A new algorithm for computing the 2-dimensional matching distance between size functions

Pattern Recognition Letters

Volumn 32, Issue 14, 2011, Pages 1735-1746

  Biasotti, Silvia ^b   Cerri, Andrea ^a,c   Frosini, Patrizio ^a   Giorgi, Daniela ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF GENOA   (Italy)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Multi dimensional size function; Shape comparison; Size Theory

Indexed keywords

3D OBJECT; ERROR THRESHOLD; REAL-VALUED FUNCTIONS; SHAPE COMPARISON; SHAPE DESCRIPTORS; SIZE FUNCTIONS; SIZE THEORY; THEORETICAL RESULT;

APPROXIMATION ALGORITHMS;

EID: 80052523850     PISSN: 01678655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patrec.2011.07.014     Document Type: Article

References (41)

1. S. Biasotti, A. Cerri, P. Frosini, D. Giorgi, and C. Landi Multidimensional size functions for shape comparison J. Math. Imaging Vis. 32 2 2008 161 179
2. S. Biasotti, A. Cerri, and D. Giorgi k-dimensional size functions for shape description and comparison R. Cucchiara, ICIAP 2007 IEEE Computer Society 795 800
3. 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 Comput. Surv. 40 4 2008 1 87
4. S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno Size functions for comparing 3d models Pattern Recognit. 41 9 2008 2855 2873
5. A.M. Bronstein, M.M. Bronstein, M. Ovsjanikov, and L.J. Guibas Shape google: Geometric words and expressions for invariant shape retrieval ACM Trans. Graphics (TOG) 30 1 2011 1 20
6. G. Carlsson, G. Singh, and A. Zomorodian Computing multidimensional persistence Y. Dong, D.-Z. Du, O.H. Ibarra, ISAAC Lecture Notes in Computer Science vol. 5878 2009 Springer 730 739
7. G. Carlsson, and A. Zomorodian The theory of multidimensional persistence J. Erickson, Symposium on Computational Geometry 2007 ACM 184 193 (Pubitemid 47582061)
8. Cerri, A., Di Fabio, B., Ferri, M., Frosini, P., Landi, C., 2010. Betti Numbers in Multidimensional Persistent Homology are Stable Functions. Technical Report, no. 2923, Universit di Bologna. http://amsacta.cib.unibo.it/2923/.
9. A. Cerri, M. Ferri, and D. Giorgi Retrieval of trademark images by means of size functions Graph. Models 68 5 2006 451 471 (Pubitemid 44648828)
10. Cerri, A., Frosini, P., 2010. Invariance Properties of the Multidimensional Matching Distance in Persistent Topology and Homology. Technical Report no. 2765, Universit di Bologna, http://amsacta.cib.unibo.it/ 2765/.
11. D.-Y. Chen, X.-P. Tian, Y.-T. Shen, and M. Ouhyoung On visual similarity based 3d model retrieval Comput. Graph. Forum 22 3 2003 223 232
12. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer Stability of persistence diagrams J.S.B. Mitchell, G. Rote, Symposium on Computational Geometry 2005 ACM 263 271 (Pubitemid 43283469)
13. D. Cohen-Steiner, H. Edelsbrunner, and D. Morozov Vines and vineyards by updating persistence in linear time SCG '06: Proceedings of the twenty-second Annual Symposium on Computational Geometry 2006 ACM New York, NY, USA 119 126 (Pubitemid 44300779)
14. d'Amico, M., 2002. Aspetti computazionali delle funzioni di taglia. Ph.D. thesis, Universit di Bologna, (in Italian).
15. M. d'Amico, P. Frosini, and C. Landi Using matching distance in Size Theory: A survey Int. J. Imag. Syst. Tech. 16 5 2006 154 161 (Pubitemid 46588678)
16. M. d'Amico, P. Frosini, and C. Landi Natural pseudo-distance and optimal matching between reduced size functions Acta. Appl. Math. 109 2010 527 554
17. F. Dibos, P. Frosini, and D. Pasquignon The use of size functions for comparison of shapes through differential invariants J. Math. Imaging Vis. 21 2 2004 107 118
18. P. Donatini, and P. Frosini Natural pseudodistances between closed manifolds Forum Mathematicum 16 5 2004 695 715 (Pubitemid 39392477)
19. P. Donatini, and P. Frosini Natural pseudodistances between closed surfaces Journal of the European Mathematical Society 9 2 2007 231 253
20. P. Donatini, and P. Frosini Natural pseudodistances between closed curves Forum Mathematicum 21 6 2009 981 999
21. Edelsbrunner, H., Harer, J., 2008. Persistent homology - a survey. In: Surveys on discrete and computational geometry, vol. 453 of Contemp. Math. Amer. Math. Soc., Providence, RI, pp. 257-282.
22. H. Edelsbrunner, and J. Harer Computational Topology: An Introduction 2009 American Mathematical Society
23. H. Edelsbrunner, D. Letscher, and A. Zomorodian Topological persistence and simplification Discr. Comput. Geom. 28 4 2002 511 533 (Pubitemid 36161396)
24. P. Frosini, and C. Landi Size Theory as a topological tool for computer vision Pattern Recogn. and Image Anal. 9 1999 596 603
25. P. Frosini, and C. Landi Size functions and formal series Appl. Algebra Engrg. Comm. Comput. 12 4 2001 327 349 (Pubitemid 32933362)
26. Frosini, P., Landi, C., 2010a. Stability of multidimensional persistent homology with respect to domain perturbations, arXiv:1001.1078v2 [math.AT].
27. Frosini, P., Landi, C., 2010b. Uniqueness of Models in Persistent Homology: The Case of Curves. Technical Report. no. 2933, Universit di Bologna, http://amsacta.cib.unibo.it/2933/.
28. P. Frosini, and C. Landi No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit Applied Mathematics Letters 24 2011 1654 1657
29. P. Frosini, and M. Mulazzani Size homotopy groups for computation of natural size distances Bull. of the Belg. Math. Soc. 6 3 1999 455 464
30. Giorgi, D., Biasotti, S., Paraboschi, L., 2007. Watertight Models track. Technical Report no. 09, CNR - IMATI, Genova, Italy.
31. M. Hilaga, Y. Shinagawa, T. Kohmura, and T.L. Kunii Topology matching for fully automatic similarity estimation of 3d shapes SIGGRAPH '01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques 2001 ACM Press 203 212 (Pubitemid 33047305)
32. A.K. Jain, M.N. Murty, and P.J. Flynn Data clustering: A review ACM Comput. Surv. 31 3 1999 264 323
33. Kazhdan, M., Funkhouser, T., Rusinkiewicz, S., 2003. Rotation invariant spherical harmonic representation of 3d shape descriptors. In: Proc. SGP '03. pp. 156-164.
34. R. Litman, A.M. Bronstein, and M.M. Bronstein Diffusion-geometric maximally stable component detection in deformable shapes Computers & Graphics 35 3 2011 549 560
35. Non-rigid World, http://tosca.cs.technion.ac.il/.
36. A. Smeulders, M. Worring, S. Santini, A. Gupta, and R. Jain Content-based image retrieval at the end of the early years IEEE Trans. PAMI 22 12 2000
37. Sun, J., Ovsjanikov, M., Guibas, L., 2009. A concise and provably informative multi-scale signature based on heat diffusion. In: Proc. SGP '09. pp. 1383-1392.
38. J. Tangelder, and R. Veltkamp A survey of content-based 3D shape retrieval methods Multimedia Tools and Applications 39 3 2008 441 471
39. C. Uras, and A. Verri Computing size functions from edge maps Int. J. Comput. Vision 23 2 1997 169 183 (Pubitemid 127507403)
40. A. Verri, C. Uras, P. Frosini, and M. Ferri On the use of size functions for shape analysis Biol. Cybern. 70 1993 99 107
41. L. Vincent, and P. Soille Watersheds in digital spaces: An efficient algorithm based on immersion simulations IEEE Trans. PAMI 13 6 1991