基于小波分析和自适应网格拟合的逆向工程研究
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摘要
复杂曲面重构是逆向工程实现自由曲面零件数字化仿制和改进的一项重要技术,拥有非常广阔的应用前景。一般的曲面重构都是由测量点云经过预处理,三角网格剖分,点云分块,然后对分块点云分别进行曲面重构。这类方法中的自由曲面重构过程相当繁琐费时,而且精度难以保证。由此,我们派生出由整块的三角网格直接进行曲面重构的思想,并且能够实现自动化,它可跳过复杂且难以控制的点云分块环节。
通常对实物进行采样的测量方法应用较多的是非接触式测量,我们一般运用的是激光扫描仪,这种测量方法所采得的数据点会包含许多随机噪点,这些点的存在对点云的曲面重构质量有很大的影响。基于这些随机噪点是一种较高频率分量的信号,我们派生出利用小波分析理论进行降噪,滤除这些随机噪点,为接下来的复杂曲面重构提供有利条件。
本文首先通过研究现有的测量设备数据采集的原理、方法及特点,通过大量零件表面数据的测量,比较自由曲面测量的各种手段,并采用TDV800型激光扫描仪测得典型零件的含有随机噪声散乱点云作为研究对象,对数据点进行数据拼合、滤波、精简及坐标变换等预处理操作,其主要是研究利用小波技术进行降噪,即对信号进行多次小波分解,分解后得到近似系数和细节系数,再对细节系数作用阈值抑制噪声,重建信号达到降噪的目的。小波分解后,可以在各个层次选择阈值,对噪声成分进行抑制,手段更加灵活。更重要的是可以根据某些频段分离出来的系数随时间的变化,通过某些准则来确定其是信号本身所包含的信息,还是噪声。
另外,在拓扑结构重构过程中,将散乱点云进行等间隔区域分割,采用三角网格剖分手段来建立点云在空间的完整拓扑结构,同时设计三角面片的存储数据结构并保存输出三角面片,将所得三角面片进行四边形划分,利用参数化的曲线拟合所得的四边形曲线网格的边界线以及边界线上的法线,再利用参数化曲面对四边形面片进行整体构造,通过将参数化面片与被构造的数据点进行误差比较,在误差超出预设置值的情况下,再次对四边形面片进行细分,再次拟合,直至达到要求为止。
针对本文各项研究,采用VC++编程开发工具结合OpenGL开放式图形库设计可视化应用软件以及MATLAB应用软件,通过叶子、叶片以及人脸等“点云”演示了软件的可操作性及本文中提出的小波降噪理论以及自适应网格拟合理论。
Complex surface reconstruction in Reverse engineering (RE) is an important technology that can realize digital duplication of free-form surface parts and improvements, and it has a wide prospect. In general procedures of surface reconstruction, the measured point cloud is to pre-process, mesh, segment and then reconstruct surface that is segmented. In these ways, the process is proceeded slowly and cost-time, also can not promise the precision. Then direct surface reconstruction is arised, and it can realize the automation easily, also can pass the complex and un-controllable point segmentation process.
Normally, non-contact measurement method is mostly used in data acquiring on surface. The laser we use that will make many randam noise data in the point cloud that is affect the quality of the reconstruct surface. For those randam noise data points are at high frequency, it arises that wavelet analysis theory can be applied in noise reduction, that can prove the quality of the surface reconstruction.
In the paper, the theories, methods and characteristic of exiting measurement machine is studied. In the meanwhile, every method of free-form surface measurement is also comparied by a lot of parts’measurement. Based on the point cloud which is acquired by TDV800 laser scanner, pre-processing which includes data merge, filtering, noise reduction and coordinate transformation were observed, mostly in applying wavelet technology in denosing cloudy data. Denoising cloudy data based wavelet is the process of decomposing signal with wavelet, aquiring approximate coefficients and detail coefficient, acting detailed coefficient with threshold to suppress noises, then reconstruting signal to get the goal of denoising. After decomposing signal of wavelet, threshold value can be chosen in different level to suppress noises, that means the method is flexible. Most important is that the cloudy data can be judged whether it is a noise point data or not, by some principle.
Besides, in the process of topology reconstruction, the scattered point cloud was divided at equal intervals, then be meshed to finish the point cloud reconstruction. The mesh is saved in the software and can be exported, then the mesh is divided to quadrilateral patch. The boudary curve of quadrilateral patch and the normal line to boundary curve are fitted by parametric curve, and a parametric surface will be constructed by fitting the boundary curve, normal line and the points. After that, the error between parametric surface and the mesh point data will be caculated. If the error is larger than the setting value, the quadrilateral patch will be divided, then fitted until the error is not larger than the setting value.
Focus on the research contents of this paper, visual software was designed by using VC++ programming and OpenGL graphics library and MATLAB. The operation of this software and the realize procedure of wavelet denoising and adaptive mesh fitting were demonstrated by point cloud samples of“leaf”,“vane”and“face”.
通常对实物进行采样的测量方法应用较多的是非接触式测量,我们一般运用的是激光扫描仪,这种测量方法所采得的数据点会包含许多随机噪点,这些点的存在对点云的曲面重构质量有很大的影响。基于这些随机噪点是一种较高频率分量的信号,我们派生出利用小波分析理论进行降噪,滤除这些随机噪点,为接下来的复杂曲面重构提供有利条件。
本文首先通过研究现有的测量设备数据采集的原理、方法及特点,通过大量零件表面数据的测量,比较自由曲面测量的各种手段,并采用TDV800型激光扫描仪测得典型零件的含有随机噪声散乱点云作为研究对象,对数据点进行数据拼合、滤波、精简及坐标变换等预处理操作,其主要是研究利用小波技术进行降噪,即对信号进行多次小波分解,分解后得到近似系数和细节系数,再对细节系数作用阈值抑制噪声,重建信号达到降噪的目的。小波分解后,可以在各个层次选择阈值,对噪声成分进行抑制,手段更加灵活。更重要的是可以根据某些频段分离出来的系数随时间的变化,通过某些准则来确定其是信号本身所包含的信息,还是噪声。
另外,在拓扑结构重构过程中,将散乱点云进行等间隔区域分割,采用三角网格剖分手段来建立点云在空间的完整拓扑结构,同时设计三角面片的存储数据结构并保存输出三角面片,将所得三角面片进行四边形划分,利用参数化的曲线拟合所得的四边形曲线网格的边界线以及边界线上的法线,再利用参数化曲面对四边形面片进行整体构造,通过将参数化面片与被构造的数据点进行误差比较,在误差超出预设置值的情况下,再次对四边形面片进行细分,再次拟合,直至达到要求为止。
针对本文各项研究,采用VC++编程开发工具结合OpenGL开放式图形库设计可视化应用软件以及MATLAB应用软件,通过叶子、叶片以及人脸等“点云”演示了软件的可操作性及本文中提出的小波降噪理论以及自适应网格拟合理论。
Complex surface reconstruction in Reverse engineering (RE) is an important technology that can realize digital duplication of free-form surface parts and improvements, and it has a wide prospect. In general procedures of surface reconstruction, the measured point cloud is to pre-process, mesh, segment and then reconstruct surface that is segmented. In these ways, the process is proceeded slowly and cost-time, also can not promise the precision. Then direct surface reconstruction is arised, and it can realize the automation easily, also can pass the complex and un-controllable point segmentation process.
Normally, non-contact measurement method is mostly used in data acquiring on surface. The laser we use that will make many randam noise data in the point cloud that is affect the quality of the reconstruct surface. For those randam noise data points are at high frequency, it arises that wavelet analysis theory can be applied in noise reduction, that can prove the quality of the surface reconstruction.
In the paper, the theories, methods and characteristic of exiting measurement machine is studied. In the meanwhile, every method of free-form surface measurement is also comparied by a lot of parts’measurement. Based on the point cloud which is acquired by TDV800 laser scanner, pre-processing which includes data merge, filtering, noise reduction and coordinate transformation were observed, mostly in applying wavelet technology in denosing cloudy data. Denoising cloudy data based wavelet is the process of decomposing signal with wavelet, aquiring approximate coefficients and detail coefficient, acting detailed coefficient with threshold to suppress noises, then reconstruting signal to get the goal of denoising. After decomposing signal of wavelet, threshold value can be chosen in different level to suppress noises, that means the method is flexible. Most important is that the cloudy data can be judged whether it is a noise point data or not, by some principle.
Besides, in the process of topology reconstruction, the scattered point cloud was divided at equal intervals, then be meshed to finish the point cloud reconstruction. The mesh is saved in the software and can be exported, then the mesh is divided to quadrilateral patch. The boudary curve of quadrilateral patch and the normal line to boundary curve are fitted by parametric curve, and a parametric surface will be constructed by fitting the boundary curve, normal line and the points. After that, the error between parametric surface and the mesh point data will be caculated. If the error is larger than the setting value, the quadrilateral patch will be divided, then fitted until the error is not larger than the setting value.
Focus on the research contents of this paper, visual software was designed by using VC++ programming and OpenGL graphics library and MATLAB. The operation of this software and the realize procedure of wavelet denoising and adaptive mesh fitting were demonstrated by point cloud samples of“leaf”,“vane”and“face”.
引文
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2. Finkelstein, A.. Salesin D.H..Multiresolution Curves[J].SIGGRAPH’94 Proceedings,1994,261-268
3. Lounsbery,M.,DeRose,T. and Warren J.Multiresolution Surfaces of Arbitrary Topological Type[J].ACM Transations on Graphics.1997,16(1):34-73
4. Eck ,M.,DeRose,T.and Warren J.,Multiresolution Analysis of Arbitrary Meshes[J].SIGGRAPH’95 Proceedings,1995,173-182
5. Certain.A..Interactive Multiresolution Surface Viewing[J].SIGGRAPH’96 Proceedings,1996,91-98
6. Gortler,S.J. and Cohen,M.F.,Hierachical and Variational Geometric Modeling with Wavelets[J].In Proc.Symp. on Interative 3D Graphic,May1995
7.孙延奎,朱心雄,唐泽圣.准均匀B样条曲面小波分解的快速算法[J].清华大学学报(自然科学版),2001,41:209-213
8.孙延奎,朱心雄.曲线分层表示的小波方法[J] .工程图学学报,1999,1:40-44
9.孙延奎,朱心雄.任意B样条曲面的多分辨率表示及光顺[J].工程图学学报,1998,3:49-54
10.赵罡,朱心雄等.均匀B样条曲线曲面的小波表示[J].工程图学学报,2001,l:80-88
11.吴维勇,王小椿.基于小波分析的散乱测量数据的压缩算法[J].小型微型计算机系统,2002,23(11):1384-1386
12.潘洋宇.面向逆向工程的小波技术与研究[D]
13.李道军,刘德平,上官建林.逆向工程中测量数据点的滤波[J].现代制造工程,2006,3:92-94
14. ECK M,HOPPE H.Automatic reconstruction of B-spline surface of arbitrary topological type[J].SIGGRAPH’96 Proceedings,1996:325- 333.
15. Krishnamurthy, V., Levoy, M., 1996. Fitting smooth surfaces to dense polygon meshes[J]. In: Computer Graphics (Proceedings of SIGGRAPH’96):313-324.
16. Milroy, M.J., Bradley, C., Vickera, G.W., Weir, D.J., 1995. G1 continuity of B-spline surface patches in reverse engineering[J].Computer-Aided Design 27:471-478
17. Xiquan Shi, Tianjun Wang, Peiru Wu, Fengshan Liu. Reconstruction of convergent G1 smooth B-spline surfaces[J]. Computer Aided Geometric Design 21 (2004): 893–913
18. Hongwei Lin, Wei Chen, Hujun Bao. Adaptive patch-based mesh fitting for reverseengineering[J]. Computer-Aided Design 39 (2007): 1134–1142
19. L.Y. Zhang, R.R. Zhou, J.Y. Zhu(l), X. Wu. Piecewise B-spline Surfaces Fitting to Arbitrary Triangle Meshes[J].
20.许智钦,闫明,张宝峰,王宝华,郑义忠,叶声华.逆向工程技术三维激光扫描测量[J].天津大学学报,2001,5:404-408
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23.曾华明.逆向工程中的曲面重构技术研究[D]
24.潘洋宇,李东波,童一飞.基于小波技术的数据降噪[J].机械设计,2006,31-32
25. David F.Roger著,石教英,彭群生等译.计算机图形学的算法基础[M].机械工程出版社,2002
26. FISCHER A.Utilizing image processing techniques for 3Dreconstruction of laser–scanned data[J].Annals of the CIRP,1999,48(1):99-102.
27.金涛,童水光.逆向工程技术[M].机械工业出版社,2003
28. Hoope H, DeRose, Duchamp T, et al. Surface Reconstruction from Unorganized Points[J]. In: Proceeding of SIGGRA-PH’92. Danvers: Assison-Wssley Publishing Company,1992:71-78
29.董洪伟.散乱点云的三角网格重构.计算机工程,2005,31(15):30-31
30. Lin A C, Lin S Y, Fang T H. Automated sequence arrangement of 3D point data for surface fitting in reverse engineering[J].Computers in Industry, 1998, 35(2): 149-173
31. Zhong Gang. Research on curve and surface reconstruction[J].Hangzhou: Zhejiang University, 2002(in Chinese)
32. Liu Yunfeng, Ke Yinglin. Hybrid slicing technology in reverse engineering[J]. Journal of Computer-Aided Design& Computer Graphics, 2003, 15(6):741-745
33. Wu Y F, Wong Y S, Loh H T, et al. Modeling cloud data using an adaptive slicing approach[J]. Computer-Aided Design, 2004, 36(1): 231-240
34. Amenta N , Bern M , Eppstein D. The crust and theβ2skeleton :Combinatorial curve reconstruction [J]. Graphical Models and Image Processing , 1998 , 60 (2) : 125-135
35. Giesen J. Curve reconstruction , the traveling salesman problem and Menger’s theorem on length [A] : Proceedings of the 15th Annual ACM Symposium on Computer Geometry , Miami , 1999, 1: 207-216
36.柯映林.反求工程中的点云切片算法研究[J].计算机辅助设计与图形学学报,2005,17(8):1798-1802
37.潘洋宇.点云数据曲面重构和小波分解研究[J].计算机集成制造系统,2005,11(10):1496-1500
38. Tsukasa K, Takeshi K, Katsumas S. Machining system based on inverse offset method[J]. J Jap Soc Precision Eng, 1998, 54(5): 971-976
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2. Finkelstein, A.. Salesin D.H..Multiresolution Curves[J].SIGGRAPH’94 Proceedings,1994,261-268
3. Lounsbery,M.,DeRose,T. and Warren J.Multiresolution Surfaces of Arbitrary Topological Type[J].ACM Transations on Graphics.1997,16(1):34-73
4. Eck ,M.,DeRose,T.and Warren J.,Multiresolution Analysis of Arbitrary Meshes[J].SIGGRAPH’95 Proceedings,1995,173-182
5. Certain.A..Interactive Multiresolution Surface Viewing[J].SIGGRAPH’96 Proceedings,1996,91-98
6. Gortler,S.J. and Cohen,M.F.,Hierachical and Variational Geometric Modeling with Wavelets[J].In Proc.Symp. on Interative 3D Graphic,May1995
7.孙延奎,朱心雄,唐泽圣.准均匀B样条曲面小波分解的快速算法[J].清华大学学报(自然科学版),2001,41:209-213
8.孙延奎,朱心雄.曲线分层表示的小波方法[J] .工程图学学报,1999,1:40-44
9.孙延奎,朱心雄.任意B样条曲面的多分辨率表示及光顺[J].工程图学学报,1998,3:49-54
10.赵罡,朱心雄等.均匀B样条曲线曲面的小波表示[J].工程图学学报,2001,l:80-88
11.吴维勇,王小椿.基于小波分析的散乱测量数据的压缩算法[J].小型微型计算机系统,2002,23(11):1384-1386
12.潘洋宇.面向逆向工程的小波技术与研究[D]
13.李道军,刘德平,上官建林.逆向工程中测量数据点的滤波[J].现代制造工程,2006,3:92-94
14. ECK M,HOPPE H.Automatic reconstruction of B-spline surface of arbitrary topological type[J].SIGGRAPH’96 Proceedings,1996:325- 333.
15. Krishnamurthy, V., Levoy, M., 1996. Fitting smooth surfaces to dense polygon meshes[J]. In: Computer Graphics (Proceedings of SIGGRAPH’96):313-324.
16. Milroy, M.J., Bradley, C., Vickera, G.W., Weir, D.J., 1995. G1 continuity of B-spline surface patches in reverse engineering[J].Computer-Aided Design 27:471-478
17. Xiquan Shi, Tianjun Wang, Peiru Wu, Fengshan Liu. Reconstruction of convergent G1 smooth B-spline surfaces[J]. Computer Aided Geometric Design 21 (2004): 893–913
18. Hongwei Lin, Wei Chen, Hujun Bao. Adaptive patch-based mesh fitting for reverseengineering[J]. Computer-Aided Design 39 (2007): 1134–1142
19. L.Y. Zhang, R.R. Zhou, J.Y. Zhu(l), X. Wu. Piecewise B-spline Surfaces Fitting to Arbitrary Triangle Meshes[J].
20.许智钦,闫明,张宝峰,王宝华,郑义忠,叶声华.逆向工程技术三维激光扫描测量[J].天津大学学报,2001,5:404-408
21.王霄.逆向工程技术及其应用[M].化学工业出版社,2004
22.许智钦,孙长库.3D逆向工程技术[M].中国计量出版社,2002
23.曾华明.逆向工程中的曲面重构技术研究[D]
24.潘洋宇,李东波,童一飞.基于小波技术的数据降噪[J].机械设计,2006,31-32
25. David F.Roger著,石教英,彭群生等译.计算机图形学的算法基础[M].机械工程出版社,2002
26. FISCHER A.Utilizing image processing techniques for 3Dreconstruction of laser–scanned data[J].Annals of the CIRP,1999,48(1):99-102.
27.金涛,童水光.逆向工程技术[M].机械工业出版社,2003
28. Hoope H, DeRose, Duchamp T, et al. Surface Reconstruction from Unorganized Points[J]. In: Proceeding of SIGGRA-PH’92. Danvers: Assison-Wssley Publishing Company,1992:71-78
29.董洪伟.散乱点云的三角网格重构.计算机工程,2005,31(15):30-31
30. Lin A C, Lin S Y, Fang T H. Automated sequence arrangement of 3D point data for surface fitting in reverse engineering[J].Computers in Industry, 1998, 35(2): 149-173
31. Zhong Gang. Research on curve and surface reconstruction[J].Hangzhou: Zhejiang University, 2002(in Chinese)
32. Liu Yunfeng, Ke Yinglin. Hybrid slicing technology in reverse engineering[J]. Journal of Computer-Aided Design& Computer Graphics, 2003, 15(6):741-745
33. Wu Y F, Wong Y S, Loh H T, et al. Modeling cloud data using an adaptive slicing approach[J]. Computer-Aided Design, 2004, 36(1): 231-240
34. Amenta N , Bern M , Eppstein D. The crust and theβ2skeleton :Combinatorial curve reconstruction [J]. Graphical Models and Image Processing , 1998 , 60 (2) : 125-135
35. Giesen J. Curve reconstruction , the traveling salesman problem and Menger’s theorem on length [A] : Proceedings of the 15th Annual ACM Symposium on Computer Geometry , Miami , 1999, 1: 207-216
36.柯映林.反求工程中的点云切片算法研究[J].计算机辅助设计与图形学学报,2005,17(8):1798-1802
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