地图空间信息量的度量方法研究
摘要
地图通常表达着复杂的空间地理环境信息,人们通过地图可以便捷地认识自然和社会经济现象。早在60年代捷克制图学家Koldcny把信息的概念引入地图制图学时,地图传输信息的功能在制图学界产生了巨大影响,开创了现代地图学的一个新领域—地图信息传输理论(亦称地图信息论)。地图空间信息量度量是地图信息传输理论的一个最基础的问题,定量计算地图空间信息量一方面可以为地图设计、地图分析评价提供依据；另一方面亦为地图综合提供选取标准,控制地图综合的评价指标。鉴于此,本论文紧紧围绕地图空间信息量的度量这一基础研究问题,分别从地图元素层次和专题地图层次研究空间信息量度量的方法,并探讨地图空间信息量度量在地图信息传输和制图综合中的初步应用。具体地,主要研究内容包括：
1.系统地分析了地图空间信息量度量的当前进展,包括地图空间信息的分类、度量方法及其应用等方面,详细分析了现有研究中存在的主要问题。进而,为了建立合理的地图空间信息量度量模型,本文归纳分析了不同领域的信息定义,指出了信息产生的本质即多样性或差异性特征,并结合地图制图的特点,系统地阐述了地图空间信息的定义、分类方法、度量准则以及基于特征的信息量度量的数学模型。
2.系统地研究了点要素、线要素和面要素的空间信息量度量方法。针对点要素的空间信息量度量,研究提出了一种改进的弧比弦算法,并用来定量描述节点的重要性程度,进而建立了节点的空间信息量度量方法。针对线要素和面要素,提出了基于认知的线、面要素几何形态分解方法,给出了定量的描述指标。在此基础上,采用层次策略,分别提出了基于弯曲的线要素空间信息量度量方法和基于凸包的面要素空间信息量度量方法。最后,采用实际的地图要素数据对所提出的方法进行了实验验证和分析,结果表明了所提方法的正确性。
3.系统地研究了点状专题图、线状专题图和面状专题图的空间信息量度量方法。采用“专题地图空间信息的认知→空间信息内容构成→空间信息内容描述→空间信息量的层次度量”的研究思路,重点研究提出了专题图空间信息的层次分类和描述方法,包括元素层次的结构形态信息、邻域层次的拓扑邻接信息和整体层次的空间分布信息,并分别建立了各层次空间信息量的计算模型。最后,采用实际地图数据对所提出的方法进行了合理性验证和对比实验分析,结果表明所提方法的合理性和优越性。
4.研究了地图空间信息量的度量方法在地图数据渐进性传输和地图综合算法性能评价方面的初步应用。首先,以面要素为例,采取具有代表性的面要素渐进式传输变化累积模型,研究建立了面要素渐进性传输过程中空间信息量变化分析方法,建立了空间信息传递状况的定量评价指标。然后,以一些最具代表性的线要素化简算法为例,建立了基于层次空间信息量的线要素化简算法性能评价方法。最后,采用实际地图数据对所提出的方法进行了实验验证和对比分析,结果表明所提方法的合理性和优越性。
最后,总结了本文的研究成果,并展望了该方向进一步研究的若干问题。
Map is a visualization representation of geospatial entities and their distribution. Users often can obtain large amount of information through reading a map, and further solve their application requirements, or better understand the local natural environment, phenomenon and even all over the world. As early in1960s, Kolacny introduced the concept of information into the domain of cartography. This pioneering work promotes the development of theoretical cartography and a new research topic, i.e. map information transmission theory, is paid more and more attention by the scholars from the international cartographic association.
The measurement of map information content is one of the most important basic research issues in the theory of map information transmission. It has been preliminarily applied to evaluation of map generalization, geospatial information service and visualization of mobile map, geospatial information transmission, the production and updating of multi-scale maps, etc. As a matter of fact, information content has been considered as an important indicator for evaluating the efficiency of map design, map generalization algorithm and the transmission of spatial information. Therefore, this dissertation is focused on the quantitative measurement of geospatial information content of a map, that is, to develop a methodology for the measurement of geospatial information content. It includes two levels, one is to measure the information content of spatial feature, i.e. feature level; the other is measure the information content of a thematic map, i.e. thematic map level. The applications of the proposed methods to map information transmission and map generalization algorithms evaluation are also concerned. In the following, the main work of this dissertation is elaborated.
1. Many representative methods for measuring map information content are reviewed in detail. These methods are developed based on the Shannon information theory. Indeed, it also should be pointed out that, there are many problems for further consideration. For this purpose, this dissertation firstly analyzes the definition of information in various domains such as information science, computer science and cognition science and discovers the connotation of information, and discovers the essence of information content, i.e. variability or diversity. Further, the definitions of information are naturally extended to map information content, and a scientific definition of map information content is stated by considering the property of cartography. The types of map information content are further analyzed and summarized into statistical information, geometric information, topological information and thematic information. On this basis, the standards of measuring map information content are elaborated and related mathematical foundation (e.g. various types of information entropy) is highlighted.
2. At feature level, this dissertation systematically discusses the measurement of geospatial information content of point, line and area features. For a point feature, the most common-used local length ratio algorithm is analyzed and an improved local length ratio algorithm is proposed, which is further utilized to describe the importance of vertices. On this basis, a computational model of point information content is developed. For line and area features, their geometric shape is deemed to be the carrier of geospatial information content. Therefore, the partition of a line or an area feature is proposed from the view of spatial cognition, and further quantitative indicators are defined for the description of geometric shape. Sequentially, the computational models are developed to measure the geospatial information content of individual line or area features, which are based upon their partitions, i.e. the bends of individual line and the convex hull of individual area. At last, practical examples are provided to illustrate the rational of the proposed methods.
3. At thematic map level, this dissertation systematically discusses the measurement of spatial information contents of point-, line-and area-shaped thematic maps, which involves the spatial cognition of thematic map information, the type and description of thematic map information contents, and the computational methods. This dissertation places the emphases on the hierarchical classification of thematic map information contents (i.e. the geometrical structural information at element level, the topological adjacency information at neighborhood level and the spatial distribution information at global level) and their computational models. Finally, some practical examples are provided to illustrate the rational and advantages of the proposed models and methods.
4. This dissertation investigates the applications of above-mentioned models and methods of map information content to the progressive transmission of geospatial data and the performance evaluation of map generalization algorithms. For the former, the changes accumulation model is chosen as the model of information transfer, and the computational model of geospatial information content is employed to analyze quantitatively the geometrical information transferred in the progressive transmission of area features. Moreover, a set of evaluation indicators of transmission information are put forward to the quantitative analysis of transfer status. The result of the experiments shows that the proposed indicators of information content are feasible to control the transmission process and thus to improve the transmission efficiency of geometrical information. For the latter, the representative line simplification algorithms are chosen as example, and the difference of information content before and after line simplification is computed and utilized to evaluate performance of line simplification algorithms. A river network dataset is used to test the performance evaluations of seven common-used line simplification algorithms by using the indicator of information content. It is proven that this new indicator is very rational to evaluate the performance of these line simplification algorithms. At the meantime, a comparative test is made to show the advantages of the new indicator.
Finally, this dissertation summarizes the new findings among the above investigations, and highlights some of valuable issues for further research in the future.
1.系统地分析了地图空间信息量度量的当前进展,包括地图空间信息的分类、度量方法及其应用等方面,详细分析了现有研究中存在的主要问题。进而,为了建立合理的地图空间信息量度量模型,本文归纳分析了不同领域的信息定义,指出了信息产生的本质即多样性或差异性特征,并结合地图制图的特点,系统地阐述了地图空间信息的定义、分类方法、度量准则以及基于特征的信息量度量的数学模型。
2.系统地研究了点要素、线要素和面要素的空间信息量度量方法。针对点要素的空间信息量度量,研究提出了一种改进的弧比弦算法,并用来定量描述节点的重要性程度,进而建立了节点的空间信息量度量方法。针对线要素和面要素,提出了基于认知的线、面要素几何形态分解方法,给出了定量的描述指标。在此基础上,采用层次策略,分别提出了基于弯曲的线要素空间信息量度量方法和基于凸包的面要素空间信息量度量方法。最后,采用实际的地图要素数据对所提出的方法进行了实验验证和分析,结果表明了所提方法的正确性。
3.系统地研究了点状专题图、线状专题图和面状专题图的空间信息量度量方法。采用“专题地图空间信息的认知→空间信息内容构成→空间信息内容描述→空间信息量的层次度量”的研究思路,重点研究提出了专题图空间信息的层次分类和描述方法,包括元素层次的结构形态信息、邻域层次的拓扑邻接信息和整体层次的空间分布信息,并分别建立了各层次空间信息量的计算模型。最后,采用实际地图数据对所提出的方法进行了合理性验证和对比实验分析,结果表明所提方法的合理性和优越性。
4.研究了地图空间信息量的度量方法在地图数据渐进性传输和地图综合算法性能评价方面的初步应用。首先,以面要素为例,采取具有代表性的面要素渐进式传输变化累积模型,研究建立了面要素渐进性传输过程中空间信息量变化分析方法,建立了空间信息传递状况的定量评价指标。然后,以一些最具代表性的线要素化简算法为例,建立了基于层次空间信息量的线要素化简算法性能评价方法。最后,采用实际地图数据对所提出的方法进行了实验验证和对比分析,结果表明所提方法的合理性和优越性。
最后,总结了本文的研究成果,并展望了该方向进一步研究的若干问题。
Map is a visualization representation of geospatial entities and their distribution. Users often can obtain large amount of information through reading a map, and further solve their application requirements, or better understand the local natural environment, phenomenon and even all over the world. As early in1960s, Kolacny introduced the concept of information into the domain of cartography. This pioneering work promotes the development of theoretical cartography and a new research topic, i.e. map information transmission theory, is paid more and more attention by the scholars from the international cartographic association.
The measurement of map information content is one of the most important basic research issues in the theory of map information transmission. It has been preliminarily applied to evaluation of map generalization, geospatial information service and visualization of mobile map, geospatial information transmission, the production and updating of multi-scale maps, etc. As a matter of fact, information content has been considered as an important indicator for evaluating the efficiency of map design, map generalization algorithm and the transmission of spatial information. Therefore, this dissertation is focused on the quantitative measurement of geospatial information content of a map, that is, to develop a methodology for the measurement of geospatial information content. It includes two levels, one is to measure the information content of spatial feature, i.e. feature level; the other is measure the information content of a thematic map, i.e. thematic map level. The applications of the proposed methods to map information transmission and map generalization algorithms evaluation are also concerned. In the following, the main work of this dissertation is elaborated.
1. Many representative methods for measuring map information content are reviewed in detail. These methods are developed based on the Shannon information theory. Indeed, it also should be pointed out that, there are many problems for further consideration. For this purpose, this dissertation firstly analyzes the definition of information in various domains such as information science, computer science and cognition science and discovers the connotation of information, and discovers the essence of information content, i.e. variability or diversity. Further, the definitions of information are naturally extended to map information content, and a scientific definition of map information content is stated by considering the property of cartography. The types of map information content are further analyzed and summarized into statistical information, geometric information, topological information and thematic information. On this basis, the standards of measuring map information content are elaborated and related mathematical foundation (e.g. various types of information entropy) is highlighted.
2. At feature level, this dissertation systematically discusses the measurement of geospatial information content of point, line and area features. For a point feature, the most common-used local length ratio algorithm is analyzed and an improved local length ratio algorithm is proposed, which is further utilized to describe the importance of vertices. On this basis, a computational model of point information content is developed. For line and area features, their geometric shape is deemed to be the carrier of geospatial information content. Therefore, the partition of a line or an area feature is proposed from the view of spatial cognition, and further quantitative indicators are defined for the description of geometric shape. Sequentially, the computational models are developed to measure the geospatial information content of individual line or area features, which are based upon their partitions, i.e. the bends of individual line and the convex hull of individual area. At last, practical examples are provided to illustrate the rational of the proposed methods.
3. At thematic map level, this dissertation systematically discusses the measurement of spatial information contents of point-, line-and area-shaped thematic maps, which involves the spatial cognition of thematic map information, the type and description of thematic map information contents, and the computational methods. This dissertation places the emphases on the hierarchical classification of thematic map information contents (i.e. the geometrical structural information at element level, the topological adjacency information at neighborhood level and the spatial distribution information at global level) and their computational models. Finally, some practical examples are provided to illustrate the rational and advantages of the proposed models and methods.
4. This dissertation investigates the applications of above-mentioned models and methods of map information content to the progressive transmission of geospatial data and the performance evaluation of map generalization algorithms. For the former, the changes accumulation model is chosen as the model of information transfer, and the computational model of geospatial information content is employed to analyze quantitatively the geometrical information transferred in the progressive transmission of area features. Moreover, a set of evaluation indicators of transmission information are put forward to the quantitative analysis of transfer status. The result of the experiments shows that the proposed indicators of information content are feasible to control the transmission process and thus to improve the transmission efficiency of geometrical information. For the latter, the representative line simplification algorithms are chosen as example, and the difference of information content before and after line simplification is computed and utilized to evaluate performance of line simplification algorithms. A river network dataset is used to test the performance evaluations of seven common-used line simplification algorithms by using the indicator of information content. It is proven that this new indicator is very rational to evaluate the performance of these line simplification algorithms. At the meantime, a comparative test is made to show the advantages of the new indicator.
Finally, this dissertation summarizes the new findings among the above investigations, and highlights some of valuable issues for further research in the future.
引文
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