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孙国道, 王云超, 李藏, 蒋莉, 梁荣华. 基于二阶优化的地图重构算法[J]. 计算机辅助设计与图形学学报, 2020, 32(9): 1367-1376. DOI: 10.3724/SP.J.1089.2020.18139
引用本文: 孙国道, 王云超, 李藏, 蒋莉, 梁荣华. 基于二阶优化的地图重构算法[J]. 计算机辅助设计与图形学学报, 2020, 32(9): 1367-1376. DOI: 10.3724/SP.J.1089.2020.18139
Sun Guodao, Wang Yunchao, Li Cang, Jiang Li, Liang Ronghua. Map Reconstruction Algorithm Based on Quadratic Optimization[J]. Journal of Computer-Aided Design & Computer Graphics, 2020, 32(9): 1367-1376. DOI: 10.3724/SP.J.1089.2020.18139
Citation: Sun Guodao, Wang Yunchao, Li Cang, Jiang Li, Liang Ronghua. Map Reconstruction Algorithm Based on Quadratic Optimization[J]. Journal of Computer-Aided Design & Computer Graphics, 2020, 32(9): 1367-1376. DOI: 10.3724/SP.J.1089.2020.18139

基于二阶优化的地图重构算法

Map Reconstruction Algorithm Based on Quadratic Optimization

  • 摘要: 空间数据可视化是信息可视化的重要组成部分,而地图则是空间数据可视化最常用的载体.生成与传统地图相似的简化地图能够提高研究人员与普通民众对空间数据分析和可视查看的效率和准确率.然而传统通过人工绘制得到重构地图的过程十分烦琐,现有算法生成的重构地图大都由矩形形式组成,导致地图结构化信息缺失.这些因素都会影响重构地图的可视化效果.通过数据简化以缩减边界数据量、直角化与去噪声以规范图形边界和消除边界毛刺、二阶优化求解以得到最优布局效果这3个步骤,实现地图重构及可视化的完整流程.文中选择我国部分省份以及美国除夏威夷和阿拉斯加外的地区作为测试样本.对比现有的空间有序正方化布局算法,该算法能更好地维持重构地图与实际地图在区域形状和邻域关系的相似度.

     

    Abstract: Spatial data visualization is an important part of information visualization,and geographical map is the most common carrier of spatial data visualization.Generating simplified maps similar to traditional maps can improve the efficiency and accuracy of researchers and general public in analyzing and viewing spatial data.However,traditional process of reconstructing maps manually is tedious,and the reconstructed maps generated by existed algorithms are all composed of rectangular areas,which results in the loss of structural information.All of these factors may affect the visual perception of reconstructed maps.Our process of map reconstruction and visualization consists of following three steps,namely,reducing the amount of boundary data through data simplification,normalizing and removing boundary burrs through rectangularity and de-noise,and obtaining the optimal layout effect through quadratic optimization.In this paper,some provinces in China and regions of the United States except Hawaii and Alaska are selected as test sample.Compared with existed spatial ordered square layout algorithm,the proposed algorithm could better maintain the similarity between the reconstructed map and the original map with respect to the area shape and neighborhood relationship.

     

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