牙模数据拼合重建系统的研究与实现
|
摘要
非接触式光学三维测量技术具有非接触、速度快、精度高等特点,近年来在机械设计与制造、航空航天、生物医学工程、计算机视觉与虚拟现实、文物修复等领域的应用越来越广泛。牙模具有外形复杂且体积小等特点,因此针对牙模的非接触式光学三维测量系统的研究和开发具有重要的理论意义和工程应用价值。
非接触式光学三维测量系统主要有两个部分组成:一是被测物体的表面数据的获取;二是曲面重建。本文的研究工作主要有光学三维测量系统的控制系统、多视点云拼接和以三角网格为基础的曲面重建技术,具体内容涵盖:
(1)设计光学三维测量系统精确稳定的测量转台。主要包括光栅投影模块和电动旋转台控制模块。计算机控制投影仪向被测物体投射4幅光栅条纹,相机采集经过物体表面高度调制的变形条纹图像转化为三维坐标数据,旋转台在步进电机的控制下,获得被测物体的多个不同视角的数据点云,测量一周后完成物体表面轮廓的360°三维全场测量。
(2)研究点云噪声的去除和多视点云的拼接,用手动选取三个参考点的方法实现点云的预拼接和ICP算法实现多视点云的精确拼接。
(3)用二维Delaunay三角剖分实现空间散乱点集的三角网格化,该方法克服了三维Delaunay三角剖分高复杂度和投影Delaunay三角网格算法质量难以保证的缺点,研究通过对空间散乱数据进行适当分区,提高k近邻搜索算法的速度。
(4)研究了VTK可视化类库和HOOPS 3D图形应用接口与Microsoft Visual Studio .NET 2003的系统整合。
(5)开发了三维重建软件原型系统,并用该系统对牙模的点云数据进行了拼合和重建,取得了很好的效果。
Non-contact optical 3D measurement technology has the advantages of non-contact, fast speed and high precision in measuring process, so it has been applied more and more extensively in machine design and manufacture field, aerospace industry, biomedical engineering, computer vision, virtual reality and cultural relic restoration recently. Teeth model is a kind of object with complicated surface and small volume. Hence the research and develop on a set of Non-contact optical measuring system for dental model means a lot on both theoretical and engineering application.
Optical 3D measurement system includes two main aspects: One is surface data acquisition of measured object, the other is surface reconstruction. This thesis includes control system of optical 3D measurement device, multi-view point cloud registration, and surface reconstruction technology based triangular mesh. The concrete content of this research includes five subtopics:
(1) An accurate and stable motorized rotary stage of optical 3D measurement device is developed。It mainly includes grating projection module and rotary electrical servo. After measured object is perfectly fit on the motorized rotary stage driven by the step motor, the computer controls projector to project four grating fringes on it, then transforms the deformed fringe images modulated by the object’s height into 3D coordinate data. Motorized rotary stage is driven by the step motor and the multi-view point clouds of measured object can be obtained. After measuring around the object with one circle, 360-deg 3D full-court measurement of object’s surface profiles will be completed.
(2) Study on unorganized point cloud denoising method and multi-view point cloud registration. The method using manual selection of three points is realized pre-registration of point cloud data and precise registration based on ICP algorithm.
(3) 3D Delaunay neighbors of any points are searched by the map from 2D triangulation to space unorganized points, which solves high complexity of 3D Delaunay triangulation and shortcomings of quality not guaranteed of projection Delaunay algorithm. This thesis increases searching speed of k-nearest neighbor by proper partition of space unorganized point cloud data.
(4) Study on system integration of VTK(Visualization Toolkit) ,HOOPS 3D Application Framework and Microsoft Visual Studio .NET.
(5) 3D reconstruction software prototype system has been established, and the point cloud of detal models have been aqured by this system. after sequential merging and reconstruction, the result shows that the system has a good performance.
非接触式光学三维测量系统主要有两个部分组成:一是被测物体的表面数据的获取;二是曲面重建。本文的研究工作主要有光学三维测量系统的控制系统、多视点云拼接和以三角网格为基础的曲面重建技术,具体内容涵盖:
(1)设计光学三维测量系统精确稳定的测量转台。主要包括光栅投影模块和电动旋转台控制模块。计算机控制投影仪向被测物体投射4幅光栅条纹,相机采集经过物体表面高度调制的变形条纹图像转化为三维坐标数据,旋转台在步进电机的控制下,获得被测物体的多个不同视角的数据点云,测量一周后完成物体表面轮廓的360°三维全场测量。
(2)研究点云噪声的去除和多视点云的拼接,用手动选取三个参考点的方法实现点云的预拼接和ICP算法实现多视点云的精确拼接。
(3)用二维Delaunay三角剖分实现空间散乱点集的三角网格化,该方法克服了三维Delaunay三角剖分高复杂度和投影Delaunay三角网格算法质量难以保证的缺点,研究通过对空间散乱数据进行适当分区,提高k近邻搜索算法的速度。
(4)研究了VTK可视化类库和HOOPS 3D图形应用接口与Microsoft Visual Studio .NET 2003的系统整合。
(5)开发了三维重建软件原型系统,并用该系统对牙模的点云数据进行了拼合和重建,取得了很好的效果。
Non-contact optical 3D measurement technology has the advantages of non-contact, fast speed and high precision in measuring process, so it has been applied more and more extensively in machine design and manufacture field, aerospace industry, biomedical engineering, computer vision, virtual reality and cultural relic restoration recently. Teeth model is a kind of object with complicated surface and small volume. Hence the research and develop on a set of Non-contact optical measuring system for dental model means a lot on both theoretical and engineering application.
Optical 3D measurement system includes two main aspects: One is surface data acquisition of measured object, the other is surface reconstruction. This thesis includes control system of optical 3D measurement device, multi-view point cloud registration, and surface reconstruction technology based triangular mesh. The concrete content of this research includes five subtopics:
(1) An accurate and stable motorized rotary stage of optical 3D measurement device is developed。It mainly includes grating projection module and rotary electrical servo. After measured object is perfectly fit on the motorized rotary stage driven by the step motor, the computer controls projector to project four grating fringes on it, then transforms the deformed fringe images modulated by the object’s height into 3D coordinate data. Motorized rotary stage is driven by the step motor and the multi-view point clouds of measured object can be obtained. After measuring around the object with one circle, 360-deg 3D full-court measurement of object’s surface profiles will be completed.
(2) Study on unorganized point cloud denoising method and multi-view point cloud registration. The method using manual selection of three points is realized pre-registration of point cloud data and precise registration based on ICP algorithm.
(3) 3D Delaunay neighbors of any points are searched by the map from 2D triangulation to space unorganized points, which solves high complexity of 3D Delaunay triangulation and shortcomings of quality not guaranteed of projection Delaunay algorithm. This thesis increases searching speed of k-nearest neighbor by proper partition of space unorganized point cloud data.
(4) Study on system integration of VTK(Visualization Toolkit) ,HOOPS 3D Application Framework and Microsoft Visual Studio .NET.
(5) 3D reconstruction software prototype system has been established, and the point cloud of detal models have been aqured by this system. after sequential merging and reconstruction, the result shows that the system has a good performance.
引文
[1] Chen F, Brown G M, Song M. Overview of three-dimensional shape measurement using optical methods[J]. Optical Engineering, 2000, 39: 10.
[2] Sansoni G, Docchio F. Three-dimensional optical measurements and reverse engineering for automotive applications[J]. Robotics and Computer Integrated Manufacturing, 2004, 20(5): 359-367.
[3] Flisch A, Wirth J, Zanini R, et al. Industrial computed tomography in reverse engineering applications[J]. Proc. of Computerized Tomography for Industrial Applications and Image Processing in Radiology, 1999, .
[4] Tilley H A, Orgun M A, Corrie B D, et al. A Reverse Engineering Environment Based on Spatial and Visual Software Interconnection Models[J].
[5]田晓东,史桂蓉.复杂曲面实物的逆向工程及其关键技术[J].机械设计与制造工程, 2000, 29(4): 1-3.
[6] Hain T, Eckhardt R, Kunzi-rapp K, et al. Indications for Optical Shape Measurements in Orthopaedics and Dermatology[J]. Medical Laser Application, 2002, 17(1): 55-58.
[7] Dropps S H. Reverse Engineering Using X-Ray Scan Technique[J]. 1998, .
[8] Salvi J. An Approach to Coded Structured Light to Obtain Three Dimensional Information[J]. Universitat de Girona, Departament d'ElectrYonica, InformYatica I AutomYatica, 1997, .
[9] Rusinkiewicz S, Hall-holt O, Levoy M. Real-time 3D model acquisition[J]. ACM Transactions on Graphics (TOG), 2002, 21(3): 438-446.
[10] Hilton A, Stoddart A J, Illingworth J, et al. Reliable surface reconstruction from multiple range images[J]. LECTURE NOTES IN COMPUTER SCIENCE, 1996, : 117-126.
[11] Vosniakos G C, Giannakakis T. Reverse engineering of simple surfaces of unknown shape with touch probes: scanning and compensation issues[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2003, 217(4): 563-568.
[12] Fuchs H, Kedem Z M, Uselton S P. Optimal surface reconstruction from planar contours[J]. Communications of the ACM, 1977, 20(10): 693-702.
[13]吴焕明,方漪.基于计算机立体视觉的图像测量技术[J].工程图学学报, 2002, 23(004): 60-67.
[14] Goesele M, Curless B, Seitz S M. Multi-view stereo revisited[C]. 2006. 2402-2409.
[15] Bruce P I, Hu B S, Glover G H, et al. Magnetization transfer time-of-flight magnetic resonance angiography[J]. Magnetic resonance in medicine, 1992, 25(2): 372-379.
[16] Campbell I H, Smith D L, Neef C J, et al. Consistent time-of-flight mobility measurements and polymer light-emitting diode current–voltage characteristics[J]. Applied Physics Letters, 1999, 74: 2809.
[17] Keferstein C P, Marxer M. Testing bench for laser triangulation sensors[J]. Sensor Review, 1998, 18(3): 183-187.
[18]牛小兵,林玉池.光栅投影三维轮廓测量及关键技术分析[J].光电子.激光, 2002, 13(009): 983-986.
[19] Pauly M, Gross M. Spectral processing of point-sampled geometry[C]. ACM New York, NY, USA, 2001. 379-386.
[20] Alexa M, Behr J, Cohen-or D, et al. Point set surfaces[C]. IEEE Computer Society Washington, DC, USA, 2001. 21-28.
[21] Jones T R, Durand F, Desbrun M. Non-iterative, feature-preserving mesh smoothing[J]. ACM Transactions on Graphics, 2003, 22(3): 943-949.
[22] Shashar F, Iddo D, Cohen-or D. Bilateral mesh denoising [A][C]. 2003. 950-953.
[23] Varady T, Martin R R, Coxt J. Reverse engineering of geometric models: an introduction[J]. Computer-aided design, 1997, 29(4): 255-268.
[24] Besl P J, Mckay N D. A method for registration of 3-D shapes[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(2): 239-256.
[25] Chen Y, Medioni G. Object modeling by registration of multiple range images[C]. 1991. 2724-2729.
[26] Fan K C, Tsai T H. Optimal shape error analysis of the matching image for a free-form surface[J]. Robotics and Computer Integrated Manufacturing, 2001, 17(3): 215-222.
[27] Masuda T, Yokoya N. A robust method for registration and segmentation of multiple rangeimages[C]. 1994. 106-113.
[28] Johnson A, Hebert M. Surface registration by matching oriented points[C]. 12-15.
[29] Ristic M, Brujic D. Efficient registration of NURBS geometry[J]. Image and Vision Computing, 1997, 15(12): 925-935.
[30]罗先波,钟约先,李仁举.三维扫描系统中的数据配准技术[J].清华大学学报:自然科学版, 2004, 44(8): 1104-1106.
[31]王磊,邢渊.反向工程中数据点云的拼合[J].模具技术, 2004, (1): 47-49.
[32]张舜德,朱东波,等.反求工程中三维几何形状测量及数据预处理[J].机电工程技术, 2001, 30(1): 7-10.
[33]张丽艳,周儒荣,等.海量测量数据简化技术研究[J].计算机辅助设计与图形学学报, 2001, 13(11): 1019-1023.
[34]石教英,蔡文立.科学计算可视化算法与系统[J].科学出版社l996, .
[35]李晓梅,黄朝晖,蔡勋,等.并行与分布式可视化技术及应用[Z].北京:国防工业出版社,2001.
[36] Lorensen W E, Cline H E. Marching cubes: A high resolution 3D surface construction algorithm[C]. ACM New York, NY, USA, 1987. 163-169.
[37] Hoppe H, Derose T, Duchamp T, et al. Surface Reconstruction from Unorganized Points[C]. 1992. 71-78.
[38] Edelsbrunner H, M E P. Three-dimensional alpha shapes[C]. ACM New York, NY, USA, 1992. 75-82.
[39] Amenta N, Bern M, Eppstein D. The Crust and theβ-Skeleton: Combinatorial Curve Reconstruction[J]. Graphical Models and Image Processing, 1998, 60(2): 125-135.
[40] Amenta N, Choi S, Dey T K, et al. A simple algorithm for homeomorphic surface reconstruction[C]. ACM New York, NY, USA, 2000. 213-222.
[41] Amenta N, Choi S, Kolluri R K. The power crust, unions of balls, and the medial axis transform[J]. Computational Geometry, 2001, 19(2): 127-153.
[42] Kuo C C, Yau H T. A Delaunay-based region-growing approach to surface reconstruction from unorganized points[J]. Computer-Aided Design, 2005, 37(8): 825-835.
[43] Bajaj C L, Bernardini F, Chen J, et al. Automatic Reconstruction of 3D CAD Models[C]. 1996.
[44] Gopi M, Krishnan S. A Fast and Efficient Projection-Based Approach for Surface Reconstruction[C]. 1834. 02.
[45] G J. Dense 3-d surface acquisition by structured light using off-the-shelf components[J]. Videometrics and Optical Methods for 3D Shape Measurement, 2001, 4309: 220–231.
[46] Sansoni G, Corini S, Lazzari S, et al. Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications[J]. APPLIED OPTICS, 1997, 36(19).
[47] Schroeder W J, Martin K M, Avila L S, et al. The VTK User’s Guide. Kitware[J]. Inc., June, 1999, .
[48] Schroeder W, Martin K, Lorensen B. The Visualization Toolkit An Object-Oriented Approach To 3D Graphics, Kitware[J]. Inc. publishers, 2004, 2.
[49] Weyrich T, Pauly M, Keiser R, et al. Post-processing of scanned 3D surface data[C]. 2004. 85–94.
[50]董明晓,郑康平.一种点云数据噪声点的随机滤波处理方法[J].中国图象图形学报: A辑, 2004, 9(002): 245-248.
[51] Ooi B C, Clayton V. Spatial kd-Tree: A Data Structure for Geographic Database[C]. Springer, 1987.
[52]金涛,单岩,等.实物测量造型中的测量数据重定位方法[J].计算机辅助设计与图形学学报, 2001, 13(4): 315-318.
[53]单岩,梁建国.反向工程中三坐标测量重定位整合[J].模具工业, 2001, (008): 8-11.
[54] Li Q, Griffiths J G. Iterative closest geometric objects registration[J]. Computers and Mathematics with Applications, 2000, 40(10-11): 1171-1188.
[55] Hamann B. A data reduction scheme for triangulated surfaces[J]. Computer Aided Geometric Design, 1994, 11(2): 197-214.
[56]王青,王融清.散乱数据点的增量快速曲面重建算法[J].软件学报, 2000, 11(9): 1221-1227.
[57] Bern M, Eppstein D. Mesh Generation and Optimal Triangulation[M]. Xerox Corporation, 1992.
[58]张三元,查红彬,鲍虎军,等.数字几何处理及其应用的最新进展[J].计算机辅助设计与图形学学报, 2005, 17(6): 1129-1138.
[59] Miles R E. Solution to Problem 67-15 (Probability Distribution of a Network of Triangles)[J]. SIAM, 1969, 11(3): 399-402.
[60] Sibson R. Locally equiangular triangulations[J]. The Computer Journal, 1978, 21(3): 243-245.
[61] Lingus A. The Greedy and Delaunay triangulations are not bad in the average case[J]. Information Processing Letters, 1986, 22(1): 25-31.
[62] Tsai V J. Delaunay triangulations in TIN creation: an overview and a linear-time algorithm[J]. International Journal of Geographical Information Science, 1993, 7(6): 501-524.
[63]周儒荣,张丽艳,苏旭,等.海量散乱点的曲面重建算法研究[M]. 2001. 249-255.
[64]黄淼,张海朝,李超.基于八叉树空间分割的k近邻搜索算法[J].计算机应用, 2008, 28(8): 2046-2048.
[65]马长胜,姜晓峰,强鹤群.散乱数据点的k近邻快速搜索算法[J].微电子学与计算机, 2007, 24(12): 206-209.
[66]吴丽娟,郑冕,张彩明.海量空间数据点k近邻的快速搜索算法[J].小型微型计算机系统, 2007, 28(1): 70-74.
[67] Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes*[J]. The Computer Journal, 1981, 24(2): 167-172.
[68]张明亮,史小路.基于运动控制卡的步进电机随动系统设计[J].机电产品开发与创新, 2007, 20(1): 138-139.
[69]严晓照,张兴国.增量式PID控制在温控系统中的应用[J].南通大学学报:自然科学版, 2006, 5(4): 48-51.
[70]吕迅.试验机的增量式PID控制系统研制[J].浙江树人大学学报, 2002, 2(4): 75-77.
[2] Sansoni G, Docchio F. Three-dimensional optical measurements and reverse engineering for automotive applications[J]. Robotics and Computer Integrated Manufacturing, 2004, 20(5): 359-367.
[3] Flisch A, Wirth J, Zanini R, et al. Industrial computed tomography in reverse engineering applications[J]. Proc. of Computerized Tomography for Industrial Applications and Image Processing in Radiology, 1999, .
[4] Tilley H A, Orgun M A, Corrie B D, et al. A Reverse Engineering Environment Based on Spatial and Visual Software Interconnection Models[J].
[5]田晓东,史桂蓉.复杂曲面实物的逆向工程及其关键技术[J].机械设计与制造工程, 2000, 29(4): 1-3.
[6] Hain T, Eckhardt R, Kunzi-rapp K, et al. Indications for Optical Shape Measurements in Orthopaedics and Dermatology[J]. Medical Laser Application, 2002, 17(1): 55-58.
[7] Dropps S H. Reverse Engineering Using X-Ray Scan Technique[J]. 1998, .
[8] Salvi J. An Approach to Coded Structured Light to Obtain Three Dimensional Information[J]. Universitat de Girona, Departament d'ElectrYonica, InformYatica I AutomYatica, 1997, .
[9] Rusinkiewicz S, Hall-holt O, Levoy M. Real-time 3D model acquisition[J]. ACM Transactions on Graphics (TOG), 2002, 21(3): 438-446.
[10] Hilton A, Stoddart A J, Illingworth J, et al. Reliable surface reconstruction from multiple range images[J]. LECTURE NOTES IN COMPUTER SCIENCE, 1996, : 117-126.
[11] Vosniakos G C, Giannakakis T. Reverse engineering of simple surfaces of unknown shape with touch probes: scanning and compensation issues[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2003, 217(4): 563-568.
[12] Fuchs H, Kedem Z M, Uselton S P. Optimal surface reconstruction from planar contours[J]. Communications of the ACM, 1977, 20(10): 693-702.
[13]吴焕明,方漪.基于计算机立体视觉的图像测量技术[J].工程图学学报, 2002, 23(004): 60-67.
[14] Goesele M, Curless B, Seitz S M. Multi-view stereo revisited[C]. 2006. 2402-2409.
[15] Bruce P I, Hu B S, Glover G H, et al. Magnetization transfer time-of-flight magnetic resonance angiography[J]. Magnetic resonance in medicine, 1992, 25(2): 372-379.
[16] Campbell I H, Smith D L, Neef C J, et al. Consistent time-of-flight mobility measurements and polymer light-emitting diode current–voltage characteristics[J]. Applied Physics Letters, 1999, 74: 2809.
[17] Keferstein C P, Marxer M. Testing bench for laser triangulation sensors[J]. Sensor Review, 1998, 18(3): 183-187.
[18]牛小兵,林玉池.光栅投影三维轮廓测量及关键技术分析[J].光电子.激光, 2002, 13(009): 983-986.
[19] Pauly M, Gross M. Spectral processing of point-sampled geometry[C]. ACM New York, NY, USA, 2001. 379-386.
[20] Alexa M, Behr J, Cohen-or D, et al. Point set surfaces[C]. IEEE Computer Society Washington, DC, USA, 2001. 21-28.
[21] Jones T R, Durand F, Desbrun M. Non-iterative, feature-preserving mesh smoothing[J]. ACM Transactions on Graphics, 2003, 22(3): 943-949.
[22] Shashar F, Iddo D, Cohen-or D. Bilateral mesh denoising [A][C]. 2003. 950-953.
[23] Varady T, Martin R R, Coxt J. Reverse engineering of geometric models: an introduction[J]. Computer-aided design, 1997, 29(4): 255-268.
[24] Besl P J, Mckay N D. A method for registration of 3-D shapes[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(2): 239-256.
[25] Chen Y, Medioni G. Object modeling by registration of multiple range images[C]. 1991. 2724-2729.
[26] Fan K C, Tsai T H. Optimal shape error analysis of the matching image for a free-form surface[J]. Robotics and Computer Integrated Manufacturing, 2001, 17(3): 215-222.
[27] Masuda T, Yokoya N. A robust method for registration and segmentation of multiple rangeimages[C]. 1994. 106-113.
[28] Johnson A, Hebert M. Surface registration by matching oriented points[C]. 12-15.
[29] Ristic M, Brujic D. Efficient registration of NURBS geometry[J]. Image and Vision Computing, 1997, 15(12): 925-935.
[30]罗先波,钟约先,李仁举.三维扫描系统中的数据配准技术[J].清华大学学报:自然科学版, 2004, 44(8): 1104-1106.
[31]王磊,邢渊.反向工程中数据点云的拼合[J].模具技术, 2004, (1): 47-49.
[32]张舜德,朱东波,等.反求工程中三维几何形状测量及数据预处理[J].机电工程技术, 2001, 30(1): 7-10.
[33]张丽艳,周儒荣,等.海量测量数据简化技术研究[J].计算机辅助设计与图形学学报, 2001, 13(11): 1019-1023.
[34]石教英,蔡文立.科学计算可视化算法与系统[J].科学出版社l996, .
[35]李晓梅,黄朝晖,蔡勋,等.并行与分布式可视化技术及应用[Z].北京:国防工业出版社,2001.
[36] Lorensen W E, Cline H E. Marching cubes: A high resolution 3D surface construction algorithm[C]. ACM New York, NY, USA, 1987. 163-169.
[37] Hoppe H, Derose T, Duchamp T, et al. Surface Reconstruction from Unorganized Points[C]. 1992. 71-78.
[38] Edelsbrunner H, M E P. Three-dimensional alpha shapes[C]. ACM New York, NY, USA, 1992. 75-82.
[39] Amenta N, Bern M, Eppstein D. The Crust and theβ-Skeleton: Combinatorial Curve Reconstruction[J]. Graphical Models and Image Processing, 1998, 60(2): 125-135.
[40] Amenta N, Choi S, Dey T K, et al. A simple algorithm for homeomorphic surface reconstruction[C]. ACM New York, NY, USA, 2000. 213-222.
[41] Amenta N, Choi S, Kolluri R K. The power crust, unions of balls, and the medial axis transform[J]. Computational Geometry, 2001, 19(2): 127-153.
[42] Kuo C C, Yau H T. A Delaunay-based region-growing approach to surface reconstruction from unorganized points[J]. Computer-Aided Design, 2005, 37(8): 825-835.
[43] Bajaj C L, Bernardini F, Chen J, et al. Automatic Reconstruction of 3D CAD Models[C]. 1996.
[44] Gopi M, Krishnan S. A Fast and Efficient Projection-Based Approach for Surface Reconstruction[C]. 1834. 02.
[45] G J. Dense 3-d surface acquisition by structured light using off-the-shelf components[J]. Videometrics and Optical Methods for 3D Shape Measurement, 2001, 4309: 220–231.
[46] Sansoni G, Corini S, Lazzari S, et al. Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications[J]. APPLIED OPTICS, 1997, 36(19).
[47] Schroeder W J, Martin K M, Avila L S, et al. The VTK User’s Guide. Kitware[J]. Inc., June, 1999, .
[48] Schroeder W, Martin K, Lorensen B. The Visualization Toolkit An Object-Oriented Approach To 3D Graphics, Kitware[J]. Inc. publishers, 2004, 2.
[49] Weyrich T, Pauly M, Keiser R, et al. Post-processing of scanned 3D surface data[C]. 2004. 85–94.
[50]董明晓,郑康平.一种点云数据噪声点的随机滤波处理方法[J].中国图象图形学报: A辑, 2004, 9(002): 245-248.
[51] Ooi B C, Clayton V. Spatial kd-Tree: A Data Structure for Geographic Database[C]. Springer, 1987.
[52]金涛,单岩,等.实物测量造型中的测量数据重定位方法[J].计算机辅助设计与图形学学报, 2001, 13(4): 315-318.
[53]单岩,梁建国.反向工程中三坐标测量重定位整合[J].模具工业, 2001, (008): 8-11.
[54] Li Q, Griffiths J G. Iterative closest geometric objects registration[J]. Computers and Mathematics with Applications, 2000, 40(10-11): 1171-1188.
[55] Hamann B. A data reduction scheme for triangulated surfaces[J]. Computer Aided Geometric Design, 1994, 11(2): 197-214.
[56]王青,王融清.散乱数据点的增量快速曲面重建算法[J].软件学报, 2000, 11(9): 1221-1227.
[57] Bern M, Eppstein D. Mesh Generation and Optimal Triangulation[M]. Xerox Corporation, 1992.
[58]张三元,查红彬,鲍虎军,等.数字几何处理及其应用的最新进展[J].计算机辅助设计与图形学学报, 2005, 17(6): 1129-1138.
[59] Miles R E. Solution to Problem 67-15 (Probability Distribution of a Network of Triangles)[J]. SIAM, 1969, 11(3): 399-402.
[60] Sibson R. Locally equiangular triangulations[J]. The Computer Journal, 1978, 21(3): 243-245.
[61] Lingus A. The Greedy and Delaunay triangulations are not bad in the average case[J]. Information Processing Letters, 1986, 22(1): 25-31.
[62] Tsai V J. Delaunay triangulations in TIN creation: an overview and a linear-time algorithm[J]. International Journal of Geographical Information Science, 1993, 7(6): 501-524.
[63]周儒荣,张丽艳,苏旭,等.海量散乱点的曲面重建算法研究[M]. 2001. 249-255.
[64]黄淼,张海朝,李超.基于八叉树空间分割的k近邻搜索算法[J].计算机应用, 2008, 28(8): 2046-2048.
[65]马长胜,姜晓峰,强鹤群.散乱数据点的k近邻快速搜索算法[J].微电子学与计算机, 2007, 24(12): 206-209.
[66]吴丽娟,郑冕,张彩明.海量空间数据点k近邻的快速搜索算法[J].小型微型计算机系统, 2007, 28(1): 70-74.
[67] Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes*[J]. The Computer Journal, 1981, 24(2): 167-172.
[68]张明亮,史小路.基于运动控制卡的步进电机随动系统设计[J].机电产品开发与创新, 2007, 20(1): 138-139.
[69]严晓照,张兴国.增量式PID控制在温控系统中的应用[J].南通大学学报:自然科学版, 2006, 5(4): 48-51.
[70]吕迅.试验机的增量式PID控制系统研制[J].浙江树人大学学报, 2002, 2(4): 75-77.