面向设计的三维CAD模型搜索技术研究
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摘要
在机械产品设计领域，相同的或相似的零部件经常在不同的产品中出现；强经验弱理论产品设计的成败在很大程度上依赖于设计者的相关设计经验；而企业已有的、被工程实践证明了的成功设计案例，是可以利用的、最为丰富和最具代表性的设计经验。因此，在新产品设计中重用现有的设计方案是一个务实和必然的选择。有调查显示，现实中40%零部件可以采用现成设计，40%可以通过修改已有的设计完成，只有20%的需要全新设计。为了寻找参考设计方案，设计者60%的时间用于资料搜索；工业界仍然普遍存在着的重复设计和制造现象，使企业蒙受巨大经济损失；其根源是缺乏有效的设计资源管理和搜索工具。
三维CAD系统的推广应用使得设计资源的主要形式是三维CAD模型；对于以几何表达为主体的CAD模型，由于模型文本记录的语义随CAD系统、设计者和设计时间的变化呈极大的不确定性，文本记录对模型结构形状描述的准确性是极其有限的，导致单纯基于文本的管理与搜索技术有严重的局限性。因此，近十多年来，基于几何形状比较分析的CAD模型管理与搜索技术成为CAD领域中人们普遍关注的热点问题之一。本论文沿着这一方向对CAD模型搜索技术开展了进一步的研究，具体包括以下几个方面：
(1)为弥补现有的三维CAD模型搜索方法难以搜索到不同近似程度的相似度模型的缺陷，提出一种基于非精确面属性邻接图匹配的CAD模型搜索方法。首先应用CAD模型中的B-rep信息，将搜索输入和搜索目标CAD模型分别转化为面属性邻接图；然后分别计算搜索输入与搜索目标CAD模型面属性邻接图之间的顶点以及边相似度矩阵，并由此建立2个CAD模型相似度度量作为选择不同顶点匹配矩阵M的优化目标函数；最后将匹配矩阵M的不等式约束松弛为等式约束后，运用经典的拉格朗日乘子法求解该优化问题。
(2)提出一种基于李群梯度流的CAD模型局部搜索方法。首先应用CAD模型的B-rep信息，将搜索输入CAD模型局部形状和数据库CAD模型整体形状分别表示为子图和大图，于是CAD模型的局部形状搜索转化为在大图中寻找匹配的子图问题；接着将子图匹配问题转化为优化约束问题，优化目标函数是相比较的2个图顶点和边之间的相似度度量，优化变量是面属性邻接图的顶点映射匹配矩阵。不同于现有的子图匹配方法，引入了齐次变换矩阵描述子图匹配过程中的顶点映射，其平移子矩阵在大图中选择用于图匹配的顶点，其旋转子矩阵给出了小图顶点与其具有同样顶点数量的大图选择顶点的置换变换；最后用特殊欧氏群SE(n)里的梯度流方法寻找最优匹配矩阵。
(3)提出一种基于B-rep分割的CAD模型搜索方法。首先充分考虑机械零件模型的形状特征较为显著、表面与表面之间分界较为明显的特点，在不破坏模型B-rep结构的前提下，依据CAD模型的边界将模型分割成一组数量最少的、有一定工程意义的、由一些相互连接的面组成的面区域集合；接着对分割形成的面区域及其邻接关系属性进行编码，生成CAD模型形状描述子；最后由面区域及其邻接关系属性编码的相似度比较，得到相比较CAD模型的相似度。该方法既支持CAD模型的整体相似度评价，又支持CAD模型的局部形状搜索。
(4)提出一种基于零件属性邻接图(component attributed relational graph, CARG)匹配的装配体模型相似度评价方法。首先装配体模型在CAD系统中产生，并完整地提取装配体模型中除联接与传动件以外的组成零件个体信息，同时自动或交互式得到装配体模型装配组成关系信息，用CARG表征装配体模型；接着由相比较装配体模型组成零件以及装配组成关系之间的相似度建立组成零件相似度映射矩阵，作为相比较装配体模型之间相似度度量；最后用最优匹配Kuhn-Munkres算法求解CARG图匹配。
在以上的CAD模型形状描述和搜索方法的指导下，基于Visual C++开发环境、ACIS几何引擎和HOOPS显示核心开发了一个三维CAD模型搜索原型系统。该系统能实现CAD模型的非精确搜索、CAD模型局部形状精确搜索以及基于B-rep分割的CAD模型整体和局部搜索，同时用实例验证了研究成果的正确性和有效性。
In the field of mechanical engineering, different products often have the same orsimilar parts. The successful product designs with strong experience and weak theorydepend heavily on the designer's relevant design experience. And the existing design casesthat have been proved to be correct in practice can be modified to meet the requirement fornew products. Consequently, reuse of existing design in new product design is a pragmaticand inevitable choice. Some surveys show that about40%of product designs can directlyuse the existing design resources, about40%of product designs can modify the previousdesign cases to get the new designs, and only20%of product designs need to start fromscratch. In order to locate the reference cases, the designers used their60%of the time tosearch for desired design resources. Even so, there are widespread repeat design andmanufacturing phenomenon in the manufacturing industry, which cause huge economiclosses for enterprise. The reason is the lack of effective design resources management andsearch tools.
The popularity of three-dimensional (3D) CAD systems in the product design ofmanufacturing industry brings about the emergence of a large number of3D CAD models.Since CAD models are geometry expression the text-based management and searchtechnologies have serious limitations. First, the descriptive texts for CAD model are ofgreat uncertainty as the change of CAD systems, designers and design dates. Second, theaccuracy of the shape description based on text is poor. Thus, in the last decade,content-based CAD model search has received extensive attention in the academiccommunity.
This dissertation mainly studies the CAD model retrieval methods for mechanicalproduct design, which includes the following aspects:
(1) A CAD model retrieval method based on inexact graph matching is presented inorder to resolve the problem that the exact graph matching is unable to support the similarmodel retrieval. First, a representation of face attributed relational graph (ARG) for eachCAD model is extracted from its B-Rep model. Then, the vertex compatibility matrix andedge compatibility matrix between the ARGs of the target and searched model arecalculated, and the measure of the two model’s similarity is created from the compatibilitymatrices, which serves as the objective function for optimally selecting vertex mappingmatrix M between the two models. At last, the optimal vertex mapping matrix M is foundusing Lagrange multiplier method for the optimization problem after relaxing itsinequality constraints to be equal.
(2) Based on the gradient flows in Lie group, a partial retrieval approach for CAD models is presented. First, a representation of the face ARG for a CAD model is createdfrom its B-rep model and thus partial retrieval is converted to a subgraph matchingproblem. Then, an optimization method is adopted to solve the matching problem, wherethe optimization variable is the vertex mapping and the objective function is themeasurement of compatibility between the mapped vertices and between the mappededges. Different from most previously proposed methods, a homogeneous transformationmatrix is introduced to represent the vertex mapping in subgraph matching, whosetranslational sub-matrix gives the vertex selection in the larger graph and whoseorthogonal sub-matrix presents the vertex permutation for the same-sized mapping fromthe selected vertices to the smaller graph’s vertices. Finally, a gradient flow method isdeveloped to search for the optimal matching matrix in Special Euclidean group SE(n).
(3) A CAD model retrieval method based on B-rep decomposition is presented. First,according to the salient geometric features of the mechanical part, the surface boundary ofa solid model is divided into local convex, concave and planar regions with the minimalnumber. Then, we give a kind of region codes that describe the surface region and theirlinks in CAD model. At last, the similarity between two models is measured by thecomparison of their region codes. The retrieval for CAD model can be applied to theglobal and partial search.
(4) A similarity evaluation for assembly model based on component attributedrelational graph (CARG) is presented. First, assembly models are created from CADsystems. The information of constitute parts, excluding for connection and transmissionparts, and the complex relationships between them in an assembly are extractedautomatically or manually; meanwhile, assembly model is described as CARG. Then, thepart compatibility matrix between two assemblies are calculated, which serve as themeasure of their similarity. Finally, the optimal matching under the measures is calculatedusing Kuhn-Munkres algorithm.
Based on the methodologies mentioned above, a3D retrieval system is developedusing Visual C++6.0, geometry engine ACIS and display engine HOOPS. The systemsupports the inexact retrieval, the exact partial retrieval, globe and local retrieval for CADmodel. Meanwhile, some experimental results show their correctness and effectiveness.
三维CAD系统的推广应用使得设计资源的主要形式是三维CAD模型；对于以几何表达为主体的CAD模型，由于模型文本记录的语义随CAD系统、设计者和设计时间的变化呈极大的不确定性，文本记录对模型结构形状描述的准确性是极其有限的，导致单纯基于文本的管理与搜索技术有严重的局限性。因此，近十多年来，基于几何形状比较分析的CAD模型管理与搜索技术成为CAD领域中人们普遍关注的热点问题之一。本论文沿着这一方向对CAD模型搜索技术开展了进一步的研究，具体包括以下几个方面：
(1)为弥补现有的三维CAD模型搜索方法难以搜索到不同近似程度的相似度模型的缺陷，提出一种基于非精确面属性邻接图匹配的CAD模型搜索方法。首先应用CAD模型中的B-rep信息，将搜索输入和搜索目标CAD模型分别转化为面属性邻接图；然后分别计算搜索输入与搜索目标CAD模型面属性邻接图之间的顶点以及边相似度矩阵，并由此建立2个CAD模型相似度度量作为选择不同顶点匹配矩阵M的优化目标函数；最后将匹配矩阵M的不等式约束松弛为等式约束后，运用经典的拉格朗日乘子法求解该优化问题。
(2)提出一种基于李群梯度流的CAD模型局部搜索方法。首先应用CAD模型的B-rep信息，将搜索输入CAD模型局部形状和数据库CAD模型整体形状分别表示为子图和大图，于是CAD模型的局部形状搜索转化为在大图中寻找匹配的子图问题；接着将子图匹配问题转化为优化约束问题，优化目标函数是相比较的2个图顶点和边之间的相似度度量，优化变量是面属性邻接图的顶点映射匹配矩阵。不同于现有的子图匹配方法，引入了齐次变换矩阵描述子图匹配过程中的顶点映射，其平移子矩阵在大图中选择用于图匹配的顶点，其旋转子矩阵给出了小图顶点与其具有同样顶点数量的大图选择顶点的置换变换；最后用特殊欧氏群SE(n)里的梯度流方法寻找最优匹配矩阵。
(3)提出一种基于B-rep分割的CAD模型搜索方法。首先充分考虑机械零件模型的形状特征较为显著、表面与表面之间分界较为明显的特点，在不破坏模型B-rep结构的前提下，依据CAD模型的边界将模型分割成一组数量最少的、有一定工程意义的、由一些相互连接的面组成的面区域集合；接着对分割形成的面区域及其邻接关系属性进行编码，生成CAD模型形状描述子；最后由面区域及其邻接关系属性编码的相似度比较，得到相比较CAD模型的相似度。该方法既支持CAD模型的整体相似度评价，又支持CAD模型的局部形状搜索。
(4)提出一种基于零件属性邻接图(component attributed relational graph, CARG)匹配的装配体模型相似度评价方法。首先装配体模型在CAD系统中产生，并完整地提取装配体模型中除联接与传动件以外的组成零件个体信息，同时自动或交互式得到装配体模型装配组成关系信息，用CARG表征装配体模型；接着由相比较装配体模型组成零件以及装配组成关系之间的相似度建立组成零件相似度映射矩阵，作为相比较装配体模型之间相似度度量；最后用最优匹配Kuhn-Munkres算法求解CARG图匹配。
在以上的CAD模型形状描述和搜索方法的指导下，基于Visual C++开发环境、ACIS几何引擎和HOOPS显示核心开发了一个三维CAD模型搜索原型系统。该系统能实现CAD模型的非精确搜索、CAD模型局部形状精确搜索以及基于B-rep分割的CAD模型整体和局部搜索，同时用实例验证了研究成果的正确性和有效性。
In the field of mechanical engineering, different products often have the same orsimilar parts. The successful product designs with strong experience and weak theorydepend heavily on the designer's relevant design experience. And the existing design casesthat have been proved to be correct in practice can be modified to meet the requirement fornew products. Consequently, reuse of existing design in new product design is a pragmaticand inevitable choice. Some surveys show that about40%of product designs can directlyuse the existing design resources, about40%of product designs can modify the previousdesign cases to get the new designs, and only20%of product designs need to start fromscratch. In order to locate the reference cases, the designers used their60%of the time tosearch for desired design resources. Even so, there are widespread repeat design andmanufacturing phenomenon in the manufacturing industry, which cause huge economiclosses for enterprise. The reason is the lack of effective design resources management andsearch tools.
The popularity of three-dimensional (3D) CAD systems in the product design ofmanufacturing industry brings about the emergence of a large number of3D CAD models.Since CAD models are geometry expression the text-based management and searchtechnologies have serious limitations. First, the descriptive texts for CAD model are ofgreat uncertainty as the change of CAD systems, designers and design dates. Second, theaccuracy of the shape description based on text is poor. Thus, in the last decade,content-based CAD model search has received extensive attention in the academiccommunity.
This dissertation mainly studies the CAD model retrieval methods for mechanicalproduct design, which includes the following aspects:
(1) A CAD model retrieval method based on inexact graph matching is presented inorder to resolve the problem that the exact graph matching is unable to support the similarmodel retrieval. First, a representation of face attributed relational graph (ARG) for eachCAD model is extracted from its B-Rep model. Then, the vertex compatibility matrix andedge compatibility matrix between the ARGs of the target and searched model arecalculated, and the measure of the two model’s similarity is created from the compatibilitymatrices, which serves as the objective function for optimally selecting vertex mappingmatrix M between the two models. At last, the optimal vertex mapping matrix M is foundusing Lagrange multiplier method for the optimization problem after relaxing itsinequality constraints to be equal.
(2) Based on the gradient flows in Lie group, a partial retrieval approach for CAD models is presented. First, a representation of the face ARG for a CAD model is createdfrom its B-rep model and thus partial retrieval is converted to a subgraph matchingproblem. Then, an optimization method is adopted to solve the matching problem, wherethe optimization variable is the vertex mapping and the objective function is themeasurement of compatibility between the mapped vertices and between the mappededges. Different from most previously proposed methods, a homogeneous transformationmatrix is introduced to represent the vertex mapping in subgraph matching, whosetranslational sub-matrix gives the vertex selection in the larger graph and whoseorthogonal sub-matrix presents the vertex permutation for the same-sized mapping fromthe selected vertices to the smaller graph’s vertices. Finally, a gradient flow method isdeveloped to search for the optimal matching matrix in Special Euclidean group SE(n).
(3) A CAD model retrieval method based on B-rep decomposition is presented. First,according to the salient geometric features of the mechanical part, the surface boundary ofa solid model is divided into local convex, concave and planar regions with the minimalnumber. Then, we give a kind of region codes that describe the surface region and theirlinks in CAD model. At last, the similarity between two models is measured by thecomparison of their region codes. The retrieval for CAD model can be applied to theglobal and partial search.
(4) A similarity evaluation for assembly model based on component attributedrelational graph (CARG) is presented. First, assembly models are created from CADsystems. The information of constitute parts, excluding for connection and transmissionparts, and the complex relationships between them in an assembly are extractedautomatically or manually; meanwhile, assembly model is described as CARG. Then, thepart compatibility matrix between two assemblies are calculated, which serve as themeasure of their similarity. Finally, the optimal matching under the measures is calculatedusing Kuhn-Munkres algorithm.
Based on the methodologies mentioned above, a3D retrieval system is developedusing Visual C++6.0, geometry engine ACIS and display engine HOOPS. The systemsupports the inexact retrieval, the exact partial retrieval, globe and local retrieval for CADmodel. Meanwhile, some experimental results show their correctness and effectiveness.
引文
[1] Regli WC, Cicirelll VA. Managing digital libraries for computer aided design.Compute-Aided Design,2000,32(2):119–132.
[2] William CR, Michela S. Introduction to shape similarity detection and search forCAD/CAE applications. Computer-Aided Design,2006,38(1):937–938.
[3] Ullman DG. The Mechanical Design Process. McGraw-Hill, New York,1997.
[4] Gunn TG. The mechanization of design and manufacturing. Sci Am1982,247(3):86–108.
[5] Leizerowicz W, Lin J, Fox MS. Collaborative designs using. Proceedings of theWET-ICE’96, CERC, University of West Virginia1996.
[6] Vrnaic D, Suape D. A feature vector approach for retrieval of3D objects in theContext of MPEG-7. In: Proceedings of the International Conference onAugmented. Virtual Environments and Three-Dimensional Imaging (ICAV3D2001).Mykonos, Greece,2001:37–40.
[7] Wang J, He Y, Tian H, Cai H. Retrieving3D CAD model by freehand sketches fordesign reuse. Advanced Engineering Informatics,2008,22(3):385–392.
[8] Li M, Zhang YF, Fuh JYH, et al. Toward effective mechanical design reuse: CADmodel retrieval based on general and partial shapes. Journal of Mechanical Design,2009,131(12):124501-1~124501-8.
[9] Bosche F, Haas CT. Automated retrieval of3D CAD model objects in constructionrange images. Automation in Construction,2008,17(4):499–512.
[10] Pu J, Lou K and Karthik R. A2D sketch-based user interface for3D CAD modelretrieval. Computer-Aided Design&Applications,2005,2(6):717–725.
[11]陶松桥,王书亭,郑坛光,黄正东.基于非精确图匹配的CAD模型搜索方法.计算机辅助设计与图形学学报，2010,22(3):545–552.
[12] Vrnaic D, Suape D. A feature vector approach for retrieval of3D objects in theContext of MPEG-7. In: Proceedings of the International Conference onAugmented. Virtual Environments and Three-Dimensional Imaging (ICAV3D2001).Mykonos, Greece,2001:37–40.
[13] Tangelder JWH, Veltkamp RC. A survey of content based3D shape retrievalmethods. Multimedia Tools and Applications,2008,39(3):441–471.
[14] AIM@SHAPE shape repository. http://shapes.aim-at-shape.net.
[15]3D model similarity search engine. http://merkur01.inf.uni-konstanz.de/CCCC.
[16]3D model search engine. http://shape.cs.princeton.edu.
[17] Paquet E and Rioux M. Nefertiti: A query by content software forthree-dimensional models databases management.3dim,1997.
[18] Paquet E, Rioux M, Murching A, Naveen T, and Tabatabai A. Description of shapeinformation for2-d and3-d objects. Signal Processing: Image Communication,2000,16(9):103–122.
[19] Koenderink JJ, Doorn AJ. Surface shape and curvature scales. Image and visioncomputing,1992,10(8):557–565.
[20] Vandeborre JP, Couillet V, and Daoudi M. A practical approach for3D modelindexing by combining local and global invariants. In1st IEEE InternationalSymposium on3D Data Processing Visualization Transmission (3DPVT’02),Padova, Italy, June,2002:19–21.
[21] Zaharia T and Preteux F.3D shape-based retrieval within the MPEG-7framework.In SPIE Conf. on Nonlinear Image Processing and Pattern Analysis XII, January2001,4304:133–145.
[22] Berchtold S, Keim DA, Kriegel HP. Section Coding: Ein Verfahren zur Ahnlichkeitssuche in CAD-Datenbanken (Section Coding: a Technique for SimilaritySearch in CAD Databases) In: Proceedings7GI-Fachtagung Datenbanksysteme inBuro, Technik und Wissenschaft, Ulm Germany1997:152–71.
[23] Ankerst M, Kastenmulle G, Kriegel HP, et al.3D Shape Histograms for SimilaritySearch and Classification in Spatial Databases. In: Proceeding of6th InternationalSymposium on Advances in Spatial Databases (SSD).Hong Kong, China,1999:207–228.
[24] Ankerst M, Kastenmuller G, Kriegel HP, Seidl T.3D shape histograms forsimilarity search and classification in spatial databases. Lecture Notes in ComputerScience. Berlin: Springer,1999,1651:207–226.
[25] Osada R, Funkhouser T, Chazelle B, et al. Shape distributions.ACM Transactionson Graphics,2002,21(4):807–832.
[26] Ohbuchi R, Minamitani T, Takei T. Shape similarity search of3D models by usingenhanced shape functions. Proceedings of Theory and Practice in ComputerGraphics2003, Birmingham, UK2003.
[27] Ip CY, Lapadat D, Sieger L, Regli WC. Using shape distributions to compare solidmodels. Proceedings of ACM Symposium on Solid Modeling and Applications,2002:273–280.
[28] Cardone A, Gupta SK, Karnik M. A Survey of Shape Similarity AssessmentAlgorithms for Product Design and Manufacturing Applications. Journal ofComputing and Information Science in Engineering,2003,3(6),109–118.
[29] Belongie S, Malik J, Puzicha J. Shape matching and object recognition using shapecontexts. IEEE Trans Pattern Anal Mach Intell,2002,24(4):509–22.
[30] Ko¨rtgen M, Park GJ, Novotni M, Klein R.3D shape matching with3D shapecontexts. In: Proceedings of the Seventh Central European Seminar on ComputerGraphics, Budmerice, and Slovakia2003.
[31] Horn BKP. Extended Gaussian images. Proc IEEE,1984,72(12):1671–1686.
[32] Xu JZ, Sku M, Ranka S. Hierarchical EGI: a new method for object representation.3rd International Conference on Signal Processing, Beijing, China,2,1996:926–929.
[33] Riehard CW, Hemmai H. Identification of three-dimensional objects using Fourierdescriptors of the boundary curve. IEEE Transactions on Systems Man andCybernetics,1974,4(4):371–378.
[34] Pauly M, Gross M. Spectral processing of point-sampled geometry. In:SIGGRAPH’01,2001:379–386.
[35] Vranic DV, SauPe D.3D Shape Descriptor Based on3D Fourier Transform. InProceedings of the EURASPI Con. on Digital Signal Processing of MultimediaCommunications and Services，September2001:271–274.
[36] Miroslaw Bober. Mpeg-7visual shape descriptors. IEEE Transactions on Circuitsand Systems for Video Technology,2001,11(6):716–719.
[37] Rieard J, Coeurjolly D and Baskurt A. ART extension for description, indexing andretrieval of3D objects. International Conference on Pattern Recognition,2004:23–26.
[38] Vranic D, Saupe D, Richter J. Tools for3D object retrieval: Karhunen–Loevetransform and spherical harmonics. Proceedings of the IEEE2001Workshop onMultimedia Signal Processing2001,2001:293–298.
[39] Saupe D, Vranic D.3D model retrieval with spherical harmonics and moments.Proceedings of the DAGM2001, Munich, Germany,2001:392–397.
[40] Kazhdan M, Funkhouser T. Harmonic3D shape matching. SIGGRAPH2002Technical Sketches2002:191–196.
[41] Kazhdan M, Funkhouser T, Rusinkiewicz S. Rotation invariant spherical harmonicrepresentation of3D shape descriptors. In: Proceedings of the ACM/Euro graphicsSymposium on Geometry Processing,2003:167–175.
[42] Papadakisa P, Pratikakisa I, Perantonisa S, Theoharis T. Efficient3D shapematching and retrieval using a concrete radicalized spherical projectionrepresentation. Pattern Recognition,2007,40(9):2437–2452.
[43]辛谷雨,查红彬.一种基于旋转不变量的三维形状描述子.北京大学学报(自然科学版)，2007,43(3):428–433.
[44]刘玉杰,李宗民,李华.用于3D模型检索的扩展距离球面调和表达.计算机辅助设计与图形学学报,2006,15(11):1671–1676.
[45]章志勇,杨柏林.一种基于球面调和描述子的3D模型相似性比较算法.中国图像图形学报,2007,12(3):541–555.
[46]章志勇,杨柏林.球面调和描述子在图像形状匹配中的应用.自动化学报,2007,33(7):683–687.
[47] Novotni M, Klein R. Shape retrieval using3D Zernike descriptors.Computer-Aided Design,2004,36(11):1047–1062.
[48] Gain J, Seott J. Fast polygon mesh querying by example. International Conf onComputer Graphics and Interactive Techniques (SIGGRAPH99)， California,United States,1999,241–247.
[49] Pastor L, Rodrmguez A, Espadero JM, Rincon L.3D wavelet-based multiresolutionobject representation. Pattern Recognition,2001,34(12):2497–2513.
[50] Schroder P, Sweldens W. Spherical Wavelets: Efficiently representing functions onthe sphere. Proceedings of the22ndAnnual ACM Conference on computer Graphicsand iterative Techniques,1995,161–172.
[51] Laga H, Takahashi H. Spherical wavelet descriptors for content-based3D modelretrieval. Proceedings of IEEE International Conference on Shape Modeling andApplications, SMI2006,2006:15–15.
[52] Laga H, Nakajima M. Statistical spherical wavelet moments for content-based3Dmodel Retrieval. In the Computer Graphics International (CGI2007),2007,47–54.
[53] Nain D, Haker S, Bobiek A, et al. Multi-scale3D shape representation andsegmentation using spherical wavelets. Proceedings of IEEE Transactions onMedical Imaging,2007,26(4):598–618.
[54] Daras P, Axenopoulos A. A3D shape retrieval framework supporting multimodalqueries. Int J Comput Vis,2010,89:229–247.
[55] Mahmoudi S, Daoudi M.3D models retrieval by using characteristic views.Processing of16thinternational conference on pattern recognition,2002:457-460.
[56] Funkhouser T, Min P, Kazhdan M, et al. A search engine for3D models. ACMTransactions on graphics,2003,22(l):83–105.
[57] Super BJ, Lu H. Evaluation of a hypothesizer for silhouette-based3-D objectrecognition. Pattern Recognition,2003,36(1):69–78.
[58] Chen DY, Tian XP, Shen YT, Ouhyoung M. On visual similarity based3D modelretrieval. Comput. Graphics Forum,2003,22(3):223–232.
[59] Shih JL, Lee CH, Wang JT. A new3D model retrieval approach based on theelevation descriptor. Pattern Recognition,2007,40(1):283–295.
[60] Ohbuchi R, Osada K, Furuya T, Banno T. Salient local visual features for shapebased3d model retrieval. In: Proceedings of IEEE Conference on Shape Modelingand Applications,2008, pp.1–10.
[61] Lowe D. Distinctive image features from scale-invariant key points. InternationalJournal of Computer Vision,2004,60(2):91–110.
[62] Gao Y, Yang Y, Dai Q, Zhang N.3d object retrieval with bag-of-region-words. In:Proceedings of ACM Conference on Multimedia,2010.
[63] Culver T, Keyser J, Manoeha D. Accurate computation of the medial axis of aPolyhedron. Proceeding of the Symposium on Solid Modeling and Applications,1999:179–190.
[64] Sherbrooke EC, Patrikalakis NM, Brisson E. An algorithm for the medial axistransform of3D polyhedral solids. IEEE Trans. Visualization and ComputerGraphics,1996,2(l):44–61.
[65] Borgefors G, Nystrom I, Gabriella Sanniti di Baja. Surface skeletonization ofvolume objects. Proceedings of SSPR,96: Advances in Structural and SyntacticalPattern Recognition,1996:251–259.
[66] Foskey M, Lin MC, Manocha D. Efficient computation of a simplified medial axis.Proceedings of the symposium on Solid modeling and applications,2003:96–107.
[67] Hilaga M, Shinagawa Y, Kohmura T, Kunii T. Topology matching for fullyautomatic similarity estimation of3d shapes. In: Proceedings of ACM SIGGRAPH,Los Angeles, USA,2001:203–212.
[68] Chen DY, Ouhyoung M. A3D Object Retrieval System Based on Multi-ResolutionReeb Graph. Proceedings of Computer Graphics Workshop, Taiwan, June2002:16–20.
[69] Bespalov D, Regli WC, Shokoufandeh A. Reeb graph-based shape retrieval forCAD. Proceedings of the ASME DETC03Computers and Information inEngineering (CIE) Conference, Chicago, IL2003.
[70] Tung T, Schmitt F. Augmented reeb graphs for content-based retrieval of3D meshmodels. In: Proc. shape modeling international2004:157–166.
[71] Sundar H, Silver D, Gagvani N, Dickenson S. Skeleton based shape matching andretrieval. In: Proc. shape modeling international2004:130–139.
[72] Gagvani N, Silver D. Parameter controlled volume thinning. Graph Models ImageProcess1999,61(3):149–164.
[73] Iyer N, Kalyanaraman Y, Lou K, Jayanti S, Ramani K. A reconfigurable3Dengineering shape search system Part I: shape representation. Proceedings ofASME DETC03Computers and Information in Engineering (CIE) Conference,Chicago, IL2003.
[74] Lou K, Jayanti S, Iyer N, Kalyanaraman Y, Ramani K, Prabhakar S. Areconfigurable3D engineering shape search system. Part II: database indexing,retrieval and clustering. Proceedings of ASME DETC03Computers andInformation in Engineering (CIE) Conference, Chicago, IL2003.
[75] Kim D, Yun D, Lee S. Graph representation by medial axis transformation for3Dimage retrieval. Proceedings of SPIE, San Jose, CA,2001,4298:223–230.
[76] Nagasaka Y, Nakamura M, Murakami T. Extracting and learning geometric featuresbased on a voxel based mapping method for manufacturing design. Proc IPPM2001,2001:1–10.
[77] Gao W, Gao SM and Liu YS.3D CAD model similarity assessment and retrievalusing DBS. Proceeding of ASME DETC2005Computers and Information inEngineering (CIE) Conference,2005.
[78] Ogniewicz RL, Kubler O. Hierarchical voronoi skeletons. Pattern Recognition,1995,28(3):343–359.
[79] Sun TL, Su CJ, Mayer RJ, Wysk RA. Shape similarity assessment of mechanicalparts based on solid models. In: Gadh R, editor.ASME Design for ManufacturingConference, Symposium on Computer Integrated Concurrent Design, ASME,Boston, MA, September17–21,1995:953–62.
[80] El-Mehalawi M, Miller R. A database system of mechanical components based ongeometric and topological similarity. Part I: representation. Computer-Aided Des2003;35:83–94.
[81]马露杰,黄正东,吴青松.基于面形位编码的CAD模型检索.计算机辅助设计与图形学学报,2008,20(1):19–25.
[82] Cicirello V, Regli WC. Machining feature-based comparisons of mechanical parts.ACM International Conference on Shape Modeling and Applications, Genova, Italy2001:176–85.
[83] Cicirello V. Intelligent retrieval of solid models. Drexel University, Philadelphia,1999.
[84] Cicirello V, Regli WC. Resolving non-uniqueness in design feature histories. In:Proceedings of the Fifth ACM Symposium on Solid Modeling and Applications,New York.
[85] Chu CH, and Hsu YC. Similarity Assessment of3D Mechanical Components forDesign Reuse. Robot. Robotics and Computer-Integrated Manufacturing,2006,22(4):332–341.
[86] Li M, Zhang YF, Fuh JYH, et al. Retrieving Reusable3D CAD Models UsingKnowledge-Driven Dependency Graph Partitioning. Computer-Aided Design&Applications,2010,7(3):417–430
[87] Ramesh M, Yip-Hoi D, Dutta D. Feature based shape similarity measurement formechanical parts. ASME Journal Compute Information Science,2001,1(3):245–56.
[88] Cardone A, Gupta SK, Deshmukh A. Machining feature-based similarityassessment algorithms for prismatic machined parts. Computer-Aided Design,2006,38(9):954–972.
[89] Cardone A, Gupta SK, Deshmukh A. Identifying similar parts for assisting costestimation of prismatic machined parts. Proceedings of ASME: Design EngineeringTechnical Conference2004October2,2004, Salt Lake City.
[90] Hoffman, DD, Singh M. Salience of visual parts. In Cognition,1997,63(1).29–78.
[91] Gal R, Cohen-Or D. Salient Geometric Features for Partial Shape Matching andSimilarity. ACM Transactions on Graphics,2006,25(1):130–150.
[92] Hu J, Hua J. Salient spectral geometric features for shape matching and retrieval.The Visual Computer,2009,25(5-7):667–675.
[93] Bai J, Gao S, Tang W, et al. Design reuse oriented partial retrieval of CAD model.Computer-Aided Design,2010,42(12):1069–1084.
[94]白静.面向设计重用的三维CAD模型检索.浙江大学博士论文,2009.
[95] Kim YS, Jung YH, Kang BG. Feature-Based Part Similarity Assessment MethodUsing Convex Decomposition. In Proc. of ASME DETC2003Computers andInformation in Engineering (CIE),2003, Chicago, Illinois, United States．
[96] Bespalov D, Regli WC, Shokoufandeha A. Local feature extraction and matchingpartial objects. Computer-Aided Design,2006,38(9):1020–1037.
[97] Suzuki MT, Yaginuma Y., and Shimizu Y. A partial shape matching technique for3d model retrieval systems. In ACM SIGGRAPH2005Posters, page128, NewYork, NY, USA,2005, ACM Press.
[98] Suzuki MT, Yaginuma Y, and Shimizu Y. A3dmodel retrieval based oncombinations of partial shape descriptors. In Proceedings of IEEE North AmericanFuzzy Information Processing Society Annual Conference (NAFIPS2006),Montreal, Canada, June2006:273–278.
[99] Katz S, Tal A. Hierarchical mesh decomposition using fuzzy clustering and cuts.ACM Transactions on Graphics (TOG),2003,22(3):954–961.
[100] Mademlis A, Daras P, Axenopoulos A, Tzovaras D, and Strintzis MG. Combiningtopological and geometrical features for global and partial3-D shape retrieval.IEEE Transactions on Multimedia,2008,10(5):819–831.
[101]徐敬华,张树有.基于递归分割的机械零件三维形状结构检索方法.机械工程学报,2009,45(11),186–183.
[102] Schreck T, Bustos B, Walter M. A query-by-example concept and user interface forglobal and partial3D object retrieval. Eurographics Workshop on3D ObjectRetrieval (2009).
[103] Ferreira A, Marini S, Attene M, et al. Thesaurus-based3D object retrieval withpart-in-whole matching. International Journal of Computer Vision,2010,89:327–347.
[104] Philipp-Foliguet S, Jordan M, Najman L, Cousty J. Artwork3D model databaseindexing and classification. Pattern Recognition,2011,44(3):588–597.
[105] Iyer S and Nagi R. Automated retrieval and ranking of similar parts in agilemanufacturing. IEEE Transactions,1997,29:859–876．
[106] Srinivas G, Fasse ED, and Marefat MM. Retrieval of similarly shaped parts from aCAD database. IEEE International Conference on1998,2809–2814．
[107] Tsai Chieh-Yuan and Chang CA. A two-stage fuzzy approach to feature-baseddesign retrieval. Computers in Industry,2005,56(5):493–505．
[108] Zhang R, Zhou X. Similarity Assessment of Mechanical Parts Based on IntegratedProduct Information Model. Journal of Computing and Information Science inEngineering,2011,11(3):011001-1–011001-12.
[109] Mehlhorn K. Graph Algorithms and NP-completeness. Springer-Verlag New York,Inc., New York, NY, USA,1984.
[110] Ullmann JR. An algorithm for subgraph isomorphism. Journal of the Associationfor Computing Machinery,1976,23(1):31–42.
[111] Cordella LP, Foggia P, Sansone C and Vento M. Fast graph matching for detectingCAD image components. In Proc.15th Int. Conf. Pattern Recognition,2000:1034–1037.
[112] Cordella LP, Foggia P, Sansone C and Vento M. An improved algorithm formatching large graphs. In Proc.3rd IAPR-TC15Workshop Graph-BasedRepresentations in Pattern Recognition,2001,149–159.
[113] Bunke H and Messmer BT. Recent advances in graph matching. Journal of PatternRecognition and Art. Intelligence,1997,11(1):169–203.
[114] Messmer BT, Bunke H. A decision tree approach to graph and subgraphisomorphism detection. Pattern Recognition,1999,32(12):1979–1998.
[115] Lazarescu M, Bunke H and Venkatesh S. Graph matching: fast candidateelimination using machine learning techniques. In Proc. Joint IAPR Int. WorkshopsSSPR and SPR,2000:236–245.
[116] Irniger C and Bunke H. Graph matching: filtering large databases of graphs usingdecision trees. In Proc.3rd IAPR-TC15Workshop Graph-Based Representations inPattern Recognition,2001:239–249.
[117] Berretti S, Bimbo AD and Vicario E. A look-ahead strategy for graph matching inretrieval by spatial arrangement. Int. Conf. Multimedia and Expo,2000:1721–1724.
[118] Berretti S, Bimbo AD and Vicario E. The computational aspect of retrieval byspatial arrangement. In Proc.15th Int. Conf. Pattern Recognition,2000:1047-1051.
[119] Berretti S, Bimbo AD and Vicario E. Efficient matching and indexing of graphmodels in content-based retrieval. IEEE Trans. Pattern Anal. Machine Intelligence.2001,23(10):1089–1105.
[120] Christmas MWJ, Kittler J. Structural matching in computer vision usingprobabilistic relaxation. IEEE Trans. Pattern Anal. Machine Intelligence,1995,17(8):749–764.
[121] Finch EH, Wilson RC. Matching Delaunay graphs. Pattern Recognition,1997,30(1):123–140.
[122] Gold S, Rangarajan A. A graduated assignment for graph matching. IEEE Trans.Pattern Anal. Machine Intellence,1996,18(4):377–388.
[123] Wilson R, Hancock E. A bayesian compatibility model for graph matching. PatternRecognition Letter,1996,17:263–276.
[124] Kuner P., Ueberreiter B. Pattern recognition by graph matching: Combinatorialversus continuous optimization. Internat. J. Pattern Recognition Artif. Intell.,1988,2(3):527–542.
[125] Suganthan DMPN, Teoh EK. Pattern recognition by graph matching using the pottsmft neural networks. Pattern Recognition,1995,28(7):997–1009.
[126] Suganthan DMPN, Teoh EK. Pattern recognition by homomorphic graph matchingusing hopfield neural networks. Image Vision Computer,1995,13(1):45–60.
[127] Cross EH ADJ, Wilson RC. Inexact graph matching using genetic search. PatternRecognition,1997,30(6):953–970.
[128] Ford GP, Zhang J. Structural graph-matching approach to image understanding.Intell. Robots Comput. Vision X: Algorithms Technique,1992,1607(1):559–569.
[129] Jiang X, Münger A, Bunke H. Synthesis of representative graphical symbols bycomputing generalized median graph. In: Chhabra, A.K., Dori, D.,(Eds.), GraphicsRecognition: Recent Advances,2000:183–192.
[130] Umeyama S. An Eigen decomposition approach to weighted graph matchingproblem. IEEE Transaction on Pattern Analysis and Machine Intelligence,1988,10(5):695–703.
[131] Xu L and King I. A PCA approach for fast retrieval of structural patterns inattributed graphs. IEEE Trans. Syst. Man Cybern.,2001, B31:812–817.
[132] Kosinov S and Caelli T. Inexact multisubgraph matching using graph eigenspaceand clustering models. In Proc. Joint IAPR Int. Workshops SSPR and SPR,2002:133–142.
[133] Snead CS. Group Technology: Foundations for Competitive Manufacturing. NewYork: Van Nostrand Reinhold,1989.
[134] IP CY. Automatic classification of CAD models. Drexel University,2005.
[135] Vapnik VN. Statistical learning theory. New York: Wiley,1998.
[136] Nilesh V Patel and Ishwar KS. Video shot detection and characterization for videodatabases. Pattern Recognition,1997,30(4):583–592.
[137] Jones S, Van Rijsbergen CJ. Information retrieval test collections. Journal ofDocumentation,1976,32:59–75.
[138] Shilane P, Min P, Kazhdan M, Funkhouser T. The Princeton shape benchmark.Proceedings of the Shape Modeling International,2004,167–178.
[139] Iyer N, Jayanti S, Lou K, Kalyanaraman Y, Ramani K. Developing an engineeringshape benchmark for cad models. Computer-Aided Design,2006,38(9):939–953.
[140] http://www.designrepository.org/datasets/.
[141]张旭堂,刘文剑.基于二分图的装配体检索研究.计算机辅助设计与图形学学报,2005,17(9):2106–2111.
[142]周炜,郑建荣,颜建军.基于子图同构与事例匹配的装配体局部结构相似性分析.计算机辅助设计与图形学学报,2010,22(2):299–305.
[143] Abhijit SD, Ashis GB, Satyandra KG, et al. Content-based assembly search: A steptowards assembly reuse. Computer-Aided Design,2008,40(2):244–261.
[144]董雁,徐静.基于装配结构相似的零件三维模型检索方法.机械工程学报,2009,45(4):273–280.
[145]唐韦华,基于高效图匹配的三维CAD模型相似评价.浙江大学硕士论文,2010.
[146] Chen X, Guo S, Bai J, Gao S. Assembly retrieval in top-down product Design.2010Asian Conference on Design&Digital Engineering,2010, Jeju Republic ofKorea:39–52.
[147] Gold S, Rangarajan A. A graduated assignment algorithm for graph matching.IEEE Transactions on Pattern Analysis and Machine Intelligence,1996,18(4):377–388.
[148] Gold S, Rangarajan A. Graph Matching by Graduated Assignment. In Proc. ofCVPR’96, San Francisco, CA,1996,239–244.
[149] Rangarajan A, Yuille A, and Mjolsness E. Conver-gence properties of thesoftassign quadratic assignment algorithm. Neural Computation,1999,11:1455–1474.
[150] Ullmann JR. An algorithm for subgraph isomorphism. Journal of the Associationfor Compu tin g Machinery,1976,23(1):31–42.
[151] Zavlanos MM, Pappas GJ. A dynamical systems approach to weighted graphmatching. Automatica,2008,44(11):2817–2824.
[152] Munthe KH. Runge-Kutta methods on lie group. BIT,1998,38:92–111.
[153] Gallier J, Xu D. Computing exponentials of skew-symmetric matrices andlogarithms of orthogonal matrices. International Journal of Robotics andAutomation,2003,18(1):10–20.
[154] Buono ND, Lopez L, Peluso R. Computation of the exponential of large sparseskew-symmetric matrices. SIAM J. Sci. Comput.,2005,27(1):278–293.
[155] Bespalov D, Regli WC, Shokoufandeha A. Local feature extraction and matchingpartial objects. Computer-Aided Design,2006,38(9):1020–1037.
[156]马露杰,黄正东,梁良,郑坛光. CAD模型表面区域分割方法[J].计算机辅助设计与图形学学报,2009,21(2):148–153
[157]马露杰.三维CAD模型形状结构分析方法.华中科技大学博士论文,2009.
[158] Biederman I. Recognition by Components: A Theory of Human ImageUnderstanding. Psychological Review,1987,94(2):115–147.
[159] Biederman H. Visual Object Recognition. In An Invitation to Cognitive Science,Visual Cognition. S. Kosslyn, D. Osherson, Eds. MIT Press,1995,2:121–65.
[160]孙晓鹏,李华.三维网格模型的分割及应用综述.计算机辅助设计与图形学学报,2005,17(8):1647–1655).
[161] Philip R K. ISO TC184/SC4: Product Data Representation and Exchange, Part:44,Title: Industrial Automation Systems and Integration Product Data Representationand Exchange–Integrated Generic Resources: Product Structure Configuration(November1994), ISO,1994.
[162] Sugimura N and Ohtaka A. ISO TC184/SC4/WG12N597, JNC Proposal of STEPAssembly Model for Products (June2000), ISO,2000.
[163]孙惠泉.图论及其应用.北京:科学出版社,2004:89–92.
[2] William CR, Michela S. Introduction to shape similarity detection and search forCAD/CAE applications. Computer-Aided Design,2006,38(1):937–938.
[3] Ullman DG. The Mechanical Design Process. McGraw-Hill, New York,1997.
[4] Gunn TG. The mechanization of design and manufacturing. Sci Am1982,247(3):86–108.
[5] Leizerowicz W, Lin J, Fox MS. Collaborative designs using. Proceedings of theWET-ICE’96, CERC, University of West Virginia1996.
[6] Vrnaic D, Suape D. A feature vector approach for retrieval of3D objects in theContext of MPEG-7. In: Proceedings of the International Conference onAugmented. Virtual Environments and Three-Dimensional Imaging (ICAV3D2001).Mykonos, Greece,2001:37–40.
[7] Wang J, He Y, Tian H, Cai H. Retrieving3D CAD model by freehand sketches fordesign reuse. Advanced Engineering Informatics,2008,22(3):385–392.
[8] Li M, Zhang YF, Fuh JYH, et al. Toward effective mechanical design reuse: CADmodel retrieval based on general and partial shapes. Journal of Mechanical Design,2009,131(12):124501-1~124501-8.
[9] Bosche F, Haas CT. Automated retrieval of3D CAD model objects in constructionrange images. Automation in Construction,2008,17(4):499–512.
[10] Pu J, Lou K and Karthik R. A2D sketch-based user interface for3D CAD modelretrieval. Computer-Aided Design&Applications,2005,2(6):717–725.
[11]陶松桥,王书亭,郑坛光,黄正东.基于非精确图匹配的CAD模型搜索方法.计算机辅助设计与图形学学报，2010,22(3):545–552.
[12] Vrnaic D, Suape D. A feature vector approach for retrieval of3D objects in theContext of MPEG-7. In: Proceedings of the International Conference onAugmented. Virtual Environments and Three-Dimensional Imaging (ICAV3D2001).Mykonos, Greece,2001:37–40.
[13] Tangelder JWH, Veltkamp RC. A survey of content based3D shape retrievalmethods. Multimedia Tools and Applications,2008,39(3):441–471.
[14] AIM@SHAPE shape repository. http://shapes.aim-at-shape.net.
[15]3D model similarity search engine. http://merkur01.inf.uni-konstanz.de/CCCC.
[16]3D model search engine. http://shape.cs.princeton.edu.
[17] Paquet E and Rioux M. Nefertiti: A query by content software forthree-dimensional models databases management.3dim,1997.
[18] Paquet E, Rioux M, Murching A, Naveen T, and Tabatabai A. Description of shapeinformation for2-d and3-d objects. Signal Processing: Image Communication,2000,16(9):103–122.
[19] Koenderink JJ, Doorn AJ. Surface shape and curvature scales. Image and visioncomputing,1992,10(8):557–565.
[20] Vandeborre JP, Couillet V, and Daoudi M. A practical approach for3D modelindexing by combining local and global invariants. In1st IEEE InternationalSymposium on3D Data Processing Visualization Transmission (3DPVT’02),Padova, Italy, June,2002:19–21.
[21] Zaharia T and Preteux F.3D shape-based retrieval within the MPEG-7framework.In SPIE Conf. on Nonlinear Image Processing and Pattern Analysis XII, January2001,4304:133–145.
[22] Berchtold S, Keim DA, Kriegel HP. Section Coding: Ein Verfahren zur Ahnlichkeitssuche in CAD-Datenbanken (Section Coding: a Technique for SimilaritySearch in CAD Databases) In: Proceedings7GI-Fachtagung Datenbanksysteme inBuro, Technik und Wissenschaft, Ulm Germany1997:152–71.
[23] Ankerst M, Kastenmulle G, Kriegel HP, et al.3D Shape Histograms for SimilaritySearch and Classification in Spatial Databases. In: Proceeding of6th InternationalSymposium on Advances in Spatial Databases (SSD).Hong Kong, China,1999:207–228.
[24] Ankerst M, Kastenmuller G, Kriegel HP, Seidl T.3D shape histograms forsimilarity search and classification in spatial databases. Lecture Notes in ComputerScience. Berlin: Springer,1999,1651:207–226.
[25] Osada R, Funkhouser T, Chazelle B, et al. Shape distributions.ACM Transactionson Graphics,2002,21(4):807–832.
[26] Ohbuchi R, Minamitani T, Takei T. Shape similarity search of3D models by usingenhanced shape functions. Proceedings of Theory and Practice in ComputerGraphics2003, Birmingham, UK2003.
[27] Ip CY, Lapadat D, Sieger L, Regli WC. Using shape distributions to compare solidmodels. Proceedings of ACM Symposium on Solid Modeling and Applications,2002:273–280.
[28] Cardone A, Gupta SK, Karnik M. A Survey of Shape Similarity AssessmentAlgorithms for Product Design and Manufacturing Applications. Journal ofComputing and Information Science in Engineering,2003,3(6),109–118.
[29] Belongie S, Malik J, Puzicha J. Shape matching and object recognition using shapecontexts. IEEE Trans Pattern Anal Mach Intell,2002,24(4):509–22.
[30] Ko¨rtgen M, Park GJ, Novotni M, Klein R.3D shape matching with3D shapecontexts. In: Proceedings of the Seventh Central European Seminar on ComputerGraphics, Budmerice, and Slovakia2003.
[31] Horn BKP. Extended Gaussian images. Proc IEEE,1984,72(12):1671–1686.
[32] Xu JZ, Sku M, Ranka S. Hierarchical EGI: a new method for object representation.3rd International Conference on Signal Processing, Beijing, China,2,1996:926–929.
[33] Riehard CW, Hemmai H. Identification of three-dimensional objects using Fourierdescriptors of the boundary curve. IEEE Transactions on Systems Man andCybernetics,1974,4(4):371–378.
[34] Pauly M, Gross M. Spectral processing of point-sampled geometry. In:SIGGRAPH’01,2001:379–386.
[35] Vranic DV, SauPe D.3D Shape Descriptor Based on3D Fourier Transform. InProceedings of the EURASPI Con. on Digital Signal Processing of MultimediaCommunications and Services，September2001:271–274.
[36] Miroslaw Bober. Mpeg-7visual shape descriptors. IEEE Transactions on Circuitsand Systems for Video Technology,2001,11(6):716–719.
[37] Rieard J, Coeurjolly D and Baskurt A. ART extension for description, indexing andretrieval of3D objects. International Conference on Pattern Recognition,2004:23–26.
[38] Vranic D, Saupe D, Richter J. Tools for3D object retrieval: Karhunen–Loevetransform and spherical harmonics. Proceedings of the IEEE2001Workshop onMultimedia Signal Processing2001,2001:293–298.
[39] Saupe D, Vranic D.3D model retrieval with spherical harmonics and moments.Proceedings of the DAGM2001, Munich, Germany,2001:392–397.
[40] Kazhdan M, Funkhouser T. Harmonic3D shape matching. SIGGRAPH2002Technical Sketches2002:191–196.
[41] Kazhdan M, Funkhouser T, Rusinkiewicz S. Rotation invariant spherical harmonicrepresentation of3D shape descriptors. In: Proceedings of the ACM/Euro graphicsSymposium on Geometry Processing,2003:167–175.
[42] Papadakisa P, Pratikakisa I, Perantonisa S, Theoharis T. Efficient3D shapematching and retrieval using a concrete radicalized spherical projectionrepresentation. Pattern Recognition,2007,40(9):2437–2452.
[43]辛谷雨,查红彬.一种基于旋转不变量的三维形状描述子.北京大学学报(自然科学版)，2007,43(3):428–433.
[44]刘玉杰,李宗民,李华.用于3D模型检索的扩展距离球面调和表达.计算机辅助设计与图形学学报,2006,15(11):1671–1676.
[45]章志勇,杨柏林.一种基于球面调和描述子的3D模型相似性比较算法.中国图像图形学报,2007,12(3):541–555.
[46]章志勇,杨柏林.球面调和描述子在图像形状匹配中的应用.自动化学报,2007,33(7):683–687.
[47] Novotni M, Klein R. Shape retrieval using3D Zernike descriptors.Computer-Aided Design,2004,36(11):1047–1062.
[48] Gain J, Seott J. Fast polygon mesh querying by example. International Conf onComputer Graphics and Interactive Techniques (SIGGRAPH99)， California,United States,1999,241–247.
[49] Pastor L, Rodrmguez A, Espadero JM, Rincon L.3D wavelet-based multiresolutionobject representation. Pattern Recognition,2001,34(12):2497–2513.
[50] Schroder P, Sweldens W. Spherical Wavelets: Efficiently representing functions onthe sphere. Proceedings of the22ndAnnual ACM Conference on computer Graphicsand iterative Techniques,1995,161–172.
[51] Laga H, Takahashi H. Spherical wavelet descriptors for content-based3D modelretrieval. Proceedings of IEEE International Conference on Shape Modeling andApplications, SMI2006,2006:15–15.
[52] Laga H, Nakajima M. Statistical spherical wavelet moments for content-based3Dmodel Retrieval. In the Computer Graphics International (CGI2007),2007,47–54.
[53] Nain D, Haker S, Bobiek A, et al. Multi-scale3D shape representation andsegmentation using spherical wavelets. Proceedings of IEEE Transactions onMedical Imaging,2007,26(4):598–618.
[54] Daras P, Axenopoulos A. A3D shape retrieval framework supporting multimodalqueries. Int J Comput Vis,2010,89:229–247.
[55] Mahmoudi S, Daoudi M.3D models retrieval by using characteristic views.Processing of16thinternational conference on pattern recognition,2002:457-460.
[56] Funkhouser T, Min P, Kazhdan M, et al. A search engine for3D models. ACMTransactions on graphics,2003,22(l):83–105.
[57] Super BJ, Lu H. Evaluation of a hypothesizer for silhouette-based3-D objectrecognition. Pattern Recognition,2003,36(1):69–78.
[58] Chen DY, Tian XP, Shen YT, Ouhyoung M. On visual similarity based3D modelretrieval. Comput. Graphics Forum,2003,22(3):223–232.
[59] Shih JL, Lee CH, Wang JT. A new3D model retrieval approach based on theelevation descriptor. Pattern Recognition,2007,40(1):283–295.
[60] Ohbuchi R, Osada K, Furuya T, Banno T. Salient local visual features for shapebased3d model retrieval. In: Proceedings of IEEE Conference on Shape Modelingand Applications,2008, pp.1–10.
[61] Lowe D. Distinctive image features from scale-invariant key points. InternationalJournal of Computer Vision,2004,60(2):91–110.
[62] Gao Y, Yang Y, Dai Q, Zhang N.3d object retrieval with bag-of-region-words. In:Proceedings of ACM Conference on Multimedia,2010.
[63] Culver T, Keyser J, Manoeha D. Accurate computation of the medial axis of aPolyhedron. Proceeding of the Symposium on Solid Modeling and Applications,1999:179–190.
[64] Sherbrooke EC, Patrikalakis NM, Brisson E. An algorithm for the medial axistransform of3D polyhedral solids. IEEE Trans. Visualization and ComputerGraphics,1996,2(l):44–61.
[65] Borgefors G, Nystrom I, Gabriella Sanniti di Baja. Surface skeletonization ofvolume objects. Proceedings of SSPR,96: Advances in Structural and SyntacticalPattern Recognition,1996:251–259.
[66] Foskey M, Lin MC, Manocha D. Efficient computation of a simplified medial axis.Proceedings of the symposium on Solid modeling and applications,2003:96–107.
[67] Hilaga M, Shinagawa Y, Kohmura T, Kunii T. Topology matching for fullyautomatic similarity estimation of3d shapes. In: Proceedings of ACM SIGGRAPH,Los Angeles, USA,2001:203–212.
[68] Chen DY, Ouhyoung M. A3D Object Retrieval System Based on Multi-ResolutionReeb Graph. Proceedings of Computer Graphics Workshop, Taiwan, June2002:16–20.
[69] Bespalov D, Regli WC, Shokoufandeh A. Reeb graph-based shape retrieval forCAD. Proceedings of the ASME DETC03Computers and Information inEngineering (CIE) Conference, Chicago, IL2003.
[70] Tung T, Schmitt F. Augmented reeb graphs for content-based retrieval of3D meshmodels. In: Proc. shape modeling international2004:157–166.
[71] Sundar H, Silver D, Gagvani N, Dickenson S. Skeleton based shape matching andretrieval. In: Proc. shape modeling international2004:130–139.
[72] Gagvani N, Silver D. Parameter controlled volume thinning. Graph Models ImageProcess1999,61(3):149–164.
[73] Iyer N, Kalyanaraman Y, Lou K, Jayanti S, Ramani K. A reconfigurable3Dengineering shape search system Part I: shape representation. Proceedings ofASME DETC03Computers and Information in Engineering (CIE) Conference,Chicago, IL2003.
[74] Lou K, Jayanti S, Iyer N, Kalyanaraman Y, Ramani K, Prabhakar S. Areconfigurable3D engineering shape search system. Part II: database indexing,retrieval and clustering. Proceedings of ASME DETC03Computers andInformation in Engineering (CIE) Conference, Chicago, IL2003.
[75] Kim D, Yun D, Lee S. Graph representation by medial axis transformation for3Dimage retrieval. Proceedings of SPIE, San Jose, CA,2001,4298:223–230.
[76] Nagasaka Y, Nakamura M, Murakami T. Extracting and learning geometric featuresbased on a voxel based mapping method for manufacturing design. Proc IPPM2001,2001:1–10.
[77] Gao W, Gao SM and Liu YS.3D CAD model similarity assessment and retrievalusing DBS. Proceeding of ASME DETC2005Computers and Information inEngineering (CIE) Conference,2005.
[78] Ogniewicz RL, Kubler O. Hierarchical voronoi skeletons. Pattern Recognition,1995,28(3):343–359.
[79] Sun TL, Su CJ, Mayer RJ, Wysk RA. Shape similarity assessment of mechanicalparts based on solid models. In: Gadh R, editor.ASME Design for ManufacturingConference, Symposium on Computer Integrated Concurrent Design, ASME,Boston, MA, September17–21,1995:953–62.
[80] El-Mehalawi M, Miller R. A database system of mechanical components based ongeometric and topological similarity. Part I: representation. Computer-Aided Des2003;35:83–94.
[81]马露杰,黄正东,吴青松.基于面形位编码的CAD模型检索.计算机辅助设计与图形学学报,2008,20(1):19–25.
[82] Cicirello V, Regli WC. Machining feature-based comparisons of mechanical parts.ACM International Conference on Shape Modeling and Applications, Genova, Italy2001:176–85.
[83] Cicirello V. Intelligent retrieval of solid models. Drexel University, Philadelphia,1999.
[84] Cicirello V, Regli WC. Resolving non-uniqueness in design feature histories. In:Proceedings of the Fifth ACM Symposium on Solid Modeling and Applications,New York.
[85] Chu CH, and Hsu YC. Similarity Assessment of3D Mechanical Components forDesign Reuse. Robot. Robotics and Computer-Integrated Manufacturing,2006,22(4):332–341.
[86] Li M, Zhang YF, Fuh JYH, et al. Retrieving Reusable3D CAD Models UsingKnowledge-Driven Dependency Graph Partitioning. Computer-Aided Design&Applications,2010,7(3):417–430
[87] Ramesh M, Yip-Hoi D, Dutta D. Feature based shape similarity measurement formechanical parts. ASME Journal Compute Information Science,2001,1(3):245–56.
[88] Cardone A, Gupta SK, Deshmukh A. Machining feature-based similarityassessment algorithms for prismatic machined parts. Computer-Aided Design,2006,38(9):954–972.
[89] Cardone A, Gupta SK, Deshmukh A. Identifying similar parts for assisting costestimation of prismatic machined parts. Proceedings of ASME: Design EngineeringTechnical Conference2004October2,2004, Salt Lake City.
[90] Hoffman, DD, Singh M. Salience of visual parts. In Cognition,1997,63(1).29–78.
[91] Gal R, Cohen-Or D. Salient Geometric Features for Partial Shape Matching andSimilarity. ACM Transactions on Graphics,2006,25(1):130–150.
[92] Hu J, Hua J. Salient spectral geometric features for shape matching and retrieval.The Visual Computer,2009,25(5-7):667–675.
[93] Bai J, Gao S, Tang W, et al. Design reuse oriented partial retrieval of CAD model.Computer-Aided Design,2010,42(12):1069–1084.
[94]白静.面向设计重用的三维CAD模型检索.浙江大学博士论文,2009.
[95] Kim YS, Jung YH, Kang BG. Feature-Based Part Similarity Assessment MethodUsing Convex Decomposition. In Proc. of ASME DETC2003Computers andInformation in Engineering (CIE),2003, Chicago, Illinois, United States．
[96] Bespalov D, Regli WC, Shokoufandeha A. Local feature extraction and matchingpartial objects. Computer-Aided Design,2006,38(9):1020–1037.
[97] Suzuki MT, Yaginuma Y., and Shimizu Y. A partial shape matching technique for3d model retrieval systems. In ACM SIGGRAPH2005Posters, page128, NewYork, NY, USA,2005, ACM Press.
[98] Suzuki MT, Yaginuma Y, and Shimizu Y. A3dmodel retrieval based oncombinations of partial shape descriptors. In Proceedings of IEEE North AmericanFuzzy Information Processing Society Annual Conference (NAFIPS2006),Montreal, Canada, June2006:273–278.
[99] Katz S, Tal A. Hierarchical mesh decomposition using fuzzy clustering and cuts.ACM Transactions on Graphics (TOG),2003,22(3):954–961.
[100] Mademlis A, Daras P, Axenopoulos A, Tzovaras D, and Strintzis MG. Combiningtopological and geometrical features for global and partial3-D shape retrieval.IEEE Transactions on Multimedia,2008,10(5):819–831.
[101]徐敬华,张树有.基于递归分割的机械零件三维形状结构检索方法.机械工程学报,2009,45(11),186–183.
[102] Schreck T, Bustos B, Walter M. A query-by-example concept and user interface forglobal and partial3D object retrieval. Eurographics Workshop on3D ObjectRetrieval (2009).
[103] Ferreira A, Marini S, Attene M, et al. Thesaurus-based3D object retrieval withpart-in-whole matching. International Journal of Computer Vision,2010,89:327–347.
[104] Philipp-Foliguet S, Jordan M, Najman L, Cousty J. Artwork3D model databaseindexing and classification. Pattern Recognition,2011,44(3):588–597.
[105] Iyer S and Nagi R. Automated retrieval and ranking of similar parts in agilemanufacturing. IEEE Transactions,1997,29:859–876．
[106] Srinivas G, Fasse ED, and Marefat MM. Retrieval of similarly shaped parts from aCAD database. IEEE International Conference on1998,2809–2814．
[107] Tsai Chieh-Yuan and Chang CA. A two-stage fuzzy approach to feature-baseddesign retrieval. Computers in Industry,2005,56(5):493–505．
[108] Zhang R, Zhou X. Similarity Assessment of Mechanical Parts Based on IntegratedProduct Information Model. Journal of Computing and Information Science inEngineering,2011,11(3):011001-1–011001-12.
[109] Mehlhorn K. Graph Algorithms and NP-completeness. Springer-Verlag New York,Inc., New York, NY, USA,1984.
[110] Ullmann JR. An algorithm for subgraph isomorphism. Journal of the Associationfor Computing Machinery,1976,23(1):31–42.
[111] Cordella LP, Foggia P, Sansone C and Vento M. Fast graph matching for detectingCAD image components. In Proc.15th Int. Conf. Pattern Recognition,2000:1034–1037.
[112] Cordella LP, Foggia P, Sansone C and Vento M. An improved algorithm formatching large graphs. In Proc.3rd IAPR-TC15Workshop Graph-BasedRepresentations in Pattern Recognition,2001,149–159.
[113] Bunke H and Messmer BT. Recent advances in graph matching. Journal of PatternRecognition and Art. Intelligence,1997,11(1):169–203.
[114] Messmer BT, Bunke H. A decision tree approach to graph and subgraphisomorphism detection. Pattern Recognition,1999,32(12):1979–1998.
[115] Lazarescu M, Bunke H and Venkatesh S. Graph matching: fast candidateelimination using machine learning techniques. In Proc. Joint IAPR Int. WorkshopsSSPR and SPR,2000:236–245.
[116] Irniger C and Bunke H. Graph matching: filtering large databases of graphs usingdecision trees. In Proc.3rd IAPR-TC15Workshop Graph-Based Representations inPattern Recognition,2001:239–249.
[117] Berretti S, Bimbo AD and Vicario E. A look-ahead strategy for graph matching inretrieval by spatial arrangement. Int. Conf. Multimedia and Expo,2000:1721–1724.
[118] Berretti S, Bimbo AD and Vicario E. The computational aspect of retrieval byspatial arrangement. In Proc.15th Int. Conf. Pattern Recognition,2000:1047-1051.
[119] Berretti S, Bimbo AD and Vicario E. Efficient matching and indexing of graphmodels in content-based retrieval. IEEE Trans. Pattern Anal. Machine Intelligence.2001,23(10):1089–1105.
[120] Christmas MWJ, Kittler J. Structural matching in computer vision usingprobabilistic relaxation. IEEE Trans. Pattern Anal. Machine Intelligence,1995,17(8):749–764.
[121] Finch EH, Wilson RC. Matching Delaunay graphs. Pattern Recognition,1997,30(1):123–140.
[122] Gold S, Rangarajan A. A graduated assignment for graph matching. IEEE Trans.Pattern Anal. Machine Intellence,1996,18(4):377–388.
[123] Wilson R, Hancock E. A bayesian compatibility model for graph matching. PatternRecognition Letter,1996,17:263–276.
[124] Kuner P., Ueberreiter B. Pattern recognition by graph matching: Combinatorialversus continuous optimization. Internat. J. Pattern Recognition Artif. Intell.,1988,2(3):527–542.
[125] Suganthan DMPN, Teoh EK. Pattern recognition by graph matching using the pottsmft neural networks. Pattern Recognition,1995,28(7):997–1009.
[126] Suganthan DMPN, Teoh EK. Pattern recognition by homomorphic graph matchingusing hopfield neural networks. Image Vision Computer,1995,13(1):45–60.
[127] Cross EH ADJ, Wilson RC. Inexact graph matching using genetic search. PatternRecognition,1997,30(6):953–970.
[128] Ford GP, Zhang J. Structural graph-matching approach to image understanding.Intell. Robots Comput. Vision X: Algorithms Technique,1992,1607(1):559–569.
[129] Jiang X, Münger A, Bunke H. Synthesis of representative graphical symbols bycomputing generalized median graph. In: Chhabra, A.K., Dori, D.,(Eds.), GraphicsRecognition: Recent Advances,2000:183–192.
[130] Umeyama S. An Eigen decomposition approach to weighted graph matchingproblem. IEEE Transaction on Pattern Analysis and Machine Intelligence,1988,10(5):695–703.
[131] Xu L and King I. A PCA approach for fast retrieval of structural patterns inattributed graphs. IEEE Trans. Syst. Man Cybern.,2001, B31:812–817.
[132] Kosinov S and Caelli T. Inexact multisubgraph matching using graph eigenspaceand clustering models. In Proc. Joint IAPR Int. Workshops SSPR and SPR,2002:133–142.
[133] Snead CS. Group Technology: Foundations for Competitive Manufacturing. NewYork: Van Nostrand Reinhold,1989.
[134] IP CY. Automatic classification of CAD models. Drexel University,2005.
[135] Vapnik VN. Statistical learning theory. New York: Wiley,1998.
[136] Nilesh V Patel and Ishwar KS. Video shot detection and characterization for videodatabases. Pattern Recognition,1997,30(4):583–592.
[137] Jones S, Van Rijsbergen CJ. Information retrieval test collections. Journal ofDocumentation,1976,32:59–75.
[138] Shilane P, Min P, Kazhdan M, Funkhouser T. The Princeton shape benchmark.Proceedings of the Shape Modeling International,2004,167–178.
[139] Iyer N, Jayanti S, Lou K, Kalyanaraman Y, Ramani K. Developing an engineeringshape benchmark for cad models. Computer-Aided Design,2006,38(9):939–953.
[140] http://www.designrepository.org/datasets/.
[141]张旭堂,刘文剑.基于二分图的装配体检索研究.计算机辅助设计与图形学学报,2005,17(9):2106–2111.
[142]周炜,郑建荣,颜建军.基于子图同构与事例匹配的装配体局部结构相似性分析.计算机辅助设计与图形学学报,2010,22(2):299–305.
[143] Abhijit SD, Ashis GB, Satyandra KG, et al. Content-based assembly search: A steptowards assembly reuse. Computer-Aided Design,2008,40(2):244–261.
[144]董雁,徐静.基于装配结构相似的零件三维模型检索方法.机械工程学报,2009,45(4):273–280.
[145]唐韦华,基于高效图匹配的三维CAD模型相似评价.浙江大学硕士论文,2010.
[146] Chen X, Guo S, Bai J, Gao S. Assembly retrieval in top-down product Design.2010Asian Conference on Design&Digital Engineering,2010, Jeju Republic ofKorea:39–52.
[147] Gold S, Rangarajan A. A graduated assignment algorithm for graph matching.IEEE Transactions on Pattern Analysis and Machine Intelligence,1996,18(4):377–388.
[148] Gold S, Rangarajan A. Graph Matching by Graduated Assignment. In Proc. ofCVPR’96, San Francisco, CA,1996,239–244.
[149] Rangarajan A, Yuille A, and Mjolsness E. Conver-gence properties of thesoftassign quadratic assignment algorithm. Neural Computation,1999,11:1455–1474.
[150] Ullmann JR. An algorithm for subgraph isomorphism. Journal of the Associationfor Compu tin g Machinery,1976,23(1):31–42.
[151] Zavlanos MM, Pappas GJ. A dynamical systems approach to weighted graphmatching. Automatica,2008,44(11):2817–2824.
[152] Munthe KH. Runge-Kutta methods on lie group. BIT,1998,38:92–111.
[153] Gallier J, Xu D. Computing exponentials of skew-symmetric matrices andlogarithms of orthogonal matrices. International Journal of Robotics andAutomation,2003,18(1):10–20.
[154] Buono ND, Lopez L, Peluso R. Computation of the exponential of large sparseskew-symmetric matrices. SIAM J. Sci. Comput.,2005,27(1):278–293.
[155] Bespalov D, Regli WC, Shokoufandeha A. Local feature extraction and matchingpartial objects. Computer-Aided Design,2006,38(9):1020–1037.
[156]马露杰,黄正东,梁良,郑坛光. CAD模型表面区域分割方法[J].计算机辅助设计与图形学学报,2009,21(2):148–153
[157]马露杰.三维CAD模型形状结构分析方法.华中科技大学博士论文,2009.
[158] Biederman I. Recognition by Components: A Theory of Human ImageUnderstanding. Psychological Review,1987,94(2):115–147.
[159] Biederman H. Visual Object Recognition. In An Invitation to Cognitive Science,Visual Cognition. S. Kosslyn, D. Osherson, Eds. MIT Press,1995,2:121–65.
[160]孙晓鹏,李华.三维网格模型的分割及应用综述.计算机辅助设计与图形学学报,2005,17(8):1647–1655).
[161] Philip R K. ISO TC184/SC4: Product Data Representation and Exchange, Part:44,Title: Industrial Automation Systems and Integration Product Data Representationand Exchange–Integrated Generic Resources: Product Structure Configuration(November1994), ISO,1994.
[162] Sugimura N and Ohtaka A. ISO TC184/SC4/WG12N597, JNC Proposal of STEPAssembly Model for Products (June2000), ISO,2000.
[163]孙惠泉.图论及其应用.北京:科学出版社,2004:89–92.
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