Lidar点云三维模型于Morse理论下特征提取及应用  

Lidar Point Cloud 3D Model for Feature Extraction and Application Based on Morse Theory

作　　者：游晨宇 张春亢[1] 张亚宁 王朝 

机构地区：[1]贵州大学矿业学院,贵州 贵阳

出　　处：《应用数学进展》2022年第12期8901-8907,共7页Advances in Applied Mathematics

摘　　要：针对传统的特征提取技术特征提取粗略,拓扑信息大量丢失,拓扑关系难以简化等问题,本文实现了基于分段线性Morse理论的特征提取算法,确定了一种新特征线度量指标。首先以三角网格顶点曲率计算为基础,构建了三维表面模型的Morse理论指标函数;采用最大(小)邻点算法连接指标函数所提取特征点,完成特征线构建;针对Morse-Smale复形在三维表面模型中冗余或错误特征过多,采用单复形拓扑模型进行特征提取;以三维表面模型Morse单复形“持续值法”思想为参照,确定了一种点线结合特征线提取度量指标,并基于该指标完成特征线额拓扑简化。实验结果表明,对棱角线完整性和存在性存在关键作用,在零件模型点云压缩率为26.02%,在苹果模型点云压缩率为39.33%,提高了拓扑特征提取效率,为点云后续处理奠定良好基础。In response to the problems of rough feature extraction, massive loss of topological information, and difficulty in simplifying topological relationships by traditional feature extraction techniques, this study implements a feature extraction algorithm based on segmented linear Morse theory and de-termines a new feature line metric. The Morse index function of the 3D surface model is constructed based on the calculation of the triangular mesh vertex curvature;the maximum (small) neighbor-hood algorithm is used to connect the extracted feature points of the index function to complete the construction of the feature line;in view of the excessive redundant or wrong features of the Morse-Smale complex in the 3D surface model, the single complex topological model is used for feature extraction;the 3D surface model is used as the “Morse single complex” continuous model. The Morse single complex shape “continuous value method” is used as a reference, and a point-line combination feature line extraction metric is determined. And based on this index, the topological simplification of the characteristic line is completed. The experimental results show that it has a key effect on the integrity and existence of angular lines, and the compression rate of the point cloud is 26.02% in the part model and 39.33% in the apple model, which improves the efficiency of topological feature extraction and lays a good foundation for the subsequent processing of the point cloud.

关 键 词：分段线性Morse理论 曲率 持续值 拓扑特征 提取与简化 

分 类 号：O18[理学—数学]