Proceedings of 2018 IEEE International Conference on Mechatronics and Automation August 5 - 8, Changchun, China
Research on Key Technologies of Lidar 3D Point Cloud Imaging Yanxin Yu, Yuxin Li and Chunyang Wang*
Department of Electronics and Information Engineering,
Department of Optoelectronic Engineering,
Changchun University of Science and Technology,
Xi’an Technological University,
*Corresponding Author:[email protected]
three-dimensional reconstruction technology  is to reproduce the three-dimensional virtual model of the surface of a real object in a computer. The three-dimensional point cloud data is mainly obtained by the three-dimensional scanning apparatus. It is a three-dimensional point set of spatial distribution and surface characteristics of an object expressed in the same spatial reference system. Because it does not require any topology structure and the advantages of simple data structure for easy storage and transmission, it has been widely used in many fields. People can obtain three-dimensional data  of an object in a computer in many different ways. Since the measurement process is affected by human factors and scanner parameters, the point cloud data contains noise. Therefore, point cloud data must be smoothed. Finally, the point cloud data undergoes a series of preprocessing, and the 3D point cloud data model is reconstructed. The research content of this paper is to use the scattered point cloud data obtained by the three-dimensional laser scanning to obtain a 3D point cloud data model that can more accurately represent the target object through filtering. On this basis, the point cloud data model is reconstructed to complete a series of operations on point cloud data processing. This article simply summarizes the denoising, and reconstruction methods mentioned above.
Abstract-The three-dimensional laser scanning technology can directly obtain the spatial sample points or point cloud data on the surface of real objects. The use of point cloud data can reconstruct the surface of three-dimensional objects, which greatly promotes the development of reverse engineering. On the basis of introducing the definition of laser radar three-dimensional scanning technology and the imaging principle of laser radar, the current research status of point cloud data measurement, data preprocessing and surface reconstruction are analyzed. Firstly, the classifications of point cloud data measurement methods are introduced, then the denoising methods of point cloud data are summarized, and the methods of point cloud data surface reconstruction are summarized. Index Terms-Laser radar; Denoising reconstruction; Reverse engineering
I. INTRODUCTION Laser radar, the laser detection and ranging system, is a radar that uses a laser as a radiation source, using laser light waves instead of radio waves. Lidar uses pulse or continuous wave two kinds of work methods, detection methods are divided into direct detection and heterodyne detection. After the laser pulse emitted by the laser passes through the beam splitter, it is divided into two channels and enters the receiver all the way. The other way is reflected by the mirror to the surface of the obstructed object. The reflected light is also returned to the receiver via the reflector. The frequency of the emitted light and the reflected light is exactly same. The distance of the measured object is measured by measuring the time interval between the transmitted pulse and the reflected pulse and multiplying the speed of light. Lidar 3D scanning technology is a fast and accurate 3D measurement technology. It can obtain 3D point cloud data with simple structure and accurate measurement, analyzes and processes the collected point cloud data. Further, reconstruction of the target model is one of the core topics in the field of three-dimensional intelligent information processing, and has been widely used in computer vision, measurement, reverse engineering, archeology, and other fields. With the rapid development and wide application of optical scanning equipment, the acquisition of 3D point cloud data  is no longer a problem, but to obtain accurate object model data, point cloud data needs to be processed. The
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II. POINT CLOUD DATA COLLECTION The point cloud data collection refers to the process of extracting the three-dimensional coordinate information of the surface of the object through some measurement device or technical means, that is, the process of expressing the object model with point cloud data. The data collection of point clouds is the first step in the reconstruction of three-dimensional surfaces. The accuracy of the point cloud data directly affects the effect of preprocessing the object surface, denoising and smoothing, and registration. According to whether or not the measurement probe is in contact with the measured object, the measurement of the point cloud data can be roughly classified into contact type and non-contact type. The contact measurement is a method in which the sensor of a measuring instrument is in directly contact with the surface of the measured object. The contact method has the advantages of high precision, high reliability, and good
repeatability. The disadvantages are slow speed and low efficiency. Non-contact methods use a physical phenomenon that interacts with the surface of the object such as light, electromagnetics to obtain its three-dimensional information. The non-contact method has the advantages of no contact, rapid measurement. The disadvantage is that the material to be measured has strict requirements. If the laser measurement is used, the measured object material must not be transparent, and the surface cannot be too bright. Moreover, there are certain errors in the collection of straight-wall and steep-slope data, and the accuracy is not as good as that of contact measurement. The three-dimensional laser scanning system adopts a non-contact measurement method. The characteristics of the laser are single coloration, high height, strong directionality, and the speed of reflection is light speed. Therefore, it isn’t easily affected by factors such as on-site lighting conditions. The measurement speed of the laser can reach more than 1000 points per second, ranging from several hundred meters, so a large number of point clouds can be scanned in a short time. III. POINT CLOUD FILTER The filtering of the point cloud model is an important part of the three-dimensional point cloud data preprocessing and modeling. The purpose is to leave the data points reflecting the true surface of the object generated in the measurement process, and to remove the “bad points” generated by various interference factors, especially non-random factors, thereby improving the quality of the generated point cloud. The main goals of point cloud denoising are: (i) denoising while maintaining the geometric surface features of the point cloud model; (ii) improving the efficiency of denoising; (iii) reducing the volume contraction and preventing the deformation of the model; (iv) improving the robustness of noise reduction. Noise is usually expressed as high-frequency information. The common denoising methods are to filter out high-frequency information and preserve low-frequency information. However, in the 3D point cloud data model, the sharp geometric features are also high-frequency information. Filtering high-frequency information may mistakenly delete sharp geometric features and lose feature information. Therefore, how to effectively maintain the geometric characteristics of the object surface while removing the noise has always been a hot spot for researchers at home and abroad. The denoising methods commonly used for ordered point clouds include direct observation, Gaussian filtering, mean filtering and median filtering. The weight distribution of the Gaussian filter in the specified area is Gaussian distribution, that is to take several data points before and after the data point to be weighted average, as the required distribution value. The mean filtering takes the statistical average of sampled data points in the filter window as an alternative to the center point of the window, so that the distribution of the point cloud data tends to be flat, which may cause some details of the surface of the point cloud model to be lost. The median filtering takes the point in the middle of the filter
window as the median point instead of the center point in the window. It can eliminate glitches and data with a lot of noise in the data. The median filtering is often used to eliminate the randomly generated impulse noise and can well maintain the inherent detail of the model. The current denoising methods for scattered point cloud data can be divided into the following categories: (1) Statistical-based filtering methods Schall et al.  used the kernel-based clustering method to filter point clouds. They define the global probability distribution function to move the sampling point to the most likely position, and utilize the iterative scheme of the mean shifting technique to smooth the point cloud. The method achieves the filtering in anomaly detection and robustness. However, the sharp features of object surface are ignored in their method. Jenke et al.  used Bayesian statistical method to perform point clouds denoising, modeled the sampling points and prior knowledge as probability distribution, and achieved denoising while reserving features by obtaining the maximum probability value. Based on the Bayesian theory, Yang Jun  derives a new point colud prior probability according to the normal vector field and spatial position to achieve denoising. Kalogerakis et al.  provided a powerful statistical framework for point cloud denoising. In their framework, the iterative least squares (IRIS) method is used to estimate the curvature tensor, and weights are assigned to the samples in each iteration to refine the points around each point. The calculated curvature and the final statistical weight are used to correct the average level. Based on the global energy minimization process, robust estimation of the curve can drive outlier exclusion in a way that features are reserved and denoising point cloud. Orts-Escolano et al.  first used 3D filtering and downsampling techniques based on the growing neural gas(GNG)  network. This is a growth process that used to generate a GNG network. A primitive point cloud is represented by a set of three-dimensional neurons and their interconnections. Fig.1 shows the ability of the proposed method to create colour meshes of different types of models. The method preserves the topological structure of point cloud and handles the outliers in the point cloud. Hence, the GNG-filtered point clouds can improve the performance of key point detection  and obtain better recognition results . The method produces a GNG mesh mapping to the point cloud.
Fig. 1 Reconstructed models using the extended GNG method for facereconstruction and without applyingpost-processing steps. Top: Stanford bunny. Bottom: builder helmet.
combination of bilateral filter and fuzzy C-means clustering for point cloud denoising. Zhang Xin et al.  utilized the trilateral filter function to filter and optimize the point cloud respectively. The algorithm can preserve the characteristics of the model surface. Sun et al.  limited the local neighborhood of the sampling point to the similar region of the normal vector and modified the normal vector. In order to reduce the smoothness at the feature, a modified method based on bilateral filter was proposed in . The literature  considered the existence of singularity in the point cloud, the normal vector is adjusted by the minimum spanning tree method, which has a high efficiency. Sun et al.  used the R*-tree spatial index structure to implement a weighted mean adaptive filtering method for scattered point cloud data based on the point cloud local surface. However, the size of the neighborhood has a great influence on the filtering effect. (3) Projection-based filtering methods The projection-based filtering techniques adjust the position of each point in the point cloud through different projection methods, so as to achieve the purpose of filtering point cloud. In recent years, the denoising method based on Moving Least Squares (MLS) has been widely concerned by scholars. Alex et al.  processed the noise problem by projecting point iteration to MLS surface, but solving MLS surface needs to nonlinear optimization problems with low efficiency. Amenta et al.  proposed to calculate the sampling surface by the weighted centroid and gradient domain, which avoids the planar parameterization of sparse sampling. However, the method will become unstable when the sampling rate decreased. In order to solve this problem, Guennebaud et al.  utilized algebraic sphere fitting instead of plane fitting to realize more stable projection operations. In fact, MLS can be regarded as an isotropic low-pass filter that can smooth shape of the point cloud. To maintain sharp features, Fleishman et al.  proposed a robust moving least squares approach based on the forward search paradigm to handle noise, outliers and sharp features. However, the technique requires dense point clouds and time-consuming. Oztireli et al.  proposed a robust projection algorithm that uses a similar approach to trilateral filter to preserve features, and the algorithm has a high efficiency. (4) Signal processing based filtering methods Laplacian-based signal processing techniques were first applied by Taubin  to grid processing. Subsequently, Linsen  refers to the Laplacian denoising idea in the grid, and proposes a point cloud denoising method that considers the geometric properties. Pauly et al.  deal with point clouds based on Laplacian ideas. However, this kind of algorithm may have the phenomenon of smooth features and vertex drift. Pauly and Gross  applied Fourier-based spectral methods in image processing to process point clouds and use spectral analysis to remove noise. (5) PDE-based filtering methods The Filter methods based on partial differential equations are derived from grid denoising, and Clarenz  constructed partial differential representations based on local finite elements to achieve anisotropic denoising. Lange  used an
(2) Neighborhood-based filtering methods The neighborhood-based filtering technique uses the similarity measure between the point and its neighborhood to determine the filtering position of the point, which has an important influence on the efficiency and effectiveness of the filtering method . Initially, the bilateral filter introduced by Tomasi  is an edge-preserving smoothing filter. Subsequently, Fleishman et al.  and Jones et al.  improved the bilateral filtering of images to the 3D mesh model and proposed a bilateral filtering technique for mesh denoising. Since this method doesn’t involve the topology connection structure, it is also suitable for denoising point models. Bilateral filtering is a robust noise reduction technology. The algorithm performs anisotropic denoising by assigning different weight functions to the influence domain and the spatial domain, has a good noise reduction effect, and can maintain the geometric characteristics of the point model. However, the outliers cannot be handled well and the sharpest part of the model can be easily deleted. Fig.2 demonstrates the results of the outliers removal algorithm in different models.
Fig. 2 Results of the outliers removing algorithm: (a) Left: Bunny pointcloud with uniformly distributed noise, Right: Corresponding point cloudafter using the methodused in this research, (b) Left: Point cloud model of a carwith outliers data, Right: Carmodel after removing outliers.
Choudhury et al.  proposed a trilateral filtering algorithm for denoising of 3D mesh models. The algorithm perform local clustering and integration of sampling points by the degree of normal similarity, and restrict filtering in gradient-similar regions. Meanwhile, the algorithm achieves better denoising and feature preserving by triangulation at the sampling point. Through the three-side smoothing, better results than noise reduction and feature retention are obtained with bilateral filtering. In the process of noise reduction, the selection of the nearest neighbor points has a direct effect on filtering, so we often assign different weights according to distance and gradient. Hu et al.  adaptively searched the neighborhood based on the mean-shift technique and propose an anisotropic filter algorithm based on three-dimensional mean shift by considering the vertex normal, curvature and position. The denoising and smoothing of noise reduction points can effectively maintain the sharp features of the object surface, but the amount of calculation is large. In , the non-local denoising method of images is extended to the point model. The geometric feature of the data point is described as “geometric gray value” and the self-prediction is carried out through the global weighting. The method can also achieve the effect of maintaining the feature. Yang Jun  proposed an effective point cloud multilateral filter denoising method, which can keep the geometric salient feature well. Wang et al.  proposed the
average curvature flow to perform anisotropic denoising. Xiao  proposed a point cloud data denoising algorithm based on dynamic equilibrium curvature flow, which provided a point-model-based smoothing method against vertex drift, volume preservation and feature preservation. The filter technologies based on PDEs need to calculate differential properties, so the complexity of the algorithm is high. IV. POINT CLOUD SURFACE RECONSTRUCTION TECHNOLOGIES The 3D point cloud surface reconstruction technology is the core step of 3D point cloud data processing. Hoppe  proposed the concept of surface reconstruction. In recent years, the issue has received intense attention from domestic and foreign scholars. Surface reconstruction is the process of reconstructing a triangular mesh model that can reflect the true geometric shape of a target object according to the sample surface point cloud of the object. In general, according to the representation of the reconstructed surface, it can be divided into five kinds of surface reconstruction methods, namely parametric surface reconstruction, implicit surface reconstruction, mesh surface reconstruction, deformed surface reconstruction, and subdivision surface reconstruction. (1) Parametric surface reconstruction Parameter surface is the most common method for surface reconstruction, and it’s one of the main tools for describing geometric shapes. It has the characteristics of convenient display, no deformation, and easy control. Common parametric surfaces include Bezier surface, B-spline surface and Non-Uniform rational B-spline (NURBS) surface. It has the characteristics of convenient display, no deformation and easy control. Bezier proposed the Bezier surface in 1972. The advantage is that changing the surface shape only requires moving the control vertices. The disadvantage is that it cannot handle continuous splicing. Gordon first proposed a reconstruction method based on B-spline surface, and used it to construct the normal vector of the surface corresponding to the target object. The disadvantage is that the surface of the object with sharp corners cannot be reconstructed. Later, after the improvements of Piegl and Tiller et al., NURBS has become the mainstream way of reconstructing surface representations. Compared with B-spline surfaces, NURBS surfaces can represent freeform surfaces more accurately and have higher flexibility and efficiency. The disadvantages are that they can only deal with relatively simple object surfaces and increase the complexity of the algorithm due to the introduction of new weights. Zeng  proposed NURBS modeling after the point cloud data preprocessing phase, and used Geomagic Studio deviation analysis module to compare point cloud data and reconstructuring curve model. The experimental results show that the NURBS model has good visual effect and high reconstruction precision, it satisfies the purpose of high precision model. (2) Implicit surface reconstruction In the implicit function surface, the inner model of geometric object is represented by an implicit function surface,
so the implicit function surface representation method of the model can easily realize the operation of the intersection of the surface. The implicit function and surface representation of curves and surfaces is more and more widely used. The reconstruction algorithm of the implicit function surface generally needs to increase the constraint conditions, and the calculation amount is large. Carr et al.  applied the RBF function interpolation method to the surface reconstruction of point cloud data. The algorithm uses scattered data points as the radial basis function interpolation center, and calculates weights to construct an interpolation function to approximate the expression function of the model surface. The advantage is that there is no need to know the topology between any data points, but when the number of point clouds increases, the calculation is very time consuming. Ohtake  proposed multi-level partition of unity implicits (MPU) algorithm. Firstly, the input cloud data was partitioned and stored using octree. According to the location of the data points in each sub-domain and the normal vector relations, select different local functions to fit the surface represented by the local point set, and then calculate the weight of each local function. Finally, using these weights, the local function is stitched into the global implicit function to represent the model surface. Reconstruction from scattered point data with MPU implicits is robust with respect to variations of point density, as demonstrated in Fig.3. Its advantage is that the memory consumption is small and the running time is fast, but this algorithm does not have anti-noise performance, and it is required that the scattered point cloud data cannot contain noise. Jia et al.  presented
a surface reconstruction algorithm based on three-dimensional Delaunay triangulation, it is essentially a greedy algorithm, and combined with the idea of surface region growing algorithm. The experiment results show that the quality of the surface generated by the algorithm is choiceness, and the efficiency of reconstruction is faster, it can be better applied in the field of 3D modeling.
Fig. 3 Reconstruction from a scattered point data set with non-uniform density of points.
(3) Mesh surface reconstruction The principle is to establish a polygon mesh on the surface of the object, and then to interpolate or approximate the data points for reconstruction. The mesh surface can represent a set of data points with a complex topology, but the surface reconstructed using multiple patches is less continuous. At present, the methods of grid reconstruction are mainly based on the carving method  and regional growth method. The sculpture-based grid reconstruction method belongs
technology. Finally, the original surface is reconstructed by selecting an appropriate reconstruction algorithm.
to a local reconstruction method. The basic steps of this method are: first triangulate the original data point set, and all data point sets form a convex hull consisting of a tetrahedral mesh. Then the convex hulls are peeled off layer by layer in a quasi-sculpture manner. Finally, with the original topology unchanged, the number of point clouds is greatly reduced, and the point cloud data on the surface of the object is visible. In other words, the remaining tetrahedron is the simplest tetrahedron, and there is no possibility to delete it again, resulting in the final triangulation mesh. Zhang et al.  proposed a two-level implicit function interpolation algorithm based on compactly supported radial basis function (CSRBF). Firstly, a threshold for center reduction is set before interpolation, so the center points of CSRBF are reduced and the linear system based on CSRBF is simplified. Secondly, the point cloud model is approximated by interpolating in the coarse scale. Then, the surface is fitted in the fine scale and it sums up the coarse surface and the fine surface. Finally, a regularization parameter is introduced to regularize the CSRBF matrix to deal with the noise of 3D point cloud models. (4) Deformed surface reconstruction It constructs an initial surface model and then assigns certain physical properties to the surface firstly. Then according to the external environment of the object itself and the physical characteristics possessed by the object, the initial surface is deformed according to a certain direction, and finally a new surface to be constructed is formed. The deformed surface reconstruction method can reflect the geometric features of the object, and can reconstruct a smooth continuous surface. The disadvantage is that the initial position needs to be as close to the real surface of the object as possible, and the reconstruction effect is not ideal for the complex features of the object. (5) Subdivision surface reconstruction The proposed subdivision surface reconstruction solves the problem of surface reconstruction of objects with complex topological structures. First, the point cloud model is polygon meshed, and then each vertex on the new mesh is recursively calculated according to the requirements of the subdivision rules. When the number of subdivisions is sufficient, the initial polyhedral mesh is subdivided into countless times and eventually converges to a smooth surface, which is called a subdivision surface. The disadvantage of this method is that its initial control grid is not easily determined, limiting the implementation of this method.
REFERENCES  Rusu R.B., Cousins S., “3d is here: Point cloud library (pcl)”,IEEE InternationalConference on Robotics and Automation, vol. 47, no. 10, pp. 1-4, 2011.  Aldoma A., Marton Z.C., Tombari F., Wohlkinger W., Potthast C., Zeisl B., et al., “Tutorial: Point Cloud Library: Three-Dimensional Object Recognition and 6 DOFPoseEstimation.” IEEE Robot. Autom. Mag., vol. 19, no. 3, pp. 80-91, 2012.  Saval-Calvo M., Orts-Escolano S., Azorin-Lopez J.,Garcia-Rodriguez J, Fuster-Guillo A., Morell-Gimenez V., et al., “A comparative study of downsampling techniquesfor non-rigid point set registration using color.” Bioinspired Computation inArtificial Systems, Springer, pp. 281-290, 2015.  O. Schall, A. Belyaev and H.P. Seidel, “Robust filtering of noisy scattered point data,”Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, Stony Brook, NY, USA, pp. 71–77, June 2005.  M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D.Levin and C.T. Silva, “Point set surfaces,”Proceedings of the Conference on Visualization, San Diego, CA, USA, pp. 21-28, October 2001.  Jun Yang. “Study on denoising and 3D reconstruction for point-based models,”Xi’an Jiao Tong University, Chengdu,pp. 20-125, 2007.  E. Kalogerakis, D. Nowrouzezahrai, P. Simari and K. Singh, “Extracting lines of curvature from noisy point clouds,” Computer Aided Design,vol. 41, no. 4, pp. 282-292, Januray 2009.  S. Orts-Escolano, V. Morell, J. Garcia-Rodriguez and M. Cazorla, “Point cloud data filtering and downsampling using growing neural gas,”Proceedings of International Joint Conference on Neural Networks, Dallas, TX, pp. 1-8, August 2013.  S. Orts-Escolano, J. Garcia-Rodriguez, V. Morell, M. Cazorla, J.A.S. Perez and A. Garcia-Garcia, “3d surface reconstruction of noisy point clouds using growing neural gas: 3d object/scene reconstruction,” Neural Process, vol. 43, no. 2, pp. 401-423, 2016.  M. Saval-Calvo, S. Orts-Escolano, J. Azorin-Lopez, J. Garcia-Rodriguez, A. Fuster-Guillo, V. Morell-Gimenez, et al., “Non-rigid point set registration using color and data downsampling,” Proceedings of the International Joint Conference on Neural Networks, Killarney, pp. 1-8, July 2015.  B. Fritzke, “A growing neural gas network learns topologies,” Adv. Neural Inf. Process.Syst.,vol. 7, 625-632, 1994.  J. Garcia-Rodriguez, M. Cazorla, S. Orts-Escolano and V. Morell, “Improving 3d keypoint detection from noisy data using growing neural gas,” International Conference on Artificial Neural Networks: Advences in Computational Intelligence, pp.480-487, 2013.  J.C. Rangel, V. Morell, M. Cazorla, S. Orts-Escolano and J. García-Rodríguez, “Object recognition in noisy rgb-d data using gng,” PAA Pattern Anal. Appl.,pp. 1-16, 2015.  O. Schall, A. Belyaev and H.P. Seidel,“Adaptive feature-preserving non-local denoising of static and time-varying range data,” Comput. Aided Des.,vol. 40, no. 6,pp. 701-707, 2008.  C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” International Conference on Computer Vision, Bombay, pp. 839-846, January 1998.  E.A.L. Narváez and N.E.L. Narváez, “Point cloud denoising using robust principal component analysis,”Proceedings of the First International Conference on Computer Graphics Theory and Applications, Setúbal, Portugal, pp. 51-58, February 2006.  F. Zaman, Y.P. Wong and B.Y. Ng, “Density-based denoising of point cloud,” Springer Singapore, 2017.  Choudhury P and Tumblin J. “The trilateral filter for high contrast images and meshes,”Eurographics Symposium on Rendering, pp. 1-11, 2003.  G. Hu, Q. Peng and A.R. Forrest, “Mean shift denoising of point-sampled surfaces,” Visual Computer, vol. 22, no. 3,pp. 147-157, 2006.  Miu Y, Feng Q, Wang J and R. Pajarola,“A Multi-Channel Salience Based Detail Exaggeration Technique for 3D Relief Surfaces,” Journal of Computer Science and Technology, vol. 27, no. 6, pp. 1100-1109, November 2012.  Wang L.H,“Study on data processing technology of 3d cloud points,”Beijing Jiaotong University, Beijing,pp. 13-28, May 2011.
V. CONCLUSION With the development of laser measurement technology, the point cloud data collected on the surface of the measured model within a short time has become a reality. However, the point cloud collected by the laser scanner is scattered and massive. How to deal with these scattered point clouds efficiently is one of the core aspects of reverse engineering. This article focuses on three key issues in the point cloud processing technology. After the point cloud data is collected by the measurement equipment, the effectiveness of the point cloud model is enhanced by the denoising and filtering 2219
 Zhang X, Wang Z.Y., Fan H.Q., Wang B.Y. and Peng Q.S., “A feature preserving denoising approach for scanned models based on trilateral filtering,” Journal of Computer Aided Design and Computer Graphics, vol. 21, no. 7, pp. 936-942, July 2009.  Sun X.F., Rosin P.L, Martin R.R. and Langbein F.C,“Random Walks for Feature-preserving Mesh Denoising,” Computer Aided Geometric Design, vol. 25, no.7, pp. 437-456, January 2008.  Öztireli A.C., Guennebaud G and Gross M,“Feature preserving point set surfaces based on non-linear kernel regression,”Computer Graphics Forum, vol. 28, no. 2, pp. 493-501, 2009.  Sun J.H., Zhou L.S. and An L.L., “Optimal algorithm for normal adjustment of point clouds,” Journal of Image and Graphics, vol.18, no.7, pp. 844-851, July 2013.  Sun D.Z., Sun Y.W., Li Y.R. and Song Y, “Node splitting algorithm of R*-tree based on self-adaptation clustering,” Journal of Beijing University of Aeronautics and Astronautics, vol.39, no.3, pp. 344-348, March 2013.  Alexa M, Behr J, Cohen-Or D, Fleishman S, Levin D and Silva C.T.,“Computing and rendering point set surfaces,” IEEE Transactions on Visualization andComputer Graphics, vol. 9, no. 1, pp.3-15, 2003.  Amenta N and Kil Y,“Defining Point-Set Surfaces,” ACM Transactions on Graphics, vol.23, no.3, pp. 264-270, 2004.  Guennebaud G and Gross M,“Algebraic Point Set Surfaces,” ACM Transactions on Graphics, vol. 26, no. 3, pp. 23, 2007.  Fleishman S, Cohen-or D and Silva C.T,“Robust moving least-squares fitting with sharp features,”ACM Trans. Graph, vol. 24, no. 3, pp. 544-552, 2005.  Taubin G,“A Signal Processing Approach to Fair Surface Design,”The 22nd Annual Conference on Computer Graphics and Interactive Techniques, vol. 29, pp. 351-358, 1995.  Linsen L,“Point Cloud Representation,” Karlsruhe: Faculty of Computer Science, University of Karlsruhe, pp. 3-8, 2001.  Pauly M, Gross M and Kobbelt L.P.,“Multiresolution Modeling Of Point-Sampled Geometry,” ETH Zurich: Computer Science Department, pp. 1-10, 2002.  Pauly M and Gross M,“Spectral processing of point-sampled geometry,” Computer Graphics, vol. 35, no. 4, pp. 379-386, 2001.  Clarenz U, Droske M, Henn S, Rumpf M and Witsch K,“Computational Methods for Nonlinear Image Registration,”Mathematical Models for Registration and Applications to Medical Imaging Mathematics in industry, vol. 10, pp. 81-101, 2006.  Lange C and Polthier K,“Anisotropic Smoothing of Point Sets,” Computer Aided Geometric Design, vol. 22, no. 7, pp. 680-692, 2005.  Xiao C.X.,“Multi-level partition of unity algebraic point set surfaces,” Journal of Computer Science and Technology, vol.26, no. 2, pp. 229-238, March 2011.  Hoppe H, Derose T, Duchamp T, Mcdonald J and Stuetzle W,“Surface reconstruction fromunorganized points,”Conference on Computer Graphics and Interactive Technologies, vol. 26, no. 2, pp. 71-78, 1992.  Zeng F.X. and Li L, “Surface reconstruction technology of ground-based Lidar point cloud,” Laser Journal, vol. 38, no. 6,pp. 108-111, 2017.  Carr J.C., Beatson R.K.,Cherrie J.B., Mitchell T.J.,Fright W.R.,McCallum B.C. and Evans T.R.,“Reconstruction and representation of 3D objects with radial basis functions,” Proceedings of ACM Siggraph, vol. 100, no. 2, pp. 67-76, 2001.  Ohtake Y, Belyaev A, Alexa M, Turk G and Seidel H.P,“Multi-level partition of unity implicits,” Proceedings of ACM Siggraph, vol. 22, no. 3, pp. 463-470, 2003.  Jia J.H., Huang M and Liu X.L., “Surface reconstruction algorithm based on 3d delaunay triangulation,” Acta Geodaetica et Cartographica Sinica, vol. 47, no. 2, pp. 281-290, February 2018.  Amenta N, Bern M and Kamvysselis M,“A new Voronoi-based surface reconstruction algorithm,” pp. 415-421, 1998.  DeyT.K., Goswami S,“Provable surface reconstruction from noisy samples,” Computational Geometry, vol. 35, no. 1, pp. 24-141, 2006.  Zhang J, Hou J, Wu T.T., Zhong L.T., Gong S and Tang Y.H., “Rapid surface reconstruction algorithm for 3d scattered point cloud model,” Journal of Computer Aided Design and Computer Graphics, vol.30, no. 2, pp. 235-243, February 2018.