分段线性Morse理论支持下的三维点云拓扑特征提取与简化  

Extraction and Simplification of three-dimensional Point Cloud Topological Features Using Piecewise Linear Morse Theory

作　　者：韦永昱 张春亢[1] 邵小美 吉雨田 尹耀 Wei Yongyu;Zhang Chunkang;Shao Xiaomei;Ji Yutian;Yin Yao(College of Mining,Guizhou University,Guiyang 550025,Guizhou,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18期449-455,共7页Laser & Optoelectronics Progress

基　　金：国家自然科学基金(41701464);贵州大学培育项目(贵大培育[2019]26号);贵州省科技计划(黔科合平台人才[2017]5788);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：针对目前基于Morse理论的三维点云拓扑特征提取算法难以删除“伪特征”点,简化后存在噪声特征线的问题,提出了一种基于分段线性Morse理论的三维点云特征提取与简化算法。首先计算函数指标,对特征点进行提取,以各特征点为顶点所包含的三角形为一个集合,计算该集合中两两相邻的三角形法向量的点积,将其最大值作为该点权重,并设置合适的阈值去除“伪特征”点;其次通过特征点生成特征线,完成下降Morse复形的构建;最后选择特征线上不同点的函数指标值,分别计算持续值和考虑特征线实际留存价值的保留系数,两者结合对原有“持续值”法进行改进,得到新的特征线重要性度量指标,并基于该指标实现对三维点云拓扑特征的简化与表达。结果表明,相较其他算法,所提特征提取算法显著减少了“伪特征”点提取,使下降Morse复形构建的时间效率提高了70.37%,点云压缩率提高了22.48%。新的特征线重要性度量方法能获取更简洁、连续且结构完整的特征线,且特征提取与简化过程表现出较强的抗噪性。In this paper,we proposed a feature extraction and simplification algorithm for threedimensional(3D)point cloud based on piecewise linear Morse theory to solve problems in difficultly deleting pseudo feature points,and generating noise characteristic lines after simplification of existing 3D point cloud topological feature extraction algorithms based on Morse theory.First,we calculated the function index to extract the feature points.Regarding the triangles comprising each feature points as a collection,we calculated the dot product of the normal vectors of two adjacent triangles in the collection.Herein,the dot product maximum was considered the weight of the point,and the appropriate threshold was set to remove the pseudo feature points.Second,feature lines were produced by connecting feature points to complete the construction of descending Morse complex.Finally,the persistence and the retention index considering the actual retention value of the feature lines were calculated,respectively,by choosing the function index value of different points on the feature lines.With both indexes,the origin persistence method can be improved to attain a new feature line measurement index and the simplification and expression of 3D point cloud topological feature can be accomplished.The results show that,compared with other algorithms,the proposed feature extraction algorithm significantly reduces pseudo feature points.Furthermore,the time efficiency of the proposed algorithm for constructing the descending Morse complex increases by 70.37%,and the point cloud compression rate increases 22.48%.Additionally,the new importance measurement method for feature lines attains more concise,continuous,and structural complete feature lines,and the feature extraction and simplification processes show strong antinoise performance.

关 键 词：分段线性Morse理论 权重计算 保留系数 拓扑简化 三维点云 

分 类 号：P208[天文地球—地图制图学与地理信息工程]