分段线性Morse理论下的地表拓扑特征提取与简化  

Extraction and Simplification of Terrain Surface Topological Features Based on PiecewiseLinear Morse Theory

作　　者：吉雨田 张春亢[1] 尹耀 Ji Yutian;Zhang Chunkang;Yin Yao(College of Mining,Guizhou University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州大学矿业学院,贵州贵阳550025

出　　处：《激光与光电子学进展》2022年第8期308-314,共7页Laser & Optoelectronics Progress

基　　金：国家自然科学基金项目(41701464);贵州大学培育项目(贵大培育[2019]26号);贵州省矿山动力灾害预警与控制技术科技创新人才团队项目(黔科合平台人才〔2019〕5619)。

摘　　要：针对传统地表特征提取算法存在特征识别不完整,拓扑关系构建复杂,难以进行拓扑简化的问题,本文实现了基于分段线性Morse理论的特征提取,并提出一种新的特征重要性度量指标进行拓扑简化。首先识别关键点构成关键线,生成Morse-Smale复形完成地表拓扑特征构建;然后提出一种新的特征重要性度量指标,利用Morse-Smale复形的平均特征值反算关键点的特征值,使其对Morse-Smale复形的特征重要性进行双重评估;最后基于该度量指标实现了地表拓扑特征的简化与表达。实验结果表明,地表特征被清晰提取并构建了良好的拓扑结构,特征提取点云压缩率达36.29%,拓扑简化的点云压缩率达70.73%,大大缩减了点云数据量,并将冗余拓扑结构剔除,为后续地表点云的表达与应用奠定良好的数据基础。This study implements a feature extraction based on piecewise linear Morse theory to solve the problems of incomplete feature recognition in traditional surface feature extraction algorithms,complex topological relationship construction,and difficulty in topological simplification.In addition,it proposes a new feature importance measurement index for topological simplification.Firstly,critical points are identified to form critical lines,which generates Morse-Smale complex to complete the construction of surface topological features.Thereafter,a new feature importance metric is proposed using the average eigenvalue of MorseSmale complex to backcalculate the eigenvalues of critical points,making a double evaluation of the feature importance of this complex.Finally,the simplification and the expression of the topological features of the surface are realized based on the metric.The experimental results show that the surface features are extracted and a good topology structure is constructed.The feature extraction point cloud compression rate reaches 36.29%,and the topology simplified point cloud compression rate reaches 70.73%.This considerably reduces the massive point cloud data and eliminates redundant topology,laying a good data foundation for the subsequent expression and the application of surface point clouds.

关 键 词：遥感 分段线性Morse理论 地形特征提取 拓扑简化 重要性度量 

分 类 号：P208[天文地球—地图制图学与地理信息工程]