基于空间拓扑条件控制的等高线化简方法  

Contour Line Simplification Methods Based on the Control of Spatial Topological Conditions

作　　者：李元復 孙群 温伯威 周炤 朱蕊 LI Yuanfu;SUN Qun;WEN Bowei;ZHOU Zhao;ZHU Rui(Institute of Geospatial Information,PLA Strategic Support Force Information Engineering University,Zhengzhou 450052,China)

机构地区：[1]中国人民解放军战略支援部队信息工程大学地理空间信息学院,郑州450052

出　　处：《地球信息科学学报》2024年第7期1659-1671,共13页Journal of Geo-information Science

基　　金：国家自然科学基金项目(42101458、42101455、42101454);河南省中原学者资助项目(202101510001);智慧中原地理信息技术河南省协同创新中心和时空感知与智能处理自然资源部重点实验室基金资助项目(212102)。

摘　　要：等高线是地形图上的重要要素之一,其化简过程需要兼顾主要地形结构特征的保持、数据精度的控制以及相交和视觉混淆的避免等问题,现有研究大多没有同时兼顾这3个方面。针对上述问题,本文在现有方法使用的误差带的基础上,进一步引入隔离带的概念,并对它们在几何中的定义进行数学描述,提出将空间拓扑条件应用于等高线化简的策略。根据这一策略,对谷地弯曲选取(Valley Bend Selection,VBS)算法和Douglas-Peucker(DP)算法进行改进,从而得到空间拓扑条件控制下的VBS(Spatial-Topologic-Condition-Controlled VBS,STCC-VBS)算法和空间拓扑条件控制下的DP(Spatial-Topologic-Condition-Controlled DP,STCC-DP)算法。最后,将这2种方法应用于1:5万比例尺地形图等高线化简生成1:10万比例尺地形图等高线的任务中,并与现有的2种单纯以误差带控制的等高线化简方法进行对比。实验结果表明,STCC-VBS算法和STCC-DP算法都有效避免了相交问题,同时以改进前的方法为参考,在算法参数相同的情况下,分别在节点约减率降低8.33%和2.06%同时,使等高线偏移率降低了22.97%和12.65%,化简效果得到显著改善。其中,STCC-VBS算法在约减54.58%的节点的同时,仍能使地形特征线保持率达到94.73%,在有效约减数据量的前提下,较好地保持了主要地形特征。2种算法在效率方面均优于2种单纯以误差带控制的等高线化简方法。Contour lines are the most important elements on a topographic map.Realizing the automatic simplification of contour lines can significantly increase map compilation efficiency.When simplifying contour lines,it is crucial to maintain the main topographic features,control the data precision,and avoid intersection and visual confusion.However,most existing methods do not consider these issues simultaneously.To address this,this paper introduces the concept of error band from existing research,describes its mathematical definition in geometry,and proposes a method to extract error bands using digital elevation model.In addition,this paper proposes the concept of isolation band,describes its mathematical definition in geometry,and generates it using angular bisector method.This paper limits maximum deviation distance to control the deviation of points on contours.Finally,this paper puts forward a strategy to apply spatial topological condition to contour line simplification.Based on this strategy,improvements are made to the Valley Bend Selection(VBS)algorithm and the DouglasPeucker(DP)algorithm.This also leads to the development of the Spatial-Topologic-Condition-Controlled VBS(STCC-VBS)algorithm and Spatial-Topologic-Condition-Controlled DP(STCC-DP)algorithm.Finally,these two methods are employed to generate simplified contour lines,i.e.,to generate a 1:100,000-scale topographic map from the 1:50,000-scale topographic map,and the results are compared with two existing contour simplification results solely controlled by error bands.Our experimental results show that both the STCC-VBS algorithm and STCC-DP algorithm can effectively avoid the intersection issue,which is important for visual interpretation of maps.Compared to the methods prior to improvement,the reduction of deviation of contour lines simplified by the improved methods is both significantly greater than that of point reduction rate.To be specific,compared with VBS algorithm and DP algorithm,STCC-VBS algorithm and STCC-DP algorithm can reduce the node r

关 键 词：地形 等高线 数字高程模型 制图综合 线化简 误差带 隔离带 空间拓扑条件 

分 类 号：P284[天文地球—地图制图学与地理信息工程] P208[天文地球—测绘科学与技术]