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Issue No.02 - Feb. (2013 vol.19)
pp: 306-318
Min Wan , Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore
Yu Wang , CGGVeritas Co., Singapore, Singapore
E. Bae , Dept. of Math., Univ. of Bergen, Bergen, Norway
Xue-Cheng Tai , Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore
Desheng Wang , Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore
ABSTRACT
A novel graph-cuts-based method is proposed for reconstructing open surfaces from unordered point sets. Through a Boolean operation on the crust around the data set, the open surface problem is translated to a watertight surface problem within a restricted region. Integrating the variational model, Delaunay-based tetrahedral mesh and multiphase technique, the proposed method can reconstruct open surfaces robustly and effectively. Furthermore, a surface reconstruction method with domain decomposition is presented, which is based on the new open surface reconstruction method. This method can handle more general surfaces, such as nonorientable surfaces. The algorithm is designed in a parallel-friendly way and necessary measures are taken to eliminate cracks and conflicts between the subdomains. Numerical examples are included to demonstrate the robustness and effectiveness of the proposed method on watertight, open orientable, open nonorientable surfaces and combinations of such.
INDEX TERMS
mesh generation, Boolean functions, computer graphics, graph theory, watertight surfaces, graph-cuts-based method, unordered point sets, Boolean operation, open surface problem, Delaunay-based tetrahedral mesh, multiphase technique, domain decomposition, open surface reconstruction method, open nonorientable surfaces, Surface reconstruction, Level set, Surface cracks, Surface treatment, Reconstruction algorithms, Minimization, Robustness, Delaunay triangulation, Graph cuts, open surface, domain decomposition
CITATION
Min Wan, Yu Wang, E. Bae, Xue-Cheng Tai, Desheng Wang, "Reconstructing Open Surfaces via Graph-Cuts", IEEE Transactions on Visualization & Computer Graphics, vol.19, no. 2, pp. 306-318, Feb. 2013, doi:10.1109/TVCG.2012.119
REFERENCES
[1] T. Dey, Curve and Surface Reconstruction: Algorithms with Mathematical Analysis, pp. 6-7. Cambridge Univ Press, 2007.
[2] H. Edelsbrunner and E. Mucke, "Three-Dimensional Alpha Shapes," Proc. Workshop Vol. Visualization, pp. 75-82, 1992.
[3] N. Amenta, M. Bern, and M. Kamvysselis, "A New Voronoi-Based Surface Reconstruction Algorithm," Proc. 25th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 415-421, 1998.
[4] F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva, and G. Taubin, "The Ball-Pivoting Algorithm for Surface Reconstruction," IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 4, pp. 349-359, Oct.-Dec. 1999.
[5] U. Adamy, J. Giesen, and M. John, "New Techniques for Topologically Correct Surface Reconstruction," Proc. Conf. Visualization '00, pp. 373-380, 2000.
[6] T.K. Dey and S. Goswami, "Tight Cocone: A Water-Tight Surface Reconstructor," Proc. Eighth ACM Symp. Solid Modeling and Applications (SM '03), pp. 127-134, 2003.
[7] M. Zhao, "Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method," Computer Vision and Image Understanding, vol. 80, no. 3, pp. 295-314, 2000.
[8] E. Franchini, S. Morigi, and F. Sgallari, "Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds," Numerical Math.: Theory, Methods and Applications, vol. 3, pp. 405-430, 2010.
[9] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, "Surface Reconstruction from Unorganized Points," Proc. 19th Ann. Conf. Computer Graphics and Interactive Techniques (SIGGRAPH '92), pp. 71-78, 1992.
[10] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C. Silva, "Point Set Surfaces," Proc. IEEE Conf. Visualization, vol. 1, pp. 21-28, 2001.
[11] H. Zhao, S. Osher, and R. Fedkiw, "Fast Surface Reconstruction Using the Level Set Method," Proc. IEEE Workshop Variational and Level Set Methods (VLSM '01), pp. 194-201, 2001.
[12] E. Franchini, S. Morigi, and F. Sgallari, "Segmentation of 3D Tubular Structures by a PDE-Based Anisotropic Diffusion Model," Proc. Seventh Int'l Conf. Math. Methods for Curves and Surfaces , pp. 224-241, 2010.
[13] J. Barhak and A. Fischer, "Parameterization and Reconstruction from 3D Scattered Points Based on Neural Network and pde Techniques," IEEE Trans. Visualization and Computer Graphics, vol. 7, no. 1, pp. 1-16, Jan.-Mar. 2001.
[14] J. Solem and A. Heyden, "Reconstructing Open Surfaces from Unorganized Data Points," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 2, 2004.
[15] A. Jalba and J. Roerdink, "Efficient Surface Reconstruction Using Generalized Coulomb Potentials," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp. 1512-1519, Nov.-Dec. 2007.
[16] R. Paulsen, J. Baerentzen, and R. Larsen, "Markov Random Field Surface Reconstruction," IEEE Trans. Visualization and Computer Graphics, vol. 16, no. 4, pp. 636-646, July/Aug. 2009.
[17] K. Zhou, M. Gong, X. Huang, and B. Guo, "Data-Parallel Octrees for Surface Reconstruction," IEEE Trans. Visualization and Computer Graphics, vol. 17, no. 5, pp. 669-681, May 2011.
[18] S. Paris, F. Sillion, and L. Quan, "A Surface Reconstruction Method Using Global Graph Cut Optimization," Int'l J. Computer Vision, vol. 66, no. 2, pp. 141-161, 2006.
[19] G. Zeng, S. Paris, L. Quan, and F. Sillion, "Accurate and Scalable Surface Representation and Reconstruction from Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 1, pp. 141-158, Jan. 2007.
[20] V.S. Lempitsky and Y. Boykov, "Global Optimization for Shape Fitting," Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), 2007.
[21] S. Paris, F. Sillion, and L. Quan, "A Surface Reconstruction Method Using Global Graph Cut Optimization," Int'l J. Computer Vision, vol. 66, no. 2, pp. 141-161, 2006.
[22] A. Hornung and L. Kobbelt, "Robust Reconstruction of Watertight 3D Models from Non-Uniformly Sampled Point Clouds without Normal Information," Geometry Processing '06: Proc. Fourth Eurographics Symp. Geometry Processing, p. 41, 2006.
[23] S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer Verlag, 2002.
[24] Y. Yu, "Surface Reconstruction from Unorganized Points Using Self-Organizing Neural Networks," Proc. IEEE Visualization, vol. 99, pp. 61-64, 1999.
[25] C. Kuo and H. Yau, "A Delaunay-Based Region-Growing Approach to Surface Reconstruction from Unorganized Points," Computer-Aided Design, vol. 37, no. 8, pp. 825-835, 2005.
[26] J. Solem and A. Heyden, "Reconstructing Open Surfaces from Image Data," Int'l J. Computer Vision, vol. 69, no. 3, pp. 267-275, 2006.
[27] T. Kohlberger, C. Schnörr, A. Bruhn, and J. Weickert, "Domain Decomposition for Parallel Variational Optical Flow Computation," Proc. 25th German Conf. Pattern Recognition, pp. 196-203, 2003.
[28] T. Kohlberger, C. Schnörr, A. Bruhn, and J. Weickert, "Domain Decomposition for Nonlinear Problems: A Control-Theoretic Approach," technical report, Computer Science Series, 2005.
[29] T. Kohlberger, C. Schnörr, A. Bruhn, and J. Weickert, "Parallel Variational Motion Estimation by Domain Decomposition and Cluster Computing," Proc. Eighth European Conf. Computer Vision (ECCV '04), pp. 205-216, 2004.
[30] X. Tai and J. Xu, "Global and Uniform Convergence of Subspace Correction Methods for Some Convex Optimization Problems," Math. of Computation, vol. 71, no. 237, pp. 105-124, 2002.
[31] Y. Duan and X. Tai, "Domain Decomposition Methods with Graph Cuts Algorithms for Total Variation Minimization," Advances in Computational Math., pp. 1-25, 2011.
[32] P. Strandmark and F. Kahl, "Parallel and Distributed Graph Cuts by Dual Decomposition," Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), pp. 2085-2092, 2010.
[33] M. Wan, Y. Wang, and D. Wang, "Variational Surface Reconstruction Based on Delaunay Triangulation and Graph Cut," Int'l J. Numerical Methods in Eng., vol. 85, no. 2, pp. 206-229, 2011.
[34] V. Caselles, R. Kimmel, G. Sapiro, and C. Sbert, "Minimal Surfaces Based Object Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 4, pp. 394-398, Apr. 1997.
[35] V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic Active Contours," Int'l J. Computer Vision, vol. 22, no. 1, pp. 61-79, 1997.
[36] A. Hornung and L. Kobbelt, "Hierarchical Volumetric Multi-View Stereo Reconstruction of Manifold Surfaces Based on Dual Graph Embedding," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 1, 2006.
[37] E. Bae and X.-C. Tai, "Graph Cut Optimization for the Piecewise Constant Level Set Method Applied to Multiphase Image Segmentation," Proc. Second Int'l Conf. Scale Space and Variational Methods in Computer Vision (SSVM), X.-C. Tai, K. Morken, M. Lysaker, and K.-A. Lie eds., pp. 1-13, 2009.
[38] J. Lie, M. Lysaker, and X. Tai, "A Variant of the Level Set Method and Applications to Image Segmentation," Math. of Computation, vol. 75, no. 255, pp. 1155-1174, 2006.
[39] P. George and H. Borouchaki, Delaunay Triangulation and Meshing: Application to Finite Elements. Kogan Page, 1998.
[40] R. Gray and D. Neuhoff, "Quantization," IEEE Trans. Information Theory, vol. 44, no. 6, pp. 2325-2383, 2002.
[41] F. Labelle and J. Shewchuk, "Isosurface Stuffing: Fast Tetrahedral Meshes with Good Dihedral Angles," Proc. ACM SIGGRAPH '07 Papers, p. 57, 2007.
[42] Q. Du and D. Wang, "Tetrahedral Mesh Generation and Optimization Based on Centroidal Voronoi Tessellations," Int'l J. Numerical Methods in Eng., vol. 56, pp. 1355-1373, 2002.
[43] M. Wan, D. Wang, and X. Tai, "Surface Reconstruction with Feature Preservation Based on Graph-Cuts," UCLA CAM Report 12-58.
[44] V. Kolmogorov and R. Zabin, "What Energy Functions can be Minimized via Graph Cuts?" IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 147-159, Feb. 2004.
[45] Y. Boykov and V. Kolmogorov, "An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124-1137, Sept. 2004.
[46] Y. Boykov, O. Veksler, and R. Zabih, "Fast Approximate Energy Minimization via Graph Cuts," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 11, pp. 1222-1239, Nov. 2001.
[47] H. Ishikawa, "Exact Optimization for Markov Random Fields with Convex Priors," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1333-1336, Oct. 2003.
[48] R. Adams and L. Bischof, "Seeded Region Growing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 6, pp. 641-647, June 1994.
[49] E. Hodneland, X. Tai, and H. Gerdes, "Four-Color Theorem and Level Set Methods for Watershed Segmentation," Int'l J. Computer Vision, vol. 82, no. 3, pp. 264-283, 2009.
[50] H. Edelsbrunner and N. Shah, "Incremental Topological Flipping Works for Regular Triangulations," Algorithmica, vol. 15, no. 3, pp. 223-241, 1996.
[51] "Cgal, Computational Geometry Algorithms Library," http:/www.cgal.org, 1997.
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