一种基于Morse复形的地形特征线构建改进算法  

An Improved Algorithm of Constructing Terrain Feature Lines Based on Morse Complex

作　　者：王洪斌[1,2] 赵学胜[2] 张春亢[2] 郭俊枫 

机构地区：[1]核工业北京地质研究院,北京100029 [2]中国矿业大学(北京),北京100083

出　　处：《武汉大学学报（信息科学版）》2015年第9期1220-1224,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41171306);高校博士点专项科研基金资助项目(20130023110001)~~

摘　　要：地形特征线的正确拓扑表达是进行地表形态描述、地形拓扑简化和地貌综合的基础。传统的基于Morse复形从三角格网地形提取特征线的算法,存在山谷线与山脊线在正则点处"交叉"及无法识别"宏"鞍点等问题。本文利用Morse复形的对偶特征,提出了一种较为通用的改进算法。该算法将下降(或上升)Morse复形的边界作为提取其对偶复形边界的约束线,并使"宏鞍线"按相应已建复形边界线寻径,不仅消除了传统算法出现的"交叉"现象,而且能够识别"宏"鞍点,实现了整个地形特征线的完整构建。The correct connection of the topological relationships between critical points （or lines） is the basis of the earth＇s surface description, terrain topological simplification, or geomorphic generalization of relief. However, valley and ridge line often intersect at regular points; the macro-saddles cannot be identified when terrain feature lines are extracted by the traditional algorithms based on Morse complex. In this paper, an improved and universal algorithm is proposed using the duality of Morse complex. In our approach, the separatrix of descending （or ascending） Morse complex is regarded as the constrained boundary for extracting the separatrix of the dual complex. Moreover, the ＂macro-saddle line＂ coincides exactly with the corresponding separatrix of the constructed complex. As a result, intersections can be prevented and the macro-saddles can be identified with the complete decomposition of the whole terrain surface. In the end, an experiment validated the correctness and feasibility of this algorithm.

关 键 词：Morse复形 地形特征线 “宏”鞍点 交叉 

分 类 号：P208[天文地球—地图制图学与地理信息工程] P283.1[天文地球—测绘科学与技术]