Research On Feature Representation Of 3D Point Cloud By Persistent Homology And Conformal Mapping

The feature analysis of 3D point cloud is a research hotspot in the field of computer vision and the core technology in the data processing of 3D point cloud.The existing feature analysis of 3D point cloud mostly targets rigid objects with relatively simple structures,while there are many kinds of 3D point clouds in real life,and the factors affecting their feature description capabilities are complicated.Therefore,studying some feature representation methods with wide applicability and strong robustness to meet the needs of different levels in practical applications is the focus and difficulty in the research on feature representation of 3D point cloud.In this paper,we study the feature representation methods of point cloud under complex 3D transformation from two perspectives of persistent homology and conformal mapping.The main contents include as follows.Firstly,the construction method of topological relations anmong scattered 3D points is studied.It provides structured 3D data for subsequent geometric and topological feature analysis.In the topology onstruction process of point cloud,the key problems such as the definitions of vertex and edge weight and the determination of nested level are analysed.A multi-scale representation method based on minimum spanning tree is proposed to build the topology structure of nested complexes for 3D point cloud.Comparing to the single-scale method depending on specific threshold,the topology structure established by the multi-scale method has richer information,more stable performance and more practicability.Secondly,the topological feature representation of point cloud based on persistent homology is studied.The connected component aggregation cost is introduced based on the zero-dimensional Betti number.A novel integrated persistence feature(IPF)and the univariate feature SIP refined from IPF are proposed.The theory of Betti number is extented,and the spatial evolution process of nested complexes is more fully characterized.The proposed SIP can be used to measure the topology changes of complexed point clouds.The experimental results show that the proposed topological feature SIP has better statistical performance than graph-based features and may become a potential imaging biomarker for Alzheimer's disease.Thirdly,the conformal mapping method under the hyperbolic flow is studied,and a general framework and algorithm for measuring conformal structure in hyperbolic geometric space are proposed.The 3D point cloud of any genus can be consistently embed onto the Poincarédisk disk,a hyperbolic conformal feature descriptor is constructed by calculating the coordinates of the simply connected domain in the Teichmüller space.The experimental results show that the proposed feature descriptor is not only insensitive to singularity selection,but also effectively improves the performance of facial expression recognition.Finally,the feature analysis method combining persistent homology and conformal mapping is studied.A hybrid geometric topological descriptor based on persistent homology and conformal mapping is proposed,and a classification algorithm based on two-level feature selection is designed.The classification performance of proposed feature descriptor is studied in the structural and functional magnetic resonance imaging of Alzheimer's disease.The results show that the proposed hybrid geometric topological features have better classification performance comparing to sepearted features under persistent homology or conformal mapping.