弯曲面积头尾断裂分类的曲线综合方法Curve generalization method based on area of bends classification using head/tail breaks
王杭宇;闫浩文;
摘要(Abstract)：
针对现有基于曲线弯曲的综合方法存在算法复杂、计算量大,过于关注局部相邻弯曲之间的关系,忽略整体弯曲之间联系,现有算法有用于筛选弯曲的阈值设置基于经验不合理等问题。该文借助头尾断裂分类法,提出了一种根据弯曲面积分类,以达到化简曲线目的的综合方法。该方法采用斜拉式曲线划分方法,将曲线划分为若干弯曲,以曲线首尾的连线为轴线,计算各个弯曲与相应轴线围成的面积,然后利用头尾断裂对其进行分类,将面积位于数据"头部"的弯曲予以保留,并提取"尾部"弯曲中距离轴线最远的点作为特征点,最后,合并弯曲与特征点作为综合结果。实验表明,该方法简单高效,可以迭代地在顾及整体弯曲数据且不使用经验阈值的情况下,舍去细小弯曲,保留原有曲线的特征弯曲,以获取不同细节层次下都符合自然规律且与原图高度相似的综合结果。
关键词(KeyWords)： 弯曲面积;头尾断裂;曲线综合
基金项目(Foundation): 国家自然科学基金项目（41671447,71563025）;; 兰州交通大学优秀平台支持项目（201806）
作者(Authors): 王杭宇;闫浩文;
DOI: 10.16251/j.cnki.1009-2307.2019.12.019
参考文献(References)：
- [1]毋河海．地图信息自动综合基本问题研究[J]．武汉测绘科技大学学报，2000(5):377-386.(WU Hehai.Research on fundamental theory and technical approaches of automated map generalization[J].Journal of Wuhan Technical University of Surveying and Mapping,2000(5):377-386.)
- [2]邓敏，樊子德，刘慧敏．层次信息量的线要素化简算法评价研究[J]．测绘学报，2013,42(5):767-773,781.(DENG Min,FAN Zide,LIU Huimin.Performance evaluation of line simplification algorithms based on hierarchical information content[J].Acta Geodaetica et Cartographica Sinica,2013,42(5):767-773,781.)
- [3]张青年，廖克．基于结构分析的曲线概括方法[J]．中山大学学报（自然科学版），2001(5):118-121.(ZHANG Qingnian,LIAO Ke.Line generalization based on structure analysis[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2001(5):118-121.)
- [4] ZHILIN L I,STAN OPENSHAW.Algorithms for automated line generalization based on a natural principle of objective generalization[J].International Journal of Geographical Information Systems,1992,6(5):373-389.
- [5] VISVALINGM M,WHYATT J.Line Generalization by Repeated Elimination of Points[J]. The Cartographic Journal,1993,30(7):46-51.
- [6]郭庆胜．线状要素图形综合的渐进方法研究[J]．武汉测绘科技大学学报，1998(1):54-58.(GUO Qinsheng.Study on progressive approach to graphic generalization of linear feature[J].Journal of Wuhan Technical University of Surveying and Mapping,1998(1):54-58.)
- [7] SHENG Zhou,CHRISTOPHER B J.Shape-aware line generalisation with weighted effective area[C]∥FISHER Peter F.Developments in Spatial Data Handling.Berlin:Springer,2005:369-380.
- [8] GUILBERT E,SAUX E.Cartographic generalisation of lines based on a B-spline snake model[J].International Journal of Geographical Information Science,2008,22(8):847-870.
- [9]祝国瑞，郭礼珍，尹贡白，等．地图设计与编绘[M]．武汉：武汉大学出版社，2001.(ZHU Guorui,GUO Lizhen,YIN Gongbai,et al.Map design and compilation[M].Wuhan:Wuhan University Press,2001.)
- [10]钱海忠，武芳，陈波，等．采用斜拉式弯曲划分的曲线化简方法[J]．测绘学报，2007(4):443-449,456.(QIAN Haizhong,WU Fang,CHEN Bo,et al.Simplifying line with oblique dividing curvemethod[J].Acta Geodaetica et Cartographica Sinica,2007(4):443-449,456.)
- [11]钱海忠，何海威，王骁，等．采用三元弯曲组划分的线要素化简方法[J]．武汉大学学报（信息科学版），2017,42(8):1096-1103.(QIAN Haizhong,HE Haiwei,WANG Xiao,et al.Line simplification method based on threebends groups division[J].Geomatics and Information Science of Wuhan University,2017,42(8):1096-1103.)
- [12]杜佳威，武芳，巩现勇，等．采用双向斜拉式弯曲划分的曲线渐进化简方法[J]．中国图象图形学报，2017,22(10):1455-1466.(DU Jiawei,WU Fang,GONG Xianyong,et al.Progressive line simplification approach based on the double-oblique-dividing-curve method[J].Journal of Image and Graphics,2017,22(10):1455-1466.)
- [13]JIANG Bin,LIU Xintao,JIA tao.Scaling of geographic space as a universal rule for map generalization[J].Annals of the Association of American Geographers,2013,103(4):844-855.
- [14]杜佳威，武芳，李靖涵，等．采用多元弯曲组划分的线要素化简方法[J]．计算机辅助设计与图形学学报，2017,29(12):2189-2196.(DU Jiawei,WU Fang,LI Jinghan,et al.Line simplification method based on multi-bends groups division[J].Journal of ComputerAided Design&Computer Graphics,2017,29(12):2189-2196.)
- [15]QIAN H Z,ZHANG M,WU F.A new simplification approach based on the oblique-dividing-curve method for contour lines[J].International Journal of GeoInformation,2016,5(9):153-173.
- [16]JIANG Bin,YIN Junjun.Ht-Index for quantifying the fractal or scaling structure of geographic features[J].Annals of the Association of American Geographers,2014,104(3):530-540.
- [17]JIANG Bin.Head/tail breaks:a new classification scheme for data with a heavy-tailed distribution[J].The Professional Geographer,2013,65(3):482-494.
- [18]操震洲，李满春，程亮．曲线弯曲的多叉树表达[J]．测绘学报，2013,42(4):602-607.(CAO Zhenzhou,LI Manchun,CHENG Liang.Multi-way trees representation for curve bends[J].Acta Geodaetica et Cartographica Sinica,2013,42(4):602-607.)
- [19]武芳，朱鲲鹏．线要素化简算法几何精度评估[J]．武汉大学学报（信息科学版），2008,33(6):600-603.(WU Fang,ZHU Kunpeng.Geometric accuracy assessment of linear features’simplification algorithms[J].Geomatics and Information Science of Wuhan University,2008,33(6):600-603.)
- [20]SHI Wenzhong,CHEUNG Chuikwan.Performance evaluation of line simplification algorithms for vector generalization[J].The Cartographic Journal,2006,43(1):27-44.