Shape approximation by differential properties of scalar functions

Computers and Graphics (Pergamon)

Volumn 34, Issue 3, 2010, Pages 252-262

  Biasotti, Silvia ^a   Patané, Giuseppe ^a   Spagnuolo, Michela ^a   Falcidieno, Bianca ^a   Barequet, Gill ^b,c  

^a UNIVERSITY OF GENOA   (Italy)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c Tufts University   (United States)

Author keywords

Morse theory; Shape approximation; Shape chartification; Shape reconstruction

Indexed keywords

ITERATIVE METHODS;

DIFFERENTIAL PROPERTIES; ITERATIVE REFINEMENT; MORSE THE-ORY; SCALAR FUNCTION; SHAPE APPROXIMATION; SHAPE CHARTIFICATION; SHAPE RECONSTRUCTION; SURFACE APPROXIMATION;

TOPOLOGY;

EID: 77955273865     PISSN: 00978493     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cag.2010.03.013     Document Type: Conference Paper

References (53)

1. C.L. Bajaj, E.J. Coyle, and K.-N. Lin Arbitrary topology shape reconstruction from planar cross sections Graphical Models and Image Processing 58 6 1996 524 543
2. T.F. Banchoff Critical points and curvature for embedded polyhedral surfaces American Mathematical Monthly 77 1970 475 485
3. G. Barequet, M.T. Goodrich, A. Levi-Steiner, and D. Steiner Contour interpolation by straight skeletons Graphical Models 66 4 2004 245 260
4. G. Barequet, and M. Sharir Filling gaps in the boundary of a polyhedron Computer Aided Geometric Design 12 2 1995 207 229
5. G. Barequet, and M. Sharir Piecewise-linear interpolation between polygonal slices Computer Vision and Image Understanding 63 2 1996 251 272
6. S. Biasotti, L. De Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, and M. Spagnuolo Describing shapes by geometrical-topological properties of real functions ACM Computing Surveys 40 4 2008 1 87
7. Biasotti S, Falcidieno B, Frosini P, Giorgi D, Landi C, Patan G, Spagnuolo M. 3D shape description and matching based on properties of real functions. In: Eurographics 2007 tutorial proceedings, 2007. p. 949-98.
8. S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno Reeb graphs for shape analysis and applications Theoretical Computer Science 392 13 2008 5 22
9. Biasotti S, Mortara M, Spagnuolo M. Surface compression and reconstruction using Reeb graphs and shape analysis. In: Spring conference on computer graphics, Bratislava; 2000. p. 174-85.
10. Bohn JH, Wozny MJ. Automatic CAD-model repair: shell-closure. In: Proceedings of solid free form fabrication symposium. Dept. of Mech. Eng., University of Texas at Austin; 1993.
11. Boissonnat J-D, Memari P. Shape reconstruction from unorganized cross-sections. In: Proceedings of symposium on geometry processing, Eurographics Association, 2007. p. 89-98.
12. D. Bommes, H. Zimmer, and L. Kobbelt Mixed-integer quadrangulation ACM Transactions on Graphics 28 3 2009 1 10
13. P.-T. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci A topological hierarchy for functions on triangulated surfaces IEEE Transactions on Visualization and Computer Graphics 10 4 2004 385 396
14. Y.-K. Choi, and K.H. Park A heuristic triangulation algorithm for multiple planar contours using an extended double branching procedure The Visual Computer 10 7 1994 372 387
15. H.N. Christiansen, and T.W. Sederberg Conversion of complex contour line definitions into polygonal element mosaics Computer Graphics 13 1978 187 192
16. D. Cohen-Steiner, P. Alliez, and M. Desbrun Variational shape approximation ACM SIGGRAPH 2004 905 914
17. Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. In: Proceedings of the symposium on computational geometry, 2003. p. 344-50.
18. Desbrun M, Hirani AN, Marsden JE. Discrete exterior calculus for variational problems in computer vision and graphics. In: Proceedings of decision and control, 2003. Dec. 2003. 5, p. 49027.
19. M. Desbrun, M. Meyer, P. Schrder, and A.H. Barr Implicit fairing of irregular meshes using diffusion and curvature flow ACM SIGGRAPH 1999 317 324
20. S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J.C. Hart Spectral surface quadrangulation ACM Transactions on Graphics 25 3 2006 1057 1066
21. S. Dong, S. Kircher, and M. Garland Harmonic functions for quadrilateral remeshing of arbitrary manifolds Computer Aided Geometric Design 22 5 2005 392 423
22. H. Edelsbrunner, J. Harer, and A. Zomorodian Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds Discrete and Computational Geometry 30 2003 87 107
23. Edelsbrunner H, Morozov D, Pascucci V. Persistence-sensitive simplification functions on 2-manifolds. In: Proceedings of the symposium on computational geometry, ACM; 2006. p. 127-34.
24. M.S. Floater, and K. Hormann Surface parameterization: a tutorial and survey Advances in multiresolution for geometric modelling 2005 Springer 157 186
25. H. Fuchs, Z.M. Kedem, and S.P. Uselton Optimal surface reconstruction from planar contours Communications of the ACM 20 10 1977 693 702
26. S. Ganapathy, and T.G. Dennehy A new general triangulation method for planar contours ACM SIGGRAPH 16 3 1982 69 75
27. K. Gebal, J. Andreas Bærentzen, H. Aanæs, and R. Larsen Shape analysis using the auto diffusion function Computer Graphics Forum 28 5 2009 1405 1413
28. X. Gu, S.J. Gortler, and H. Hoppe Geometry images ACM Transactions on Graphics 21 3 2002 355 361
29. Gu X, Yau S-T. Global conformal surface parameterization. In: Proceedings of symposium on geometry processing, 2003. p. 127-37.
30. J. Huang, M. Zhang, J. Ma, X. Liu, L. Kobbelt, and H. Bao Spectral quadrangulation with orientation and alignment control ACM Transactions on Graphics 27 5 2008 1 9
31. J.-D. Boissonnat Shape reconstruction from planar cross sections Computer Vision, Graphics, and Image Processing 44 1 1988 1 29
32. D. Julius, V. Kraevoy, and A. Sheffer D-charts: quasi-developable mesh segmentation Computer Graphics Forum 24 3 2005 581 590
33. Kel M, Dolenc A. Some efficient procedures for correcting triangulated models. In: Proceedings of solid free form fabrication symposium, Dept. of Mech. Eng., Univ. of Texas at Austin, 1993.
34. E. Keppel Approximating complex surfaces by triangulation of contour lines IBM Journal of Research and Development 19 1 1975 2 11
35. L. Liu, C. Bajaj, J. Deasy, D.A. Low, and T. Ju Surface reconstruction from non-parallel curve networks Computer Graphics Forum 27 2 2008 155 163
36. Rong Liu, and Hao Zhang Mesh segmentation via spectral embedding and contour analysis Computer Graphics Forum 26 2007 385 394
37. A. Mebarki, P. Alliez, and O. Devillers Farthest point seeding for efficient placement of streamlines Visualization 2005 479 486
38. X. Ni, M. Garland, and J.C. Hart Fair Morse functions for extracting the topological structure of a surface mesh ACM ToG 23 3 2004 613 622
39. V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas Robust on-line computation of Reeb graphs: simplicity and speed ACM Transactions on Graphics 26 3 2007 58 67
40. G. Patan, and B. Falcidieno Computing smooth approximations of scalar functions with constraints Computer & Graphics 33 33 2009 399 413
41. G. Patan, M. Spagnuolo, and B. Falcidieno Para-graph: graph-based parameterization of triangle meshes with arbitrary genus Computer Graphics Forum 23 4 2004 783 797
42. Patan G, Spagnuolo M, Falcidieno B. A minimal contouring approach to the computation of the Reeb Graph. IEEE Transactions on Visualization and Computer Graphics, 2009.
43. U. Pinkall, and K. Polthier Computing discrete minimal surfaces and their conjugates Experimental Mathematics 2 1 1993 15 36
44. N. Ray, W.C. Li, B. Lvy, A. Sheffer, and P. Alliez Periodic global parameterization ACM Transactions on Graphics 25 4 2006 1460 1485
45. G. Reeb Sur les points singulirs d'une forme de Pfaff compltement intgrable ou d'une fonction numrique Comptes Rendu Hebdomadaires des Sances de l'Acadmie des Sciences 1946 847 849
46. A. Shamir A survey on mesh segmentation techniques Computer Graphics Forum 37 6 2008 1539 1556
47. O. Sorkine, D. Cohen-Or, D. Irony, and S. Toledo Geometry-aware bases for shape approximation IEEE Transactions on Visualization and Computer Graphics 11 2 2005 171 180
48. J. Tierny, J.P. Vandeborre, and M. Daoudi Enhancing 3D mesh topological skeletons with discrete contour constrictions The Visual Computer 24 3 March 2008 155 172
49. Y. Tong, P. Alliez, D. Cohen-Steiner, M. Desbrun, Designing quadrangulations with discrete harmonic forms. In: Proceedings of symposium on geometry processing, 2006. p. 201-10.
50. B. Vallet, and B. Levy Spectral geometry processing with manifold harmonics Computer Graphics Forum 27 2 2008
51. Y.F. Wang, and J.K. Aggarwal Surface reconstruction and representation of 3-D scenes Pattern Recognition 19 3 1986 197 207
52. Z. Wood, H. Hoppe, M. Desbrun, and P. Schrder Removing excess topology from isosurfaces ACM Transactions on Graphics 23 2 2004 190 208
53. E. Zhang, K. Mischaikow, and G. Turk Feature-based surface parameterization and texture mapping ACM Transactions on Graphics 24 1 2005 1 27