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

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。

Abstract: 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.