A correspondence-less approach to matching of deformable shapes

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6667 LNCS, Issue , 2012, Pages 592-603

  Pokrass, Jonathan ^a   Bronstein, Alexander M ^a   Bronstein, Michael M ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF LUGANO   (Switzerland)

Author keywords

deformable shapes; diffusion geometry; heat kernel signature; Laplace Beltrami operator; Mumford Shah regularization; partial correspondence; partial matching; partial similarity; shape descriptors

Indexed keywords

DEFORMABLE SHAPES; HEAT KERNEL; LAPLACE-BELTRAMI OPERATOR; MUMFORD-SHAH; PARTIAL CORRESPONDENCE; PARTIAL MATCHING; PARTIAL SIMILARITY; SHAPE DESCRIPTORS;

COMPUTER VISION;

DEFORMATION;

EID: 84855679610     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-24785-9_50     Document Type: Conference Paper

References (33)

1. Ambrosio, L., Tortorelli, V.M.: Approximation of functionals depending on jumps by elliptic functionals via-convergence. Comm. Pure Appl. Math. 43(8), 999-1036 (1990)
2. Bronstein, A.M., Bronstein, M.: Not only size matters: regularized partial matching of nonrigid shapes. In: Prof. NORDIA (2008)
3. Bronstein, A.M., Bronstein, M.M.: Regularized partial matching of rigid shapes. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 143-154. Springer, Heidelberg (2008)
4. Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M., Kimmel, R.: Partial similarity of objects, or how to compare a centaur to a horse. IJCV 84(2), 163-183 (2009)
5. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. National Academy of Science (PNAS) 103(5), 1168-1172 (2006)
6. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical geometry of non-rigid shapes. Springer-Verlag New York Inc., Secaucus (2008)
7. Bronstein, A.M., Bronstein, M.M., Bustos, B., Castellani, U., Crisani, M., Falcidieno, B., Guibas, L.J., Kokkinos, I., Murino, V., Ovsjanikov, M., et al.: SHREC 2010: robust feature detection and description benchmark. In: Proc. 3DOR (2010)
8. Bronstein, A.M., Bronstein, M.M., Castellani, U., Dubrovina, A., Guibas, L.J., Horaud, R.P., Kimmel, R., Knossow, D., von Lavante, E., Mateus, D., et al.: SHREC 2010: robust correspondence benchmark. In: Eurographics Workshop on 3D Object Retrieval (2010)
9. Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Proc. CVPR (2010)
10. Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Processing 10(2), 266-277 (2001)
11. Clarenz, U., Rumpf, M., Telea, A.: Robust feature detection and local classification for surfaces based on moment analysis. Trans. Visualization and Computer Graphics 10(5), 516-524 (2004)
12. Domokos, C., Kato, Z.: Affine puzzle: Realigning deformed object fragments without correspondences. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6312, pp. 777-790. Springer, Heidelberg (2010)
13. Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in Multiresolution for Geometric Modelling, vol. 1 (2005)
14. Gromov, M.: Structures Métriques Pour les Variétés Riemanniennes. Textes Mathématiques, vol. (1) (1981)
15. Jacobs, D., Weinshall, D., Gdalyahu, Y.: Class representation and image retrieval with non-metric distances. Trans. PAMI 22(6), 583-600 (2000)
16. Johnson, A.E., Hebert, M.: Using spin images for efficient object recognition in cluttered 3D scenes. Trans. PAMI 21(5), 433-449 (1999)
17. Lévy, B.: Laplace-Beltrami eigenfunctions towards an algorithm that "understands"geometry. In: Proc. Shape Modeling and Applications (2006)
18. Manay, S., Hong, B.W., Yezzi, A.J., Soatto, S.: Integral invariant signatures. LNCS, pp. 87-99 (2004)
19. Mémoli, F., Sapiro, G.: A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics 5, 313-346 (2005)
20. Meyer, M., Desbrun, M., Schroder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. Visualization and Mathematics III, 35-57 (2003)
21. Mitra, N.J., Guibas, L.J., Giesen, J., Pauly, M.: Probabilistic fingerprints for shapes. In: Proc. SGP (2006)
22. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on pure and applied mathematics 42(5), 577-685 (1989)
23. Ovsjanikov, M., Bronstein, A.M., Guibas, L.J., Bronstein, M.M.: Shape Google: a computer vision approach to invariant shape retrieval. In: Proc. NORDIA, Citeseer (2009)
24. Pauly, M., Keiser, R., Gross, M.: Multi-scale feature extraction on point-sampled surfaces. In: Computer Graphics Forum, vol. 22, pp. 281-289 (2003)
25. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2(1), 15-36 (1993)
26. Reuter, M., Wolter, F.-E., Peinecke, N.: Laplace-spectra as fingerprints for shape matching. In: Proc. ACM Symp. Solid and Physical Modeling, pp. 101-106 (2005)
27. Sipiran, I., Bustos, B.: A robust 3D interest points detector based on Harris operator. In: Proc. 3DOR, pp. 7-14. Eurographics (2010)
28. Sivic, J., Zisserman, A.: Video Google: a text retrieval approach to object matching in videos. In: Proc. CVPR (2003)
29. Sun, J., Ovsjanikov, M., Guibas, L.: A Concise and Provably Informative Multi- Scale Signature Based on Heat Diffusion. In: Computer Graphics Forum, vol. 28, pp. 1383-1392 (2009)
30. Toldo, R., Castellani, U., Fusiello, A.: Visual vocabulary signature for 3D object retrieval and partial matching. In: Proc. 3DOR (2009)
31. Wardetzky, M., Mathur, S., Kälberer, F., Grinspun, E.: Discrete Laplace operators: no free lunch. In: Conf. Computer Graphics and Interactive Techniques (2008)
32. Zaharescu, A., Boyer, E., Varanasi, K., Horaud, R.: Surface feature detection and description with applications to mesh matching. In: Proc. CVPR (2009)
33. Zhang, C., Chen, T.: Efficient feature extraction for 2D/3D objects in mesh representation. In: Proc. ICIP, vol. 3 (2001)