地图信息论:从狭义到广义的发展回顾
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摘要
地图是人类认识客观世界的有力工具。地图的核心功能是传输空间信息。自20世纪60年代源自通信领域的信息论被引入地图信息度量.现代地图学已经发展了一个崭新的研究领域——地图信息论。本文旨在对近50年来地图信息论的发展历程进行回顾,论述从狭义到广义地图信息论的基本概念、研究进展及应用领域,最后对地图信息论的发展进行了展望。
Map is a kind of powerful means to help people in understanding the objective world.The key function of map is to transmit spatial information.The measurement of spatial information of maps dates back to 1960 s,when the information theory of communication was introduced to the field of cartography.The introduction led to a new branch of cartography,i.e.cartographic information theory.This paper provides a review of the development of cartographic information theory over the past 50 years.Emphasis is on the evolution from the special to the general cartographic information theory.
Map is a kind of powerful means to help people in understanding the objective world.The key function of map is to transmit spatial information.The measurement of spatial information of maps dates back to 1960 s,when the information theory of communication was introduced to the field of cartography.The introduction led to a new branch of cartography,i.e.cartographic information theory.This paper provides a review of the development of cartographic information theory over the past 50 years.Emphasis is on the evolution from the special to the general cartographic information theory.
引文
[1]WOOD D,FELS J.The Power of Maps[M].New York:Guilford Press,1992.
[2]WOOD D,FELS J,PICKLES J.The Natures of Maps:Cartographic Constructions of the Natural World[M].Chicago:University of Chicago Press,2009.
[3]ROBINSON A H.The Look of Maps[M].Madison:University of Wisconsin Press,1952.
[4]KEATES J S.The Perception of Colour in Cartography[C]//Proceedings of the Cartographic Symposium.Edinburgh:[s.n.],1962:19-28.
[5]SHANNON C E.A Mathematical Theory of Communication[J].The Bell System Technical Journal,1948,27(3):379-423.
[6]SUKHOV V 1.Information Capacity of a Map Entropy[J].Geodesy and Aerophotography,1967,10(4):212-215.
[7]邓敏,徐震.赵彬彬.等.地图概括中空间目标几何信息传递模型研究[J].地球信息科学学报,2010,12(5):655-661.DENG Min.XU Zhen,ZHAO Binbin.et al.A Transmission Model of Geometrical Information for Individual Spatial Objects in Cartographic Generalization[J].Journal of GeoInformation Science,2010,12(5):655-661.
[8]COVER T M,THOMAS J A.Elements of Information Theory[M].2nd ed.New Jersey:John Wiley&Sons,2006.
[9]KOLACCNY A.Cartographic Information—A Fundamental Concept and Term in Modern Cartography[J].Cartographica:The International Journal for Geographic Information and Geovisualization,1977,14(1):39-45.
[10]祝国瑞,黄采芝.一览图上居民地要素语义信息量的测度[J].武汉测绘学院学报,1985.10(4):89-96.ZHU Guorui,HUANG Caizhi.On the Measurement of Map Information of Settlements[J].Journal of Wuhan Technical University of Surveying and Mapping,1985,10(4):89-96.
[11]何宗宜.地图信息含量的量测研究[J].武汉测绘科技大学学报,1987,12(1):70-80.HE Zongyi.A Study of the Method for Measuring the Information Content of Map[J].Journal of Wuhan Technical University of Surveying and Mapping,1987,12(1):70-80.
[12]NEUMANN J.The Topological Information Content of a Map An Attempt at a Rehabilitation of Information Theory in Cartography[J].Cartographica.1994.31(1):26-34.
[13]KNOPFLI R.Communication Theory and Generalization[M]//TAYLOR D R F.Graphic Communication and Design in Contemporary Cartography.New York,Chichester:John Wiley&Sons,1983:177-218.
[14]BJ0RKE J T.Exploration of Information Theoretic Arguments for the Limited Amount of Information in a Map[J].Cartography and Geographic Information Science,2012,39(2):88-97.
[15]BJ0RKE J T.Framework for Entropy-Based Map Evaluation[J].Cartography and Geographic Information Systems,1996,23(2):78-95.
[16]刘宏林.地图信息的科学含义再探[J].测绘学院学报,1992(2):51-55.LIU Honglin.Exploring the Scientific Implication of Map Information Again[J].Journal of the Institute of Surveying and Mapping,1992(2):51-55.
[17]SHANNON C E,WEAVER W.The Mathematical Theory of Communication[M].Urbana:University of Illinois Press.1964.
[18]LI Zhilin,HUANG Peizhi.Quantitative Measures for Spatial Information of Maps[J].International Journal of Geographical Information Science,2002,16(7):699-709.
[19]王少一,王昭,杜清运.顾及地图要素级别的几何信息量量测方法[J].测绘科学,2007.32(4):60-62.WANG Shaoyi,WANG Zhao,DU Qingyun.A Measurement Method of Geometrical Information Considering MultiLevel Map Feature[J].Science of Surveying and Mapping,2007.32(4):60-62
[20]王昭.费立凡.基于语法层的地图综合信息量原则[J].测绘科学,2007,32(6):21-23.WANG Zhao.FE1 Lifan.Syntax-Based Information Quantity Rule for Automatic Map Generalization[J].Science of Surveying and Mapping,2007,32(6):21-23.
[21]艾廷华,何亚坤,杜欣.GIS数据尺度变换中的信息熵变化[J].地理与地理信息科学,2015,3i(2):7-11.AI Tinghua,HE Yakun,DU Xin.Information Entropy Change in GIS Data Scale Transformation[J].Geography and Geo-Information Science,2015,31(2):7-11.
[22]张辉.地图信息度量的方法及其应用[J].测绘与空间地理信息.2010.33(3):236-239.ZHANG Hui.The Approach and Application of Map Information Measurement[J],Geomatics cV Spatial Information Technology,2010,33(3):236-239.
[23]刘慧敏,樊子德,邓敏,等.地图上等高线信息度量的层次方法研究[J].测绘学报,2012,41(5):777-783.LIU Huimin,FAN Zide,DENG Min,et al.A Hierarchical Approach to Measuring the Information Content of the Contours in a Map[J].Acta Geodaetica et Cartographica Sinica,2012,41(5):777-783.
[24]陈杰,邓敏,徐枫,等.面状地图空间信息度量方法研究EJ].测绘科学,2010,35(1):74-76,49.CHEN Jie,DENG Min,XU Feng,et al.A Measurement Approach for Spatial Information of Area Map[J].Science of Surveying and Mapping,2010,35(1):74-76,49.
[25]刘慧敏.地图空间信息量的度量方法研究[D].长沙:中南大学,2012.LIU Huimin.Methods of Measuring the Spatial Information Content of a Map[D].Changsha:Central South University,2012.
[26]WU Huayi,ZHU Haijun,LIU Yi.A Raster-based Map Information Measurement for QoS[J],The International Archives of the Photogrammetry,Remote Sensing and Spatial Information Sciences.2004,35(B2):365-370.
[27]HARRIE L,STIGMAR H.An Evaluation of Measures for Quantifying Map Information[J].ISPRS Journal of Photogrammetry and Remote Sensing,2010,65(3):266-274.
[28]STIGMAR H,HARRIE L.Evaluation of Analytical Measures of Map Legibility[J].The Cartographic Journal,2011,48(1):41-53.
[29]HARRIE L,STIGMAR H,DJORDJEVIC M.Analytical Estimation of Map Readability[J].ISPRS International Journal of Geo-Information,2015,4(2):418-446.
[30]刘文锴,乔朝飞,陈云浩,等.等高线图信息定量度量研究[J].武汉大学学报(信息科学版),2008,33(2):157-159.LIU Wenkai,QIAO Chaofei.CHEN Yunhao,et al.Quantitative Measures for Spatial Information of Contour Maps[J].Geomatics and Information Science of Wuhan University,2008,33(2):157-159.
[31]王红.基础地理信息地形数据库信息量度量方法研究[D].阜新:辽宁工程技术大学,2010.WANG Hong.Research on Quantity Measurement of Basic Geographic Information in Topographic Database[D].Fuxin:Liaoning Technical University,2010.
[32]LI Zhilin,HUANG Peizhi.Transformations of Spatial Information in Multi-scale Representation[C]//Proceedings of the 20th International Cartographic Conference.Beijing:Scientific and Technical Program Committee,2001.
[33]邓敏,樊子德.刘慧敏.层次信息量的线要素化简算法评价研究[J].测绘学报.2013,42(5):767-773.DENG Min.FAN Zide,LIU Huimin.Performance Evaluation of Line Simplification Algorithms Based on Hierarchical Information Content[J].Acta Geodaetica et Cartographica Sinica,2013,42(5):767-773.
[34]王昭,吴中恒,费立凡,等.基于几何信息熵的面状要素注记配置[J].测绘学报,2009,38(2):183-188.WANG Zhao,WU Zhongheng,FEI Lifan,et al.Automatic Name Placement of Area Feature:A Metric Information Approach[J].Acta Geodaetica et Cartographica Sinica,2009,38(2):183-188.
[35]张恒,冯德俊,朱军,等.遥感影像信息量与空间分辨率的关系研究[J].应用光学,2014,35(3):409-413.ZHANG Heng,FENG Dejun,ZHU Jun,et al.Relationship between Information Content and Spatial Resolution of Remote Sensing Images[J].Journal of Applied Optics,2014,35(3):409-413.
[36]韩鹏,龚健雅,李志林,等.遥感影像分类中的空间尺度选择方法研究[J].遥感学报.2010,14(3):507-518.HAN Peng,GONG Jianya,LI Zhilin,et al.Selection of Optimal Scale in Remotely Sensed Image Classification[J].Journal of Remote Sensing,2010,14(3):507-518.
[37]林宗坚,张永红.遥感与地理信息系统数据的信息量及不确定性[J].武汉大学学报(信息科学版).2006,31(7):569-572.LIN Zongjian.ZHANG Yonghong.Measurement of Information and Uncertainty of Remote Sensing and GIS Data[J].Geomatics and Information Science of Wuhan University,2006,31(7):569-572.
[38]张盈,张景雄.顾及空间相关性的遥感影像信息量的度量方法[J].测绘学报,2015,44(10):1117-1124.DOI:10.11947/J.AGCS.2015.0140417.ZHANG Ying.ZHANG Jingxiong.Measure of Information Content of Remotely Sensed Images Accounting for Spatial Correlation[J].Acta Geodaetica et Cartographica Sinica,2015,44(10):1117-1124.DOI:10.11947/j.AGCS.2015.0140417.
[39]HU Lujin,HE Zongyi,LIU Jiping,et al.Method for Measuring the Information Content of Terrain from Digital Elevation Models[J].Entropy.2015.17(10),7021-7051.
[40]王家耀.关于信息时代地图学的再思考[J].测绘科学技术学报.2013,30(4):329-333.WANG Jiayao.Rethinking about the Information Age Cartography[J].Journal of Geomatics Science and Technology,2013,30(4):329-333.
[41]周成虎,朱欣焰,王蒙,等.全息位置地图研究[J].地理科学进展,2011,30(11):1331-1335.ZHOU Chenghu,ZHU Xinyan,WANG Meng,et al.Panoramic Location-based Map[J].Progress in Geography,2011,30(11):1331-1335.
[2]WOOD D,FELS J,PICKLES J.The Natures of Maps:Cartographic Constructions of the Natural World[M].Chicago:University of Chicago Press,2009.
[3]ROBINSON A H.The Look of Maps[M].Madison:University of Wisconsin Press,1952.
[4]KEATES J S.The Perception of Colour in Cartography[C]//Proceedings of the Cartographic Symposium.Edinburgh:[s.n.],1962:19-28.
[5]SHANNON C E.A Mathematical Theory of Communication[J].The Bell System Technical Journal,1948,27(3):379-423.
[6]SUKHOV V 1.Information Capacity of a Map Entropy[J].Geodesy and Aerophotography,1967,10(4):212-215.
[7]邓敏,徐震.赵彬彬.等.地图概括中空间目标几何信息传递模型研究[J].地球信息科学学报,2010,12(5):655-661.DENG Min.XU Zhen,ZHAO Binbin.et al.A Transmission Model of Geometrical Information for Individual Spatial Objects in Cartographic Generalization[J].Journal of GeoInformation Science,2010,12(5):655-661.
[8]COVER T M,THOMAS J A.Elements of Information Theory[M].2nd ed.New Jersey:John Wiley&Sons,2006.
[9]KOLACCNY A.Cartographic Information—A Fundamental Concept and Term in Modern Cartography[J].Cartographica:The International Journal for Geographic Information and Geovisualization,1977,14(1):39-45.
[10]祝国瑞,黄采芝.一览图上居民地要素语义信息量的测度[J].武汉测绘学院学报,1985.10(4):89-96.ZHU Guorui,HUANG Caizhi.On the Measurement of Map Information of Settlements[J].Journal of Wuhan Technical University of Surveying and Mapping,1985,10(4):89-96.
[11]何宗宜.地图信息含量的量测研究[J].武汉测绘科技大学学报,1987,12(1):70-80.HE Zongyi.A Study of the Method for Measuring the Information Content of Map[J].Journal of Wuhan Technical University of Surveying and Mapping,1987,12(1):70-80.
[12]NEUMANN J.The Topological Information Content of a Map An Attempt at a Rehabilitation of Information Theory in Cartography[J].Cartographica.1994.31(1):26-34.
[13]KNOPFLI R.Communication Theory and Generalization[M]//TAYLOR D R F.Graphic Communication and Design in Contemporary Cartography.New York,Chichester:John Wiley&Sons,1983:177-218.
[14]BJ0RKE J T.Exploration of Information Theoretic Arguments for the Limited Amount of Information in a Map[J].Cartography and Geographic Information Science,2012,39(2):88-97.
[15]BJ0RKE J T.Framework for Entropy-Based Map Evaluation[J].Cartography and Geographic Information Systems,1996,23(2):78-95.
[16]刘宏林.地图信息的科学含义再探[J].测绘学院学报,1992(2):51-55.LIU Honglin.Exploring the Scientific Implication of Map Information Again[J].Journal of the Institute of Surveying and Mapping,1992(2):51-55.
[17]SHANNON C E,WEAVER W.The Mathematical Theory of Communication[M].Urbana:University of Illinois Press.1964.
[18]LI Zhilin,HUANG Peizhi.Quantitative Measures for Spatial Information of Maps[J].International Journal of Geographical Information Science,2002,16(7):699-709.
[19]王少一,王昭,杜清运.顾及地图要素级别的几何信息量量测方法[J].测绘科学,2007.32(4):60-62.WANG Shaoyi,WANG Zhao,DU Qingyun.A Measurement Method of Geometrical Information Considering MultiLevel Map Feature[J].Science of Surveying and Mapping,2007.32(4):60-62
[20]王昭.费立凡.基于语法层的地图综合信息量原则[J].测绘科学,2007,32(6):21-23.WANG Zhao.FE1 Lifan.Syntax-Based Information Quantity Rule for Automatic Map Generalization[J].Science of Surveying and Mapping,2007,32(6):21-23.
[21]艾廷华,何亚坤,杜欣.GIS数据尺度变换中的信息熵变化[J].地理与地理信息科学,2015,3i(2):7-11.AI Tinghua,HE Yakun,DU Xin.Information Entropy Change in GIS Data Scale Transformation[J].Geography and Geo-Information Science,2015,31(2):7-11.
[22]张辉.地图信息度量的方法及其应用[J].测绘与空间地理信息.2010.33(3):236-239.ZHANG Hui.The Approach and Application of Map Information Measurement[J],Geomatics cV Spatial Information Technology,2010,33(3):236-239.
[23]刘慧敏,樊子德,邓敏,等.地图上等高线信息度量的层次方法研究[J].测绘学报,2012,41(5):777-783.LIU Huimin,FAN Zide,DENG Min,et al.A Hierarchical Approach to Measuring the Information Content of the Contours in a Map[J].Acta Geodaetica et Cartographica Sinica,2012,41(5):777-783.
[24]陈杰,邓敏,徐枫,等.面状地图空间信息度量方法研究EJ].测绘科学,2010,35(1):74-76,49.CHEN Jie,DENG Min,XU Feng,et al.A Measurement Approach for Spatial Information of Area Map[J].Science of Surveying and Mapping,2010,35(1):74-76,49.
[25]刘慧敏.地图空间信息量的度量方法研究[D].长沙:中南大学,2012.LIU Huimin.Methods of Measuring the Spatial Information Content of a Map[D].Changsha:Central South University,2012.
[26]WU Huayi,ZHU Haijun,LIU Yi.A Raster-based Map Information Measurement for QoS[J],The International Archives of the Photogrammetry,Remote Sensing and Spatial Information Sciences.2004,35(B2):365-370.
[27]HARRIE L,STIGMAR H.An Evaluation of Measures for Quantifying Map Information[J].ISPRS Journal of Photogrammetry and Remote Sensing,2010,65(3):266-274.
[28]STIGMAR H,HARRIE L.Evaluation of Analytical Measures of Map Legibility[J].The Cartographic Journal,2011,48(1):41-53.
[29]HARRIE L,STIGMAR H,DJORDJEVIC M.Analytical Estimation of Map Readability[J].ISPRS International Journal of Geo-Information,2015,4(2):418-446.
[30]刘文锴,乔朝飞,陈云浩,等.等高线图信息定量度量研究[J].武汉大学学报(信息科学版),2008,33(2):157-159.LIU Wenkai,QIAO Chaofei.CHEN Yunhao,et al.Quantitative Measures for Spatial Information of Contour Maps[J].Geomatics and Information Science of Wuhan University,2008,33(2):157-159.
[31]王红.基础地理信息地形数据库信息量度量方法研究[D].阜新:辽宁工程技术大学,2010.WANG Hong.Research on Quantity Measurement of Basic Geographic Information in Topographic Database[D].Fuxin:Liaoning Technical University,2010.
[32]LI Zhilin,HUANG Peizhi.Transformations of Spatial Information in Multi-scale Representation[C]//Proceedings of the 20th International Cartographic Conference.Beijing:Scientific and Technical Program Committee,2001.
[33]邓敏,樊子德.刘慧敏.层次信息量的线要素化简算法评价研究[J].测绘学报.2013,42(5):767-773.DENG Min.FAN Zide,LIU Huimin.Performance Evaluation of Line Simplification Algorithms Based on Hierarchical Information Content[J].Acta Geodaetica et Cartographica Sinica,2013,42(5):767-773.
[34]王昭,吴中恒,费立凡,等.基于几何信息熵的面状要素注记配置[J].测绘学报,2009,38(2):183-188.WANG Zhao,WU Zhongheng,FEI Lifan,et al.Automatic Name Placement of Area Feature:A Metric Information Approach[J].Acta Geodaetica et Cartographica Sinica,2009,38(2):183-188.
[35]张恒,冯德俊,朱军,等.遥感影像信息量与空间分辨率的关系研究[J].应用光学,2014,35(3):409-413.ZHANG Heng,FENG Dejun,ZHU Jun,et al.Relationship between Information Content and Spatial Resolution of Remote Sensing Images[J].Journal of Applied Optics,2014,35(3):409-413.
[36]韩鹏,龚健雅,李志林,等.遥感影像分类中的空间尺度选择方法研究[J].遥感学报.2010,14(3):507-518.HAN Peng,GONG Jianya,LI Zhilin,et al.Selection of Optimal Scale in Remotely Sensed Image Classification[J].Journal of Remote Sensing,2010,14(3):507-518.
[37]林宗坚,张永红.遥感与地理信息系统数据的信息量及不确定性[J].武汉大学学报(信息科学版).2006,31(7):569-572.LIN Zongjian.ZHANG Yonghong.Measurement of Information and Uncertainty of Remote Sensing and GIS Data[J].Geomatics and Information Science of Wuhan University,2006,31(7):569-572.
[38]张盈,张景雄.顾及空间相关性的遥感影像信息量的度量方法[J].测绘学报,2015,44(10):1117-1124.DOI:10.11947/J.AGCS.2015.0140417.ZHANG Ying.ZHANG Jingxiong.Measure of Information Content of Remotely Sensed Images Accounting for Spatial Correlation[J].Acta Geodaetica et Cartographica Sinica,2015,44(10):1117-1124.DOI:10.11947/j.AGCS.2015.0140417.
[39]HU Lujin,HE Zongyi,LIU Jiping,et al.Method for Measuring the Information Content of Terrain from Digital Elevation Models[J].Entropy.2015.17(10),7021-7051.
[40]王家耀.关于信息时代地图学的再思考[J].测绘科学技术学报.2013,30(4):329-333.WANG Jiayao.Rethinking about the Information Age Cartography[J].Journal of Geomatics Science and Technology,2013,30(4):329-333.
[41]周成虎,朱欣焰,王蒙,等.全息位置地图研究[J].地理科学进展,2011,30(11):1331-1335.ZHOU Chenghu,ZHU Xinyan,WANG Meng,et al.Panoramic Location-based Map[J].Progress in Geography,2011,30(11):1331-1335.