三坐标机与立体视觉的系统集成与信息融合的关键技术研究
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摘要
在逆向工程中,自由曲线曲面的测量一直以来是逆向工程的重要组成部分,受到众多学者的关注。计算机视觉与三坐标机是反求工程中不同的两种测量手段的代表,他们各具有自己的优缺点。作为非接触式测量的代表,计算机立体视觉测量具有速度快、灵活、采样范围广、有利于整体形状信息的获取等优点,可以方便地提取物体的边界轮廓与特征信息,其缺点是测量精度较差;三坐标机作为接触测量的设备之一,其优点是测量精度高,适应性强,鲁棒性能优越,但作为逐点测量的设备,是在人为制定的测量规则指导下,对产品原型进行测量获取三维坐标数据,实现产品表面的数字化,其测量效率低,测量过程过分依赖于测量者的经验,特别是在未知产品几何数值模型的前提下,难以保证测点分布的合理性。
     基于线结构光-立体视觉与三坐标机信息集成技术的集成式测量以其测量精度高、速度快、智能化程度高而成为一种很有前途的测量方法,特别是如能实现二者信息的融合,将势必大大提高集成系统的测量速度和精度。本文就线结构光-立体视觉与三坐标机系统集成与信息融合的一些关键性技术
     展开了研究,其主要内容包括:
     1)主动轮廓提取技术。主动轮廓(又称为蛇形轮廓)为计算机立体视觉提供了获取线激光器扫描曲线在摄像机图像中曲线轮廓的方法。线结构光测量数据在每条扫描线内测量点排列密集、杂乱,且测量点之间没有明显的拓扑关系,无法直接应用于CAD系统中建模。主动轮廓提取的曲线则为测量点之间建立了拓扑关系。
     2) B样条最佳逼近。以差分法提取的主动轮廓包含了大量的曲线数据,不利于数据的保存与结果后处理。利用B样条曲线去逼近轮廓曲线,大大减少了轮廓曲线的数据存储量,且使得曲线变得更为光滑,也给曲线的后处理带来了方便。
     3) B样条曲线变形(修改)技术。基于物理模型的B样条曲线变形是在尽量维持曲线整体轮廓特征的基础上产生的。它不像其它局部变形技术那样会产生局部的“肿块”,从而影响了曲线的整体轮廓特征。基于物理模型的B样条曲线变形在力学上类似于一根曲杆在外力作用下产生整体变形,其数学模型上就好像在原有曲线的基础上,加上了一条光滑的误差拟合曲线。本文将此技术应用于线结构光-立体视觉与三坐标机信息的融合,实现利用三标机测量的精确数据去修正立体视觉测量的曲线,从而提高视觉测量的精度,减少利用三坐标测量机测量的数据量,提高了测量效率与测量精度。
     4)摄像机的标定。摄像机的标定建立了三维数据点与摄像机像点之间的对应关系,是实现立体视觉系统最为重要的一环。利用三坐标机的测头实现摄像机的标定为立体视觉测量系统和三坐标机的集成建立了数据点坐标间的关系,实现了立体视觉测量的世界坐标系与三坐标机的世界坐标系相统一。
     5)测头半径补偿。测头半径补偿问题是三坐标机测量中的一个关键问题,影响着三坐标机的测量精度。在已知截面轮廓线的情况下,可以计算出测头接触工件的法线方向,并由此可以计算出测头接触工件的位置,解决了测头的半径补偿问题,并同时实现了测头半径向一个平面内补偿问题。
Measuring a free curve or surface is an important component in the reverse engineering. Many researchers and scholars have fixed their eyes upon it. Computer stereo vision and coordinate measuring machine(CMM) belong to two kind of measuring equipment respectively. They have their respective merits and drawbacks. As a representative of non-touching measuring equipment, computer stereo vision has many merits, such as fast measuring speed, agility, broad sampling scope and convenience of extracting the boundary contours and characters. However, the drawback is its lower measuring precision. As a touching equipment, CMM has many advantages such as higher measuring precision, strong adaptability and robusticity. However, being a point-by-point touching measuring equipment, its obtaining the three dimensional measuring data of prototype is directed by the man-made measuring rules. It is much lower efficiency, and is excessively depended on the experience of manipulator to digitize the product. When there is no digital geometric prototype of product, it is difficult to properly distribute the measuring points.
     An integrated measuring equipment is suggested which is composed of seam-laser stereo vision equipment and CMM. It is a promising measuring equipment due to its high efficiency, high precision and high intelligentizing. The efficiency and the precision will become much higher if we can fuse the information obtained by these two different types of equipments.
     This paper will devote to investigate some key techniques of information fusion between the seam-laser stereo vision equipment and CMM. The contents include the following:
     1) Active contour models. Active contour models (or snake models) provide a method of obtaining the curve contour in the image produced by seam-laser stereo vision. The measuring data are dense, unorderly, and there is no topology relationship between them. They can not be applied to erect CAD models directly. Active contour models establish a topology relationship among these measuring data.
     2) B-spline approaching. The solution to active contour models is traditionally through the difference method, which includes large amount of curve data. It is not convenient to save them and to manipulate in the following procedure. Approaching the curve by B-spline will largely cut down the amount of curve data to be stored. It also makes the curve smoother and is easier to manipulate in the following procedures.
     3) Deformation of B-spline curve. The Physical model based deformation of B-spline curve keeps the contour character of the whole curve well. It will not produce local bump like the local curve deformation to hurt the contour character of the whole curve. The deformation is just like a crooked stick to produce a deformation under the external forces in mechanics, or like a smooth error curve fitted by given conditions adding up to original curve in mathematics. This paper will apply this deformation technique of B-spline curve to realize the information fusion between the seam-laser stereo vision equipment and CMM, in order to revise the curve measured by seam-laser stereo vision through the accurate data measured by CMM. This will increase the measuring precision measured by seam-laser stereo vision, and cut down the amount of data measured by CMM, so the efficiency and the precision will be promoted.
     4) Calibration of camera. The calibration of camera erects a corresponding relationship between the space points and the points in the camera images. It is a very important step to realize stereo vision. The tip center of the CMM touch probe is regarded as the space points to calibrate the camera, which set up a relationship of coordinate systems between two measuring equipments, and the two coordinate systems are unified into unitary CMM coordinate systems.
     5) Compensating of tip radius of CMM. Compensating of tip radius is a key problem in CMM. It has a great influence to its measuring accuracy. According to the contour curves which have been figured out,the normals of touching points can be computed, and the postions of touching points also can be decided. Hence, the proplem of compensating of tip radius of CMMM is solved, and at the same time the compensating of tip radius in a plane is also realized.
引文
[1]金涛.逆向工程技术[M].北京:机械工业出版社, 2003.
    [2]康剑莉,陈罡.逆向工程在纺织机械引进技术国产化中的应用[J].纺织器材, 2006, 33(1): 23-25.
    [3] Nashman, Marilyn. The Use of Vision and Touch Sensors for Dimensional Inspection [J]. Manufacturing Review, 1993, 6(2): 155-162.
    [4] Marilyn Nashman, Billibon Yoshimi, Tsai Hong Hong, et al. A Unique Sensor Fusion System for Coordinate Measuring Machine Tasks[J]. Proceedings of the SPIE International Symposium on Intelligent Systems and Advanced Manufacturing, 1997, 3209.
    [5] Billibon Yoshimi, Tsai-Hong Hong, Martin Herman, et al., Integrated Vision and Touch Sensing for CMMs[C]. SME Applied Machine Vision Conference. 1997.
    [6] Chan V.H., Bradley C.,Vickers G.W. A Multi-Sensor Approach for Rapid Digitization and Data Segmentation in Reverse Engineering [J]. Journal of Manufacturing Science and Engineering 2000, 122(4): 725-733.
    [7] V. Carbone, M. Carocci, E. Savio, et al. Combination of a Vision System and a Coordinate Measuring Machine for the Reverse Engineering of Freeform Surfaces [J]. The International Journal of Advanced Manufacturing Technology, 2001, 17(4): 263-271.
    [8] Tzung-Sz Shen, Jianbing Huang, Chia-Hsing Menq, Multiple-sensor integration for rapid and high-precision coordinate metrology[C], International Conference on Advanced Intelligent Mechatronics, 1999:908-915
    [9] Tzung-Sz Shen, Jianbing Huang, Chia-Hsiang Menq. Multiple-Sensor Planning and Information Integration for Automatic Coordinate Metrology [J]. Journal of Computing and Information Science in Engineering 2001, 1(2): 167-179.
    [10] Tzung-Sz Shen, Jianbing Huang,Chia-Hsing Menq. Multiple-sensor integration for rapid and high-precision coordinate metrology [J]. IEEE/ASME Transaction on mechatronic, 2000, 5(2): 110-121.
    [11] Chen L.-C., Lin G.C.I. A vision-aided reverse engineering approach to reconstructing free-form surfaces [J]. Robotics and Computer-Integrated Manufacturing, 1997, 13(4): 323-336.
    [12] Chen L.-C., Lin G.C.I. An integrated reverse engineering approach to reconstructing free-form surfaces [J]. Computer Integrated Manufacturing Systems, 1997, 10(1): 49-60(12).
    [13]方勇,刘志刚,林志航等.立体视觉指导下的CMM集成智能检测系统在逆向工程中的应用[J].机械科学与技术, 1999(04): 675-677, 681.
    [14]何炳蔚,林志航.逆向工程中线激光—机器视觉集成坐标测量系统研究[J].机械, 2002(06): 7-10, 30.
    [15]何炳蔚,林志航.易与CMM集成的线激光视觉传感器建模及标定技术[J].机器人, 2002(06): 513-516.
    [16]刘志刚,陈康宁,刘布昆等.逆向工程中基于线结构光视觉传感器的光学坐标测量系统研究[J].制造业自动化, 1999(05): 36-39.
    [17] Kass M, Witkin A, Terzopoulos D., Snakes: Active Contour Models[C], First international conference of Computer Vision, London, 1987:259-269
    [18] Venkatesh, Y. V., S. Kumar Raja,N. Ramya. Multiple Contour Extraction From Graylevel Images Using an Artificial Neural Network [J]. IEEE Transactions on Image Processing, 2006, 15(4): 892 - 899.
    [19] Nakagawa, T., T. Hara, H. Fujita, et al. Automated contour extraction of mammographic mass shadow using an improved active contour model [J]. International Congress Series, 2004, 1268: 882 - 885.
    [20]侯志强,韩崇昭.基于力场分析的主动轮廓模型[J].计算机学报, 2004(06): 743-749.
    [21]郑林,韩崇昭,左东广等.基于信息融合的运动目标自动提取[J].西安交通大学学报, 2003(08): 853-856,877.
    [22] Gastaud, Muriel, Michel Barlaud,Gilles Aubert. Combining Shape Prior and Statistical Features for Active Contour Segmentation[J]. IEEE Transactions on Circuits & Systems for Video Technology, 2004, 14(5): 726 - 734.
    [23]朱莉,朱音,黄贤武.基于主动轮廓模型提取运动目标的图像分割技术[J].微电子学与计算机, 2004(01): 106-108,113.
    [24] Radeva, P., J. Serrat,E. Marti, A snake for model-based segmentation[C]. International Conference on Computer Vision, 1995:816-821
    [25] Wang, Kejun, Qingchang Guo,Dayan Zhuang. An Image Segmentation Method Based on the Improved Snake Model[J]. Proceedings of the 2006 IEEE,International Conference on Mechatronics and Automation, 2006: 532-536.
    [26] McInerney, T.,D. Terzopoulos. A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4d image analysis[J]. Computerized Medical Imaging and Graphics, 1995, 19(1): 69-83.
    [27] Tsechpenakis, G., K. Rapantzikos, N. Tsapatsoulis, et al. A snake model for object tracking innatural sequences[J]. Signal Processing: Image Communication, 2004, 19(3): 219 -238.
    [28] Bascle, B.,Rachid Deriche, Region Tracking through Image Sequences[M], 1995:302-307
    [29] Ray, Nilanjan, Scott T. Acton. Active contours for cell tracking[J]. Fifth IEEE Southwest Symposium on Image Analysis and Interpretation, 2002.
    [30] Sanz-Requena, Roberto, David Moratal, GarcSánchezDiego, et al. Automatic segmentation and 3D reconstruction of intravascular ultrasound images for a fast preliminar evaluation of vessel pathologies[J]. Computerized Medical Imaging & Graphics, 2007, 31(2): 71 - 80.
    [31] Auer, Martin, Rudolf Stollberger, Peter Regitnig, et al. 3-D Reconstruction of Tissue Components for Atherosclerotic Human Arteries Using Ex Vivo High-Resolution MRI[J]. IEEE Transactions on Medical Imaging, 2006, 25(3): 345 - 357.
    [32] Huysmans, T., B. Haex, Audekercke R. Van, et al. Three-dimensional mathematical reconstruction of the spinal shape, based on active contours[J]. Journal of Biomechanics, 2004, 37(11): 1793 - 1798.
    [33] Pietroni, Nico, Fabio Ganovelli, Andrea Giachetti. Robust segmentation of anatomical structures with 3D active contours and marching cubes[J]. International Congress Series, 2005: 1278-1281.
    [34] Fuping, Zhu Ramin,Jie Tian. Modified fast marching and level set method for medical image segmentation[J]. Journal of X-Ray Science & Technology, 2003, 11(4): 193 - 204.
    [35]李培华,张田文.主动轮廓线模型(蛇模型)综述[J].软件学报, 2000(06): 751-757.
    [36] Cohen, L. D. On active contour models and balloons[J]. Computer Vision, Graphics, and Image Processing. Image Understanding, 1991, 53(2): 211-218.
    [37]尤建洁,周则明,王平安等.基于模拟退火的简化Snake弱边界医学图像分割[J].中国图象图形学报, 2004, 9(1): 11-17.
    [38] Kass M, Witkin A. Terzopoulos D. Snakes:Active contour models[J]. International Journal of Computer Vision, 1987, 1: 321-331.
    [39]苑玮琦,马军防,狄文彬.基于主动轮廓线的虹膜定位方法[J].计算机工程与应用, 2003(34): 104-107.
    [40] Chenyang Xu,Jerry L. Prince. Generalized gradient vector flow external forces for active contours[J]. Signal Processing, 1998, 71: 131-139.
    [41] Lean, C.C.H;See, A.K.B;Shanmugam,S.A., An Enhanced Method for the Snake Algorithm, 2006:240-243
    [42] Luo Suhuai, Li Rongxin,Sebastien Ourselin, A New Deformable Model Using Dynamic Gradient Vector Flow, in Third International Conference on Information Technology andApplications. 2005: Sydney p. 9-14.
    [43] Chenyang Xu, Jerry L. Prince, Gradient Vector Flow: A New External Force for Snakes, IEEE Proc. Conf. on Comp. Vis. Patt. Recog, 1997:66-71
    [44] Chenyang Xu, Jerry L. Prince. Snakes, Shapes, and Gradient Vector Flow[J]. IEEE Transactions On Image Processing, 1998, 7(3): 359-369.
    [45] Schunck Ramesh Jain, Rangachar Kasturi, Brian G. Machine Vision[M]. 2003,机械工业出版社:北京.
    [46] Jerry L.Prince, Chenyang Xu, A new external force model for snakes[J], Image and Multidimensional Signal Processing Workshop, 1996:30-31
    [47]李弼程,彭天强,彭波等.智能图像处理技术[M],北京:电子工业出版社, 2004.
    [48] J.F.Canny. A computational approach to edge detection[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(6): 679-798.
    [49] Meer, P.,B. Georgescu. Edge detection with embedded confidence[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(12): 1351-1365.
    [50]万力,易昂,傅明.一种基于Canny算法的边缘提取改善方法[J].计算机与自动化, 2003, 22(1): 24-26.
    [51] Rueckert, Daniel,Peter Burger, A Multiscale Approach to Contour Fitting for MR Images[C], SPIE Conference on Medical Imaging: Image Processing, 1996:289-300
    [52] Schnabel, Julia A., Simon R. Arridge. Multiscale shape description of MR brain images using active contour models[J]. Medical Imaging: Image Processing, 1996, volume Proc SPIE 2710: 596-606.
    [53] Julia A. Schnabel, Simon R. Arridge, Active Contour Models for Shape Description Using Multiscale Differential Invariants[C], British Machine Vision Conference, 1995:197-206
    [54] Schnabel, Julia A., Simon R. Arridge, Multi-Scale Active Shape Description[M]. Scale-Space Theories in Computer Vision. 1997. p. 337-340.
    [55] Cohen Laurent D., Cohen Isaac. Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images[J]. PAMI, 1993, 15(11): 1131-1147.
    [56]黄志彦,曹春红,徐剑.基于小波多尺度分析与GVF Snake的空中目标提取[J].电光与控制, 2002(04): 32-35.
    [57]宋新,罗军,王鲁平等.基于GVF Snake的运动目标跟踪方法[J].红外与激光工程, 2007(02): 226-228,256.
    [58] Horn B K P, Schunck B G. Determining optical flow[J]. AI, 1981, 17: 185-203.
    [59]高文,陈熙霖.计算机视觉-算法与系统原理[M].清华大学出版社、广西科学技术出版社,1999.
    [60]老大中.变分法基础[M].北京:国防工业出版社, 2004.
    [61] Tim McInerney, Demetri Terzopoulos. A Dynamic Finite Element Surface Model for Segmentation and Tracking in Multidimensional Medical Images with Application to Cardiac 4D Image Analysis[J]. Journal of Computerized Medical Imaging and Graphics., 1995, 19(1): 69-83.
    [62] Tim McInerney, Demetri Terzopoulos. Deformable models in medical images analysis: a survey[J]. Medical Image Analysis, 1996, 1(2): 91-108.
    [63] Curry H. B, Schoenberg I. On Spline Distributions and Their Limits: The Polya Distribution Functions.[J]. Journal of the American Mathematical Society, 1947, 53: 1114.
    [64] Schoenberg I. Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions.[J]. Quarterly of Applied Mathematics, 1946, 4: 45-99,112-141.
    [65] Schoenberg I, On spline function.[M], NewYork: Academic press, 1967.
    [66] Riesenfeld R. F. Applications of B-Spline Approximation to Geometric Problems of CAD[D]. Syracuse University, 1973
    [67] Gordon W. J., Riesenfeld R. F. Bernstein-Bezier Methods for the Computer-Aided Design of Free-Form Curves and Surface[J]. Journal of the Association for Computing Machinery, 1974, 21(2): 293-310.
    [68] Gordon W. J., Riesenfeld R. F., B-Spline Curves and Surfaces[M]. Computer Aided Geometric Design., R. E. Barnhill.R. F. Riesenfeld, Editors. 1974, Academic Press.
    [69] Coons S. A., Surface Patches and B-Spline Curves[M]. Computer Aided Geometric Design, Academic Press,1974.
    [70] Versprille K. J. Computer-Aided Design Applications of the Rational B-Spline Approxiamtion Form[D]. Syracuse University, 1974.
    [71] Catmull E. E., Clark J. E. Recursively Generated B-Spline Surface on Arbitary Topological Meshes[J]. CAD, 1978, 10(9): 350-355.
    [72] Clark J. H. 3-D Design of Free-Form B-Spline Surfaces[D]. University of Utah, 1974.
    [73] Clark J. H., Some properties of B-Spline[C], Proc. 2nd USA-Japan computer Conference, AFIPS, Montvale, N. J., 1975:542-545
    [74] Clark J. H. Designing Surface in 3D[J]. Communications of the ACM, 1976, 19(8): 454-460.
    [75] Deboor C. On Caculating with B-Spline[J]. Journal of Approximation Theory, 1972, 6: 50-62.
    [76] Cox M. G., The Numberical Evaluation of B-Splines[R]. Report No. NPL-DNACS-4. 1971, National Physical Laboratory.
    [77] Cox M. G. The Numerical Evaluation of B-Splines[J]. The Journal of the Institute of Mathematics., 1972, 10: 134-149
    [78] Bezier P., Example of an Existing System in the Motor Industry: The UNISURF System[C], Proc. Roy. Soc. of London, 1971:207-218
    [79] Bezier P., Numerical Control-Mathematical and Applications[M], John Wiley and Sons, London, 1972.
    [80] Bezier P., The Mathematical Basis of the UNISURF CAD System[M], Butterworths, England, 1986.
    [81]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:高等教育出版社, 2001.
    [82] Imre Juhasz, Miklos Hoffmann. The Effect of Knot Modifcations on the Shape of B-spline Curves[J]. Journal for Geometry and Graphics, 2001, 5(2): 111-119.
    [83] Rony Goldenthal,Michel Bercovier, Spline Curve Approximation And Design By Optimal Control Over The Knots Using Genetic Algorithms[C], International Congress On Evolutionary Methods For Design,Optimization And Control With Applications To Industrial Problems, Eurogen, 2003:1-18
    [84] Boehm W. Inserting New Knots Into B-Spline Curves.[J]. Computer-Aided Design, 1980, 12(4): 199-201.
    [85] Yamaguchi F. A New Curve Fitting Method Using a CRT Display[J]. Computer Graphics and Image Processing, 1978, 7(3): 425-437.
    [86]朱心雄,吴瑞祥. B样条曲线曲面的原理和应用[M].北京:北京航空学院, 1980.
    [87]朱心雄.自由曲线曲面造型技术[M].北京:科学出版社, 2000.
    [88] Piegl L, Tiller W, The NURBS Book.[M], Berlin Heidelberg: Springer-Verlag, 1995.
    [89]黄文均.迭代线性最近点参数非均匀B样条曲线拟合[J].广西科学院学报, 2002, 18(4): 165-170.
    [90]肖轶军,丁明跃,彭嘉雄.基于迭代最近点的B样条曲线拟合方法研究[J].中国图象图形学报, 2000(07): 585-588.
    [91] David E. Johnson, Elaine Cohen, Minimum Distance Queries For Polygonal and Parametric Models[R], Technical Report UUCS-97-003. 1997: University of Utah, Department of Computer Science.
    [92] Limaiem, Anis and Trochu, Francois. Geometric Algorithms for the Intersection of Curves and Surfaces[J]. Computer & Graphics, 1995, 19(3): 391-403.
    [93] Baraff David. Curved Surfaces and Coherence for Non-penetrating Rigid Body Simulation.[J]. Computer & Graphics, 1990, 24(4): 19-28.
    [94] Snyder, John M. An Interactive Tool for Placing Curved Surfaces without Interpenetration[C], Proceedings of Computer Graphics, 1995:209-218
    [95] Cham, Tat-Jen.Geometric Representation and Grouping of Image Curves[D].University of Cambridge,1996:
    [96] Cham, Tat Jen, Roberto Cipolla. Automated B-Spline Curve Representation Incorporating {MDL} and Error-Minimizing Control Point Insertion Strategies[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(1): 49-53.
    [97] P. Dierckx. Curve and Surface Fitting with Spline. Clarendon Press, 1993
    [98] F. Lu, E.E Milios. Optimal spline fitting to plannar shape[J]. Signal Processing, 1994, 37: 129-140.
    [99] Piegl L, Modifying the shape of rational B-splines[M]. in Part 1: curves. Computer Aided Des. 1989. p. 509-518.
    [100] Juhasz Imre. Weight-based shape modification of NURBS curves[J]. Computer Aided Geom Des, 1999, 16: 377-383.
    [101]成思源,张湘伟.可变形B样条曲线曲面模型及其有限元求解[J].重庆大学学报, 2003, 26(2): 75-77(81).
    [102] Huang Ding, Hong Yan. NURBS curve controlled modelling for facial animation[J]. Computers & Graphics, 2003, 27(3): 373 -.
    [103] C. K. Au,M. M. F. Yuen. Unified approach to NURBS curve shape modification[J]. Computer Aided Des, 1995, 27: 85-93.
    [104] Sanchez-Reyes J. A simple technique for NURBS shape modification[J]. IEEE Computer Graphics Appl, 1997, 17: 52-59.
    [105] I.Juhasz, M.Hoffmanh. Constrained shape modification of cubic B-spline curves by means of knots[J]. Computer-Aided Design, 2004, 36: 437-445.
    [106] Juhasz Imre, Hoffmann Miklos. Modifying a knot of B-spline curves[J]. Computer Aided Geometric Design, 2003, 20(5): 243 -245.
    [107] Goldenthal, R.,M. Bercovier. Spline Curve Approximation and Design by Optimal Control Over the Knots[J]. Computing, 72(1/2): p53 - 64.
    [108] Lyche T, Morken K. The sensitivity of a spline function to perturbations of the knots[J]. BIT Numerical Mathematics, 1999, 39: 305-322.
    [109] Junji lshida. The general B-spline interpolation method and its application to the modification of curves and surfaces[J]. Computer-Aided Design, 1997, 29(11): 779-790.
    [110]范钦珊,薛克宗,王波.工程力学教程.北京:高等教育出版社[J]. 1998: 39-40.
    [111]经玲,席平,唐荣锡.有限元方法在变形曲线曲面造型中的应用[J].计算机学报, 1998, 21(3): 245-251.
    [112] Terzopoulos D, Platt J, Barr A, et al. Elastically deformable models[J]. Computer Graphics, 1987, 21(4): 205-214.
    [113] George Celniker, Dave Gossard.. Deformable Curve and Surface Finite-Elements for Free-Form Shape Design[J]. Computer Graphics, 1991, 25(4): 257-266.
    [114]席平,经玲,唐荣锡.用变形模型整体构造B样条曲面方法研究[J].北京航空航天大学学报, 1999(04): 471-473.
    [115] Gregory E. Fasshauer,Larry L. Schumaker. Minimal energy surfaces using parametric splines[J]. Computer Aided Design, 1996, 28: 251~262.
    [116] Terzopoulos D, Fleischer K. Deformable models[J]. Visual Computer, 1988, 4(6): 306-331.
    [117]姚小虹,赵亦工.基于Snake模型的快速目标检测算法的研究与仿真[J].计算机仿真, 2004(11): 181-183.
    [118] Li Min, Chandra Kambhamettu, Maureen Stone. Automatic contour tracking in ultrasound images[J]. Clinical Linguistics & Phonetics, 2005, 19(6/7): 545 - 554.
    [119] Papandreou, George,Petros Maragos. Multigrid Geometric Active Contour Models[J]. IEEE Transactions on Image Processing, 2007, 16(1): 229 - 240.
    [120]王立涛,贾明.能量法曲面光顺技术研究与探索[J].辽宁工程技术大学学报, 2003, 22(1): 110-112.
    [121]王侃昌,王玉林,王乃信.基于能量法的B样条农机工作部件曲线光顺研究[J].农业工程学报, 2004, 20(2): 126-128.
    [122]彭芳瑜,周云飞,周济.基于广义能量法的截面曲线光顺[J].工程图学学报, 2005, 26(2): 87-94.
    [123]彭芳瑜,周云飞,周艳红等.基于能量法的截面曲线自动形状修改算法[J].华中理工大学学报, 1999(06): 60-62.
    [124]穆国旺,宋秀琴,臧婷.一种选点法和能量法相结合的曲线光顺方法[J].工程图学学报, 2005(06): 118-121.
    [125]王勖成.有限单元法[M].北京:清华大学出版社, 2003.
    [126]刘巽亮.光学视觉传感[M].北京:中国科学技术出版社, 1998.
    [127] Zhang Zhengyou. A Flexible New Technique for Camera Calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(11): 2330-1334.
    [128] Haralick R. Determining camera parameters from the perspection projection of a rectangle[J]. Pattern Recognition, 1989, 22: 225-230.
    [129]罗飞路,傅恩赐. CCD摄像机内外参数快速标准确定方法[J].湖南大学学报, 1997, 24(2): 71-77.
    [130] O.D.Faugeras, G. Toscani, the calibration problem for stereo[C], Proc. of IEEE conference of Computer Vision and Pattern Recognition,1986. p. 15-20.
    [131]袁野.摄像机标定方法及边缘检测和轮廓跟踪算法研究[D].大连理工大学, 2002:124
    [132] Xiaoqiao Meng, Zhanyi Hu. A new easy camera calibration technique based on circular points[J]. Pattern Recognition, 2003, 36: 1155–1164.
    [133] M. Pollefeys., 3D modeling from images[M], CGRAPH. 2000.
    [134] J. Weng, P. Cohen, M. Herniou. Calibration of Stereo Cameras Using a Non-linear Distortion Model[C]. Proceedings of international conference on Pattern Recognition., 1990: 246-253.
    [135] Weng J, Cohen P, Herniou M. Camera calibration with distortion models and accuracy evaluation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, 14(10): 965-980.
    [136] Tsai R Y. An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision[C]. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 1986: 364-374.
    [137] Faugeras, O D. Camera Calibration for 3D Computer Vision[C]. Proc. of International Workshop on Industrial Application of Machine Vision and Machine Intelligence, 1987: 240-247.
    [138] Lenz, R., R. Tsai. Techniques for calibration of the scale. factor and image center for high accuracy 3D machine vision metrology[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence. , 1998, 10: 713-720.
    [139] Heikkila Janne. Camera calibration toolbox for Matlab[Z]. http://www.ee.oulu.fi/~jth/calibr/.
    [140]许智钦. 3D逆向工程技术[M].北京:中国计量出版社.
    [141]刘伟军,刘鹏,齐越.一种基于视觉的自由曲面三维测量系统[J].小型微型计算机系统, 2003(12): 2170-2173.
    [142] N. Guil, E.L. Zapata. Lower Order Circle and Ellipse Hough Transform[J]. J. Pattern Recognition, 1997, 30(10): 1729-1744.
    [143] Davies, E. R. A modified Hough scheme for general circle location[J]. Pattern Recognition Letters, 1998, 7(1): 37-43.
    [144] S. M. Thomas, Y. T. Chan. A simple approach for the estimation of circular arc center and its radius[J]. Computer Vision, Graphics, and Image Processing, 1989, 45: 362-370.
    [145] Suk-Hwan Suh, Sung-Kwon Lee. Compensating probe radius in free surface modeling withCMM[J]. Computer Integrated Manufacturing and Automation Technology, 1994: 222-227.
    [146] Mayer J. R. R. , MIR Y. A. , Trochu F., Vafaeesefat A., Balazinski M. . Touch probe radius compensation for coordinate measurement using kriging interpolation[J]. Proceedings of the Institution of Mechanical Engineers. Part B. Journal of engineering manufacture 1997: 11-18.
    [147] C. Menq, F. L. Chen. Curve and surface approximation from CMM measurement data[J]. Computers and Industrial Engineering 1996, 30(2): 211-225.
    [148] Chiang Y M., Chen F L. Sculptured surface reconstruction from CMM measurement data by a software iterative approach[J]. International Journal of Production Research, 1999, 37(8): 1679-1695.

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