Size functions for comparing 3D models

Pattern Recognition

Volumn 41, Issue 9, 2008, Pages 2855-2873

  Biasotti, S ^a   Giorgi, D ^a   Spagnuolo, M ^a   Falcidieno, B ^a  

^a CNR   (Italy)

Author keywords

3D shape retrieval; Matching distance; Shape comparison; Size function; Size graph; Skeletal graph

Indexed keywords

GRAPHIC METHODS; IMAGE CLASSIFICATION; IMAGE RETRIEVAL; MATHEMATICAL MODELS;

3D SHAPE RETRIEVAL; MATCHING DISTANCE; SKELETAL GRAPHS;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 44649180989     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2008.02.003     Document Type: Article

References (75)

1. M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, D. Fulk, The digital Michelangelo project: 3D scanning of large statues, in: Proceedings SIGGRAPH 2000, 2000, pp. 131-144.
2. Berman H.M., Westbrook J., Feng Z., Gilliland G., Bhat T.N., Weissig H., Shindyalov I.N., and Bourneet P.E. The protein data bank. Nucleic Acid Res. 28 (1997) 235-242
3. P. Shilane, P. Min, M. Kazhdan, T. Funkhouser, The Princeton shape benchmark, in: Proceedings of SMI 2004: International Conference on Shape Modeling and Applications, 2004, pp. 167-178.
4. 〈http://www.cs.uu.nl/centers/give/imaging/3Drecog/3Dmatching.html〉.
5. Biederman I. Recognition-by-components: a theory of human image understanding. Psychol. Rev. 94 (1987) 115-147
6. Marr D. Vision-A Computational Investigation into the Human Representation and Processing of Visual Information (1982), W.H. Freeman, San Francisco
7. Frosini P. A distance for similarity classes of submanifolds of a Euclidean space. Bull. Austr. Math. Soc. 42 (1990) 407-416
8. Verri A., Uras C., Frosini P., and Ferri M. On the use of size functions for shape analysis. Biol. Cybern. 70 (1993) 99-107
9. Frosini P., and Landi C. Size theory as a topological tool for computer vision. Pattern Recognition Image Anal. 9 (1999) 596-603
10. Kaczynski T., Mischaikow K., and Mrozek M. Computational homology. Applied Mathematical Sciences vol. 157 (2004), Springer, Berlin
11. H. Edelsbrunner, D. Letscher, A. Zomorodian, Topological persistence and simplification, in: Proceedings 41st Annual IEEE Symposium on Foundations of Computer Science, 2000, pp. 454-463.
12. Edelsbrunner H., Letscher D., and Zomorodian A. Topological persistence and simplification. Discrete Computat. Geometry 28 (2002) 511-533
13. M. Allili, D. Corriveau, D. Ziou, Morse homology descriptor for shape characterization, in: Proceedings ICPR 2004: International Conference on Pattern Recognition, vol. 4, 2004, pp. 27-30.
14. Verri A., and Uras C. Computing size functions from edge maps. Int. J. Comput. Vision 23 2 (1997) 169-193
15. Cerri A., Ferri M., and Giorgi D. Retrieval of trademark images by means of size functions. Grap. Models 68 (2006) 451-471
16. Stanganelli I., Brucale A., Calori L., Gori R., Lovato A., Magi S., Kopf B., Bacchilega R., Rapisarda V., Testori A., Ascierto P., Simeone E., and Ferri M. Computer-aided diagnosis of melanocytic lesions. Anticancer Res. 25 6C (2005) 4577-4582
17. S. Biasotti, D. Giorgi, M. Spagnuolo, B. Falcidieno, Size functions for 3D shape retrieval, in: Proceeding of the EG Symposium on Geometry Processing, 2006, pp. 239-242.
18. Bustos B., Keim D., Saupe D., Schreck T., and Vranić D. An experimental effectiveness comparison of methods for 3D similarity search. Int. J. Digital Libr. 6 1 (2006) 39-54
19. R. Osada, T. Funkhouser, B. Chazelle, D. Dobkin, Matching 3D models with shape distributions, in: Proceedings of SMI 2001: International Conference on Shape Modeling and Applications, 2001, pp. 154-166.
20. M. Novotni, R. Klein, A geometric approach to 3D object comparison, in: Proceedings of SMI 2001: International Conference on Shape Modeling and Applications, 2001, pp. 167-175.
21. Corney J., Rea H., Clark D., Pritchard J., Breaks M., and MacLeod R. Coarse filters for shape matching. IEEE Comput. Graphics Appl. 22 3 (2002) 65-74
22. M. Kazhdan, T. Funkhouser, S. Rusinkiewicz, Rotation invariant spherical harmonic representation of 3D shape descriptors, in: Proceedings SGP 2003: Eurographics Symposium on Geometry Processing, 2003, pp. 156-165.
23. Chen D., Ouhyoung M., Tian X., and Shen Y. On visual similarity based 3D model retrieval. Comput. Graphics Forum 22 (2003) 223-232
24. Del Bimbo A., and Pala P. Content-based retrieval of 3D models. ACM Trans. Multimedia Comput. Commun. Appl. 2 1 (2006) 20-43
25. Collins A., Zomorodian A., Carlsson G., and Guibas A. A barcode shape descriptor for curve point cloud data. Comput. Graphics 28 (2004) 881-894
26. G. Carlsson, A. Zomorodian, A. Collins, A. Guibas, Persistence barcodes for shapes, in: Proceedings SGP 2004: Eurographics Symposium on Geometry Processing, 2004, pp. 127-138.
27. M. Hilaga, Y. Shinagawa, T. Kohmura, T.L. Kunii, Topology matching for fully automatic similarity estimation of 3D shapes, in: Proceedings SIGGRAPH 2001, 2001, pp. 203-212.
28. S. Biasotti, S. Marini, M. Mortara, G. Patané, M. Spagnuolo, B. Falcidieno, 3D shape matching through topological structures, in: Lecture Notes in Computer Science, vol. 2886, 2003, pp. 194-203.
29. Biasotti S., Marini S., Spagnuolo M., and Falcidieno B. Sub-part correspondence by structural descriptors of 3D shapes. Comput. Aided Des. 38 9 (2006) 1002-1019
30. Zuckerberger E., Tal A., and Shlafman S. Polyedral surface decomposition with applications. Comput. Graphics 26 (2002) 733-743
31. N. Cornea, M. Demirci, D. Silver, A. Shokoufandeh, S. Dickinson, P. Kantor, 3D object retrieval using many-to-many matching of curve skeletons, in: Proceedings of SMI 2005: International Conference on Shape Modeling and Applications, 2005, pp. 366-371.
32. J. Zhang, K. Siddiqi, D. Macrini, A. Shokoufandeh, S. Dickinson, Retrieving articulated 3-D models using medial surfaces and their graph spectra, in: Proceedings EMMCVPR 2005: International Workshop On Energy Minimization Methods in Computer Vision and Pattern Recognition, 2005, pp. 285-300.
33. Demirci F., Shokoufandeh A., Keselman Y., Bretzner L., and Dickinson S. Object recognition as many-to-many feature matching. Int. J. Comput. Vision 69 2 (2006) 203-222
34. H. Sundar, D. Silver, N. Gagvani, S. Dickinson, Skeleton based shape matching and retrieval, in: Proceedings of SMI 2003: International Conference on Shape Modeling and Applications, Seoul, South Korea, 2003, pp. 130-139.
35. Iyer N., Jayanti S., Lou K., Kalyanaraman Y., and Ramani K. Shape-based searching for product lifecycle applications. Comput. Aided Des. 37 13 (2005) 1435-1446
36. Messmer B.T., and Bunke H. A new algorithm for error tolerant subgraph isomorphism detection. IEEE Trans. Pattern Anal. Mach. Intell. 20 5 (1998) 493-504
37. Pelillo M. Matching free trees, maximal cliques, and monotone game dynamics. IEEE Trans. Pattern Anal. Mach. Intell. 24 11 (2002) 1535-1541
38. Wilson R.C., Hancock E.R., and Luo B. Pattern vectors from algebraic graph theory. IEEE Trans. Pattern Anal. Mach. Intell. 27 7 (2005) 1112-1124
39. J. Tangelder, R. Veltkamp, A survey of content based 3D shape retrieval methods, in: Proceedings of SMI 2004: International Conference on Shape Modeling and Applications, 2004, pp. 145-156.
40. Iyer N., Jayanti S., Lou K., Kalyanaraman Y., and Ramani K. Three-dimensional shape searching: state-of-the-art review and future trends. Comput. Aided Des. 37 5 (2005) 509-530
41. Bustos B., Keim D., Saupe D., Schreck T., and Vranić D. Feature-based similarity search in 3D object databases. ACM Comput. Surv. 37 4 (2005) 345-387
42. P. Frosini, Measuring shapes by size functions, in: D.P. Casasent (Ed.), Proceedings SPIE: Intelligent Robots and Computer Vision X: Algorithms and Techniques, vol. 1607, Boston, MA, 1991, pp. 122-133.
43. d'Amico M., Frosini P., and Landi C. Using matching distance in size theory: a survey. Int. J. Imaging Syst. Technol. 16 5 (2005) 154-161
44. P. Frosini, C. Landi, New pseudo-distances for the size function space, in: R.A. Melter, A.Y. Wu, L.J. Latecki (Eds.), Proceedings SPIE: Vision Geometry VI, Proc. SPIE, vol. 3168, 1997, pp. 52-60.
45. Frosini P., and Landi C. Size functions and formal series. Applicable Algebra Eng. Commun. Comput. 12 (2001) 327-349
46. Cohen-Steiner D., Edelsbrunner H., and Harer J. Stability of persistence diagrams. Discrete Comput. Geometry 37 1 (2005) 103-120
47. M. d'Amico, P. Frosini, C. Landi, Optimal matching between reduced size functions, Technical Report 35, DISMI, Universitá di Modena e Reggio Emilia, 2003.
48. M. d'Amico, P. Frosini, C. Landi, Natural pseudo-distance and optimal matching between reduced size functions, Technical Report 66, DISMI, Universitá di Modena e Reggio Emilia, 2005.
49. Frosini P. Discrete computation of size functions. J. Combinatorics Inf. Syst. Sci. 17 (1992) 232-250
50. M. d'Amico, A new optimal algorithm for computing size functions of shapes, in: Proceedings CVPRIP Algorithms III: International Conference on Computer Vision, Pattern Recognition and Image Processing, 2000, pp. 107-110.
51. F. Lazarus, A. Verroust, Level set diagrams of polyhedral objects, in: W. Bronsvoort, D. Anderson (Eds.), Proceedings of Solid Modelling and Applications 1999, ACM Press, 1999, pp. 130-140.
52. Gramain A. Topologie des surfaces (1971), Presses Universitaires de France
53. S. Biasotti, Computational topology methods for shape modelling applications, Ph.D. Thesis, Universitá degli Studi di Genova, 2004.
54. Biasotti S., Falcidieno B., and Spagnuolo M. Surface shape understanding based on extended reeb graphs. In: Rana S. (Ed). Topological Data Structures for Surfaces: An Introduction for Geographical Information Science (2004), Wiley, New York 87-103
55. 〈http://shapes.aim-at-shape.net〉.
56. Mortara M., and Patané G. Shape-covering for skeleton extraction. Int. J. Shape Modelling 8 2 (2002) 245-252
57. Cormen T.H., Leiserson C.E., and Rivest R.L. Introduction to Algorithms (1994), The MIT Press, Cambridge, MA
58. Barequet G., and Har-Peled S. Efficiently approximating the minimum-volume bounding box of a point set in three dimensions. J. Algorithms 38 (2001) 91-109
59. Ackermann W. Zum hilbertschen aufbau der reellen zahlen. Math. Ann. 99 (1928) 118-133
60. P. Donatini, P. Frosini, C. Landi, Deformation energy for size functions, in: E.R. Hancock, M. Pelillo (Eds.), Proceedings EMMCVPR 1999: International Workshop On Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, vol. 1654, 1999, pp. 44-53.
61. Donatini P., and Frosini P. Lower bounds for natural pseudodistances via size functions. Arch. Inequalities Appl. 2 (2004) 1-12
62. S. Biasotti, L.D. Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, M. Spagnuolo, Describing shapes by geometrical topological properties of real functions, ACM Comput. Surv., in press.
63. K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, Loops in Reeb graphs of 2-manifolds, in: Proceedings of SCG 2003: Eurographics Symposium on Geometry Processing, 2003, pp. 344-350.
64. Tung T., and Schmitt F. The augmented multiresolution reeb graph approach for content-based retrieval of 3D shapes. Int. J. Shape Modelling 11 1 (2005) 91-120
65. Smeulders A., Worring M., Santini S., Gupta A., and Jain R. Content-based image retrieval at the end of the early years. IEEE Trans. Pattern Anal. Mach. Intell. 22 12 (2000) 1349-1380
66. Rijsbergen C.J.V. Information Retrieval (1979), Butterworths, London
67. Salton G., and McGill M. Introduction to modern information retrieval (1983), McGraw Hill, New York
68. Huijsmans D.P., and Sebe N. How to complete performance graphs in content-based image retrieval: add generality and normalize scope. IEEE Trans. Pattern Anal. Mach. Intell. 27 (2005) 245-251
69. 〈http://www.designrepository.org〉.
70. 〈http://www.hec.afrl.af.mil/HECP/Card1b.shtml#caesarsamples〉.
71. 〈http://www.cim.mcgill.ca/∼shape/benchMark/〉.
72. Eakins J., Boardman J., and Graham M. Similarity retrieval of trademark images. Multimedia 5 2 (1998) 53-63
73. 〈http://graphics.stanford.edu/data/3Dscanrep/〉.
74. A. Cerri, D. Giorgi, P. Musé, F. Sur, F. Tomassini, Shape recognition via an a contrario model for size functions, in: Proceedings of ICIAR 2006: International Conference on Image Analysis and Recognition, 2006.
75. Tarjan R.E., and van Leeuwen J. Worst-case analysis of set union algorithms. J. Assoc. Comput. Mach. 31 2 (1984) 245-281