Methods Of Measuring The Spatial Information Content Of A Map

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.