基于支持向量机的点云数据修补
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摘要
逆向工程是通过产品扫描数据来重建产品数据模型,进而进行产品开发和制造的技术。其主要包含数据采集和数据处理两方面的内容。数据处理中的数据修复可为后续的曲面重构及产品模型建立降低难度和缩短所耗时间,因此对数据修复进行研究具有较高的实用价值。本文在三维结构光测量的技术背景之下,针对缺损点云数据的修复处理进行了研究。
缺损点云中通常只包含点的三坐标信息,而不具备各点间的拓扑关系。为使边界提取算法能实现自动搜索缺损区域的边界轮廓,引入角度阈值作为修补区域边界点的判定依据;同时提出将空间点投影到最小二乘平面,再利用平面上投影线段间夹角和阈值的比较来判定边界点的方法。随后依据边界点间的距离关系,将求出的边界点连接成边界线,再确定其方向和内外关系,最终确定出所需修复的缺损区域。本研究提出利用支持向量机的非线性回归算法,来对点云数据中缺损区域进行修复,并通过实例验证该方法的可行性。论文重点分析了曲面修补效果与缺损区域边界处数据点的空间落差的对应关系,得出修补精度范围和适用场合,同时讨论了该方法在曲面修补过程中的局限性。
Reverse engineering is a advanced technology in engineering, it can exploit and produce products through rebuilding scan data model. It has two contents which are data acquisition and data processing respectively. Data repair can shorten operational time for succeeding reconstruction and model building. Therefore, research about data repair in RE in this paper has a high practical value. In the technical background of collecting data within three-dimensional structured light, the defect data repairment is researched in this paper.
Defect point cloud includes merely the coordinate value of points, it has no topological relations in points. In order to automatically search out boundary contour which needs repaired, threshold angle is introduced as the standard of judging boundary points. A new method is proposed to project space points to least-squares plane, and then uses the comparison of angles between projection line sections and threshold angle to judge the boundary points. Based on the distance between boundary points, boundary line is generated. Finally, the direction of boundary line, the internal boundary line and region which needs repaired can be found out.
The paper proposes a method to repair the defect region of scattered point cloud. The method builds mathematical model with non-linear regression algorithm of support vector machine. The feasibility of method is verified through repair examples. The relationship between the effect of surface patch and the space fall of boundary points is analyzed. At the same time, accurate repairing scope, situation of application as well as the limitations of this method are be discussed.
缺损点云中通常只包含点的三坐标信息,而不具备各点间的拓扑关系。为使边界提取算法能实现自动搜索缺损区域的边界轮廓,引入角度阈值作为修补区域边界点的判定依据;同时提出将空间点投影到最小二乘平面,再利用平面上投影线段间夹角和阈值的比较来判定边界点的方法。随后依据边界点间的距离关系,将求出的边界点连接成边界线,再确定其方向和内外关系,最终确定出所需修复的缺损区域。本研究提出利用支持向量机的非线性回归算法,来对点云数据中缺损区域进行修复,并通过实例验证该方法的可行性。论文重点分析了曲面修补效果与缺损区域边界处数据点的空间落差的对应关系,得出修补精度范围和适用场合,同时讨论了该方法在曲面修补过程中的局限性。
Reverse engineering is a advanced technology in engineering, it can exploit and produce products through rebuilding scan data model. It has two contents which are data acquisition and data processing respectively. Data repair can shorten operational time for succeeding reconstruction and model building. Therefore, research about data repair in RE in this paper has a high practical value. In the technical background of collecting data within three-dimensional structured light, the defect data repairment is researched in this paper.
Defect point cloud includes merely the coordinate value of points, it has no topological relations in points. In order to automatically search out boundary contour which needs repaired, threshold angle is introduced as the standard of judging boundary points. A new method is proposed to project space points to least-squares plane, and then uses the comparison of angles between projection line sections and threshold angle to judge the boundary points. Based on the distance between boundary points, boundary line is generated. Finally, the direction of boundary line, the internal boundary line and region which needs repaired can be found out.
The paper proposes a method to repair the defect region of scattered point cloud. The method builds mathematical model with non-linear regression algorithm of support vector machine. The feasibility of method is verified through repair examples. The relationship between the effect of surface patch and the space fall of boundary points is analyzed. At the same time, accurate repairing scope, situation of application as well as the limitations of this method are be discussed.
引文
[1]金涛,童水光.逆向工程技术.机械工业出版社,2003,8
[2]齐建雄,张淑琴,牛文杰.逆向工程技术及其在工业制造中的应用.农业装备与车辆工程,2006,8
[3]卞向娟,龚友平,刘加海.神经网络在逆向工程中进行三维实体特征识别.计算机应用技术,2006,7
[4]柯映林.反求工程CAD建模理论、方法和系统.北京:机械工业出版社,2005,7
[5]王霄.逆向工程技术及其应用.北京:化学工业出版社,2004,5
[6]Versprille KJ.Computer-Aided Design Applications of the Rational B-Spline Approximation Form.Ph.D Dissertation,Syracuse University,February,1974
[7]Riesenfeld RF.Non-Uniform B-Spline Curves.1975:551-555
[8]Cohen E,Lyche T,Riesenfeld RF.Discrete B-Splines and Subdivision Techniques in Computer-Aided Geometric Design and Computer Graphics.Computer Graphics and Image Proceedings 14,1980:87-111
[9]Lane JM,Riesenfeld RF.A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces.IEEE Transactions on Pattern Analysis and Machine Intelligence,1980,PAME-2(1):35-46
[10]Tiller W.Rational B-Splines for Curves and Surfaces Representation.IEEE CG&A,September 1983:61-69
[11]Piegl L,Tiller W.The NURBS Book.Springer,New York,1995
[12]李际军.反求工程CAD建模关键技术研究.杭州:浙江大学博士学位论文,1999
[13]李卫国.逆向工程中的曲面重构技术研究及基于Web的应用系统开发.南京:南京航空航天大学博士学位论文,2001
[14]林奕鸿.散乱数据曲面重构技术的研究.武汉:华中科技大学博士学位论文,2000
[15]武殿梁,洪军,丁玉成.逆向工程中基于能量法的参数二阶连续曲面构造方法研究.机械工程学报,2002,38(5):30-35
[16]种永民,杨海成.实物测量造型技术中的数据分块方法.机械科学与技术,1996,15(6):989-992
[17]周赫赫,颜永年,单忠德.反求工程中的三维表面重建技术.铸造技术,2001,(5):13-15
[18]郑康平.基于点云数据的曲面重构关键技术的研究[D].西安:西安交通大学博士学位论文,2002
[19]许智钦,闫明,张宝峰.逆向工程技术三维激光扫描测量[J].天津大学学报,2002,34(3):404-407
[20]刘丽梅,孙玉荣,李莉.中值滤波技术发展研究.云南师范大学学报.2004
[21]吴军.轮廓曲线数据的采集与处理.西南交通大学硕士学位论文.2005
[22]包晓敏,张云华,汪亚明.基于离散高斯滤波器的纺织品图像增强.纺织学报.2005
[23]洪军,于玉成,曹亮.逆向工程中的测量数据精简技术研究[J].西安交通大学学报,2004,38(7):661-664
[24]季劲松.逆向工程中三坐标测量数据处理的研究及系统开发[J].浙江:浙江大学硕士学位论文,2002
[25]黄国珍,卢章平.逆向工程的点云数据精简方法.机械设计与研究.(2005)03-059-03
[26]田竹友,简斌.逆向工程中数据的处理.北京机械工业学院学报.(04)02-0001-05
[27]戴静.逆向工程数据处理关键技术研究.南京理工大学硕士学位论文,2003
[28]M.C.Huang,C.C.Tai.The pre-processing of data points for curve fitting in Reversing Engineering.Int.J.Adv.Manuf.Techol.16{2000}635-642
[29]I.Budak,J.Hodolic,M.Sokovic.Development of a programme system for data-point pre-processing in Reversing Engineering.Jounal of Materials Processing Technology.162-163(2005)730-735
[30]C.Lawson.Generation a triangular grid with application of contour plotting.Technical Memo.299.Jet Propulation Laboratory,Pasadena,California.1972
[31]P.Green,R.Silbson.Computing Dirichlet tessellation in the plane.The Computer Journal.1978,2(2):168-173
[32]R.Silbson.Locally equiangular tirnagulations.The Computer Journal.1978,21(3):243-245
[33]A.Bowyer.Computing Dirichlet tessellations.The Computer Journal.1981,24(2):162-166
[34]D.Watson.Computing the n-dimensional Delaunay tessellation with application to Voronoi poltopes.The Computer Journal.1981,24(2):167-172
[35]F.Aurenhammer.Voronoi diagrams:a survey of a fundamental data structure.ACM Computing Surveys.1991,23(3):345-405
[36]徐利治,周蕴时,孙玉柏.逼近论.北京:国防工业出版社,1985,249-273
[37]B.Joe.Construction of three-dimensional Delaunay triangulations using local transformations.Computer Aided Geometric Design,1991.8:123-142
[38]Leong K.F,Chua C.K,Ng Y.M.A study of stereolithography file errors and repair.Part1:generic solution[J].International Journal of Advanced Manufacturing Technology,1996,12:407-414
[39]Leong K.F,Chua C.K,Ng Y.M.A study of stereolithography file errors and repair.Part2:special cases[J].International Journal of Advanced Manufacturing Technology,1996,12:415-422
[40]Barequet Gill,Sharir Micha.Filling gaps in the boundary of a polyhedron[J].Computer Aided Geometric Design,1995,12(2):207-229
[41]李根,陈志杨,张三元.网格曲面中复杂孔洞的自动修补算法.浙江大学学报(工学版).2007,41(3):407-411
[42]周久兵.三角网格模型的孔洞修补及B样条曲面拟合.南京航空航天大学硕士学位论文,2004
[43]Guskov.I,Sweldens.W,Schroder.P.Multiresolution signal processing for meshes.In Computer Graphics Proceedings[C].1999,325-334
[44]Nello Cristianini,John Shawe Taylor.支持向量机导论.北京:电子工业出版社,2004
[2]齐建雄,张淑琴,牛文杰.逆向工程技术及其在工业制造中的应用.农业装备与车辆工程,2006,8
[3]卞向娟,龚友平,刘加海.神经网络在逆向工程中进行三维实体特征识别.计算机应用技术,2006,7
[4]柯映林.反求工程CAD建模理论、方法和系统.北京:机械工业出版社,2005,7
[5]王霄.逆向工程技术及其应用.北京:化学工业出版社,2004,5
[6]Versprille KJ.Computer-Aided Design Applications of the Rational B-Spline Approximation Form.Ph.D Dissertation,Syracuse University,February,1974
[7]Riesenfeld RF.Non-Uniform B-Spline Curves.1975:551-555
[8]Cohen E,Lyche T,Riesenfeld RF.Discrete B-Splines and Subdivision Techniques in Computer-Aided Geometric Design and Computer Graphics.Computer Graphics and Image Proceedings 14,1980:87-111
[9]Lane JM,Riesenfeld RF.A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces.IEEE Transactions on Pattern Analysis and Machine Intelligence,1980,PAME-2(1):35-46
[10]Tiller W.Rational B-Splines for Curves and Surfaces Representation.IEEE CG&A,September 1983:61-69
[11]Piegl L,Tiller W.The NURBS Book.Springer,New York,1995
[12]李际军.反求工程CAD建模关键技术研究.杭州:浙江大学博士学位论文,1999
[13]李卫国.逆向工程中的曲面重构技术研究及基于Web的应用系统开发.南京:南京航空航天大学博士学位论文,2001
[14]林奕鸿.散乱数据曲面重构技术的研究.武汉:华中科技大学博士学位论文,2000
[15]武殿梁,洪军,丁玉成.逆向工程中基于能量法的参数二阶连续曲面构造方法研究.机械工程学报,2002,38(5):30-35
[16]种永民,杨海成.实物测量造型技术中的数据分块方法.机械科学与技术,1996,15(6):989-992
[17]周赫赫,颜永年,单忠德.反求工程中的三维表面重建技术.铸造技术,2001,(5):13-15
[18]郑康平.基于点云数据的曲面重构关键技术的研究[D].西安:西安交通大学博士学位论文,2002
[19]许智钦,闫明,张宝峰.逆向工程技术三维激光扫描测量[J].天津大学学报,2002,34(3):404-407
[20]刘丽梅,孙玉荣,李莉.中值滤波技术发展研究.云南师范大学学报.2004
[21]吴军.轮廓曲线数据的采集与处理.西南交通大学硕士学位论文.2005
[22]包晓敏,张云华,汪亚明.基于离散高斯滤波器的纺织品图像增强.纺织学报.2005
[23]洪军,于玉成,曹亮.逆向工程中的测量数据精简技术研究[J].西安交通大学学报,2004,38(7):661-664
[24]季劲松.逆向工程中三坐标测量数据处理的研究及系统开发[J].浙江:浙江大学硕士学位论文,2002
[25]黄国珍,卢章平.逆向工程的点云数据精简方法.机械设计与研究.(2005)03-059-03
[26]田竹友,简斌.逆向工程中数据的处理.北京机械工业学院学报.(04)02-0001-05
[27]戴静.逆向工程数据处理关键技术研究.南京理工大学硕士学位论文,2003
[28]M.C.Huang,C.C.Tai.The pre-processing of data points for curve fitting in Reversing Engineering.Int.J.Adv.Manuf.Techol.16{2000}635-642
[29]I.Budak,J.Hodolic,M.Sokovic.Development of a programme system for data-point pre-processing in Reversing Engineering.Jounal of Materials Processing Technology.162-163(2005)730-735
[30]C.Lawson.Generation a triangular grid with application of contour plotting.Technical Memo.299.Jet Propulation Laboratory,Pasadena,California.1972
[31]P.Green,R.Silbson.Computing Dirichlet tessellation in the plane.The Computer Journal.1978,2(2):168-173
[32]R.Silbson.Locally equiangular tirnagulations.The Computer Journal.1978,21(3):243-245
[33]A.Bowyer.Computing Dirichlet tessellations.The Computer Journal.1981,24(2):162-166
[34]D.Watson.Computing the n-dimensional Delaunay tessellation with application to Voronoi poltopes.The Computer Journal.1981,24(2):167-172
[35]F.Aurenhammer.Voronoi diagrams:a survey of a fundamental data structure.ACM Computing Surveys.1991,23(3):345-405
[36]徐利治,周蕴时,孙玉柏.逼近论.北京:国防工业出版社,1985,249-273
[37]B.Joe.Construction of three-dimensional Delaunay triangulations using local transformations.Computer Aided Geometric Design,1991.8:123-142
[38]Leong K.F,Chua C.K,Ng Y.M.A study of stereolithography file errors and repair.Part1:generic solution[J].International Journal of Advanced Manufacturing Technology,1996,12:407-414
[39]Leong K.F,Chua C.K,Ng Y.M.A study of stereolithography file errors and repair.Part2:special cases[J].International Journal of Advanced Manufacturing Technology,1996,12:415-422
[40]Barequet Gill,Sharir Micha.Filling gaps in the boundary of a polyhedron[J].Computer Aided Geometric Design,1995,12(2):207-229
[41]李根,陈志杨,张三元.网格曲面中复杂孔洞的自动修补算法.浙江大学学报(工学版).2007,41(3):407-411
[42]周久兵.三角网格模型的孔洞修补及B样条曲面拟合.南京航空航天大学硕士学位论文,2004
[43]Guskov.I,Sweldens.W,Schroder.P.Multiresolution signal processing for meshes.In Computer Graphics Proceedings[C].1999,325-334
[44]Nello Cristianini,John Shawe Taylor.支持向量机导论.北京:电子工业出版社,2004