Surface mesh smoothing, regularization, and feature detection

SIAM Journal on Scientific Computing

Volumn 31, Issue 1, 2008, Pages 74-93

  Huang, H ^a   Ascher, U ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Crease detection; K means clustering; Mesh regularization; Mesh segmentation; Multiscale anisotropic Laplacian; Umbrella operator

Indexed keywords

IMAGE SEGMENTATION;

CREASES DETECTIONS; FEATURES DETECTIONS; K-MEANS++ CLUSTERING; LAPLACIANS; MESH REGULARIZATION; MESH SEGMENTATION; MULTISCALE ANISOTROPIC LAPLACIAN; REGULARISATION; SURFACE MESH SMOOTHING; UMBRELLA OPERATOR;

MESH GENERATION;

EID: 55149099190     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/060676684     Document Type: Article

References (44)

1. M. ATTENEA, B. FALCIDIENO, AND M. SPAGNUOLO, Hierarchical segmentation based on fitting primitives, The Visual Computer, 22 (2006), pp. 181-193.
2. C. BAJAJ AND G. XU, Adaptive surface fairing by geometric diffusion, in Proceedings of the Symposium on Computer Aided Geometric Design, IEEE Computer Society, 2001, pp. 731-737.
3. G. BAJAJ AND G. XU, Anisotropic diffusion on surfaces and functions on surfaces, ACM Trans. Graphics (SIGGRAPH), 22 (2003), pp. 4-32.
4. M. J. BLACK, G. SAPIRO, D. H. MARIMONT, AND D. HEEGER, Robust anisotropic diffusion, IEEE Trans. Image Process., 7 (1998), pp. 421-432.
5. C. Y. CHEN AND K. Y. CHENG, A sharpness dependent filter for mesh smoothing, Comput. Aided Geom. Design, 22 (2005), pp. 376-391.
6. C. Y. CHEN, K. Y. CHENG, AND H. Y. LIAO, Fairing of polygon meshes via Bayesian discriminant analysis, J. WSCG, 12 (2004), pp. 1-3.
7. U. CLARENZ, U. DIEWALD, AND M. RUMPF, Anisotropic geometric diffusion in surface processing, in Proceedings of IEEE Visualization, 2000, pp. 397-405.
8. U. CLARENZ, U. DIEWALD, AND M. RUMPF, Processing textured surfaces via anisotropic geometric diffusion, IEEE Trans. Image Process., 13 (2004), pp. 248-261.
9. M. DESBRUN, M. MEYER, P. SCHRÖDER, AND A. H. BARR, Implicit fairing of irregular meshes using diffusion and curvature flow, in Proceedings of SIGGRAPH, 1999, pp. 317-324.
10. M. DESBRUN, M. MEYER, P. SCHRÖDER, AND A. H. BARR, Anisotropic feature-preserving denoising of height fields and bivariate data, in Proceedings of Graphics Interface, 2000, pp. 145-152.
11. R. O. DUDA, P. E. HART, AND D. G. STORK, Pattern Classification, 2nd ed., John Wiley & Sons, New York, 2001.
12. S. FLEISHMAN, I. DRORI, AND D. COHEN-O R, Bilateral mesh denoising, ACM Trans. Graphics (SIGGRAPH), 22 (2003), pp. 950-953.
13. K. FUJIWARA, Eigenvalues of Laplacians on a closed Riemannian manifold and its nets, Proc. Amer. Math. Soc., 123 (1995), pp. 2585-2594.
14. R. C. GONZALEZ AND R. E. WOODS, Digital Image Processing, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 2002.
15. I. GUSKOV, W. SWELDENS, AND P. SCHRÖDER, Multiresolution signal processing for meshes, in Proceedings of SIGGRAPH, 1999, pp. 325-334.
16. K. HILDEBRANDT AND K. POLTHIER, Anisotropic filtering of non-linear surface features, EUROGRAPHICS, 23 (2004), pp. 391-400.
17. H. HUANG AND U. ASCHER, Fast denoising of surface meshes with intrinsic texture, Inverse Problems, 24 (2008), article 034003.
18. S. JIN, R. R. LEWIS, AND D. WEST, A comparison of algorithms for vertex normal computation, The Visual Computer, 21 (2005), pp. 71-82.
19. T. JIRKA AND V. SKALA, Gradient Vector Estimation and Vertex Normal Computation, Technical Report DCSE/TR-2002-08, University of West Bohemia in Pilsen, Plzen, Czech Republic, 2002.
20. T. JONES, F. DURAND, AND M. DESBRUN, Non-iterative, feature preserving mesh smoothing, ACM Trans. Graphics (SIGGRAPH), 22 (2003), pp. 943-949.
21. R. KANNAN, S. VEMPALA, AND V. VETTA, On spectral clustering - good, bad and spectral, in Proceedings of the 41st Annual Symposium on Foundations of Computer Science, 2000, pp. 367-380.
22. S. KATZ, G. LEIFMAN, AND A. TAL, Mesh segmentation using feature point and core extraction, The Visual Computer, 21 (2005), pp. 649-658.
23. S. KATZ AND A. TAL, Hierarchical mesh decomposition using fuzzy clustering and cuts, ACM Trans. Graphics (SIGGRAPH), 22 (2003), pp. 954-961.
24. L. KOBBELT, S. CAMPAGNA, J. VORSATZ, AND H. P. SEIDEL, Interactive multiresolution modeling on arbitrary meshes, in Proceedings of SIGGRAPH, 1998, pp. 105-114.
25. G. LAVOUÉ, F. DUPONT, AND A. BASKURT, Constant curvature region decomposition of 3D-mesh by a mixed approach vertex-triangle, J. WSCG, 12 (2004), pp. 245-252.
26. R. LIU AND H. ZHANG, Segmentation of 3D meshes through spectral clustering, in Proceedings of Computer Graphics and Applications, IEEE Computer Society, 2004, pp. 298-305.
27. M. MEYER, M. DESBRUN, P. SCHRÖDER, AND A. H. BARR, Discrete differential-geometry operators for triangulated 2-manifolds, in Proceedings of VisMath, Berlin, Germany, 2002.
28. J. M. MORVAN AND B. THIBERT, Smooth surface and triangular mesh: Comparison of the area, the normals and the unfolding, in Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications, ACM, New York, 2002, pp. 147-158.
29. B. NADLER, S. LAFON, R. COIFMAN, AND I. KEVREKIDIS, Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators, in Advances in Neural Information Processing Systems 18, 2005.
30. A. Y. NG, I. J. MICHAEL, AND W. YAIR, On spectral clustering: Analysis and an algorithm, in Neural Information Processing Systems 14, 2002.
31. Y. OHTAKE, A. BELYAEV, AND I. A. BOGAEVSKI, Polyhedral surface smoothing with simultaneous mesh regularization, in Proceedings of Geometric Modeling and Processing, 2000, pp. 229-237.
32. P. PERONA AND W. T. FREEMAN, A factorization approach to grouping, in Proceedings of the 5th European Conference on Computer Vision, Volume I, 1998, pp. 655-670.
33. G. SAPIRO, Geometric Partial Differential Equations and Image Analysis, Cambridge, Cambridge, UK, 2001.
34. J. SHEN, B. MAXIM, AND K. AKINGBEHIN, Accurate correction of surface noises of polygonal meshes, Internat. J. Numer. Methods Engrg., 64 (2005), pp. 1678-1698.
35. J. SHI AND J. MALIK, Normalized cuts and image segmentation, IEEE Trans. Pattern Anal. Machine Intell., 22 (2000), pp. 888-905.
36. T. SHIMIZU, H. DATE, S. KANAI, AND T. KISHINAMI, A new bilateral mesh smoothing method by recognizing features, in Proceedings of the Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05), 2005, pp. 281-286.
37. T. TASDIZEN, R. WHITAKER, P. BURCHARD, AND S. OSHER, Geometric surface smoothing via anisotropic diffusion of normals, in Proceedings of IEEE Visualization, 2002, pp. 125-132.
38. G. TAUBIN, A signal processing approach to fair surface design, ACM Trans. Graphics (SIGGRAPH), 1995, pp. 351-358.
39. J. VOLLMER AND R. MENCL, Improved Laplacian smoothing of noisy surface meshes, EUROGRAPHICS, 18 (1999), pp. 131-139.
40. Y. WEISS, Segmentation using eigenvectors: A unifying view, in Proceedings of the International Conference on Computer Vision, 1999, pp. 975-982.
41. G. L. XU, Discrete Laplace-Beltrami operators and their convergence, Comput. Aided Geom. Design, 21 (2004), pp. 767-784.
42. H. YAGOU, Y. OHTAKE, AND A. BELYAEV, Mesh smoothing via mean and median filtering applied to face normals, in Proceedings of Geometric Modeling and Processing, 2002, pp. 124-131.
43. D.M. YAN, Y. LIU, AND W. P. WANG, Quadric surface extraction by variational shape approximation, in Proceedings of Geometric Modeling and Processing, Springer-Verlag, Berlin, 2006, pp. 73-86.
44. Y. YU, K. ZHOU, D. XU, X. SHI, H. BAO, B. GUO, AND H.-Y. SHUM, Mesh editing with Poisson-based gradient field manipulation, ACM Trans. Graphics (SIGGRAPH), 23 (2004), pp. 641-648.