of the change of direction distance caused by the change of element position in the balance transportation tableau. It is proved by an example that the method in the paper is simple to calculate,the direction distance is optimal,and the similarity is more accurate.
Spatial direction relation is an important branch of spatial relations,the research of its similarity has become a hot issue in the field of geographic information science. The following two aspects are improved for the spatial direction similarity model based on the direction relation matrix proposed by Goyal. Firstly,the spatial direction relation of the object and the reference object's minimum projection matrix is calculated using the reversal operation of the direction relation in the case of inclusion or intersection,which extends the using range of the direction relation matrix. Secondly,the direction distance between two multi-element direction relation matrices is calculated using the Vogel method,which is used to solve the balance transportation problem in operational research to overcome the limitation of the change of direction distance caused by the change of element position in the balance transportation tableau. It is proved by an example that the method in the paper is simple to calculate,the direction distance is optimal,and the similarity is more accurate.
引文
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[13]陈占龙,龚希,吴亮,等.顾及尺度差异的复合空间对象方向相似度定量计算模型[J].测绘学报,2016,45(3):362-371.CHEN Z L,GONG X,WU L,et al.A quantitative calculation method of composite spatial direction similarity concerning scale differences[J].Acta Geodaetica et Cartographica Sinica,2016,45(3):362-371.
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[2]李靖涵,巩现勇,武芳,等.一种改进的面目标间方向关系相似性计算模型[J].武汉大学学报(信息科学版),2016,41(7):925-931.LI J H,GONG X Y,WU F,et al.An improved model for calculating the similarity of spatial direction relations between areal objects[J].Geomatics and Information Science of Wuhan University,2016,41(7):925-931.
[3]SUN W,OUYANG J,HUO L,et al.Similarity of direction relations in spatial scenes[J].Journal of Computational Information Systems,2012,8(20):8589-8596.
[4]郭黎,崔铁军,郑海鹰,等.基于空间方向相似性的面状矢量空间数据匹配算法[J].测绘科学技术学报,2008,25(5):380-382.GUO L,CUI T J,ZHENG H Y,et al.Arithmetic for area vector spatial data matching on spatial direction similarity[J].Journal of Geomatics Science and Technology,2008,25(5):380-382.
[5]TANG X,QIN K.Direction-relation similarity model based on fuzzy close-degree[C]∥IEEE International Conference on Progress in Informatics and Computing.Beijing,2011:180-184.
[6]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;48.YAN H W,CHU Y D.On the fundamental issues of spatial similarity relations in multi-scale maps[J].Geography and Geo-Information Science,2009,25(4):42-44;48.
[7]ANTHONY S,PEGY A,CHARALAMBOS G,et al.Scale-and orientation-invariant scene similarity metrics for image queries[J].International Journal of Geographical Information Systems,2002,16(8):749-772.
[8]ZHANG Q,LI S,WANG X,et al.The effects of direction similarity in visual working memory:Behavioural and ERP studies[J].Quarterly Journal of Experimental P sychology,2015,69(9):1.
[9]GOYAL R K.Similarity assessment for cardinal directions between extended spatial objects[D].Maine:University of Maine,2000:89-93.
[10]PEUQUET D J,ZHAN C X.An algorithm to determine the directional relationship between arbitrarily-shaped polygons in the plane[J].Pattern Recognition,1987,20(1):65-74.
[11]郭庆胜,丁虹.基于栅格数据的面状目标空间方向相似性研究[J].武汉大学学报(信息科学版),2004,29(5):447-450.GUO Q S,DING H.Similarity for spatial directions between areal objects in raster data[J].Geomatics and Information Science of Wuhan University,2004,29(5):447-450.
[12]陈占龙,周林,龚希,等.基于方向关系矩阵的空间方向相似性定量计算方法[J].测绘学报,2015,44(7):813-821.CHEN Z L,ZHOU L,GONG X,et al.A quantitative calculation method of spatial direction similarity based on direction relation matrix[J].Acta Geodaetica et Cartographica Sinica,2015,44(7):813-821.
[13]陈占龙,龚希,吴亮,等.顾及尺度差异的复合空间对象方向相似度定量计算模型[J].测绘学报,2016,45(3):362-371.CHEN Z L,GONG X,WU L,et al.A quantitative calculation method of composite spatial direction similarity concerning scale differences[J].Acta Geodaetica et Cartographica Sinica,2016,45(3):362-371.
[14]郭平,刘然,林勇,等.方向关系的定性表示与推理[J].计算机工程与科学,2005,27(8):81-84.GUO P,LIU R,LIN Y,et al.Qualitative representation of the directional relationship and reasoning[J].Computer Engineering&Science,2005,27(8):81-84.
[15]胡运权.运筹学教程[M].4版.北京:清华大学出版社,2012:70-77.HU Y Q.Operational research course[M].4th ed.Beijing:Tsinghua University Press,2012:70-77.