大型锻件热态几何参数视觉测量技术研究
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摘要
大型构件是电力、船舶、航空航天等重大工程核心装备中的关键结构件,其特点是大重量和大尺寸,多用于承载力大、性能要求高的场合,通常先由锻造方法将坯料锻成所需形状、尺寸的锻件,再经切削加工制造而成。加热后的钢锭在锻造过程中需要对其尺寸进行测量,以保证锻件的锻后尺寸,由于锻造条件极为恶劣,锻造温度通常高达一千余摄氏度,导致在线测量大型锻件的热态几何参数十分困难。视觉测量具有非接触、速度快、精度高的特点,研究如何将视觉测量技术应用于大型锻件热态几何参数测量对提高锻件材料利用率、降低生产成本具有十分重要的意义。本文在相关项目的资助下,较系统的研究了大型锻件视觉测量的方法,主要针对以下几个关键问题开展了研究：
(1)针对热态锻件图像采集的难题,在分析锻件热辐射性质和反射性质的基础上提出了热态锻件光谱选择性图像采集方法,该方法借助照明光源照射热态锻件,并用黑白CCD摄像机接收锻件反射的照明光线成像,光谱范围由照明光源辐射出射度与热态锻件辐射出射度差值最大的波长位置确定；该方法可有效消除高温锻件辐射光线的影响,为测量大型锻件热态尺寸提供了基础。
(2)根据大型锻件尺寸测量现场条件,以热态锻件光谱选择性图像采集方法为基础,构建了基于双目视觉的大型锻件热态尺寸测量系统,系统中使用照明设备投射结构光到锻件表面,以增加锻件表面特征信息；分析了系统结构参数及结构光条中心线提取精度对系统测量精度的影响规律,根据分析结果并结合测量现场情况对两摄像机的间距、摄像机焦距以及测量系统到被测锻件距离等参数进行了调整。
(3)针对锻件加工车间复杂环境下测量系统难以标定的问题,研究了大型锻件热态尺寸测量系统的标定方法；该方法以主动视觉标定技术为基础,通过对正交运动前后所拍摄图像中投影标识的识别及对应点提取计算摄像机内参数；标定摄像机外参数时,先由基本矩阵求解相差一个尺度的旋转和平移矩阵,再根据内参数及旋转、平移矩阵三维重建两特定标识点,用双经纬仪系统测量两标识点间的实际间距,最后由两标识点测量间距与重建间距的比值得到尺度因子,从而实现外参数标定。
(4)针对大型锻件热态尺寸在线测量的难题,提出了由投影特征线所反映的锻件形状特征求锻件热态尺寸的方法。测量圆柱形及方形锻件热态尺寸时分别向锻件投影编码特征线和等间距特征线；对于圆柱形锻件,使用椭圆拟合在线测量其尺寸,并通过圆柱拟合检测其锻后尺寸；测量方形锻件时,根据重建特征线拟合曲线,搜索曲率大于阈值的位置,进而可求锻件长度。在锻件加工厂进行了大型锻件热态尺寸测量实验,并对该检测方法的测量精度进行了检验,实验结果表明该方法可在线测量锻件热态尺寸。
本文中热态锻件光谱选择性图像采集方法、通过重建的投影特征线反映锻件几何形状并测量其尺寸方法及研制的大型热态锻件几何参数测量系统等研究工作为大型锻件热态几何参数提供了一种有效的测量手段。
Large components are the key parts of important equipment which are widely used in the field of power, ship and aerospace. In order to let the large components can be employed in extreme condition, the blanks which are used to machine the large components are manufactured through forging. The large size forgings have to be measured in the forming process. However, the high temperature of hot large forgings and the large size make it hard to be measured accurately. Machine vision technology has been used as a high-speed, non-contact method in dimension measurement. In order to reduce the waste and production cost, the dimension measurement method with the machine vision technology is researched. This paper is mainly focuses on some key technical as follows:
(1) To solve the problem of acquiring the image of hot parts, the spectrum selective method is proposed. By analyzing the self-emitted radiation character and reflection character of hot large forging, the illumination lamp is used to acquiring image of hot large forging. When the external light source projects light toward the high temperature objects, the external light strikes the hot objects and is reflected toward CCD cameras along with the self-emitted radiation. One component of the reflected light is selectively detected by the CCD cameras, and the image of hot objects can be acquired. The range of wavelength is obtained according to the wavelength when difference between the radiant exitance of illumination lamp and the radiant exitance of hot forging is the maximum value. This method presents an important base for measuring the dimension of hot forging.
(2) Considering to the measurement condition in the forging plant, a stereo vision system which using the spectrum selective method is developed for mesuring the dimension of hot large forging. Structure light is projected toward the surface of hot forging in the dimension measurement process for increasing characteristics on it. The effect of the structural parameters of the stereo vision system on the error of the measurement is analysised. Based on the analysis results, the distance of two cameras, the focus length of cameras and the distance between the stereo vision system and the hot forging are adjusted accordingly.
(3) The camera calibration technique that can be used to calibrate the dimension measurement system in the forging plant is proposed. The intrinsic parameters of camera are calibrated according to the active vision. By recognizing the corresponding points in the images acquired after each orthogonal translation, the intrinsic parameters can be calculated. The extrinsic parameters of camera are determined up to indeterminate scale by the essential matrix. Then, scale is calculated by dividing the distance of two reconstructed feature points in 3D space by the length of the two feature points which is measured by the double-theodolite system.
(4) In order to measure the dimension of hot forging in the forming process, the method based on projected feature lines which can obtain the shape of forgings is presented. When measuring the dimension of round forging, a coded single pattern is projected toward hot forging to label characteristic lines and simplify the process of finding correspondences between image pairs. If the feature line is vertically to the axis of forging, the diameter of round forging can be estimated by fitting an ellipse using the reconstructed feature line in 3D space. Otherwise, the diameter of round forgings are acquired by fitting a cylinder with the reconstructed feature lines in 3D space. The lengths of square forgings are measured by finding the position of the curvature which is greater than the threshold.
The spectrum selective method for acquiring the image of hot part, the dimension measurement method by reconstructing the featured lines that are projected on the surface of hot forging, the measurment system presented in this paper can be used to measure the geometric parameters of hot large forging effeictively.
(1)针对热态锻件图像采集的难题,在分析锻件热辐射性质和反射性质的基础上提出了热态锻件光谱选择性图像采集方法,该方法借助照明光源照射热态锻件,并用黑白CCD摄像机接收锻件反射的照明光线成像,光谱范围由照明光源辐射出射度与热态锻件辐射出射度差值最大的波长位置确定；该方法可有效消除高温锻件辐射光线的影响,为测量大型锻件热态尺寸提供了基础。
(2)根据大型锻件尺寸测量现场条件,以热态锻件光谱选择性图像采集方法为基础,构建了基于双目视觉的大型锻件热态尺寸测量系统,系统中使用照明设备投射结构光到锻件表面,以增加锻件表面特征信息；分析了系统结构参数及结构光条中心线提取精度对系统测量精度的影响规律,根据分析结果并结合测量现场情况对两摄像机的间距、摄像机焦距以及测量系统到被测锻件距离等参数进行了调整。
(3)针对锻件加工车间复杂环境下测量系统难以标定的问题,研究了大型锻件热态尺寸测量系统的标定方法；该方法以主动视觉标定技术为基础,通过对正交运动前后所拍摄图像中投影标识的识别及对应点提取计算摄像机内参数；标定摄像机外参数时,先由基本矩阵求解相差一个尺度的旋转和平移矩阵,再根据内参数及旋转、平移矩阵三维重建两特定标识点,用双经纬仪系统测量两标识点间的实际间距,最后由两标识点测量间距与重建间距的比值得到尺度因子,从而实现外参数标定。
(4)针对大型锻件热态尺寸在线测量的难题,提出了由投影特征线所反映的锻件形状特征求锻件热态尺寸的方法。测量圆柱形及方形锻件热态尺寸时分别向锻件投影编码特征线和等间距特征线；对于圆柱形锻件,使用椭圆拟合在线测量其尺寸,并通过圆柱拟合检测其锻后尺寸；测量方形锻件时,根据重建特征线拟合曲线,搜索曲率大于阈值的位置,进而可求锻件长度。在锻件加工厂进行了大型锻件热态尺寸测量实验,并对该检测方法的测量精度进行了检验,实验结果表明该方法可在线测量锻件热态尺寸。
本文中热态锻件光谱选择性图像采集方法、通过重建的投影特征线反映锻件几何形状并测量其尺寸方法及研制的大型热态锻件几何参数测量系统等研究工作为大型锻件热态几何参数提供了一种有效的测量手段。
Large components are the key parts of important equipment which are widely used in the field of power, ship and aerospace. In order to let the large components can be employed in extreme condition, the blanks which are used to machine the large components are manufactured through forging. The large size forgings have to be measured in the forming process. However, the high temperature of hot large forgings and the large size make it hard to be measured accurately. Machine vision technology has been used as a high-speed, non-contact method in dimension measurement. In order to reduce the waste and production cost, the dimension measurement method with the machine vision technology is researched. This paper is mainly focuses on some key technical as follows:
(1) To solve the problem of acquiring the image of hot parts, the spectrum selective method is proposed. By analyzing the self-emitted radiation character and reflection character of hot large forging, the illumination lamp is used to acquiring image of hot large forging. When the external light source projects light toward the high temperature objects, the external light strikes the hot objects and is reflected toward CCD cameras along with the self-emitted radiation. One component of the reflected light is selectively detected by the CCD cameras, and the image of hot objects can be acquired. The range of wavelength is obtained according to the wavelength when difference between the radiant exitance of illumination lamp and the radiant exitance of hot forging is the maximum value. This method presents an important base for measuring the dimension of hot forging.
(2) Considering to the measurement condition in the forging plant, a stereo vision system which using the spectrum selective method is developed for mesuring the dimension of hot large forging. Structure light is projected toward the surface of hot forging in the dimension measurement process for increasing characteristics on it. The effect of the structural parameters of the stereo vision system on the error of the measurement is analysised. Based on the analysis results, the distance of two cameras, the focus length of cameras and the distance between the stereo vision system and the hot forging are adjusted accordingly.
(3) The camera calibration technique that can be used to calibrate the dimension measurement system in the forging plant is proposed. The intrinsic parameters of camera are calibrated according to the active vision. By recognizing the corresponding points in the images acquired after each orthogonal translation, the intrinsic parameters can be calculated. The extrinsic parameters of camera are determined up to indeterminate scale by the essential matrix. Then, scale is calculated by dividing the distance of two reconstructed feature points in 3D space by the length of the two feature points which is measured by the double-theodolite system.
(4) In order to measure the dimension of hot forging in the forming process, the method based on projected feature lines which can obtain the shape of forgings is presented. When measuring the dimension of round forging, a coded single pattern is projected toward hot forging to label characteristic lines and simplify the process of finding correspondences between image pairs. If the feature line is vertically to the axis of forging, the diameter of round forging can be estimated by fitting an ellipse using the reconstructed feature line in 3D space. Otherwise, the diameter of round forgings are acquired by fitting a cylinder with the reconstructed feature lines in 3D space. The lengths of square forgings are measured by finding the position of the curvature which is greater than the threshold.
The spectrum selective method for acquiring the image of hot part, the dimension measurement method by reconstructing the featured lines that are projected on the surface of hot forging, the measurment system presented in this paper can be used to measure the geometric parameters of hot large forging effeictively.
引文
[1]周秀云,杨春生,张涛.高精度无导轨大尺寸测量系统[J].实用测试技术.2002(6)：14-15.
[2]张国雄.三坐标测量机的发展趋势[J].中国机械工程.2000,11(1-2)：222-226.
[3]杨洪涛,费业泰.快速探测三坐标测量机特性参数优化研究[J].中国机械工程.2008,19(20)：2428-2432.
[4]张望先,仲思动,隋莉斌,等.基于三坐标测量机的大尺寸非接触测量[J].武汉大学学报(工学版).2004,37(5)：112-115.
[5]Abbe M, Takamasu K, Ozono S. Reliability on calibration of CMM[J]. Measurement.2003, 33(4):359-368.
[6]Franceschini F, Galetto M, Settineri L. On-line diagnostic tools for CMM performance[J]. International Journal of Advanced Manufacturing Technology.2002,19(2):125-130.
[7]Zhang Y F, Nee A Y C, Fuh J Y H, et al. A neural network approach to determining optimal inspection sampling size for CMM[J]. Computer Integrated Manufacturing Systems.1996, 9(3):161-169.
[8]Shereshevskii L M. Use of an Optical Theodolite in Engineering[J]. Measurement Techniques Ussr.1983,26(6):470-472.
[9]Magdeev V S. Error in the measurement of the coordinates of surface points of large components with two theodolites[J]. Measurement Techniques.1991,34(5):438-440.
[10]Netterville D D J, Djurfors S G. Controlling Inherent Uncertainties in Double Theodolite Measurements [J]. Journal of Applied Meteorology.1979,18(10):1371-1375.
[11]熊春宝,叶声华.经纬仪工业测量系统的模型研究[J].武汉测绘科技大学.1998,23(3)：233-237.
[12]陆敬舜.型架双经纬仪三维测量法[J].南京航空航天大学学报.1994,26(5).
[13]周富强,张广军,江沽.现场双经纬仪三维坐标测量系统[J].机械工程学报.2004,40(1)：165-169.
[14]张滋黎,邾继贵,耿娜,等.双经纬仪三维坐标测量系统设计[J].传感技术学报.2010,23(5)：660-664.
[15]黄桂平,叶声华,李广云,等.经纬仪大尺寸柔性三坐标测量系统的开发与应用[J].仪器仪表学报.2002,23(3)：607-610.
[16]黄桂平,李广云.电子经纬仪工业测量系统定向及坐标解算算法研究[J].测绘学报.2009,32(3)：256-260.
[17]Kramer P, Weckenmann A. Multi-energy image stack fusion in computed tomography[J]. Measurement Science & Technology.2010,21(4):1-7.
[18]Weckenmann A, Kramer P. Application of Computed Tomography in Manufacturing Metrology[J]. Tm-Technisches Messen.2009,76(7-8):340-346.
[19]Effenberger I. Use of industrial computerized tomography in quality assurance [J]. VDI Berichte.2005(1913):41-45.
[20]Bartscher M, Hilpert U. Industrial computerized tomography:From defect detector to a measuring tool for geometry determination[J]. VDI Berichte.2005(1914):187-199.
[21]Segal Y, Cohen B. Film Based Industrial Computerized-Tomography[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment.1987,254(1):202-209.
[22]Gao H W, Zhang L, Chen Z Q, et al. Beam hardening correction for middle-energy industrial computerized tomography[J]. Ieee Transactions on Nuclear Science.2006,53(5): 2796-2807.
[23]康克军.实验工业CT系统及其图像重建方法研究[D].北京：清华大学,1988.
[24]陈志强,李亮,冯建春.高能射线工业CT最新进展[J].CT理论与应用研究.2005,14(4)：1-4.
[25]吴斌.大型物体三维形貌数字化测量关键技术研究[D].天津：天津大学,2002.
[26]Emmett N. Leith J U. Reconstructed wave fronts and communication theory[J]. Journal of the Optical Society of America.1962,52(10):1123-1128.
[27]Shanin V I, Shanin 0 V. The use of holographic interferometry in adjustment of gyroscope units[J]. Russian Journal of Nondestructive Testing.2004,40(10):708-712.
[28]Gesualdi M R R, Soga D, Muramatsu M. Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique[J]. Optics and Lasers in Engineering.2006,44(1):56-67.
[29]Chien C H, Wu Y D, Chiou Y T, et al. Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry [J]. Optics and Lasers in Engineering.2006,44(1):80-91.
[30]Denicola S, Ferraro P, Finizio A, et al. Evaluation of rigid rotations in flexural loading tests by holographic interferometry [J]. Experimental Mechanics.1997,37(2): 154-158.
[31]Twitto A, Shamir J, Bekker A, et al. Detection of internal defects using phase shifting holographic interferometry[J]. Ndt & E International.1996,29(3):163-173.
[32]Zhizhin G N, Nikitin A K, Ryzhova T A, et al. Application of holographic interferometry to optical monitoring of solid surfaces[J]. Technical Physics Letters.2004,30(11): 927-929.
[33]Frejlich J, Garcia P M. Advances in real-time holographic interferometry for the measurement of vibrations and deformations [J]. Optics and Lasers in Engineering.1999, 32(6):515-527.
[34]Lettieri T R. Pulsed Laser Caliper for Noncontact Dimensional Measurement [J]. Applied Optics.1986,25(9):1443-1449.
[35]Lettieri T R. Noncontact Dimensional Measurement Using a Pulsed Laser Caliper[J]. Journal of the Optical Society of America a-Optics Image Science and Vision.1985, 2(13):P8.
[36]Jarvis R A. A Laser Time-of-Flight Range Scanner for Robotic Vision[J]. Ieee Transactions on Pattern Analysis and Machine Intelligence.1983,5(5):505-512.
[37]Ahola R. Heikkinen T M M.3D image acquisition by scanning time of flight measurements[C]. Pisa, Italy:North-Holland, Amsterdam, Neth,1986.
[38]Philip Garcia J P A J. Characterization of a scannerless ladar system [C]. Orlando, FL, USA:1993.
[39]严惠民,倪旭翔,陈奇霖,等.无扫描三维激光雷达的研究[J].中国激光.2000,27(9)：861-864.
[40]Busck J, Heiselberg H. Gated viewing and high-accuracy three-dimensional laser radar[J]. Applied Optics.2004,43(24):4705-4710.
[41]Kawakita M, Iizuka K, Iwama R, et al. Gain-modulated Axi-Vision Camera (high speed high-accuracy depth-mapping camera)[J]. Optics Express.2004,12(22):5336-5344.
[42]Kawakita M, Iizuka K, Aida T, et al. Axi-Vision Camera (real-time distance-mapping camera)[J]. Applied Optics.2000,39(22):3931-3939.
[43]Nellums R 0, Habbit R D, Heying M R, et al.3D scannerless LADAR for orbiter inspection-art. no.62200G[J]. Spaceborne Sensors Ⅲ.2006,6220:G2200.
[44]Mitchell J, Spence A, Hoang M, et al. Sensor fusion of laser trackers for use in large-scale precision metrology[J]. Intelligent Manufacturing.2004,5263:57-65.
[45]Zobrist T L, Burge J H, Davison W B, et al. Measurements of large optical surfaces with a laser tracker-art. no.70183U[J]. Advanced Optical and Mechanical Technologies in Telescopes and Instrumentation, Pts 1-3.2008,7018:U183.
[46]Osawa S, Takatsuji T, Hong J, et al. Evaluation of the performance of a novel laser tracker used for coordinate measurements[J]. Recent Developments in Traceable Dimensional Measurements.2001,4401:127-135.
[47]Muralikrishnan B, Sawyer D, Blackburn C, et al. ASME B89.4.19 Performance Evaluation Tests and Geometric Misalignments in Laser Trackers[J]. Journal of Research of the National Institute of Standards and Technology.2009,114(1):21-35.
[48]Ouyang J F, Liu W L, Yan Y G, et al. Angular error calibration of laser tracker system art. no.63442U[C].2006.
[49]李广云.激光跟踪测量系统原理及应用[J].测绘工程.2001,4(10)：3-8.
[50]张国雄,林永兵,李杏华,等.四路激光跟踪干涉三坐标测量系统[J].光学学报.2003,23(9)：1030-1036.
[51]张旭东,张国雄,付继有.多路激光跟踪干涉柔性坐标测量系统三自由度坐标测量方法的研究[J].电子测量与仪器学报.2000,1(14)：22-25.
[52]陈晓荣,陈淑芬.激光跟踪运动目标伺服系统设计[J].仪器仪表学报.2006(S3)：1965-1966.
[53]鞠有伦,陈德应,于欣,等.利用受激布里渊散射实现在轨运动目标激光跟踪瞄准研究[J].光学学报.2005(1)：88-92.
[54]贾云得.机器视觉[M].北京：科学出版社,2000.
[55]Park J, Kim C, Na J, et al. Using structured light for efficient depth edge detection[J]. Image and Vision Computing.2008,26(11):1449-1465.
[56]Dipanda A, Woo S. Towards a real-time 3D shape reconstruction using a structured light system[J]. Pattern Recognition.2005,38(10):1632-1650.
[57]Tsalakanidou F, Forster F, Malassiotis S, et al. Real-time acquisition of depth and color images using structured light and its application to 3D face recognition[J]. Real-Time Imaging.2005,11(5-6):358-369.
[58]Xu J, Xi N, Zhang C, et al. Real-time 3D shape inspection system of automotive parts based on structured light pattern[J]. Optics and Laser Technology.2011,43(1):1-8.
[59]Boverie S, Devy M, Lerasle F. Comparison of structured light and stereovision sensors for new airbag generations [J]. Control Engineering Practice.2003,11(12):1413-1421.
[60]Valkenburg R J, Mcivor A M. Accurate 3D measurement using a structured light system [J]. Image and Vision Computing.1998,16(2):99-110.
[61]张广军.机器视觉[M].北京：科学出版社,2005.
[62]Barrois B, Konrad M, Wohler C, et al. Resolving stereo matching errors due to repetitive structures using model information[J]. Pattern Recognition Letters.2010,31(12): 1683-1692.
[63]Bensrhair A, Miche P, Debrie R. Fast and automatic stereo vision matching algorithm based on dynamic programming method[J]. Pattern Recognition Letters.1996,17(5): 457-466.
[64]Wu M S, Leou J J. Bipartite Matching Approach to Feature Correspondence in Stereo Vision[J]. Pattern Recognition Letters.1995,16(1):23-31.
[65]Xie M. Automatic feature matching in uncalibrated stereo vision through the use of color[J]. Robotics and Autonomous Systems.1997,21(4):355-364.
[66]Shamir L. A proposed stereo matching algorithm for noisy sets of color images [J]. Computers & Geosciences.2007,33(8):1052-1063.
[67]El Ansari M, Masmoudi L, Bensrhair A. A new regions matching for color stereo images [J]. Pattern Recognition Letters.2007,28(13):1679-1687.
[68]苏中,夏艳,吴细宝.基于激光双目视觉系统的直径测量[J].半导体光电.2008,29(1)：131-134.
[69]Chen C S, Hung Y P, Chiang C C, et al. Range data acquisition using color structured lighting and stereo vision[J]. IMAGE AND VISION COMPUTING.1997,15(6):445-456.
[70]Sun J H, Zhang G J, Wei Z Z, et al. Large 3D free surface measurement using a mobile coded light-based stereo vision system[J]. SENSORS AND ACTUATORS A-PHYSICAL.2006, 132(2):460-471.
[71]Song L M, Wang D N. A novel grating matching method for 3D reconstruction[J]. NDT & E INTERNATIONAL.2006,39(4):282-288.
[72]张景利.大型锻件外形尺寸在线测量[J].一重技术.2010(1)：59-61.
[73]原玉磊,蒋理兴,张坷殊.三维激光扫描技术在大型高温锻件测量中的应用研究[J].测绘通报.2009,2009(6)：45-47.
[74]Kari M, Juha K, Risto M. Profiling of hot surfaces by pulsed time-of-flight laser range finder techniques[J]. Applied Optics.1993,32(27):5334-5347.
[75]Kari M, Juha K, Risto M. On the measurement of hot surfaces by pulsed time-of-flight laser radar techniques[C]. Hague, Neth:Publ by Int Soc for Optical Engineering, Bellingham, WA, United States,1990.
[76]于鹏,高峰,郭为忠,等.新型大锻件尺寸在线测量系统的关键技术研究[J].机械设计与研究.2008,24(3)：89-92.
[77]Tian Z, Gao F, Jin Z, et al. Dimension measurement of hot large forgings with a novel time-of-flight system[J]. Int J Adv Manuf Technol.2009,44:125-132.
[78]Rech R, Muller N, Lamm R, et al. Laser measurements on large open die forgings[J]. Stahl Und Eisen.2006,126(2):53-57.
[79]聂绍珉,唐景林,郭宝峰,等.基于CCD的大型锻件尺寸测量研究[J].塑性工程学报.2005,12(增刊)：85-88.
[80]聂绍珉,张庆,李树奎,等.大型锻件尺寸CCD测量的数学模型研究[J].塑性工程学报.2006,13(6)：110-113.
[81]刘勇,黄劫,李扬扬,等.大型锻件几何尺寸非接触在线测量系统研究[J].中国测试技术.2008,34(5)：116-118.
[82]常怀德,王建新,杨庆光.大锻件在线测量新技术初探[J].一重技术.2008(2)：65-66.
[83]日本陽,和佐泰宏,香川恭德.热间大型锻鋼品の形状计测装置の開発[J].神户製鋼技報.2007,57(3)：29-33.
[86]Dworkin S B, Nye T J. Image processing for machine vision measurement of hot formed parts[J]. Journal of Materials Processing Technology.2006,174:1-6.
[87]Wang Juan Q Z L J. Experimental research on dimensional measurement of hot parts based on CCD[C].2007.
[88]李亮,赵转萍.圆筒型热态锻件尺寸的立体视觉测量方法研究[J].传感器与微系统.2010, 29(4)：49-51,54.
[89]赵毅,王明辉,马品奎,等.热态锻件结构光三维测量技术[J].中国机械工程.2006,17(增刊)：125-128.
[90]吕炎.锻造工艺学[M].北京：机械工业出版社,1995：19-20.
[91]金伟其,胡威捷.辐射度光度与色度及其测量[M].北京：北京理工大学出版社,2006.
[92]葛绍岩,那鸿悦.热辐射性质及其测量[M].北京：科学出版社,1989：15.
[93]Dunkle R V. Thermal-Radiation Tables and Applications [J]. Trans. American Society of Mechanical Engineers.1954,76:549.
[94]赵兴梅,师建涛,郭鸿香.短波通滤光片膜系设计[J].应用光学.2006,27(5)：415-418.
[95]高光义.多媒体投影器用短弧超高压汞灯的进展[J].照明工程学报.2002,13(1)：5-10.
[96]马颂德,张止友.计算机视觉——计算理论与算法基础[M].北京：科学出版社,2003.
[97]Bleyer M, Gelautz M. A layered stereo matching algorithm using image segmentation and global visibility constraints [J]. ISPRS JOURNAL OF PHOTOGRAMMETRY AND REMOTE SENSING. 2005,59(3):128-150.
[98]张健新,段发阶,叶声华.双目传感器结构优化设计[J].光电工程.1996,23(3)：12-17.
[99]Sahabi H, Basu A. Analysis of error in depth perception with vergence and spatially varying sensing[J]. COMPUTER VISION AND IMAGE UNDERSTANDING.1996,63(3):447-461.
[100]李华,吴福朝,胡占义.一种新的线性摄像机自标定方法[J].计算机学报.2000,23(11)：1121-1129.
[101]雷成,吴福朝,胡占义.一种新的基于主动视觉系统的摄像机自标定方法[J].计算机学报.2000,23(11)：1130-1139.
[102]罗翔,席文明,颜景平.一种双目主动立体视觉系统的目标定位算法[J].东南大学学报(自然科学版).2002,32(11)：59-63.
[103]袁野,田中旭,欧宗瑛.一种基于主动视觉的线性自标定方法[J].小型微型计算机系统.2003,24(11)：2040-2042.
[104]杨长江,汪威,胡占义.一种基于主动视觉的摄像机内参数自定标方法[J].计算机学报.1998,21(5)：428-435.
[105]马永壮,刘伟军.一种基于双目主动视觉的线性自标定算法[J].机器人.2004,26(6)：486-490.
[106]吴福朝,李华,胡占义.基于主动视觉系统的摄像机自定标方法研究[J].自动化学报.2001,27(6)：752-762.
[107]胡占义,吴福朝.基于主动视觉摄像机标定方法[J].计算机学报.2002,25(11)：1149-1156.
[108]裴明涛,贾云得.基于主动视觉的摄像机线性自标定方法[J].北京理工大学学报.2006,26(1)：27-35.
[109]Dema S. A self-calibration technique for active vision systems[J]. Ieee Transactions on Robotics and Automation.1996,12(1):114-120.
[110]Longuethiggins H C. A Computer Algorithm for Reconstructing a Scene from 2 Projections [J]. Nature.1981,293(5828):133-135.
[111]孙晓明,刘庆伟,强锡富,等.经纬仪在航天产品几何尺寸检测中的应用研究[J].哈尔滨工业大学学报.1998,30(3)：56-59.
[112]冈萨雷斯.数字图像处理[M].北京：电子工业出版社,2007.
[113]Steger C. An unbiased detector of curvilinear structures [J]. Ieee Transactions on Pattern Analysis and Machine Intelligence.1998,20(2):113-125.
[114]胡坤,周富强.一种条纹中心线快速亚像素提取方法[J].光电技术应用.2005,20(6)：60-63.
[115]Zhang Z Y, Deriche R, Faugeras O, et al. A Robust Technique for Matching 2 Uncalibrated Images through the Recovery of the Unknown Epipolar Geometry[J]. Artificial Intelligence.1995,78(1-2):87-119.
[116]Acharya P K, Henderson T C. PARAMETER ESTIMATION AND ERROR ANALYSIS OF RANGE DATA. [C]. Philadelphia, PA, USA:1988.
[117]Fitzgibbon A, Pilu M, Fisher R B. Direct least square fitting of ellipses[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE.1999,21 (5):476-480.
[118]Bolles R C, Fischler M A. RANSAC-BASED APPROACH TO MODEL FITTING AND ITS APPLICATION TO FINDING CYLINDERS IN RANGE DATA.[C]. Vancouver, BC, Can:1981.
[119]Roth G, Levine M D. Geometric Primitive Extraction Using a Genetic Algorithm[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence.1994,16(9):901-905.
[120]刘元朋,张定华.逆向工程中圆柱体几何特征参数评估方法的研究[J].机械科学与技术.2005,24(3)：310-311.
[121]Gabor Lukdcs R M D M. Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation [C].1998.
[122]袭杨.空间直线拟合的一种方法[J].齐齐哈尔大学学报.2009,25(2)：64-68.
[123]李立声.运用改进的Gause-Newton优化算法拟合圆柱和空间直线[J].现代计量测试.1999(2)：26-29.
[124]Bychkov O D. Investigation of Precision in Measuring Diameters of Cylindrical Forgings by Means of Calipers[J]. Measurement Techniques.1967,10(8):920-923.
[2]张国雄.三坐标测量机的发展趋势[J].中国机械工程.2000,11(1-2)：222-226.
[3]杨洪涛,费业泰.快速探测三坐标测量机特性参数优化研究[J].中国机械工程.2008,19(20)：2428-2432.
[4]张望先,仲思动,隋莉斌,等.基于三坐标测量机的大尺寸非接触测量[J].武汉大学学报(工学版).2004,37(5)：112-115.
[5]Abbe M, Takamasu K, Ozono S. Reliability on calibration of CMM[J]. Measurement.2003, 33(4):359-368.
[6]Franceschini F, Galetto M, Settineri L. On-line diagnostic tools for CMM performance[J]. International Journal of Advanced Manufacturing Technology.2002,19(2):125-130.
[7]Zhang Y F, Nee A Y C, Fuh J Y H, et al. A neural network approach to determining optimal inspection sampling size for CMM[J]. Computer Integrated Manufacturing Systems.1996, 9(3):161-169.
[8]Shereshevskii L M. Use of an Optical Theodolite in Engineering[J]. Measurement Techniques Ussr.1983,26(6):470-472.
[9]Magdeev V S. Error in the measurement of the coordinates of surface points of large components with two theodolites[J]. Measurement Techniques.1991,34(5):438-440.
[10]Netterville D D J, Djurfors S G. Controlling Inherent Uncertainties in Double Theodolite Measurements [J]. Journal of Applied Meteorology.1979,18(10):1371-1375.
[11]熊春宝,叶声华.经纬仪工业测量系统的模型研究[J].武汉测绘科技大学.1998,23(3)：233-237.
[12]陆敬舜.型架双经纬仪三维测量法[J].南京航空航天大学学报.1994,26(5).
[13]周富强,张广军,江沽.现场双经纬仪三维坐标测量系统[J].机械工程学报.2004,40(1)：165-169.
[14]张滋黎,邾继贵,耿娜,等.双经纬仪三维坐标测量系统设计[J].传感技术学报.2010,23(5)：660-664.
[15]黄桂平,叶声华,李广云,等.经纬仪大尺寸柔性三坐标测量系统的开发与应用[J].仪器仪表学报.2002,23(3)：607-610.
[16]黄桂平,李广云.电子经纬仪工业测量系统定向及坐标解算算法研究[J].测绘学报.2009,32(3)：256-260.
[17]Kramer P, Weckenmann A. Multi-energy image stack fusion in computed tomography[J]. Measurement Science & Technology.2010,21(4):1-7.
[18]Weckenmann A, Kramer P. Application of Computed Tomography in Manufacturing Metrology[J]. Tm-Technisches Messen.2009,76(7-8):340-346.
[19]Effenberger I. Use of industrial computerized tomography in quality assurance [J]. VDI Berichte.2005(1913):41-45.
[20]Bartscher M, Hilpert U. Industrial computerized tomography:From defect detector to a measuring tool for geometry determination[J]. VDI Berichte.2005(1914):187-199.
[21]Segal Y, Cohen B. Film Based Industrial Computerized-Tomography[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment.1987,254(1):202-209.
[22]Gao H W, Zhang L, Chen Z Q, et al. Beam hardening correction for middle-energy industrial computerized tomography[J]. Ieee Transactions on Nuclear Science.2006,53(5): 2796-2807.
[23]康克军.实验工业CT系统及其图像重建方法研究[D].北京：清华大学,1988.
[24]陈志强,李亮,冯建春.高能射线工业CT最新进展[J].CT理论与应用研究.2005,14(4)：1-4.
[25]吴斌.大型物体三维形貌数字化测量关键技术研究[D].天津：天津大学,2002.
[26]Emmett N. Leith J U. Reconstructed wave fronts and communication theory[J]. Journal of the Optical Society of America.1962,52(10):1123-1128.
[27]Shanin V I, Shanin 0 V. The use of holographic interferometry in adjustment of gyroscope units[J]. Russian Journal of Nondestructive Testing.2004,40(10):708-712.
[28]Gesualdi M R R, Soga D, Muramatsu M. Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique[J]. Optics and Lasers in Engineering.2006,44(1):56-67.
[29]Chien C H, Wu Y D, Chiou Y T, et al. Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry [J]. Optics and Lasers in Engineering.2006,44(1):80-91.
[30]Denicola S, Ferraro P, Finizio A, et al. Evaluation of rigid rotations in flexural loading tests by holographic interferometry [J]. Experimental Mechanics.1997,37(2): 154-158.
[31]Twitto A, Shamir J, Bekker A, et al. Detection of internal defects using phase shifting holographic interferometry[J]. Ndt & E International.1996,29(3):163-173.
[32]Zhizhin G N, Nikitin A K, Ryzhova T A, et al. Application of holographic interferometry to optical monitoring of solid surfaces[J]. Technical Physics Letters.2004,30(11): 927-929.
[33]Frejlich J, Garcia P M. Advances in real-time holographic interferometry for the measurement of vibrations and deformations [J]. Optics and Lasers in Engineering.1999, 32(6):515-527.
[34]Lettieri T R. Pulsed Laser Caliper for Noncontact Dimensional Measurement [J]. Applied Optics.1986,25(9):1443-1449.
[35]Lettieri T R. Noncontact Dimensional Measurement Using a Pulsed Laser Caliper[J]. Journal of the Optical Society of America a-Optics Image Science and Vision.1985, 2(13):P8.
[36]Jarvis R A. A Laser Time-of-Flight Range Scanner for Robotic Vision[J]. Ieee Transactions on Pattern Analysis and Machine Intelligence.1983,5(5):505-512.
[37]Ahola R. Heikkinen T M M.3D image acquisition by scanning time of flight measurements[C]. Pisa, Italy:North-Holland, Amsterdam, Neth,1986.
[38]Philip Garcia J P A J. Characterization of a scannerless ladar system [C]. Orlando, FL, USA:1993.
[39]严惠民,倪旭翔,陈奇霖,等.无扫描三维激光雷达的研究[J].中国激光.2000,27(9)：861-864.
[40]Busck J, Heiselberg H. Gated viewing and high-accuracy three-dimensional laser radar[J]. Applied Optics.2004,43(24):4705-4710.
[41]Kawakita M, Iizuka K, Iwama R, et al. Gain-modulated Axi-Vision Camera (high speed high-accuracy depth-mapping camera)[J]. Optics Express.2004,12(22):5336-5344.
[42]Kawakita M, Iizuka K, Aida T, et al. Axi-Vision Camera (real-time distance-mapping camera)[J]. Applied Optics.2000,39(22):3931-3939.
[43]Nellums R 0, Habbit R D, Heying M R, et al.3D scannerless LADAR for orbiter inspection-art. no.62200G[J]. Spaceborne Sensors Ⅲ.2006,6220:G2200.
[44]Mitchell J, Spence A, Hoang M, et al. Sensor fusion of laser trackers for use in large-scale precision metrology[J]. Intelligent Manufacturing.2004,5263:57-65.
[45]Zobrist T L, Burge J H, Davison W B, et al. Measurements of large optical surfaces with a laser tracker-art. no.70183U[J]. Advanced Optical and Mechanical Technologies in Telescopes and Instrumentation, Pts 1-3.2008,7018:U183.
[46]Osawa S, Takatsuji T, Hong J, et al. Evaluation of the performance of a novel laser tracker used for coordinate measurements[J]. Recent Developments in Traceable Dimensional Measurements.2001,4401:127-135.
[47]Muralikrishnan B, Sawyer D, Blackburn C, et al. ASME B89.4.19 Performance Evaluation Tests and Geometric Misalignments in Laser Trackers[J]. Journal of Research of the National Institute of Standards and Technology.2009,114(1):21-35.
[48]Ouyang J F, Liu W L, Yan Y G, et al. Angular error calibration of laser tracker system art. no.63442U[C].2006.
[49]李广云.激光跟踪测量系统原理及应用[J].测绘工程.2001,4(10)：3-8.
[50]张国雄,林永兵,李杏华,等.四路激光跟踪干涉三坐标测量系统[J].光学学报.2003,23(9)：1030-1036.
[51]张旭东,张国雄,付继有.多路激光跟踪干涉柔性坐标测量系统三自由度坐标测量方法的研究[J].电子测量与仪器学报.2000,1(14)：22-25.
[52]陈晓荣,陈淑芬.激光跟踪运动目标伺服系统设计[J].仪器仪表学报.2006(S3)：1965-1966.
[53]鞠有伦,陈德应,于欣,等.利用受激布里渊散射实现在轨运动目标激光跟踪瞄准研究[J].光学学报.2005(1)：88-92.
[54]贾云得.机器视觉[M].北京：科学出版社,2000.
[55]Park J, Kim C, Na J, et al. Using structured light for efficient depth edge detection[J]. Image and Vision Computing.2008,26(11):1449-1465.
[56]Dipanda A, Woo S. Towards a real-time 3D shape reconstruction using a structured light system[J]. Pattern Recognition.2005,38(10):1632-1650.
[57]Tsalakanidou F, Forster F, Malassiotis S, et al. Real-time acquisition of depth and color images using structured light and its application to 3D face recognition[J]. Real-Time Imaging.2005,11(5-6):358-369.
[58]Xu J, Xi N, Zhang C, et al. Real-time 3D shape inspection system of automotive parts based on structured light pattern[J]. Optics and Laser Technology.2011,43(1):1-8.
[59]Boverie S, Devy M, Lerasle F. Comparison of structured light and stereovision sensors for new airbag generations [J]. Control Engineering Practice.2003,11(12):1413-1421.
[60]Valkenburg R J, Mcivor A M. Accurate 3D measurement using a structured light system [J]. Image and Vision Computing.1998,16(2):99-110.
[61]张广军.机器视觉[M].北京：科学出版社,2005.
[62]Barrois B, Konrad M, Wohler C, et al. Resolving stereo matching errors due to repetitive structures using model information[J]. Pattern Recognition Letters.2010,31(12): 1683-1692.
[63]Bensrhair A, Miche P, Debrie R. Fast and automatic stereo vision matching algorithm based on dynamic programming method[J]. Pattern Recognition Letters.1996,17(5): 457-466.
[64]Wu M S, Leou J J. Bipartite Matching Approach to Feature Correspondence in Stereo Vision[J]. Pattern Recognition Letters.1995,16(1):23-31.
[65]Xie M. Automatic feature matching in uncalibrated stereo vision through the use of color[J]. Robotics and Autonomous Systems.1997,21(4):355-364.
[66]Shamir L. A proposed stereo matching algorithm for noisy sets of color images [J]. Computers & Geosciences.2007,33(8):1052-1063.
[67]El Ansari M, Masmoudi L, Bensrhair A. A new regions matching for color stereo images [J]. Pattern Recognition Letters.2007,28(13):1679-1687.
[68]苏中,夏艳,吴细宝.基于激光双目视觉系统的直径测量[J].半导体光电.2008,29(1)：131-134.
[69]Chen C S, Hung Y P, Chiang C C, et al. Range data acquisition using color structured lighting and stereo vision[J]. IMAGE AND VISION COMPUTING.1997,15(6):445-456.
[70]Sun J H, Zhang G J, Wei Z Z, et al. Large 3D free surface measurement using a mobile coded light-based stereo vision system[J]. SENSORS AND ACTUATORS A-PHYSICAL.2006, 132(2):460-471.
[71]Song L M, Wang D N. A novel grating matching method for 3D reconstruction[J]. NDT & E INTERNATIONAL.2006,39(4):282-288.
[72]张景利.大型锻件外形尺寸在线测量[J].一重技术.2010(1)：59-61.
[73]原玉磊,蒋理兴,张坷殊.三维激光扫描技术在大型高温锻件测量中的应用研究[J].测绘通报.2009,2009(6)：45-47.
[74]Kari M, Juha K, Risto M. Profiling of hot surfaces by pulsed time-of-flight laser range finder techniques[J]. Applied Optics.1993,32(27):5334-5347.
[75]Kari M, Juha K, Risto M. On the measurement of hot surfaces by pulsed time-of-flight laser radar techniques[C]. Hague, Neth:Publ by Int Soc for Optical Engineering, Bellingham, WA, United States,1990.
[76]于鹏,高峰,郭为忠,等.新型大锻件尺寸在线测量系统的关键技术研究[J].机械设计与研究.2008,24(3)：89-92.
[77]Tian Z, Gao F, Jin Z, et al. Dimension measurement of hot large forgings with a novel time-of-flight system[J]. Int J Adv Manuf Technol.2009,44:125-132.
[78]Rech R, Muller N, Lamm R, et al. Laser measurements on large open die forgings[J]. Stahl Und Eisen.2006,126(2):53-57.
[79]聂绍珉,唐景林,郭宝峰,等.基于CCD的大型锻件尺寸测量研究[J].塑性工程学报.2005,12(增刊)：85-88.
[80]聂绍珉,张庆,李树奎,等.大型锻件尺寸CCD测量的数学模型研究[J].塑性工程学报.2006,13(6)：110-113.
[81]刘勇,黄劫,李扬扬,等.大型锻件几何尺寸非接触在线测量系统研究[J].中国测试技术.2008,34(5)：116-118.
[82]常怀德,王建新,杨庆光.大锻件在线测量新技术初探[J].一重技术.2008(2)：65-66.
[83]日本陽,和佐泰宏,香川恭德.热间大型锻鋼品の形状计测装置の開発[J].神户製鋼技報.2007,57(3)：29-33.
[86]Dworkin S B, Nye T J. Image processing for machine vision measurement of hot formed parts[J]. Journal of Materials Processing Technology.2006,174:1-6.
[87]Wang Juan Q Z L J. Experimental research on dimensional measurement of hot parts based on CCD[C].2007.
[88]李亮,赵转萍.圆筒型热态锻件尺寸的立体视觉测量方法研究[J].传感器与微系统.2010, 29(4)：49-51,54.
[89]赵毅,王明辉,马品奎,等.热态锻件结构光三维测量技术[J].中国机械工程.2006,17(增刊)：125-128.
[90]吕炎.锻造工艺学[M].北京：机械工业出版社,1995：19-20.
[91]金伟其,胡威捷.辐射度光度与色度及其测量[M].北京：北京理工大学出版社,2006.
[92]葛绍岩,那鸿悦.热辐射性质及其测量[M].北京：科学出版社,1989：15.
[93]Dunkle R V. Thermal-Radiation Tables and Applications [J]. Trans. American Society of Mechanical Engineers.1954,76:549.
[94]赵兴梅,师建涛,郭鸿香.短波通滤光片膜系设计[J].应用光学.2006,27(5)：415-418.
[95]高光义.多媒体投影器用短弧超高压汞灯的进展[J].照明工程学报.2002,13(1)：5-10.
[96]马颂德,张止友.计算机视觉——计算理论与算法基础[M].北京：科学出版社,2003.
[97]Bleyer M, Gelautz M. A layered stereo matching algorithm using image segmentation and global visibility constraints [J]. ISPRS JOURNAL OF PHOTOGRAMMETRY AND REMOTE SENSING. 2005,59(3):128-150.
[98]张健新,段发阶,叶声华.双目传感器结构优化设计[J].光电工程.1996,23(3)：12-17.
[99]Sahabi H, Basu A. Analysis of error in depth perception with vergence and spatially varying sensing[J]. COMPUTER VISION AND IMAGE UNDERSTANDING.1996,63(3):447-461.
[100]李华,吴福朝,胡占义.一种新的线性摄像机自标定方法[J].计算机学报.2000,23(11)：1121-1129.
[101]雷成,吴福朝,胡占义.一种新的基于主动视觉系统的摄像机自标定方法[J].计算机学报.2000,23(11)：1130-1139.
[102]罗翔,席文明,颜景平.一种双目主动立体视觉系统的目标定位算法[J].东南大学学报(自然科学版).2002,32(11)：59-63.
[103]袁野,田中旭,欧宗瑛.一种基于主动视觉的线性自标定方法[J].小型微型计算机系统.2003,24(11)：2040-2042.
[104]杨长江,汪威,胡占义.一种基于主动视觉的摄像机内参数自定标方法[J].计算机学报.1998,21(5)：428-435.
[105]马永壮,刘伟军.一种基于双目主动视觉的线性自标定算法[J].机器人.2004,26(6)：486-490.
[106]吴福朝,李华,胡占义.基于主动视觉系统的摄像机自定标方法研究[J].自动化学报.2001,27(6)：752-762.
[107]胡占义,吴福朝.基于主动视觉摄像机标定方法[J].计算机学报.2002,25(11)：1149-1156.
[108]裴明涛,贾云得.基于主动视觉的摄像机线性自标定方法[J].北京理工大学学报.2006,26(1)：27-35.
[109]Dema S. A self-calibration technique for active vision systems[J]. Ieee Transactions on Robotics and Automation.1996,12(1):114-120.
[110]Longuethiggins H C. A Computer Algorithm for Reconstructing a Scene from 2 Projections [J]. Nature.1981,293(5828):133-135.
[111]孙晓明,刘庆伟,强锡富,等.经纬仪在航天产品几何尺寸检测中的应用研究[J].哈尔滨工业大学学报.1998,30(3)：56-59.
[112]冈萨雷斯.数字图像处理[M].北京：电子工业出版社,2007.
[113]Steger C. An unbiased detector of curvilinear structures [J]. Ieee Transactions on Pattern Analysis and Machine Intelligence.1998,20(2):113-125.
[114]胡坤,周富强.一种条纹中心线快速亚像素提取方法[J].光电技术应用.2005,20(6)：60-63.
[115]Zhang Z Y, Deriche R, Faugeras O, et al. A Robust Technique for Matching 2 Uncalibrated Images through the Recovery of the Unknown Epipolar Geometry[J]. Artificial Intelligence.1995,78(1-2):87-119.
[116]Acharya P K, Henderson T C. PARAMETER ESTIMATION AND ERROR ANALYSIS OF RANGE DATA. [C]. Philadelphia, PA, USA:1988.
[117]Fitzgibbon A, Pilu M, Fisher R B. Direct least square fitting of ellipses[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE.1999,21 (5):476-480.
[118]Bolles R C, Fischler M A. RANSAC-BASED APPROACH TO MODEL FITTING AND ITS APPLICATION TO FINDING CYLINDERS IN RANGE DATA.[C]. Vancouver, BC, Can:1981.
[119]Roth G, Levine M D. Geometric Primitive Extraction Using a Genetic Algorithm[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence.1994,16(9):901-905.
[120]刘元朋,张定华.逆向工程中圆柱体几何特征参数评估方法的研究[J].机械科学与技术.2005,24(3)：310-311.
[121]Gabor Lukdcs R M D M. Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation [C].1998.
[122]袭杨.空间直线拟合的一种方法[J].齐齐哈尔大学学报.2009,25(2)：64-68.
[123]李立声.运用改进的Gause-Newton优化算法拟合圆柱和空间直线[J].现代计量测试.1999(2)：26-29.
[124]Bychkov O D. Investigation of Precision in Measuring Diameters of Cylindrical Forgings by Means of Calipers[J]. Measurement Techniques.1967,10(8):920-923.