Theory of Spatial Similarity Relations and Its Applications in Automated Map Generalization
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Automated map generalization is a necessary technique for the construction of multi-scale vector map databases that are crucial components in spatial data infrastructure of cities, provinces, and countries. Nevertheless, this is still a dream because many algorithms for map feature generalization are not parameter-free and therefore need human’s interference. One of the major reasons is that map generalization is a process of spatial similarity transformation in multi-scale map spaces; however, no theory can be found to support such kind of transformation. This thesis focuses on the theory of spatial similarity relations in multi-scale map spaces, aiming at proposing the approaches and models that can be used to automate some relevant algorithms in map generalization. After a systematic review of existing achievements including the definitions and features of similarity in various communities, a classification system of spatial similarity relations, and the calculation models of similarity relations in the communities of psychology, computer science, music, and geography, as well as a number of raster-based approaches for calculating similarity degrees between images, the thesis achieves the following innovative contributions. First, the fundamental issues of spatial similarity relations are explored, i.e. (1) a classification system is proposed that classifies the objects processed by map generalization algorithms into ten categories; (2) the Set Theory-based definitions of similarity, spatial similarity, and spatial similarity relation in multi-scale map spaces are given; (3) mathematical language-based descriptions of the features of spatial similarity relations in multi-scale map spaces are addressed; (4) the factors that affect human’s judgments of spatial similarity relations are proposed, and their weights are also obtained by psychological experiments; and (5) a classification system for spatial similarity relations in multi-scale map spaces is proposed. Second, the models that can calculate spatial similarity degrees for the ten types of objects in multi-scale map spaces are proposed, and their validity is tested by psychological experiments. If a map (or an individual object, or an object group) and its generalized counterpart are given, the models can be used to calculate the spatial similarity degrees between them. Third, the proposed models are used to solve problems in map generalization: (1) ten formulae are constructed that can calculate spatial similarity degrees by map scale changes in map generalization; (2) an approach based on spatial similarity degree is proposed that can determine when to terminate a map generalization system or an algorithm when it is executed to generalize objects on maps, which may fully automate some relevant algorithms and therefore improve the efficiency of map generalization; and (3) an approach is proposed to calculate the distance tolerance of the Douglas-Peucker Algorithm so that the Douglas-Peucker Algorithm may become fully automatic. Nevertheless, the theory and the approaches proposed in this study possess two limitations and needs further exploration. • More experiments should be done to improve the accuracy and adaptability of the proposed models and formulae. The new experiments should select more typical maps and map objects as samples, and find more subjects with different cultural backgrounds. • Whether it is feasible to integrate the ten models/formulae for calculating spatial similarity degrees into an identical model/formula needs further investigation. In addition, it is important to find out the other algorithms, like the Douglas-Peucker Algorithm, that are not parameter-free and closely related to spatial similarity relation, and explore the approaches to calculating the parameters used in these algorithms with the help of the models and formulae proposed in this thesis.