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Objectives: Curve simplification is of importance in automated map generalization; nevertheless, the Douglas-Peucker (DP) algorithm popularly used in map generalization is not automatic, because a key parameter called distance tolerance (ε) must be given by experienced cartographers and needs to be input before execution of the algorithm. Methods: To solve the problem, this paper proposed a method to automatically calculate ε and by which the automation of the DP algorithm is achieved. The method consists of the following steps: (1) A formula is constructed by the Hausdorff distance for calculating the similarity degree (Ssim) between a curve at a larger scale and its simplified counterpart at a smaller scale. (2) 15 linear rivers are selected, and each of them is manually simplified to get their counterparts at seven different scales. The Ssim of each original river and each of its simplified counterpart at a smaller scale can be obtained using the formula constructed by the Hausdorff distance, and 15×7=105 coordinate pairs consisting of (S,Ssim) can be got, and a function between Ssim and S are constructed by the curve fitting using the coordinates. (3) In the meanwhile, the 15 rivers are simplified using a number of ε, and the Ssim of each original river and each of its simplified counterpart at a smaller scale can be calculated using the formula constructed by the Hausdorff distance. In this way, a number of coordinate pairs (ε,Ssim) are got, and a function between ε and Ssim is constructed by the curve fitting. (4) By the function between Ssim and S and that between ε and Ssim, a formula between ε and S can be deducted. Using the formula ε can be calculated automatically, because in a map generalization task S is usually known. After this step, automation of the DP algorithm is achieved. Results: The experiment results show that (1) The proposed DP algorithm can automatically simplify the rivers in a specific geographical area to get the results at different scales; and (2) the resulting river curves generated by the proposed DP algorithm have a high degree of similarity with the ones made by experienced cartographers. Their average similarity degree is 0.927. Conclusion: The proposed DP algorithm can simplify curve features on maps automatically, and the results are highly intelligent and credible. Although only river data is tested in this paper, the principle of the proposed method can be extended to other linear features on maps. Our future work will be on improving the accuracy of the proposed DP algorithm using more river data so that the algorithm can be used in practical map generalization engineering. [ABSTRACT FROM AUTHOR]

Objectives: In the transferring process from the modern society to the post-modern society, information is transmitted via We Media, in which the maps that are made by public users and map enthusiasts is not at high accuracy, and the expressions of the maps are diversified. WeMap is a kind of public-made maps, aiming to improve the map expressions to avoid the problems generated due to the lack of spatial cognitive knowledge, and to focus on the expressions of the map users subjective information. Unlike the traditional maps, WeMap aims to express geographical features and phenomena from multiple per‐ spectives and dimensions. This paper examine the origins of the above characteristics from the postmodern philosophy perspective. Methods: Metaphoring maps and language, taking postmodern philosophical methodologies such as embodied cognitive view, prototype category theory and decentralism of cognitive linguistics as tools, this paper critically analyzes and reconstructs the fundamental problems including spatial cognition, information classification and cartographic expression of traditional maps, and forms the conceptual framework of WeMap with the characteristics of postmodern philosophy. Results: WeMap cognitive process model was proposed, consisting of two processes: Map making process which can be summarized as mental image-image schema-prototype category-geographic knowledge-WeMap, and the map reading process which can be described as visual representation-visual feature-semantic and spatial relationship-cognitive map-spatial analysis-spatial behavior. The cognitive hierarchy model of WeMaps may be classified into six levels ( from IS1 to IS6) by the image schema. IS1 is suitable for most of public users who own the basic body image schema and it corresponds to the lowest cognitive ability, while IS2, IS3, IS4, IS5 and IS6 correspond to more advanced cognition abilities. The information classification of WeMap coin‐cides with prototype category theory which can be realized according to the principle of achieving common ness with prototype and compatibility with category. WeMap advocates pluralism which embodies in fuzzy map projections, various forms of map symbols, and even the opposite generalization standards compare to traditional maps. Conclusions: WeMap is a new map form in the era of We Media whose cognitive model, classification principle and map expressions coincide with the ideas of embodied cognitive view, prototype category and decentralism of postmodern philosophy. The philosophical basis of traditional map is more inclined to metaphysical mechanical objectivism. Although it recognizes the role of human cognition in map making and use, the human here refers to map experts. Maps can only be developed under the design of map experts, which is difficult to give full play to the linguistic potential of maps. Map theories, such as adaptive maps and crowdsourcing maps, have begun to pay attention to the transformation of their philo‐sophical basis, emphasizing the transfer of the main body of cartography and map use from map experts to public users, but they are still limited by the design knowledge and ability of map experts. WeMap aims to put map experts and public users on an equal position, fully respect the individual geospatial cognitive needs and habits of each map user, the decentralization of WeMap conforms to the development trend of human post-modernist philosophy. [ABSTRACT FROM AUTHOR]

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Objectives: Quantitative expression of topological relations of contour is vital to spatial cognition, topological feature mining and map generalization. However, previous studies focus on the construction of contour tree and the generalization algorithm of contour. However, its lack of the quantitative expression of topological relations and the research of the quantitative relationship between it and map scale change, and it is still unknown whether the topological indexes of different geomorphic types vary with map scale change or not. Methods: By preprocessing of non - closed contour and constructing directed contour tree, such as topology checking, matching and non-closed contour closure, a quantitative expression model of them was proposed and constructed, and 60 groups multi-scale contour datasets from different geomorphic types in Gansu were used to explore the consistency of the relationship. Results and Conclusions: Experimental results show that the topological indexes change rules of adjacent scale is consistent with the space cognitive and reasoning, and the same power function can be used to express the quantitative relation-ship of contour from different geomorphic types, which further demonstrates that it is rationality and possibility to realization the completely automatic generalization of contour based on multi-scale spatial similarity relation. [ABSTRACT FROM AUTHOR]

Objectives: Most of the existing building simplification methods focus on one or two aspects of the three principles: Area preservation, shape characteristics enhancement and drawing rectangles if possible. In practice, map generalization is a process of mutual restriction and trade off of various influencing conditions, cartographic experts consider all the three aspects and balance them to reach reasonable results, sometimes they delete the small details on building's outlines, but it results in the area difference, sometimes they displace some points of the edges so that the area stays unchanged, but the vertices location changes. It depends on the short-edge structures and distributions. By imitating this thinking and operation process of cartographers, a method based on short-edge structure recognition and progressive simplification is proposed. Methods: Firstly, the building outline is preprocessed. Then the contour segments are grouped, and the edge structure is identified and analyzed. After this, some specific situations are analyzed in detail, and the calculation region (the sequence of vertices associated with the simplification of a set of edges less than the tolerance) is used to determine the optimal simplification method. Lastly, the area difference is distributed to the whole building so that the building's area difference is reduced while the shape is maintained. Open Street Map (OSM) buildings are selected in the experiment. Results: Experimental results show that the proposed method can effectively reduce the number of graphic vertices, enhances the shape characteristics like parallel, right angle, etc. Also, the approach can control the area differences after generalization. Conclusions: The proposed method gives consideration to three aspects of the building simplification principles and balances them, which provides a new way for building simplification. [ABSTRACT FROM AUTHOR]