Subscribe

Issue No.10 - October (2011 vol.17)

pp: 1531-1544

Huai-Yu Wu , Peking University, Beijing and Chinese Academy of Sciences, Beijing

Chunhong Pan , Chinese Academy of Sciences, Beijing

Hongbin Zha , Peking University, Beijing

Qing Yang , Chinese Academy of Sciences, Beijing

Songde Ma , Chinese Academy of Sciences, Beijing

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.231

ABSTRACT

In this paper, we propose a novel partwise framework for cross-parameterization between 3D mesh models. Unlike most existing methods that use regular parameterization domains, our framework uses nonregular approximation domains to build the cross-parameterization. Once the nonregular approximation domains are constructed for 3D models, different (and complex) input shapes are transformed into similar (and simple) shapes, thus facilitating the cross-parameterization process. Specifically, a novel nonregular domain, the convex hull, is adopted to build shape correspondence. We first construct convex hulls for each part of the segmented model, and then adopt our convex-hull cross-parameterization method to generate compatible meshes. Our method exploits properties of the convex hull, e.g., good approximation ability and linear convex representation for interior vertices. After building an initial cross-parameterization via convex-hull domains, we use compatible remeshing algorithms to achieve an accurate approximation of the target geometry and to ensure a complete surface matching. Experimental results show that the compatible meshes constructed are well suited for shape blending and other geometric applications.

INDEX TERMS

Cross-parameterization, nonregular approximation domains, convex hull, critical points, compatible remeshing, sketch-based segmentation.

CITATION

Huai-Yu Wu, Chunhong Pan, Hongbin Zha, Qing Yang, Songde Ma, "Partwise Cross-Parameterization via Nonregular Convex Hull Domains",

*IEEE Transactions on Visualization & Computer Graphics*, vol.17, no. 10, pp. 1531-1544, October 2011, doi:10.1109/TVCG.2010.231REFERENCES

- [1] B. Allen, B. Curless, and Z. Popović, “The Space of Human Body Shapes: Reconstruction and Parameterization from Range Scans,”
Proc. SIGGRAPH, pp. 587-594, 2003.- [2] V. Kraevoy and A. Sheffer, “Cross-Parameterization and Compatible Remeshing of 3D Models,”
Proc. SIGGRAPH, pp. 861-869, 2004.- [3] E. Praun, W. Sweldens, and P. Schröder, “Consistent Mesh Parameterizations,”
Proc. SIGGRAPH, pp. 179-184, 2001.- [4] S. Shlafman, A. Tal, and S. Katz, “Metamorphosis of Polyhedral Surfaces Using Decomposition,”
Eurographics, vol. 21, no. 3, pp. 219-228, 2002.- [5] E. Praun and H. Hoppe, “Spherical Parametrization and Remeshing,”
Proc. SIGGRAPH, pp. 340-349, 2003.- [6] J. Pan, H.-Y. Wu, C. Pan, and Q. Yang, “A Novel Scheme for Efficient Cross-Parameterization,”
Proc. Conf. Computer Graphics Int'l (CGI), 2007.- [7] H.-Y. Wu, C. Pan, Q. Yang, and S. Ma, “Consistent Correspondence between Arbitrary Manifold Surfaces,”
Proc. Int'l Conf. Computer Vision (ICCV), 2007.- [8] Y. Lipman and T. Funkhouser, “Möbius Voting for Surface Correspondence,”
Proc. SIGGRAPH, vol. 28, no. 3, 2009.- [9] H. Zhang, A. Sheffer, D. Cohen-Or, Q. Zhou, O. van Kaick, and A. Tagliasacchi, “Deformation-Driven Shape Correspondence,”
Computer Graphics Forum, vol. 27, no. 5, pp. 1431-1439, 2008.- [10] A.M. Bronstein, M.M. Bronstein, R. Kimmel, M. Mahmoudi, and G. Sapiro, “A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-Rigid Shape Matching,”
Int'l J. Computer Vision, vol. 89, pp. 266-286, 2009.- [11] M.R. Ruggeri, G. Patane, M. Spagnuolo, and D. Saupe, “Spectral-Driven Isometry-Invariant Matching of 3D Shapes,”
Int'l J. Computer Vision, vol. 89, pp. 248-265, 2009.- [12] L. Zhang, L. Liu, Z. Ji, and G. Wang, “Manifold Parameterization,”
Proc. Computer Graphics Int'l Conf., pp. 160-171, 2006.- [13] J. Schreiner, A. Asirvatham, E. Praun, and H. Hoppe, “Inter-Surface Mapping,”
Proc. SIGGRAPH, pp. 870-877, 2004.- [14] D. Ghosh, A. Sharf, and N. Amenta, “Feature-Driven Deformation for Dense Correspondence,”
Proc. SPIE Medical Imaging, pp. 36-40, 2009.- [15] Q.-X. Huang, B. Adams, M. Wicke, and L.J. Guibas, “Non-Rigid Registration under Isometric Deformations,”
Computer Graphics Forum, vol. 27, no. 5, pp. 1449-1457, 2008.- [16] O. van Kaick, H. Zhang, G. Hamarneh, and D. Cohen-Or, “A Survey on Shape Correspondence,”
Proc. Eurographics State-of-The-Art Report (STAR), 2010.- [17] M. Alexa, “Recent Advances in Mesh Morphing,”
Computer Graphics Forum, vol. 21, no. 2, pp. 173-196, 2002.- [18] M.S. Floater, “Mean Value Coordinates,”
Computer Aided Geometric Design, vol. 20, no. 1, pp. 19-27, 2003.- [19] J.L. Lin, J.H. Chuang, C.C. Lin, and C.C. Chen, “Consistent Parameterization by Quinary Subdivision for Remeshing and Mesh Metamorphosis,”
Proc. Int'l Conf. Computer Graphics and Interactive (GRAPHITE '03), pp. 151-158, 2003.- [20] R.W. Sumner and J. Popović, “Deformation Transfer for Triangle Meshes,”
Proc. SIGGRAPH, pp. 399-405, 2004.- [21] D.D. Hoffman and W.A. Richards, “Parts of Recognition,”
Cognition, vol. 18, pp. 65-96, 1984.- [22] R.M. Rustamov, “Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation,”
Proc. Eurographics Symp. Geometry Processing, pp. 225-233, 2007.- [23] H.-Y. Wu, H. Zha, T. Luo, X.-L. Wang, and S. Ma, “Global and Local Isometry-Invariant Descriptor for 3D Shape Comparison and Partial Matching,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), 2010.- [24] J.-M. Lien and N.M. Amato, “Approximate Convex Decomposition of Polyhedra and its Applications,”
Computer Aided Geometric Design, vol. 25, no. 7, pp. 503-522, 2008.- [25] B. Chazelle, D.P. Dobkin, N. Shouraboura, and A. Tal, “Strategies for Polyhedral Surface Decomposition: An Experimental Study,”
Computational Geometry: Theory and Applications, vol. 7, pp. 327-342, 1997.- [26] A.P. Mangan and R.T. Whitaker, “Partitioning 3D Surface Meshes Using Watershed Segmentation,”
IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 4, pp. 308-321, Oct.-Dec. 1999.- [27] S. Katz, G. Leifman, and A. Tal, “Mesh Segmentation Using Feature Point and Core Extraction,”
The Visual Computer, vol. 21, nos. 8-10, pp. 649-658, 2005.- [28] Y. Lee, S. Lee, A. Shamir, D. Cohen-Or, and H.-P. Seidel, “Mesh Scissoring with Minima Rule and Part Salience,”
Computer Aided Geometric Design, vol. 22, no. 5, pp. 444-465, 2005.- [29] L. Shapira, A. Shamir, and D. Cohen-Or, “Consistent Mesh Partitioning and Skeletonisation Using the Shape Diameter Function,”
The Visual Computer, vol. 24, no. 4, pp. 249-259, 2008.- [30] A. Golovinskiy and T.A. Funkhouser, “Consistent Segmentation of 3D Models,”
Int'l Conf. Shape Modeling and Int'l (SMI), pp. 262-269, 2009.- [31] Y. Zheng and C.-L. Tai, “Mech Decomposition with Cross-Boundary Brushes,”
Proc. Eurographics, vol. 29, no. 2, 2010.- [32] T. Igarashi, S. Matsuoka, and H. Tanaka, “Teddy: A Sketching Interface for 3D Freeform Design,”
Proc. SIGGRAPH, pp. 409-416, 1999.- [33] T. Funkhouser, M. Kazhdan, P. Shilane, P. Min, W. Kiefer, A. Tal, S. Rusinkiewicz, and D. Dobkin, “Modeling by Example,”
ACM Trans. Graphics-Proc. ACM SIGGRAPH, vol. 23, no. 3, pp. 652-663, Aug. 2004.- [34] H.-Y. Wu, C. Pan, J. Pan, Q. Yang, and S. Ma, “A Sketch-Based Interactive Framework for Real-Time Mesh Segmentation,”
Proc. Conf. Computer Graphics Int'l (CGI), 2007.- [35] O.S. Andrew Nealen, T. Igarashi, and M. Alexa, “Fibermesh: Designing Freeform Surfaces with 3D Curves,”
Proc. SIGGRAPH, vol. 26, no. 3, 2007.- [36] Z. Ji, L. Liu, Z. Chen, and G. Wang, “Easy Mesh Cutting,”
Eurographics, vol. 25, pp. 283-291, 2006.- [37] G. Taubin, “Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation,”
Int'l Conf. Computer Vision (ICCV), pp. 902-907, 1995.- [38] M. Meyer, M. Desbrun, P. Schroder, and A.H. Barr, “Discrete Differential-Geometry Operators for Triangulated 2-Manifolds,”
Visualization and Mathematics III, pp. 35-57, Springer, 2003.- [39] H. Pottmann, T. Steiner, M. Hofer, C. Haider, and A. Hanbury, “The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces,”
European Conf. Computer Vision (ECCV), pp. 560-572, 2004.- [40] I. Guskov, K. Vidimce, W. Sweldens, and P. Schröder, “Normal Meshes,”
Proc. SIGGRAPH, pp. 95-102, 2000.- [41] O. Sorkine, “Differential Representations for Mesh Processing,”
Computer Graphics Forum, vol. 25, no. 4, pp. 789-807, 2006.- [42] V. Kraevoy, D. Julius, and A. Sheffer, “Model Composition from Interchangeable Components,”
Proc. Pacific Conf. Computer Graphics and Applications, 2007.- [43] S. Toledo, “Taucs: A Library of Sparse Linear Solvers, Version 2.2,” Tel Aviv Univ., http://www.tau.ac.il/stoledotaucs/, Sept. 2003.
- [44] T. Ju, S. Schaefer, and J. Warren, “Mean Value Coordinates for Closed Triangular Meshes,”
Proc. SIGGRAPH, pp. 561-566, 2005.- [45] R. Gal and D. Cohen-Or, “Salient Geometric Features for Partial Shape Matching and Similarity,”
Proc. SIGGRAPH, pp. 130-150, 2006.- [46] L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel, “Interactive Multi-Resolution Modeling on Arbitrary Meshes,”
Proc. ACM SIGGRAPH, pp. 105-114, 1998.- [47] R. Zayer, C. Rossl, Z. Karni, and H.-P. Seidel, “Harmonic Guidance for Surface Deformation,”
Proc. Ann. Conf. European Assoc. for Computer Graphics (Eurographics), pp. 601-609, 2005.- [48] H.-Y. Wu, C. Pan, H. Zha, and S. Ma, “Model Transduction for Triangle Meshes,”
J. Computer Science and Technology , vol. 25, no. 3, pp. 584-595, 2010.- [49] P. Cignoni, C. Rocchini, and R. Scopigno, “Metro: Measuring Error on Simplified Surfaces,”
Computer Graphics Forum, vol. 17, no. 2, pp. 167-174, 1998. |