以曲率、法向量变化量等为度量指标的三维点云模型不具有基于某一参考面的对偶性, 基于Morse理论提取的点云Morse-Smale(MS)复形存在大量无意义特征, 这严重制约了模型特征的识别效率。针对这一问题, 提出单复形拓扑模型的概念, 以避免无意义特征的提取, 并基于MS复形的特性线重要性度量方法和“同态收缩算法”, 推导了单复形拓扑模型的特征线重要性度量方法和拓扑简化算法。同时, 针对模型过渡特征在拓扑简化过程中难以保留的问题, 依据单复形构建与“持续值”简化理论, 通过设定阈值, 过滤删除导致跨轮廓与非轮廓关键线生成的鞍点, 实现简化过程中过渡特征的保护。算法在多个典型三维点云模型上进行了实验验证, 结果表明, 与现有拓扑特征提取方法比较, 单复形拓扑模型提取与简化算法避免了大量无意义特征的提取, 时间效率提高了52.22%, 数据压缩率提高了5%以上; 过渡特征保护方法对过渡特征的识别率达到了100%。本文方法显著提高了三维点云模型的特征识别效率, 并有效改善了常规算法存在的过渡特征线断裂不完整问题。

A 3D point cloud model that takes curvature and variation of the normal vector as metrics is not dual with regard to a certain reference plane. This can lead to the production of numerous meaningless topological features from the point cloud Morse-Smale (MS) complex extracted based on Morse theory, severely restricting the recognition efficiency of model features. To address this problem, the concept of a single complex topology model is proposed to avoid the extraction of meaningless features. Based on the characteristic line importance measurement method of the MS complex and the homomorphic shrinkage algorithm, the characteristic line importance measurement method and topology simplification algorithm of a single complex topology model are derived. Furthermore, the model transition features are difficult to retain in the process of topology simplification; to address this, by setting thresholds based on the single complex construction and persistence simplification theory, the saddle points that lead to the generation of critical lines that cross the contours or are off the contours are filtered and deleted. The protection of transition features is achieved in the simplification process. The algorithm was experimentally validated on several typical 3D point cloud models. The results and analysis show that, in contrast to existing topological feature extraction methods, the extraction and simplification algorithm of the single complex topology model successfully avoids extracting several meaningless features. The time efficiency and data compression rate respectively increase by 52.22% and 5% or more. With this blend feature protection method, the identification rate of blend features reaches 100%. A large number of experimental data and a series of subsequent analyses demonstrate that this method significantly improves the feature recognition efficiency of the 3D point cloud model. Moreover, it effectively alleviates the problem of incompleteness and fracture in transition feature lines in conventional algorithms.