Determining an accurate flow direction is a prerequisite for hydrographic analysis and river generalization. For river networks with complex spatial structures and little semantic information, it has always been a difficult and interesting problem to automatically and objectively determine the flow direction of all rivers. In a river network with many estuaries, tributaries may either be "simple tributaries" that are associated only with a single main channel or "bridging tributaries" that link multiple main channels. The former is large in number, while the latter is few, but both of them are very important in constructing the hierarchical relationship of the whole river network.Existing studies have concentrated on simple tributaries, and flow direction reasoning for bridging tributaries is ignored, leading to a misunderstanding of the spatial structure of river networks. To address this problem, an automatic method of flow direction reasoning for bridging tributaries using adjacency relation (FDR-BR method) is proposed. First, in view of the insufficient semantic information in actual river data, the principle of "the minority is subordinate to the majority" is adopted to establish two statistical identification criteria for estuaries, and main channels are extracted by using the good continuity feature between river reaches, that is, stroke feature. Second, the K th -order adjacency fields are constructed for each main channel based on the topological connection relationships between the main channels and tributaries.Finally, the "split river reaches" are detected from the bridging tributaries, and the spatial adjacency relation is used as a constraint to identify the benchmark main channel of each bridging tributary. The FDR-BR method is validated using a geographical census dataset for a city in China. In the experimental area, simple river networks with independent main channels account for 91.67% of the networks, and complex river networks with multiple main channels account for 8.33%. For the complex river networks, 77.79% of the tributaries are simple tributaries, while 13.27% are bridging tributaries. The experimental results reveal that for all rivers in the simple river networks and the simple tributaries in the complex river networks, the flow direction reasoning results of FDR-BR method are consistent with the results of the state-of-
Road networks are the skeletal elements of topographic maps at different scales, and road selection is a prerequisite for implementing continuous multiscale spatial representations of road networks. The mesh-based approach is a common, advanced and powerful method for road selection in dense road areas in which small meshes are removed and road segments with the least importance in each mesh are eliminated. However, small meshes in a map can be classified into two types: aggregated small meshes and isolated small meshes. The number of the former is small, and that of the latter is large. Existing methods are generally applicable for the latter, and some or even most spatial characteristics will be lost when they are applied to the former; as a result, the road selection quality will be affected. Therefore, as a supplement to the mesh-based selection method, this paper proposed an automatic generalization method of dense road network areas (areas formed by aggregated small meshes) considering spatial structural features as constraints. First, the aggregated areas of small meshes were identified based on the number of adjoining small meshes, and the boundaries of aggregated areas are extracted and used as hard constraints during mesh elimination. Second, the starting meshes were redefined by simultaneously considering the edge features and mesh density of small meshes, and an ordinal elimination algorithm was proposed to eliminate the meshes in the stroke connection direction. Third, road selection was implemented by identifying the starting meshes and sequentially processing the related mesh pairs. This iterative process continued until all mesh densities of the newly formed meshes are beyond the threshold or the problem becomes a simple elimination problem involving two adjoining small meshes or one isolated small mesh. Finally, a 1:10,000 standard topographic road map for Jiangsu Province, China, was used for validation. The experimental results showed that in the aggregated areas with two small meshes, 31% of the areas obtained the same selection results by using the mesh-based method and the proposed method, and the remaining 69% obtained a more compact result with the proposed method. Moreover, for all aggregated areas with more than two small meshes, the spatial distribution structure of small meshes was preserved better by the proposed method.
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