Research On 3D Point Cloud Registration And Evaluation Method Based On Discrete Differentia Geometry Theory

With the development of 3D scanning technology,3D modeling,high-speed,and large capacity storage technology in the past 20 years,3D point cloud processing theory and technology have emerged.The large-scale output of 3D point cloud data and the growing demand for data processing put forward higher and higher requirements for the registration,difference evaluation,and subsequent algorithm implementation of 3D objects represented by these data.However,the existing 3D point cloud registration methods are faced with the problems of inconsistent sampling rate,low accuracy,and low robustness when there are many noisy data.The existing evaluation methods of point cloud shape are limited to a single geometric quantity,and lack of evaluation methods that can describe the overall extrinsic characteristics and instrinsic geometry of the shape.In this thesis,from the new perspective of the theory of discrete differential geometry,a point cloud registration algorithm based on Helmholtz-Hodge decomposition of curvature gradient field and a 3D shape difference evaluation algorithm based on Steklov operator spectrum are proposed,and a 3D point cloud algorithm processing system based on MESHLAB is developed.The validity and robustness of the algorithm are verified by several examples of registration and evaluation experiments.The main contents of this dissertation are summarized as follows:1.In view of the high requirements of 3D point cloud model registration and evaluation methods in terms of efficiency,accuracy,and robustness,this dissertation makes an in-depth investigation on the research status of 3D point cloud model processing technology at home and abroad,and sorts out the research and application progress of discrete differential geometry for 3D point cloud processing.Through the comprehensive analysis of the existing 3D point cloud model registration,the mathematical description of 3D point cloud shape evaluation,the related solutions and the shortcomings of these existing methods,the author determines the research ideas and main research contents of this thesis.2.Aiming at the problems of point cloud mesh denoising,smoothing,mesh parameterization and registration in the process of 3D point cloud model processing,this dissertation studies the theoretical framework of discrete differential geometry for 3D point cloud model application,reviews the research progress of discrete differential geometry in the field of 3D point cloud model denoising,mesh parameterization and non-rigid registration in recent years,and discusses the difficulties and future of these problems.Possible research directions are summarized.3.In view of the problems of non-convergence and local minimum of iterative closest point algorithm in dealing with point clouds with different sampling density,a new point cloud registration method based on discrete differential geometry theory is proposed,that is,on the basis of Helmholtz-Hodge decomposition theory,a point cloud registration algorithm based on vector field of point cloud model is proposed.In this algorithm,the mean curvature gradient field on the mesh is decomposed into three orthogonal parts:divergence-free vector field,curl-free vector field,and harmonic vector field;singularities in the curl-free vector field are extracted as registration reference points for ICP registration.Compared with the results of other typical methods,this algorithm has higher accuracy and robustness in a series of point cloud models.4.To solve the problem that the shape of the 3D point cloud model is difficult to evaluate accurately,a new shape evaluation algorithm based on the Steklov operator spectrum and characteristic function is proposed.Based on the potential theory,the Steklov operator spectrum problem is transformed into a weak solution problem under complex boundary conditions,and its numerical solution is obtained by using the incomplete Cholesky decomposition conjugate gradient method.For the spectrum difference evaluation problem,a histogram of Gaussian curvature is proposed to quantify the weight of different eigenvalues,and its spectrum difference evaluation function is designed to evaluate the difference of point cloud shape.Based on the point cloud shape evaluation algorithm proposed in this dissertation,the application of dental root canal shape evaluation is studied.The experimental results show that compared with the existing methods,this method can evaluate the difference of the shape of the root canal point cloud model more accurately and has higher robustness.5.Based on the above related theoretical and algorithm research,this dissertation analyzes the characteristics of MESHLAB,designs the overall architecture of the 3D point cloud model processing system based on MESHLAB.In addition to the basic functions such as the design of user-defined menu,batch import of point cloud data module,it also proposes an arbitrary order adjacency algorithm with low cycle complexity,and finally realizes the 3D point cloud registration and shape proposed in this dissertation.The effect of the system implementation is demonstrated through system operation examples.