Morse理论支持下的建筑物点云特征提取

针对传统特征提取算法的结果存在交叉紊乱、不连续、缺少拓扑关系等问题，本文提出了基于Morse理论的建筑物点云特征提取算法。首先定义三维表面模型上顶点的Morse函数指标；然后采用邻点比较法自动提取特征点；最后针对Morse-Smale复形的对偶性在建筑物拓扑特征中已无实际意义的问题，提出了单复形拓扑模型的提取与简化算法。试验结果表明，该算法能够获得清晰、连续、完整的建筑物特征线，实现对建筑物模型表面的完全分割；简化算法在保证建筑物特征线拓扑一致性的前提下，可以获取不同层次的建筑物拓扑特征，为建筑物模型的重建与可视化提供了保障。

Feature extraction of building point clouds based on Morse theory

Aiming at the problems of traditional feature extraction algorithms, such as cross disorder, discontinuity and lack of topological relationship, this paper proposes a point cloud feature extraction algorithm based on Morse theory. Firstly,the Morse function index of the vertices on the 3D surface model is defined. Secondly, the adjacent point comparison method is used to extract the feature points automatically. Finally, aiming at the problem that the duality of Morse-Smale complex has no practical significance in building topology features, a single complex topology model extraction and simplification algorithm is proposed. The experimental results show that the algorithm can obtain clear, continuous and complete building feature lines and realize the complete segmentation of the building model surface. On the premise of ensuring the topological consistency of building feature lines, the simplified algorithm can obtain different levels of building topology features, which provides a guarantee for the reconstruction and visualization of building models.