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.