基于隐式函数的曲面重构方法及其应用
|
摘要
曲面重构是复杂曲面建模的关键技术,是将测量设备采样获取的点云数据转换为光滑、封闭曲面的过程,广泛应用于诸多领域。虽然曲面重构方法众多,但在工程实际中仍面临巨大挑战,存在一些重要问题需要解决。工业现场测量的诸多因素会导致点云包含噪声、孔洞以及层叠等缺陷。缺陷数据使得现有大多数重构方法很难获得所依赖的点云一致性法矢或三角网格,需要耗时的预处理、曲面修补以及人工操作等复杂过程。对于工业中有特定功能要求的零件产品,现有重构方法只能保证重构曲面的几何精度,很难使重构曲面符合相应的功能要求。为此,本文针对这些工程应用中存在的问题,研究曲面重构的数学模型,基于隐式函数理论提出了多种有效的曲面重构和点云分割方法,并应用到工程实例中。
第一,现有重构方法没有统一的数学模型,曲面质量以及重构方法缺乏合理的评价标准,大多数方法依赖点云定向信息,其估算过程复杂,很难适用于缺陷点云重构。本文对现有方法进行总结,提出了基于度量函数和各种约束条件的曲面重构模型,对其分类、使用条件、求解方法等作详细分析与讨论。在此基础上,将数学形态学方法扩展到三维空间中,提出了一种新的点云定向信息的快速估算方法,能利用较少的步骤去除点云孔洞和层叠缺陷的影响,避免复杂的三角网格重构和预处理过程,提高了估算效率。
第二,传统点云分割方法往往依赖点云的三角网格,很难有效分割含缺陷的点云,需借助复杂的数据结构或算法。本文提出了基于活动轮廓模型的点云自动分割方法,能有效去除点云缺陷的影响,实现点云的高效分割。将中值滤波方法扩展到三维空间窄带内,实现点云噪声影响的有效去除。扩展二维空间的活动轮廓模型理论,建立了基于点云平均曲率的能量函数优化模型,通过空间曲线的自适应拓扑演化来实现点云的边界提取和区域划分。此方法采用简单的数据结构,能避免三角网格重构,在保证分割精度的基础上极大提高分割效率。
第三,针对诸多隐式曲面重构方法依赖于点云一致性法矢或三角网格,很难合理重构缺陷数据的不足,提出了一种基于双梯度场的间接重构方法。此方法不直接拟合点云,而通过构造双梯度函数来高效且合理的修复点云孔洞缺陷,融合层叠区域,避免了复杂的一致性法矢和三角网格构造过程。基于数学形态学集合运算的双梯度函数构造,利用了简单的立方网格数据结构和快速傅里叶变换的数值求解方法保证了很高的重构效率。数值试验表明,本方法对缺陷点云有很好的重构效果,既保证了重构的精度也合理的去除了点云缺陷的影响。
第四,现有曲面重构方法很难重构出具有相应性能要求的功能曲面,需要大量的拼接、人工修改等后续处理。为此,以流曲面为例,提出了结合流场约束的隐式曲面重构方法。将流体速度场作为整体约束加入到传统的隐式曲面重构方法中,配合点云的距离函数,通过曲面演化共同求解出最终曲面,不仅保证了重构曲面的几何精度要求,而且实现了曲面的流线型造型和全局光顺。解决了流体速度计算中的边界条件以及曲面演化收敛条件设定问题。结合工程实际中的发动机进气道点云实例,详细讨论了重构模型中两类约束的控制参数对最终结果的影响,数值试验证明了本方法的有效性和鲁棒性。
最后,基于曲面重构数学模型,利用VC++6.0和MATLAB平台的混合编程环境,将提出的多种重构方法整合到统一的数值仿真平台。以偏微分方程求解为核心,包含了功能选择、数学库函数添加以及输入输出接口等功能,并将多种类型的测量硬件设备和商业软件包整合,能有效处理工程实际中的点云重构和分割问题。通过此平台基础上的一系列数值试验说明了平台的实用性,为扩展今后的研究及实现工程化提供了基础。
Surfaces reconstruction is a key technology used for complex surface modeling, which is a process transforming the point clouds into continuous and watertight surface and widely used in many research fields. There are many reconstruction methods, but the most challenge comes from the defective sample points due the measurements in practice. The point clouds often have large amount data with noise, holes and overlapping regions. These defective samples make the existing surface reconstruction difficulty to evaluate the oriented information or construct triangular meshes, which is necessary for reconstruction. The know methods only guarantee the accurate result of function surface with geometric standard, but can not realize the physical performance. Aiming at the problems existing above, this paper mainly researches the surface reconstruction modeling, and proposes some effective methods based on implicit function theory for application.
Firstly, the known existing methods are lacking in the mathematical description and the suitable standard. Most methods are based on complex oriented information evaluation, hard to apply in practice. Based on the summary of the existed reconstruction methods, a general extremum model based on the metric function and constrains conditions is proposed. This paper analyzes many kinds of metric functions including the definition, conditions, resolving methods. Based on the modeling, a efficient estimation methods for oriented information of defective point clouds is proposed. The approach can handle the holes and overlapping regions, avoiding constructing triangular mesh and pre-processing, which can increase the efficiency.
Secondly, many segmentation methods rely on the triangular mesh and are hard to segment defective samples, requiring complex algorithm or data structure. This paper proposes an efficient and automatic segmentation methods based on active contour model, which can reduce the defective influence. The median filter is extended into a narrowband in 3D space to handle the noisy samples. The active contour model in image processing is also extended to create a segmentation model based on curvature and the segmentation is performed by propagating the space curves with adaptive topological changes. This method can avoid reconstruct triangular mesh, not only guarantee the accurate segment results, but also increase the efficiency with simple data structure.
Thirdly, many known reconstruction methods need the oriented information previously, however the information is often hard to evaluate automatically and accurately. For avoiding this problem, this paper proposes an implicit surface reconstruction based on dual off-set gradient functions. It does not fit the clouds, instead, it generates dual surfaces which construct a minimal surrounding space to the point clouds firstly and reconstruct the final surface then. The dual gradient functions are constructed by the mathematical morphology quickly, they are then combined as a novel minimal model, and finally the corresponding PDE is solved by fast Fourier transform (FFT) efficiently. Since this method needs not the normals estimation or the triangular mesh construction, it saves lots steps. For the FFT implementation, the compute time of reconstruction is reduced. Through the numerical examples, this method shows much effectiveness to the noise point clouds.
Fourthly, the know reconstruction method can not guarantee the physical performance of resulting surface and need complex post-processing including smoothing, modification et.al. Therefore, this paper takes stream surface as example and proposes a stream surface reconstruction method with the fluid velocity function. The main idea is to compute the fluid velocity as global constraint to the traditional minimal model, and use the surface evolution to reconstruct the final surface. It can not only generate a global smooth and accurate resulting surface, but also keep the surface as a corresponding stream modeling. The influences of each parametric are also discussed with an engine intake ports in real world.
Finally, based on the general extremum model and the methods proposed in the paper, a numerical platform is developed. The platform is programmed by the combination of VC++and MATLAB environment. It contains many function modules, such as input/output, mathematical function library, many kinds of measurement equipment and software package. Series numerical examples, which all sample from industrial products in real world, are adopted to prove these methods in the paper.
第一,现有重构方法没有统一的数学模型,曲面质量以及重构方法缺乏合理的评价标准,大多数方法依赖点云定向信息,其估算过程复杂,很难适用于缺陷点云重构。本文对现有方法进行总结,提出了基于度量函数和各种约束条件的曲面重构模型,对其分类、使用条件、求解方法等作详细分析与讨论。在此基础上,将数学形态学方法扩展到三维空间中,提出了一种新的点云定向信息的快速估算方法,能利用较少的步骤去除点云孔洞和层叠缺陷的影响,避免复杂的三角网格重构和预处理过程,提高了估算效率。
第二,传统点云分割方法往往依赖点云的三角网格,很难有效分割含缺陷的点云,需借助复杂的数据结构或算法。本文提出了基于活动轮廓模型的点云自动分割方法,能有效去除点云缺陷的影响,实现点云的高效分割。将中值滤波方法扩展到三维空间窄带内,实现点云噪声影响的有效去除。扩展二维空间的活动轮廓模型理论,建立了基于点云平均曲率的能量函数优化模型,通过空间曲线的自适应拓扑演化来实现点云的边界提取和区域划分。此方法采用简单的数据结构,能避免三角网格重构,在保证分割精度的基础上极大提高分割效率。
第三,针对诸多隐式曲面重构方法依赖于点云一致性法矢或三角网格,很难合理重构缺陷数据的不足,提出了一种基于双梯度场的间接重构方法。此方法不直接拟合点云,而通过构造双梯度函数来高效且合理的修复点云孔洞缺陷,融合层叠区域,避免了复杂的一致性法矢和三角网格构造过程。基于数学形态学集合运算的双梯度函数构造,利用了简单的立方网格数据结构和快速傅里叶变换的数值求解方法保证了很高的重构效率。数值试验表明,本方法对缺陷点云有很好的重构效果,既保证了重构的精度也合理的去除了点云缺陷的影响。
第四,现有曲面重构方法很难重构出具有相应性能要求的功能曲面,需要大量的拼接、人工修改等后续处理。为此,以流曲面为例,提出了结合流场约束的隐式曲面重构方法。将流体速度场作为整体约束加入到传统的隐式曲面重构方法中,配合点云的距离函数,通过曲面演化共同求解出最终曲面,不仅保证了重构曲面的几何精度要求,而且实现了曲面的流线型造型和全局光顺。解决了流体速度计算中的边界条件以及曲面演化收敛条件设定问题。结合工程实际中的发动机进气道点云实例,详细讨论了重构模型中两类约束的控制参数对最终结果的影响,数值试验证明了本方法的有效性和鲁棒性。
最后,基于曲面重构数学模型,利用VC++6.0和MATLAB平台的混合编程环境,将提出的多种重构方法整合到统一的数值仿真平台。以偏微分方程求解为核心,包含了功能选择、数学库函数添加以及输入输出接口等功能,并将多种类型的测量硬件设备和商业软件包整合,能有效处理工程实际中的点云重构和分割问题。通过此平台基础上的一系列数值试验说明了平台的实用性,为扩展今后的研究及实现工程化提供了基础。
Surfaces reconstruction is a key technology used for complex surface modeling, which is a process transforming the point clouds into continuous and watertight surface and widely used in many research fields. There are many reconstruction methods, but the most challenge comes from the defective sample points due the measurements in practice. The point clouds often have large amount data with noise, holes and overlapping regions. These defective samples make the existing surface reconstruction difficulty to evaluate the oriented information or construct triangular meshes, which is necessary for reconstruction. The know methods only guarantee the accurate result of function surface with geometric standard, but can not realize the physical performance. Aiming at the problems existing above, this paper mainly researches the surface reconstruction modeling, and proposes some effective methods based on implicit function theory for application.
Firstly, the known existing methods are lacking in the mathematical description and the suitable standard. Most methods are based on complex oriented information evaluation, hard to apply in practice. Based on the summary of the existed reconstruction methods, a general extremum model based on the metric function and constrains conditions is proposed. This paper analyzes many kinds of metric functions including the definition, conditions, resolving methods. Based on the modeling, a efficient estimation methods for oriented information of defective point clouds is proposed. The approach can handle the holes and overlapping regions, avoiding constructing triangular mesh and pre-processing, which can increase the efficiency.
Secondly, many segmentation methods rely on the triangular mesh and are hard to segment defective samples, requiring complex algorithm or data structure. This paper proposes an efficient and automatic segmentation methods based on active contour model, which can reduce the defective influence. The median filter is extended into a narrowband in 3D space to handle the noisy samples. The active contour model in image processing is also extended to create a segmentation model based on curvature and the segmentation is performed by propagating the space curves with adaptive topological changes. This method can avoid reconstruct triangular mesh, not only guarantee the accurate segment results, but also increase the efficiency with simple data structure.
Thirdly, many known reconstruction methods need the oriented information previously, however the information is often hard to evaluate automatically and accurately. For avoiding this problem, this paper proposes an implicit surface reconstruction based on dual off-set gradient functions. It does not fit the clouds, instead, it generates dual surfaces which construct a minimal surrounding space to the point clouds firstly and reconstruct the final surface then. The dual gradient functions are constructed by the mathematical morphology quickly, they are then combined as a novel minimal model, and finally the corresponding PDE is solved by fast Fourier transform (FFT) efficiently. Since this method needs not the normals estimation or the triangular mesh construction, it saves lots steps. For the FFT implementation, the compute time of reconstruction is reduced. Through the numerical examples, this method shows much effectiveness to the noise point clouds.
Fourthly, the know reconstruction method can not guarantee the physical performance of resulting surface and need complex post-processing including smoothing, modification et.al. Therefore, this paper takes stream surface as example and proposes a stream surface reconstruction method with the fluid velocity function. The main idea is to compute the fluid velocity as global constraint to the traditional minimal model, and use the surface evolution to reconstruct the final surface. It can not only generate a global smooth and accurate resulting surface, but also keep the surface as a corresponding stream modeling. The influences of each parametric are also discussed with an engine intake ports in real world.
Finally, based on the general extremum model and the methods proposed in the paper, a numerical platform is developed. The platform is programmed by the combination of VC++and MATLAB environment. It contains many function modules, such as input/output, mathematical function library, many kinds of measurement equipment and software package. Series numerical examples, which all sample from industrial products in real world, are adopted to prove these methods in the paper.
引文
[1]张舜德,朱东波,反求工程中三维几何形状测量及数据预处理,机电工程技术,2001,30(001)：7-10
[2]陈勇,刘雄伟,反求工程CAD建模技术,华侨大学学报：自然科学版,2001,22(004)：376-379
[3]张丽艳,周儒荣,海量测量数据简化技术研究,计算机辅助设计与图形学学报,2001,13(011)：1019-1023
[4]Veron P, Leon J C, Static polyhedron simplification using error measurements, Computer-Aided Design,1997,29 (4):287-298
[5]Besl P J, McKay H D, A method for registration of 3-D shapes, IEEE Transactions on pattern analysis and machine intelligence,1992,14 (2):239-256
[6]Mathieu D, Mark M, Peter S, et al., Anisotropic feature-preserving denoising of height fields and bivariate data, Graphics Interface,2000:145-152
[7]赵作智,林亨,采用能量方程优化零件数据模型,机械设计与制造,2000,(002)：24-26
[8]彭芳瑜,周云飞,基于广义能量法的曲面光顺,华中科技大学学报：自然科学版,2002,30(002)：5-8
[9]Vollmer J, Mencl R, Mueller H, Improved Laplacian smoothing of noisy surface meshes, Blackwell Publishing,1999:131-138
[10]Karbacher S, Haeusler G, A new approach for modeling and smoothing of scattered 3D data, Three-Dimensional Image Capture and Applications,1998,168-177
[11]Gabriel T, A signal processing approach to fair surface design, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM. 1995:351-358
[12]Chen Y, Medioni G, Object modeling by registration of multiple range images, Image and Vision Computing,1992,10 (3):145-155
[13]Farin G E, Hoschek J, Kim M S, Handbook of computer aided geometric design: North Holland,2002.
[14]Pottmann H, Huang Q X, Yang Y L, et al., Geometry and convergence analysis of algorithms for registration of 3D shapes, International Journal of Computer Vision, 2006,67 (3):277-296
[15]Flory S, Hofer M, Surface fitting and registration of point clouds using approximations of the unsigned distance function, Computer Aided Geometric Design,2009,27 (1):60-77
[16]Davis J, Marschner S R, Garr M, et al., Filling holes in complex surfaces using volumetric diffusion,3D Data Processing Visualization and Transmission,2002. Proceedings. First International Symposium on.2002:428-861
[17]Pauly M, Keiser R, Kobbelt L P, et al., Shape modeling with point-sampled geometry, ACM Transactions on Graphics,2003,22 (3):641-650
[18]Niloy J M, An N, Estimating surface normals in noisy point cloud data, Proceedings of the nineteenth annual symposium on Computational geometry. San Diego, California, USA. ACM.2003:322-328
[19]Dey T K, Li G, Sun J, Normal estimation for point clouds:a comparison study for a Voronoi based method, Point-Based Graphics,2005. Eurographics/IEEE VGTC Symposium Proceedings.2005:39-46
[20]OuYang D, Feng H Y, On the normal vector estimation for point cloud data from smooth surfaces, Computer-Aided Design,2005,37 (10):1071-1079
[21]Lange C, Polthier K, Anisotropic smoothing of point sets, Computer Aided Geometric Design,2005,22 (7):680-692
[22]Hu G, Xu J, Miao L, et al., Bilateral estimation of vertex normal for point-sampled models, Springer,2005:758-768
[23]Cazals F, Pouget M, Estimating differential quantities using polynomial fitting of osculating jets, Computer Aided Geometric Design,2005,22 (2):121-146
[24]Hoppe H, DeRose T, Duchamp T, et al., Surface reconstruction from unorganized points, Computer Graphics(ACM),1992,26 (2):71-78
[25]Weiss V, Andor L, Renner G, et al., Advanced surface fitting techniques, Computer Aided Geometric Design,2002,19 (1):19-42
[26]Chaikin G M, An algorithm for high-speed curve generation, Computer graphics and image processing,1974,3 (4):346-349
[27]Catmull E, Clark J, Recursively generated B-spline surfaces on arbitrary topological meshes, Computer Aided Design,1978,10 (6):350-355
[28]Loop C, Smooth subdivision surfaces based on triangles, Master's thesis, University of Utah, Department of Mathematics,1987.
[29]Nira D, David L, John A G, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. Graph.,1990,9 (2):160-169
[30]Thomas W S, Jianmin Z, David S, et al., Non-uniform recursive subdivision surfaces, Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM.1998:387-394
[31]Jos S, Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values, Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM.1998:395-404
[32]Pan Q, Xu G L, Fast Evaluation of the Improved Loop's Subdivision Surfaces, Proceedings of the Geometric Modeling and Processing 2004. IEEE Computer Society.2004:205-214
[33]Jorg P, Georg U, Gaussian and Mean Curvature of Subdivision Surfaces, Proceedings of the 9th IMA Conference on the Mathematics of Surfaces. Springer-Verlag.2000:59-69
[34]Schweitzer J E, Analysis and application of subdivision surfaces, University of Washington,1996.
[35]Hugues H, Tony D, Tom D, et al., Piecewise smooth surface reconstruction, Proceedings of the 21st annual conference on Computer graphics and interactive techniques. ACM.1994:295-302
[36]Hiromasa S, Shingo T, Fumihiko K, et al., Subdivision Surface Fitting to a Range of Points, Proceedings of the 7th Pacific Conference on Computer Graphics and Applications. IEEE Computer Society.1999:158-167,322
[37]Takashi K, MeshToSS:Converting Subdivision Surfaces from Dense Meshes, Proceedings of the Vision Modeling and Visualization Conference 2001. Aka GmbH.2001:325-332
[38]Weiyin M, Xiaohu M, Shiu-Kit T, et al., Subdivision Surface Fitting from a Dense Triangle Mesh, Proceedings of the Geometric Modeling and Processing; Theory and Applications (GMP'02). IEEE Computer Society.2002:94-103
[39]Chen H Y, Pottmann H, Approximation by ruled surfaces, Journal of Computational and Applied Mathematics,1999,102 (1):143-156
[40]Kjellander J A P, Smoothing of cubic parametric splines, Computer-Aided Design, 1983,15 (3):175-179
[41]Farin G, Rein G, Sapidis N, et al., Fairing cubic B-spline curves, Computer Aided Geometric Design,1987,4 (1-2):91-103
[42]Sapidis N, Farin G, Automatic fairing algorithm for B-spline curves, Computer-Aided Design,1990,22 (2):121-129
[43]Hahmann S, Konz S, Knot-removal surface fairing using search strategies, Computer Aided Design,1998,30 (2):131-8
[44]Leif K, Swen C, Jens V, et al., Interactive multi-resolution modeling on arbitrary meshes, Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM.1998:105-114
[45]Venkat K, Marc L, Fitting smooth surfaces to dense polygon meshes, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM.1996:313-324
[46]Demetri T, Hong Q, Dynamic NURBS with geometric constraints for interactive sculpting, ACM Trans. Graph.,1994,13 (2):103-136
[47]Demetri T, John P, Alan B, et al., Elastically deformable models, Proceedings of the 14th annual conference on Computer graphics and interactive techniques. ACM. 1987:205-214
[48]Zhang C, Zhang P, Cheng F, Fairing spline curves and surfaces by minimizing energy, Computer-Aided Design,2001,33 (13):913-923
[49]关志东,经玲,基于物理模型的变形曲线曲面研究及应用,计算机学报,1996,9187-194
[50]穆国旺,涂侯杰,参数三次B样条曲线的一种整体光顺方法,工程图学学报,1998,(001)：28-34
[51]穆国旺,朱心雄,曲面光顺的分片能量法,工程图学学报,1999,(001)：29-34
[52]经玲,席平,应用可变形模型进行曲线曲面光顺,软件学报,1998,9(006)：464-468
[53]Eric J S, Tony D D, David H S, Wavelets for Computer Graphics:A Primer, Part 1, IEEE Comput. Graph. Appl.,1995,15 (3):76-84
[54]Eric J S, Tony D D, David H S, Wavelets for computer graphics:theory and applications:Morgan Kaufmann Publishers Inc.,1996.
[55]童伟华,陈发来,冯玉瑜,基于偏微分方程的隐式曲面光顺方法,计算机学报,2004,27(009)：1264-1271
[56]李安平,蒋大为,三次均匀有理B样条曲线的权因子优化光顺算法,计算机辅助设计与图形学学报,1997,9(006)：562-567
[57]Kaufman E, Klass R, Smoothing surfaces using reflection lines for families of splines, Computer-Aided Design,1988,20312-316
[58]William E L, Harvey E C, Marching cubes:A high resolution 3D surface construction algorithm, Proceedings of the 14th annual conference on Computer graphics and interactive techniques. ACM.1987:163-169
[59]Jin G, Wang Q, Shen Y, et al., An improved marching cubes method for surface reconstruction of volume data, Intelligent Control and Automation 2006. Dalian, China. Piscataway United States,2006:10454-10457
[60]Kwan-Liu M, James S P, Charles D H, et al., Parallel volume rendering using binary-swap image composition, ACM SIGGRAPH ASIA 2008 courses. Singapore. ACM.2008:38
[61]Klaus E, Martin K, Thomas E, High-quality pre-integrated volume rendering using hardware-accelerated pixel shading, Proceedings of the ACM SIGGRAPH workshop on Graphics hardware. Los Angeles, California, United States. ACM. 2001:9-16
[62]Tao J, Frank L, Scott S, et al., Dual contouring of hermite data, Proceedings of the 29th annual conference on Computer graphics and interactive techniques. San Antonio, Texas. ACM.2002:339-346
[63]Piegl L A, Tiller W, Parametrization for surface fitting in reverse engineering, Computer-Aided Design,2001,33 (8):593-603
[64]Biplab S, Chia-Hsiang M, Parameter optimization in approximating curves and surfaces to measurement data, Comput. Aided Geom. Des.,1991,8 (4):267-290
[65]来新民,黄田,基于NURBS的散乱数据点自由曲面重构,计算机辅助设计与图形学学报,1999,11(005)：433-436
[66]Piegl L A, Tiller W, Surface approximation to scanned data, The Visual Computer, 2000,16 (7):386-395
[67]童伟华,冯玉瑜,陈发来,层次隐式张量积B-样条曲面及其在曲面重构中的应用,Journal of Software,2006,1711-20
[68]Yang Z, Deng J, Chen F, Fitting unorganized point clouds with active implicit B-spline curves, The Visual Computer,2005,21 (8):831-839
[69]Thomas W S, Jianmin Z, Almaz B, et al., T-splines and T-NURCCs, ACM SIGGRAPH 2003 Papers. San Diego, California. ACM.2003:477-484
[70]Thomas W S, David L C, Finnigan G T, et al., T-spline simplification and local refinement, ACM Trans. Graph.,2004,23 (3):276-283
[71]Yong-bo W, Ye-hua S, Guo-nian L V, et al., A Delaunay-based Surface Reconstruction Algorithm for Unorganized Sampling Points, Journal of Image and Graphics,2007,9:1537-1543
[72]Edelsbrunner H, Mucke E P, Three-dimensional alpha shapes, ACM Transactions on Graphics (TOG),1994,13 (1):72
[73]Amenta N, Choi S, Kolluri R K, The power crust, unions of balls, and the medial axis transform, Computational Geometry,2001,19 (2-3):127-153
[74]Ravikrishna K, Jonathan Richard S, James F O B, Spectral surface reconstruction from noisy point clouds, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing. Nice, France. ACM.2004:11-21
[75]Chandrajit L B, Fausto B, Guoliang X, Automatic reconstruction of surfaces and scalar fields from 3D scans, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM.1995:109-118
[76]YH Chen, Liu C, Robust segmentation of CMM data based on NURBS, The International Journal of Advanced Manufacturing Technology,1997,13:530-534
[77]Yang M, Lee E, Segmentation of measured point data using a parametric quadric surface approximation, Computer-Aided Design,1999,31 (7):449-457
[78]Katz S, Leifman G, Tal A, Mesh segmentation using feature point and core extraction, The Visual Computer,2005,21 (8):649-658
[79]Jianbing H, Chia-Hsiang M, Automatic data segmentation for geometric feature extraction from unorganized 3-D coordinate points, Robotics and Automation, IEEE Transactions on,2001,17 (3):268-279
[80]Hitoshi Y, Stefan G, Rhaleb Z, et al., Mesh Segmentation Driven by Gaussian Curvature, The Visual Computer,2005,21 (8-10):659-668
[81]Koschan A F, Perception-based 3D triangle mesh segmentation using fast marching watersheds, Computer Vision and Pattern Recognition,2003. Proceedings.2003 IEEE Computer Society Conference on.2003:Ⅱ-27-Ⅱ-32 vol.2
[82]Helmut Pottmann T S, Michael Hofer, Christoph Haider, Allan Hanbury, The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces, Computer Vision-ECCV 2004,2004,18-23
[83]Yu-Kun L, Shi-Min H, Ralph R M, et al., Fast mesh segmentation using random walks, Proceedings of the 2008 ACM symposium on Solid and physical modeling. Stony Brook, New York. ACM.2008:183-191
[84]Levy B, Petitjean S, Ray N, et al., Least squares conformal maps for automatic texture atlas generation, ACM Transactions on Graphics,2002,21 (3):362-371
[85]Yu-Kun L, Qian-Yi Z, Shi-Min H, et al., Robust Feature Classification and Editing, IEEE Transactions ON VISUALIZATION AND COMPUTER GRAPHICS,2007, 13(1):34-45
[86]Woo H, Kang E, Wang S, et al., A New Segmentation Method for Point Cloud Data, International Journal of Machine Tools and Manufacture,2002,42 (2):167-178
[87]Pottmann H, Leopoldseder S, Hofer M, et al., Industrial geometry:recent advances and applications in CAD, Computer-Aided Design,2005,37 (7):751-766
[88]Checchin P, Trassoudaine L, Alizon J, Segmentation of range images into planar regions,3-D Digital Imaging and Modeling,1997. Proceedings., International Conference on Recent Advances in.1997:156-163
[89]Dongming Z, Xintong Z, Range-data-based object surface segmentation via edges and critical points, Image Processing, IEEE Transactions on,1997,6 (6):826-830
[90]Koster K, Spann M, MIR:an approach to robust clustering-application to range image segmentation, Pattern Analysis and Machine Intelligence, IEEE Transactions on,2000,22 (5):430-444
[91]Michael G, Andrew W, Paul S H, Hierarchical face clustering on polygonal surfaces, Proceedings of the 2001 symposium on Interactive 3D graphics. ACM. 2001:49-58
[92]Rong L, Hao Z, Segmentation of 3D Meshes through Spectral Clustering, Proceedings of the Computer Graphics and Applications,12th Pacific Conference. IEEE Computer Society.2004:298-305
[93]Sagi K, Ayellet T, Hierarchical mesh decomposition using fuzzy clustering and cuts, ACM Trans. Graph.,2003,22 (3):954-961
[94]Lavou G, Dupont F, Baskurt A, A new CAD mesh segmentation method, based on curvature tensor analysis, Computer-Aided Design,2005,37 (10):975-987
[95]Gumhold S, Wang X, MacLeod R, Feature extraction from point clouds,2001: 293-305
[96]Mark P, Richard K, Markus G, Multi-scale Feature Extraction on Point-Sampled Surfaces, Computer Graphics Forum,2003,22 (3):281-289
[97]Provot L, Debled-Rennesson I,3D noisy discrete objects:Segmentation and application to smoothing, Pattern Recognition,2009,42 (8):1626-1636
[98]Demarsin K, Vanderstraeten D, Volodine T, et al., Detection of closed sharp edges in point clouds using normal estimation and graph theory, Computer-Aided Design, 2007,39 (4):276-283
[99]Brian C, Marc L, A volumetric method for building complex models from range images, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM.1996:303-312
[100]James F B, A Generalization of Algebraic Surface Drawing, ACM Trans. Graph., 1982,1 (3):235-256
[101]Jules B, Ken S, Convolution surfaces, Proceedings of the 18th annual conference on Computer graphics and interactive techniques. ACM.1991:251-256
[102]Yutaka O, Alexander B, Marc A, et al., Multi-level partition of unity implicits, ACM Trans. Graph.,2003,22 (3):463-470
[103]Yukie N, Yutaka O, Hiromasa S, Smoothing of Partition of Unity Implicit Surfaces for Noise Robust Surface Reconstruction, Computer Graphics Forum,2009,28 (5): 1339-1348
[104]Gelas A, Ohtake Y, Kanai T, et al., Approximation of Unorganized Point Set with Composite Implicit Surface, Image Processing,2006 IEEE International Conference on.2006:1217-1220
[105]Marc A, Johannes B, Daniel C-O, et al., Point set surfaces, Proceedings of the conference on Visualization'01. San Diego, California. IEEE Computer Society. 2001:
[106]Gael G, Markus G, Algebraic point set surfaces, ACM SIGGRAPH 2007 papers. San Diego, California. ACM.2007
[107]Phan L, Liu L, Abeysinghe S, et al., Surface reconstruction from point set using projection operator, ACM New York, NY, USA,2008:1-1
[108]Nina A, Yong Joo K, Defining point-set surfaces, ACM SIGGRAPH 2004 Papers. Los Angeles, California. ACM.2004:264-270
[109]Kass M, Witkin A, Terzopoulos D, Snakes:Active contour models, International Journal of Computer Vision,1988,1 (4):321-331
[110]Osher S, Sethian J A, Fronts Propagating With Curvature-dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics,1988,79(1):12-49
[111]Zhao H-K, Osher S, Merriman B, et al., Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method, Computer Vision and Image Understanding,2000,80 (3):295-314
[112]Sethian J, A Fast Marching Level Set Method for Monotonically Advancing Fronts, Proceedings of the National Academy of Sciences of the United States of America, 1996,93 (4):1591-1595
[113]Chopp D L, Some improvements of the fast marching method, SIAM Journal of Scientific Computing,2002,23 (1):230-244
[114]Chunming L, Chenyang X, Changfeng G, et al., Level Set Evolution Without Re-initialization:A New Variational Formulation, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Diego, California. IEEE Computer Society 2005:430-436
[115]Li C, Kao C Y, Gore J C, et al., Implicit active contours driven by local binary fitting energy, IEEE Computer Vision and Pattern Recognition (CVPR), Minneapolis, Minnesota, USA,2007,17-22
[116]Carr J C, Beatson R K, Cherrie J B, et al., Reconstruction and representation of 3D objects with radial basis functions, Proceedings of the 28th annual conference on Computer graphics and interactive techniques. ACM.2001:67-76
[117]Acosta F M A, Radial basis function and related models:An overview, Signal Processing,1995,45 (1):37-58
[118]Huong Quynh D, Turk G, Slabaugh G, Reconstructing surfaces by volumetric regularization using radial basis functions, Pattern Analysis and Machine Intelligence, IEEE Transactions on,2002,24 (10):1358-1371
[119]Lin Y, Chen C, Song M, et al., Dual-RBF based surface reconstruction, The Visual Computer,2009,25 (5):599-607
[120]Magoules F, Diago L A, Hagiwara I, Efficient preconditioning for image reconstruction with radial basis functions, Advances in Engineering Software, 2007,38 (5):320-327
[121]Greg T, James F O b, Modelling with implicit surfaces that interpolate, ACM Trans. Graph.,2002,21 (4):855-873
[122]Ohtake Y, Belyaev A, Seidel H-P, Sparse surface reconstruction with adaptive partition of unity and radial basis functions, Graphical Models,2006,68 (1):15-24
[123]Michael K, Matthew B, Hugues H, Poisson surface reconstruction, Proceedings of the fourth Eurographics symposium on Geometry processing. Cagliari, Sardinia, Italy. Eurographics Association.2006:61-70
[124]Manson J, Petrova G, Schaefer S, Streaming Surface Reconstruction Using Wavelets, Computer Graphics Forum,2008,27 (5):1411-1420
[125]Alliez P, Cohen-Steiner D, Tong Y, et al., Voronoi-based variational reconstruction of unoriented point sets, Proceedings of the fifth Eurographics symposium on Geometry processing. Barcelona, Spain. Eurographics Association.2007:39-48
[126]Boissonnat J D, Cazals F, Smooth surface reconstruction via natural neighbour interpolation of distance functions, Computational Geometry:Theory and Applications,2002,22 (1-3):185-203
[127]Alexander H, Leif K, Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information, Proceedings of the fourth Eurographics symposium on Geometry processing. Cagliari, Sardinia, Italy. Eurographics Association.2006:41-50
[128]Boykov Y, Kolmogorov V, Computing geodesics and minimal surfaces via graph cuts, Computer Vision,2003. Proceedings. Ninth IEEE International Conference on.2003 (1):26-33
[129]Xu N, Ahuja N, Bansal R, Object segmentation using graph cuts based active contours, Computer Vision and Image Understanding,2007,107 (3):210-224
[130]Barhak J, Fischer A, Adaptive reconstruction of freeform objects with 3D SOM neural network grids, Computers & Graphics,2002,26 (5):745-751
[131]Peng Q, Loftus M, Using image processing based on neural networks in reverse engineering, International Journal of Machine Tools and Manufacture,2001,41 (5): 625-640
[132]He X, Li C, Hu Y, et al., Automatic sequence of 3D point data for surface fitting using neural networks, Computers & Industrial Engineering,2009,57 (1):408-418
[133]Vladimir S, Lothar S, Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection, Proceedings of the sixth ACM symposium on Solid modeling and applications. Ann Arbor, Michigan, United States. ACM.2001:39-46
[134]Cong L, Wangge W, Youyong W, Image based reconstruction using hybrid optimization of simulated annealing and genetic algorithm, Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation. Shanghai, China. ACM.2009:875-878
[135]Kumar G S, Kalra P K, Dhande S G, Curve and surface reconstruction from points: an approach based on self-organizing maps, Applied Soft Computing Journal,2004, 5 (1):55-66
[136]Werman M, Keren D, A Bayesian method for fitting parametric and nonparametric models to noisy data, IEEE Transactions on pattern analysis and machine intelligence,2001,23 (5):528-534
[137]Diebel J R, Thrun S, Brunig M, A Bayesian method for probable surface reconstruction and decimation, ACM Transactions on Graphics (TOG),2006,25 (1):39-59
[138]Keren D, Werman M, A full bayesian approach to curve and surface reconstruction, Journal of Mathematical Imaging and Vision,1999,11 (1):27-43
[139]Jenke P, Wand M, Bokeloh M, et al., Bayesian Point Cloud Reconstruction, Computer Graphics Forum,2006,25 (3):379-388
[140]Roca-Pardinas J, Lorenzo H, Arias P, et al., From laser point clouds to surfaces: Statistical nonparametric methods for three-dimensional reconstruction, Computer-Aided Design,2008,40 (5):646-652
[141]Paulsen R R, B rentzen J A, Larsen R, Markov Random Field Surface Reconstruction, IEEE Transactions On Visualization and Computer Graphics,2009, 16 (4):636-646
[142]Xie P, McDonnell K T, Qin P, Surface Reconstruction of Noisy and Defective Data Sets, Proceedings of the conference on Visualization'04,2004,259-266
[143]Liu Y, Pottmann H, Wang W, Constrained 3D shape reconstruction using a combination of surface fitting and registration, Computer Aided Design,2006,38 (6):572-583
[144]Li X, Han C Y, Wee W G, On surface reconstruction:A priority driven approach, Computer-Aided Design,2009,41 (9):626-640
[145]Esteve J, Brunet P, Vinacua A, Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane, Computer Graphics Forum,2005,24 (4):791-807
[146]Hugues H, Tony D, Tom D, et al., Surface reconstruction from unorganized points, Proceedings of the 19th annual conference on Computer graphics and interactive techniques. ACM.1992 26 (2):71-78
[147]Terzopoulos D, Platt J, Barr A, et al., Elastically deformable models, SIGGRAPH Comput. Graph.,1987,21 (4):205-214
[148]Metaxas D, Terzopoulos D, Dynamic deformation of solid primitives with constraints, SIGGRAPH Comput. Graph.,1992,26 (2):309-312
[149]Pentland A, Williams J, Good vibrations:modal dynamics for graphics and animation, Proceedings of the 16th annual conference on Computer graphics and interactive techniques. ACM.1989:215-222
[150]Weimer H, Warren J, Subdivision schemes for fluid flow, Proceedings of the 26th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co.1999:111-120
[151]Qin H, Terzopoulos D, Triangular NURBS and their dynamic generalizations, Computer Aided Geometric Design,1997,14 (4):325-347
[152]Hong Q, Demetri T, D-NURBS:A Physics-Based Framework for Geometric Design, IEEE Transactions ON Visualization and Computer Graphics,1996,2 (1): 85-96
[153]刘国伟,流曲线概念及造型方法,计算机辅助设计与图形学学报,2006,18(012)：1891-1896
[154]Miura K T, Wang L, Cheng F, Streamline modeling with subdivision surfaces on the Gaussian sphere, Computer-Aided Design,2001,33 (13):975-987
[155]李秀娟,刘浩,何钢等,基于非均匀细分的流曲线曲面,机械科学与技术,2008,27(010)：1216-1219
[156]A Horvath, Horvath Z, Application of CFD numerical simulation for intake port shape design of a diesel engine, Journal of Computational and Applied Mechanics, 2003,4 (2):129-146
[157]Henriot S, Chaouche A, Cheve E, et al., Cfd Aided Development of a Si-Di Engine, Oil & Gas Science and Technology,1999,54 (2):279-286
[158]Wen-chao S, Shu H, ZHANG J, The Application of CFD in Designing Internal Combustion Engine, Vehicle & Power Technology,2006,1
[159]王军杰,严隽琪,汽车发动机进气道自由曲面的反求,中国机械工程,2001,12(007)：741-743
[160]王志,黄荣华,王必等,基于CAD/CAM/CFD的发动机气道研究,内燃机工程,2002,23(003)：26-29
[161]Watanabe N, Miyamoto S, Kuba M, et al., The CFD application for efficient designing in the automotive engineering, SAE SP,2003,89-96
[162]Shi-wei H, Chun-yu H, Li-jing Z, Parametric Modeling of Diesel Helical Intake Port based on ANSYS, Tractor & Farm Transporter,2007,5:28-29
[163]Yau H, Reverse engineering of engine intake ports by digitization and surface approximation, International Journal of Machine Tools and Manufacture,1997,37 (6):855-871
[164]Goldlucke B, Ihrke I, Linz C, et al., Weighted minimal hypersurface reconstruction, IEEE Transactions on pattern analysis and machine intelligence,2007,29 (7): 1194-1208
[165]Zhao H-K, A fast sweeping method for Eikonal equations, Mathematics of Computation,2004,74 (250):603-627
[166]Zhao H-K, Fast sweeping algorithms for a class of Hamilton-Jacobi equations, SIAM journal on numerical analysis,2004,41 (2):673-694
[167]Zhao H-K, Merriman B, Osher S, et al., Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach, Journal of Computational Physics,1998,143 (2):495-518
[168]Osher S, Fedkiw R, Level set methods and dynamic implicit surfaces:New York, Springer,2003.
[169]Osher S, Fedkiw R P, Level Set Methods:An Overview and Some Recent Results, Journal of Computational Physics,2001,169 (2):463-502
[170]谷超豪,复旦大学数学系,数学物理方程：上海科学技术出版社,1987.
[171]Botta E F F, Ellenbroek M H M, A modified SOR method for the Poisson equation in unsteady free-surface flow calculations, Journal of Computational Physics,1986, 60119-134
[172]Saraniti M, Rein A, Zandler G, et al., An efficient multigrid Poisson solver for device simulations, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1996,15 (2):141-150
[173]Holst M, Saied F, Multigrid solution of the Poisson-Boltzmann equation, Journal of computational chemistry,1993,14(1):105-113
[174]Banegas A, Fast Poisson solvers for problems with sparsity, Mathematics of Computation,1978,32 (142):441-446
[175]Temperton C, Direct methods for the solution of the discrete Poisson equation-Some comparisons, Journal of Computational Physics,1979,311-20
[176]Harris F J, On the use of windows for harmonic analysis with the discrete Fourier transform, Proc. IEEE,1978,66 (1):51-83
[177]Serra J, Image analysis and mathematical morphology, New York,1982,
[178]唐常青,吕宏伯,黄铮等.,数学形态学方法及其应用vol.1,1990.
[179]龚炜,石青云,程民德,数字空间中的数学形态学—理论及应用,北京：科学出版社,1997.
[180]Pottmann H, Steiner T, Hofer M, et al., The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces, Lecture Notes in Computer Science, 2004,560-572
[181]Memoli F, Sapiro G, Fast Computation of Weighted Distance Functions and Geodesics on Implicit Hyper-Surfaces, Journal of Computational Physics,2001, 173 (2):730-764
[182]Chan T F, Vese L A, Active contours without edges, Image Processing, IEEE Transactions on,2001,10 (2):266-277
[183]B hm W, Farin G, Kahmann J, A survey of curve and surface methods in CAGD, Computer Aided Geometric Design,1984,1 (1):1-60
[184]Jarke J v W, Implicit stream surfaces, Proceedings of the 4th conference on Visualization'93. San Jose, California. IEEE Computer Society.1993:245-252
[185]Hultquist J P M, Constructing stream surfaces in steady 3D vector fields, Proceedings of the 3rd conference on Visualization'92. Boston, Massachusetts. IEEE Computer Society Press.1992:171-178
[186]Hong-Kai Z, Hong-Kai Z, Osher S, et al., Fast surface reconstruction using the level set method, Variational and Level Set Methods in Computer Vision,2001. Proceedings. IEEE Workshop on.2001:194-201
[187]Smith S M, Brady J M, SUSAN—A new approach to low level image processing, International Journal of Computer Vision,1997,23 (1):45-78
[188]Tomasi C, Manduchi R, Bilateral Filtering for Gray and Color Images, Proceedings of the Sixth International Conference on Computer Vision. IEEE Computer Society. 1998:839
[189]Fredo D, Julie D, Fast bilateral filtering for the display of high-dynamic-range images, Proceedings of the 29th annual conference on Computer graphics and interactive techniques. San Antonio, Texas. ACM.2002:257-266
[190]Jones T R, Durand F, Desbrun M, Non-iterative, feature-preserving mesh smoothing, ACM Transactions on Graphics,2003,22 (3):943-949
[191]Fleishman S, Drori I, Cohen-Or D, Bilateral mesh denoising, ACM Transactions on Graphics (TOG),2003,22 (3):950-953
[2]陈勇,刘雄伟,反求工程CAD建模技术,华侨大学学报：自然科学版,2001,22(004)：376-379
[3]张丽艳,周儒荣,海量测量数据简化技术研究,计算机辅助设计与图形学学报,2001,13(011)：1019-1023
[4]Veron P, Leon J C, Static polyhedron simplification using error measurements, Computer-Aided Design,1997,29 (4):287-298
[5]Besl P J, McKay H D, A method for registration of 3-D shapes, IEEE Transactions on pattern analysis and machine intelligence,1992,14 (2):239-256
[6]Mathieu D, Mark M, Peter S, et al., Anisotropic feature-preserving denoising of height fields and bivariate data, Graphics Interface,2000:145-152
[7]赵作智,林亨,采用能量方程优化零件数据模型,机械设计与制造,2000,(002)：24-26
[8]彭芳瑜,周云飞,基于广义能量法的曲面光顺,华中科技大学学报：自然科学版,2002,30(002)：5-8
[9]Vollmer J, Mencl R, Mueller H, Improved Laplacian smoothing of noisy surface meshes, Blackwell Publishing,1999:131-138
[10]Karbacher S, Haeusler G, A new approach for modeling and smoothing of scattered 3D data, Three-Dimensional Image Capture and Applications,1998,168-177
[11]Gabriel T, A signal processing approach to fair surface design, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM. 1995:351-358
[12]Chen Y, Medioni G, Object modeling by registration of multiple range images, Image and Vision Computing,1992,10 (3):145-155
[13]Farin G E, Hoschek J, Kim M S, Handbook of computer aided geometric design: North Holland,2002.
[14]Pottmann H, Huang Q X, Yang Y L, et al., Geometry and convergence analysis of algorithms for registration of 3D shapes, International Journal of Computer Vision, 2006,67 (3):277-296
[15]Flory S, Hofer M, Surface fitting and registration of point clouds using approximations of the unsigned distance function, Computer Aided Geometric Design,2009,27 (1):60-77
[16]Davis J, Marschner S R, Garr M, et al., Filling holes in complex surfaces using volumetric diffusion,3D Data Processing Visualization and Transmission,2002. Proceedings. First International Symposium on.2002:428-861
[17]Pauly M, Keiser R, Kobbelt L P, et al., Shape modeling with point-sampled geometry, ACM Transactions on Graphics,2003,22 (3):641-650
[18]Niloy J M, An N, Estimating surface normals in noisy point cloud data, Proceedings of the nineteenth annual symposium on Computational geometry. San Diego, California, USA. ACM.2003:322-328
[19]Dey T K, Li G, Sun J, Normal estimation for point clouds:a comparison study for a Voronoi based method, Point-Based Graphics,2005. Eurographics/IEEE VGTC Symposium Proceedings.2005:39-46
[20]OuYang D, Feng H Y, On the normal vector estimation for point cloud data from smooth surfaces, Computer-Aided Design,2005,37 (10):1071-1079
[21]Lange C, Polthier K, Anisotropic smoothing of point sets, Computer Aided Geometric Design,2005,22 (7):680-692
[22]Hu G, Xu J, Miao L, et al., Bilateral estimation of vertex normal for point-sampled models, Springer,2005:758-768
[23]Cazals F, Pouget M, Estimating differential quantities using polynomial fitting of osculating jets, Computer Aided Geometric Design,2005,22 (2):121-146
[24]Hoppe H, DeRose T, Duchamp T, et al., Surface reconstruction from unorganized points, Computer Graphics(ACM),1992,26 (2):71-78
[25]Weiss V, Andor L, Renner G, et al., Advanced surface fitting techniques, Computer Aided Geometric Design,2002,19 (1):19-42
[26]Chaikin G M, An algorithm for high-speed curve generation, Computer graphics and image processing,1974,3 (4):346-349
[27]Catmull E, Clark J, Recursively generated B-spline surfaces on arbitrary topological meshes, Computer Aided Design,1978,10 (6):350-355
[28]Loop C, Smooth subdivision surfaces based on triangles, Master's thesis, University of Utah, Department of Mathematics,1987.
[29]Nira D, David L, John A G, A butterfly subdivision scheme for surface interpolation with tension control, ACM Trans. Graph.,1990,9 (2):160-169
[30]Thomas W S, Jianmin Z, David S, et al., Non-uniform recursive subdivision surfaces, Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM.1998:387-394
[31]Jos S, Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values, Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM.1998:395-404
[32]Pan Q, Xu G L, Fast Evaluation of the Improved Loop's Subdivision Surfaces, Proceedings of the Geometric Modeling and Processing 2004. IEEE Computer Society.2004:205-214
[33]Jorg P, Georg U, Gaussian and Mean Curvature of Subdivision Surfaces, Proceedings of the 9th IMA Conference on the Mathematics of Surfaces. Springer-Verlag.2000:59-69
[34]Schweitzer J E, Analysis and application of subdivision surfaces, University of Washington,1996.
[35]Hugues H, Tony D, Tom D, et al., Piecewise smooth surface reconstruction, Proceedings of the 21st annual conference on Computer graphics and interactive techniques. ACM.1994:295-302
[36]Hiromasa S, Shingo T, Fumihiko K, et al., Subdivision Surface Fitting to a Range of Points, Proceedings of the 7th Pacific Conference on Computer Graphics and Applications. IEEE Computer Society.1999:158-167,322
[37]Takashi K, MeshToSS:Converting Subdivision Surfaces from Dense Meshes, Proceedings of the Vision Modeling and Visualization Conference 2001. Aka GmbH.2001:325-332
[38]Weiyin M, Xiaohu M, Shiu-Kit T, et al., Subdivision Surface Fitting from a Dense Triangle Mesh, Proceedings of the Geometric Modeling and Processing; Theory and Applications (GMP'02). IEEE Computer Society.2002:94-103
[39]Chen H Y, Pottmann H, Approximation by ruled surfaces, Journal of Computational and Applied Mathematics,1999,102 (1):143-156
[40]Kjellander J A P, Smoothing of cubic parametric splines, Computer-Aided Design, 1983,15 (3):175-179
[41]Farin G, Rein G, Sapidis N, et al., Fairing cubic B-spline curves, Computer Aided Geometric Design,1987,4 (1-2):91-103
[42]Sapidis N, Farin G, Automatic fairing algorithm for B-spline curves, Computer-Aided Design,1990,22 (2):121-129
[43]Hahmann S, Konz S, Knot-removal surface fairing using search strategies, Computer Aided Design,1998,30 (2):131-8
[44]Leif K, Swen C, Jens V, et al., Interactive multi-resolution modeling on arbitrary meshes, Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM.1998:105-114
[45]Venkat K, Marc L, Fitting smooth surfaces to dense polygon meshes, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM.1996:313-324
[46]Demetri T, Hong Q, Dynamic NURBS with geometric constraints for interactive sculpting, ACM Trans. Graph.,1994,13 (2):103-136
[47]Demetri T, John P, Alan B, et al., Elastically deformable models, Proceedings of the 14th annual conference on Computer graphics and interactive techniques. ACM. 1987:205-214
[48]Zhang C, Zhang P, Cheng F, Fairing spline curves and surfaces by minimizing energy, Computer-Aided Design,2001,33 (13):913-923
[49]关志东,经玲,基于物理模型的变形曲线曲面研究及应用,计算机学报,1996,9187-194
[50]穆国旺,涂侯杰,参数三次B样条曲线的一种整体光顺方法,工程图学学报,1998,(001)：28-34
[51]穆国旺,朱心雄,曲面光顺的分片能量法,工程图学学报,1999,(001)：29-34
[52]经玲,席平,应用可变形模型进行曲线曲面光顺,软件学报,1998,9(006)：464-468
[53]Eric J S, Tony D D, David H S, Wavelets for Computer Graphics:A Primer, Part 1, IEEE Comput. Graph. Appl.,1995,15 (3):76-84
[54]Eric J S, Tony D D, David H S, Wavelets for computer graphics:theory and applications:Morgan Kaufmann Publishers Inc.,1996.
[55]童伟华,陈发来,冯玉瑜,基于偏微分方程的隐式曲面光顺方法,计算机学报,2004,27(009)：1264-1271
[56]李安平,蒋大为,三次均匀有理B样条曲线的权因子优化光顺算法,计算机辅助设计与图形学学报,1997,9(006)：562-567
[57]Kaufman E, Klass R, Smoothing surfaces using reflection lines for families of splines, Computer-Aided Design,1988,20312-316
[58]William E L, Harvey E C, Marching cubes:A high resolution 3D surface construction algorithm, Proceedings of the 14th annual conference on Computer graphics and interactive techniques. ACM.1987:163-169
[59]Jin G, Wang Q, Shen Y, et al., An improved marching cubes method for surface reconstruction of volume data, Intelligent Control and Automation 2006. Dalian, China. Piscataway United States,2006:10454-10457
[60]Kwan-Liu M, James S P, Charles D H, et al., Parallel volume rendering using binary-swap image composition, ACM SIGGRAPH ASIA 2008 courses. Singapore. ACM.2008:38
[61]Klaus E, Martin K, Thomas E, High-quality pre-integrated volume rendering using hardware-accelerated pixel shading, Proceedings of the ACM SIGGRAPH workshop on Graphics hardware. Los Angeles, California, United States. ACM. 2001:9-16
[62]Tao J, Frank L, Scott S, et al., Dual contouring of hermite data, Proceedings of the 29th annual conference on Computer graphics and interactive techniques. San Antonio, Texas. ACM.2002:339-346
[63]Piegl L A, Tiller W, Parametrization for surface fitting in reverse engineering, Computer-Aided Design,2001,33 (8):593-603
[64]Biplab S, Chia-Hsiang M, Parameter optimization in approximating curves and surfaces to measurement data, Comput. Aided Geom. Des.,1991,8 (4):267-290
[65]来新民,黄田,基于NURBS的散乱数据点自由曲面重构,计算机辅助设计与图形学学报,1999,11(005)：433-436
[66]Piegl L A, Tiller W, Surface approximation to scanned data, The Visual Computer, 2000,16 (7):386-395
[67]童伟华,冯玉瑜,陈发来,层次隐式张量积B-样条曲面及其在曲面重构中的应用,Journal of Software,2006,1711-20
[68]Yang Z, Deng J, Chen F, Fitting unorganized point clouds with active implicit B-spline curves, The Visual Computer,2005,21 (8):831-839
[69]Thomas W S, Jianmin Z, Almaz B, et al., T-splines and T-NURCCs, ACM SIGGRAPH 2003 Papers. San Diego, California. ACM.2003:477-484
[70]Thomas W S, David L C, Finnigan G T, et al., T-spline simplification and local refinement, ACM Trans. Graph.,2004,23 (3):276-283
[71]Yong-bo W, Ye-hua S, Guo-nian L V, et al., A Delaunay-based Surface Reconstruction Algorithm for Unorganized Sampling Points, Journal of Image and Graphics,2007,9:1537-1543
[72]Edelsbrunner H, Mucke E P, Three-dimensional alpha shapes, ACM Transactions on Graphics (TOG),1994,13 (1):72
[73]Amenta N, Choi S, Kolluri R K, The power crust, unions of balls, and the medial axis transform, Computational Geometry,2001,19 (2-3):127-153
[74]Ravikrishna K, Jonathan Richard S, James F O B, Spectral surface reconstruction from noisy point clouds, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing. Nice, France. ACM.2004:11-21
[75]Chandrajit L B, Fausto B, Guoliang X, Automatic reconstruction of surfaces and scalar fields from 3D scans, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM.1995:109-118
[76]YH Chen, Liu C, Robust segmentation of CMM data based on NURBS, The International Journal of Advanced Manufacturing Technology,1997,13:530-534
[77]Yang M, Lee E, Segmentation of measured point data using a parametric quadric surface approximation, Computer-Aided Design,1999,31 (7):449-457
[78]Katz S, Leifman G, Tal A, Mesh segmentation using feature point and core extraction, The Visual Computer,2005,21 (8):649-658
[79]Jianbing H, Chia-Hsiang M, Automatic data segmentation for geometric feature extraction from unorganized 3-D coordinate points, Robotics and Automation, IEEE Transactions on,2001,17 (3):268-279
[80]Hitoshi Y, Stefan G, Rhaleb Z, et al., Mesh Segmentation Driven by Gaussian Curvature, The Visual Computer,2005,21 (8-10):659-668
[81]Koschan A F, Perception-based 3D triangle mesh segmentation using fast marching watersheds, Computer Vision and Pattern Recognition,2003. Proceedings.2003 IEEE Computer Society Conference on.2003:Ⅱ-27-Ⅱ-32 vol.2
[82]Helmut Pottmann T S, Michael Hofer, Christoph Haider, Allan Hanbury, The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces, Computer Vision-ECCV 2004,2004,18-23
[83]Yu-Kun L, Shi-Min H, Ralph R M, et al., Fast mesh segmentation using random walks, Proceedings of the 2008 ACM symposium on Solid and physical modeling. Stony Brook, New York. ACM.2008:183-191
[84]Levy B, Petitjean S, Ray N, et al., Least squares conformal maps for automatic texture atlas generation, ACM Transactions on Graphics,2002,21 (3):362-371
[85]Yu-Kun L, Qian-Yi Z, Shi-Min H, et al., Robust Feature Classification and Editing, IEEE Transactions ON VISUALIZATION AND COMPUTER GRAPHICS,2007, 13(1):34-45
[86]Woo H, Kang E, Wang S, et al., A New Segmentation Method for Point Cloud Data, International Journal of Machine Tools and Manufacture,2002,42 (2):167-178
[87]Pottmann H, Leopoldseder S, Hofer M, et al., Industrial geometry:recent advances and applications in CAD, Computer-Aided Design,2005,37 (7):751-766
[88]Checchin P, Trassoudaine L, Alizon J, Segmentation of range images into planar regions,3-D Digital Imaging and Modeling,1997. Proceedings., International Conference on Recent Advances in.1997:156-163
[89]Dongming Z, Xintong Z, Range-data-based object surface segmentation via edges and critical points, Image Processing, IEEE Transactions on,1997,6 (6):826-830
[90]Koster K, Spann M, MIR:an approach to robust clustering-application to range image segmentation, Pattern Analysis and Machine Intelligence, IEEE Transactions on,2000,22 (5):430-444
[91]Michael G, Andrew W, Paul S H, Hierarchical face clustering on polygonal surfaces, Proceedings of the 2001 symposium on Interactive 3D graphics. ACM. 2001:49-58
[92]Rong L, Hao Z, Segmentation of 3D Meshes through Spectral Clustering, Proceedings of the Computer Graphics and Applications,12th Pacific Conference. IEEE Computer Society.2004:298-305
[93]Sagi K, Ayellet T, Hierarchical mesh decomposition using fuzzy clustering and cuts, ACM Trans. Graph.,2003,22 (3):954-961
[94]Lavou G, Dupont F, Baskurt A, A new CAD mesh segmentation method, based on curvature tensor analysis, Computer-Aided Design,2005,37 (10):975-987
[95]Gumhold S, Wang X, MacLeod R, Feature extraction from point clouds,2001: 293-305
[96]Mark P, Richard K, Markus G, Multi-scale Feature Extraction on Point-Sampled Surfaces, Computer Graphics Forum,2003,22 (3):281-289
[97]Provot L, Debled-Rennesson I,3D noisy discrete objects:Segmentation and application to smoothing, Pattern Recognition,2009,42 (8):1626-1636
[98]Demarsin K, Vanderstraeten D, Volodine T, et al., Detection of closed sharp edges in point clouds using normal estimation and graph theory, Computer-Aided Design, 2007,39 (4):276-283
[99]Brian C, Marc L, A volumetric method for building complex models from range images, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM.1996:303-312
[100]James F B, A Generalization of Algebraic Surface Drawing, ACM Trans. Graph., 1982,1 (3):235-256
[101]Jules B, Ken S, Convolution surfaces, Proceedings of the 18th annual conference on Computer graphics and interactive techniques. ACM.1991:251-256
[102]Yutaka O, Alexander B, Marc A, et al., Multi-level partition of unity implicits, ACM Trans. Graph.,2003,22 (3):463-470
[103]Yukie N, Yutaka O, Hiromasa S, Smoothing of Partition of Unity Implicit Surfaces for Noise Robust Surface Reconstruction, Computer Graphics Forum,2009,28 (5): 1339-1348
[104]Gelas A, Ohtake Y, Kanai T, et al., Approximation of Unorganized Point Set with Composite Implicit Surface, Image Processing,2006 IEEE International Conference on.2006:1217-1220
[105]Marc A, Johannes B, Daniel C-O, et al., Point set surfaces, Proceedings of the conference on Visualization'01. San Diego, California. IEEE Computer Society. 2001:
[106]Gael G, Markus G, Algebraic point set surfaces, ACM SIGGRAPH 2007 papers. San Diego, California. ACM.2007
[107]Phan L, Liu L, Abeysinghe S, et al., Surface reconstruction from point set using projection operator, ACM New York, NY, USA,2008:1-1
[108]Nina A, Yong Joo K, Defining point-set surfaces, ACM SIGGRAPH 2004 Papers. Los Angeles, California. ACM.2004:264-270
[109]Kass M, Witkin A, Terzopoulos D, Snakes:Active contour models, International Journal of Computer Vision,1988,1 (4):321-331
[110]Osher S, Sethian J A, Fronts Propagating With Curvature-dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics,1988,79(1):12-49
[111]Zhao H-K, Osher S, Merriman B, et al., Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method, Computer Vision and Image Understanding,2000,80 (3):295-314
[112]Sethian J, A Fast Marching Level Set Method for Monotonically Advancing Fronts, Proceedings of the National Academy of Sciences of the United States of America, 1996,93 (4):1591-1595
[113]Chopp D L, Some improvements of the fast marching method, SIAM Journal of Scientific Computing,2002,23 (1):230-244
[114]Chunming L, Chenyang X, Changfeng G, et al., Level Set Evolution Without Re-initialization:A New Variational Formulation, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Diego, California. IEEE Computer Society 2005:430-436
[115]Li C, Kao C Y, Gore J C, et al., Implicit active contours driven by local binary fitting energy, IEEE Computer Vision and Pattern Recognition (CVPR), Minneapolis, Minnesota, USA,2007,17-22
[116]Carr J C, Beatson R K, Cherrie J B, et al., Reconstruction and representation of 3D objects with radial basis functions, Proceedings of the 28th annual conference on Computer graphics and interactive techniques. ACM.2001:67-76
[117]Acosta F M A, Radial basis function and related models:An overview, Signal Processing,1995,45 (1):37-58
[118]Huong Quynh D, Turk G, Slabaugh G, Reconstructing surfaces by volumetric regularization using radial basis functions, Pattern Analysis and Machine Intelligence, IEEE Transactions on,2002,24 (10):1358-1371
[119]Lin Y, Chen C, Song M, et al., Dual-RBF based surface reconstruction, The Visual Computer,2009,25 (5):599-607
[120]Magoules F, Diago L A, Hagiwara I, Efficient preconditioning for image reconstruction with radial basis functions, Advances in Engineering Software, 2007,38 (5):320-327
[121]Greg T, James F O b, Modelling with implicit surfaces that interpolate, ACM Trans. Graph.,2002,21 (4):855-873
[122]Ohtake Y, Belyaev A, Seidel H-P, Sparse surface reconstruction with adaptive partition of unity and radial basis functions, Graphical Models,2006,68 (1):15-24
[123]Michael K, Matthew B, Hugues H, Poisson surface reconstruction, Proceedings of the fourth Eurographics symposium on Geometry processing. Cagliari, Sardinia, Italy. Eurographics Association.2006:61-70
[124]Manson J, Petrova G, Schaefer S, Streaming Surface Reconstruction Using Wavelets, Computer Graphics Forum,2008,27 (5):1411-1420
[125]Alliez P, Cohen-Steiner D, Tong Y, et al., Voronoi-based variational reconstruction of unoriented point sets, Proceedings of the fifth Eurographics symposium on Geometry processing. Barcelona, Spain. Eurographics Association.2007:39-48
[126]Boissonnat J D, Cazals F, Smooth surface reconstruction via natural neighbour interpolation of distance functions, Computational Geometry:Theory and Applications,2002,22 (1-3):185-203
[127]Alexander H, Leif K, Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information, Proceedings of the fourth Eurographics symposium on Geometry processing. Cagliari, Sardinia, Italy. Eurographics Association.2006:41-50
[128]Boykov Y, Kolmogorov V, Computing geodesics and minimal surfaces via graph cuts, Computer Vision,2003. Proceedings. Ninth IEEE International Conference on.2003 (1):26-33
[129]Xu N, Ahuja N, Bansal R, Object segmentation using graph cuts based active contours, Computer Vision and Image Understanding,2007,107 (3):210-224
[130]Barhak J, Fischer A, Adaptive reconstruction of freeform objects with 3D SOM neural network grids, Computers & Graphics,2002,26 (5):745-751
[131]Peng Q, Loftus M, Using image processing based on neural networks in reverse engineering, International Journal of Machine Tools and Manufacture,2001,41 (5): 625-640
[132]He X, Li C, Hu Y, et al., Automatic sequence of 3D point data for surface fitting using neural networks, Computers & Industrial Engineering,2009,57 (1):408-418
[133]Vladimir S, Lothar S, Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection, Proceedings of the sixth ACM symposium on Solid modeling and applications. Ann Arbor, Michigan, United States. ACM.2001:39-46
[134]Cong L, Wangge W, Youyong W, Image based reconstruction using hybrid optimization of simulated annealing and genetic algorithm, Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation. Shanghai, China. ACM.2009:875-878
[135]Kumar G S, Kalra P K, Dhande S G, Curve and surface reconstruction from points: an approach based on self-organizing maps, Applied Soft Computing Journal,2004, 5 (1):55-66
[136]Werman M, Keren D, A Bayesian method for fitting parametric and nonparametric models to noisy data, IEEE Transactions on pattern analysis and machine intelligence,2001,23 (5):528-534
[137]Diebel J R, Thrun S, Brunig M, A Bayesian method for probable surface reconstruction and decimation, ACM Transactions on Graphics (TOG),2006,25 (1):39-59
[138]Keren D, Werman M, A full bayesian approach to curve and surface reconstruction, Journal of Mathematical Imaging and Vision,1999,11 (1):27-43
[139]Jenke P, Wand M, Bokeloh M, et al., Bayesian Point Cloud Reconstruction, Computer Graphics Forum,2006,25 (3):379-388
[140]Roca-Pardinas J, Lorenzo H, Arias P, et al., From laser point clouds to surfaces: Statistical nonparametric methods for three-dimensional reconstruction, Computer-Aided Design,2008,40 (5):646-652
[141]Paulsen R R, B rentzen J A, Larsen R, Markov Random Field Surface Reconstruction, IEEE Transactions On Visualization and Computer Graphics,2009, 16 (4):636-646
[142]Xie P, McDonnell K T, Qin P, Surface Reconstruction of Noisy and Defective Data Sets, Proceedings of the conference on Visualization'04,2004,259-266
[143]Liu Y, Pottmann H, Wang W, Constrained 3D shape reconstruction using a combination of surface fitting and registration, Computer Aided Design,2006,38 (6):572-583
[144]Li X, Han C Y, Wee W G, On surface reconstruction:A priority driven approach, Computer-Aided Design,2009,41 (9):626-640
[145]Esteve J, Brunet P, Vinacua A, Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane, Computer Graphics Forum,2005,24 (4):791-807
[146]Hugues H, Tony D, Tom D, et al., Surface reconstruction from unorganized points, Proceedings of the 19th annual conference on Computer graphics and interactive techniques. ACM.1992 26 (2):71-78
[147]Terzopoulos D, Platt J, Barr A, et al., Elastically deformable models, SIGGRAPH Comput. Graph.,1987,21 (4):205-214
[148]Metaxas D, Terzopoulos D, Dynamic deformation of solid primitives with constraints, SIGGRAPH Comput. Graph.,1992,26 (2):309-312
[149]Pentland A, Williams J, Good vibrations:modal dynamics for graphics and animation, Proceedings of the 16th annual conference on Computer graphics and interactive techniques. ACM.1989:215-222
[150]Weimer H, Warren J, Subdivision schemes for fluid flow, Proceedings of the 26th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co.1999:111-120
[151]Qin H, Terzopoulos D, Triangular NURBS and their dynamic generalizations, Computer Aided Geometric Design,1997,14 (4):325-347
[152]Hong Q, Demetri T, D-NURBS:A Physics-Based Framework for Geometric Design, IEEE Transactions ON Visualization and Computer Graphics,1996,2 (1): 85-96
[153]刘国伟,流曲线概念及造型方法,计算机辅助设计与图形学学报,2006,18(012)：1891-1896
[154]Miura K T, Wang L, Cheng F, Streamline modeling with subdivision surfaces on the Gaussian sphere, Computer-Aided Design,2001,33 (13):975-987
[155]李秀娟,刘浩,何钢等,基于非均匀细分的流曲线曲面,机械科学与技术,2008,27(010)：1216-1219
[156]A Horvath, Horvath Z, Application of CFD numerical simulation for intake port shape design of a diesel engine, Journal of Computational and Applied Mechanics, 2003,4 (2):129-146
[157]Henriot S, Chaouche A, Cheve E, et al., Cfd Aided Development of a Si-Di Engine, Oil & Gas Science and Technology,1999,54 (2):279-286
[158]Wen-chao S, Shu H, ZHANG J, The Application of CFD in Designing Internal Combustion Engine, Vehicle & Power Technology,2006,1
[159]王军杰,严隽琪,汽车发动机进气道自由曲面的反求,中国机械工程,2001,12(007)：741-743
[160]王志,黄荣华,王必等,基于CAD/CAM/CFD的发动机气道研究,内燃机工程,2002,23(003)：26-29
[161]Watanabe N, Miyamoto S, Kuba M, et al., The CFD application for efficient designing in the automotive engineering, SAE SP,2003,89-96
[162]Shi-wei H, Chun-yu H, Li-jing Z, Parametric Modeling of Diesel Helical Intake Port based on ANSYS, Tractor & Farm Transporter,2007,5:28-29
[163]Yau H, Reverse engineering of engine intake ports by digitization and surface approximation, International Journal of Machine Tools and Manufacture,1997,37 (6):855-871
[164]Goldlucke B, Ihrke I, Linz C, et al., Weighted minimal hypersurface reconstruction, IEEE Transactions on pattern analysis and machine intelligence,2007,29 (7): 1194-1208
[165]Zhao H-K, A fast sweeping method for Eikonal equations, Mathematics of Computation,2004,74 (250):603-627
[166]Zhao H-K, Fast sweeping algorithms for a class of Hamilton-Jacobi equations, SIAM journal on numerical analysis,2004,41 (2):673-694
[167]Zhao H-K, Merriman B, Osher S, et al., Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach, Journal of Computational Physics,1998,143 (2):495-518
[168]Osher S, Fedkiw R, Level set methods and dynamic implicit surfaces:New York, Springer,2003.
[169]Osher S, Fedkiw R P, Level Set Methods:An Overview and Some Recent Results, Journal of Computational Physics,2001,169 (2):463-502
[170]谷超豪,复旦大学数学系,数学物理方程：上海科学技术出版社,1987.
[171]Botta E F F, Ellenbroek M H M, A modified SOR method for the Poisson equation in unsteady free-surface flow calculations, Journal of Computational Physics,1986, 60119-134
[172]Saraniti M, Rein A, Zandler G, et al., An efficient multigrid Poisson solver for device simulations, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1996,15 (2):141-150
[173]Holst M, Saied F, Multigrid solution of the Poisson-Boltzmann equation, Journal of computational chemistry,1993,14(1):105-113
[174]Banegas A, Fast Poisson solvers for problems with sparsity, Mathematics of Computation,1978,32 (142):441-446
[175]Temperton C, Direct methods for the solution of the discrete Poisson equation-Some comparisons, Journal of Computational Physics,1979,311-20
[176]Harris F J, On the use of windows for harmonic analysis with the discrete Fourier transform, Proc. IEEE,1978,66 (1):51-83
[177]Serra J, Image analysis and mathematical morphology, New York,1982,
[178]唐常青,吕宏伯,黄铮等.,数学形态学方法及其应用vol.1,1990.
[179]龚炜,石青云,程民德,数字空间中的数学形态学—理论及应用,北京：科学出版社,1997.
[180]Pottmann H, Steiner T, Hofer M, et al., The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces, Lecture Notes in Computer Science, 2004,560-572
[181]Memoli F, Sapiro G, Fast Computation of Weighted Distance Functions and Geodesics on Implicit Hyper-Surfaces, Journal of Computational Physics,2001, 173 (2):730-764
[182]Chan T F, Vese L A, Active contours without edges, Image Processing, IEEE Transactions on,2001,10 (2):266-277
[183]B hm W, Farin G, Kahmann J, A survey of curve and surface methods in CAGD, Computer Aided Geometric Design,1984,1 (1):1-60
[184]Jarke J v W, Implicit stream surfaces, Proceedings of the 4th conference on Visualization'93. San Jose, California. IEEE Computer Society.1993:245-252
[185]Hultquist J P M, Constructing stream surfaces in steady 3D vector fields, Proceedings of the 3rd conference on Visualization'92. Boston, Massachusetts. IEEE Computer Society Press.1992:171-178
[186]Hong-Kai Z, Hong-Kai Z, Osher S, et al., Fast surface reconstruction using the level set method, Variational and Level Set Methods in Computer Vision,2001. Proceedings. IEEE Workshop on.2001:194-201
[187]Smith S M, Brady J M, SUSAN—A new approach to low level image processing, International Journal of Computer Vision,1997,23 (1):45-78
[188]Tomasi C, Manduchi R, Bilateral Filtering for Gray and Color Images, Proceedings of the Sixth International Conference on Computer Vision. IEEE Computer Society. 1998:839
[189]Fredo D, Julie D, Fast bilateral filtering for the display of high-dynamic-range images, Proceedings of the 29th annual conference on Computer graphics and interactive techniques. San Antonio, Texas. ACM.2002:257-266
[190]Jones T R, Durand F, Desbrun M, Non-iterative, feature-preserving mesh smoothing, ACM Transactions on Graphics,2003,22 (3):943-949
[191]Fleishman S, Drori I, Cohen-Or D, Bilateral mesh denoising, ACM Transactions on Graphics (TOG),2003,22 (3):950-953