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Non-rigid 3D object retrieval using topological information guided by conformal factors

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Abstract

Combining the properties of conformal geometry and graph-based topological information, a non-rigid 3D object retrieval methodology is proposed, which is both robust and efficient in terms of retrieval accuracy and computation speed. While graph-based methods are robust to non-rigid object deformations, they require intensive computation which can be reduced by the use of appropriate representations, addressed through geometry-based methods. In this respect, we present a 3D object retrieval methodology, which combines the above advantages in a unified manner. Furthermore, we propose a string matching strategy for the comparison of graphs which describe 3D objects.

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References

  1. Agathos, A., Pratikakis, I., Papadakis, P., Perantonis, S.J., Azariadis, P.N., Sapidis, N.S.: 3D articulated object retrieval using a graph-based representation. Vis. Comput. 1301–1319 (2010)

  2. Beckman, F.S. Jr.: On isometries of Euclidean spaces. Proc. Am. Math. Soc. 4(5), 810–815 (1953). doi:10.2307/2032415

    Article  MathSciNet  MATH  Google Scholar 

  3. Ben-Chen, M., Gotsman, C.: Characterizing shape using conformal factors. In: 3DOR, pp. 1–8 (2008)

    Google Scholar 

  4. Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci. 392(1–3), 5–22 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Biasotti, S., Patané, G., Spagnuolo, M., Falcidieno, B., Barequet, G.: Shape approximation by differential properties of scalar functions. Comput. Graph. 34, 252–262 (2010). doi:10.1016/j.cag.2010.03.013

    Article  Google Scholar 

  6. Bimbo, A.D., Pala, P.: Content-based retrieval of 3D models. ACM Trans. Multimed. Comput. Commun. Appl. 2, 20–43 (2006)

    Article  Google Scholar 

  7. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Efficient computation of isometry-invariant distances between surfaces. SIAM J. Sci. Comput. 28, 1812–1836 (2006). doi:10.1137/050639296

    Article  MathSciNet  MATH  Google Scholar 

  8. Bronstein, A., Bronstein, M., Kimmel, R.: Numerical Geometry of Non-Rigid Shapes, 1 edn. Springer, Berlin (2008)

    MATH  Google Scholar 

  9. Bronstein, A.M., Bronstein, M.M., Kimmel, R., Mahmoudi, M., Sapiro, G.: A Gromov-hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int. J. Comput. Vis. 89, 266–286 (2010)

    Article  Google Scholar 

  10. Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.: Persistence barcodes for shapes. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP’04, pp. 124–135. ACM Press, New York (2004)

    Chapter  Google Scholar 

  11. Chen, D.Y., Shen, Y.T., Tian, X.P., Ouhyoung, M.: On visual similarity based 3D model retrieval. In: Eurographics Computer Graphics Forum, pp. 223–232 (2003)

    Google Scholar 

  12. Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Loops in reeb graphs of 2-manifolds. Discrete Comput. Geom. 32, 231–244 (2004). doi:10.1007/s00454-004-1122-6. http://portal.acm.org/citation.cfm?id=1013907.1013914

    Article  MathSciNet  MATH  Google Scholar 

  13. de Berg, M., van Kreveld, M.: Trekking in the alps without freezing or getting tired. In: Lengauer, T. (ed.) Algorithms—ESA’93. Lecture Notes in Computer Science, vol. 726, pp. 121–132. Springer, Berlin/Heidelberg (1993)

    Google Scholar 

  14. Dey, T., Giesen, J., Goswami, S.: Shape segmentation and matching with flow discretization. In: Algorithms and Data Structures. Lecture Notes in Computer Science, vol. 2748, pp. 25–36. Springer, Berlin/Heidelberg (2003)

    Chapter  Google Scholar 

  15. Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1285–1295 (2003). doi:10.1109/TPAMI.2003.1233902

    Article  Google Scholar 

  16. Floyd, R.W.: Algorithm 97: shortest path. Commun. ACM 5, 345 (1962). doi:10.1145/367766.368168

    Article  Google Scholar 

  17. Gal, R., Shamir, A., Cohen-Or, D.: Pose-oblivious shape signature. IEEE Trans. Vis. Comput. Graph. 13(2), 261–271 (2007)

    Article  Google Scholar 

  18. Giorgi, D., Biasotti, S., Paraboschi, L.: Shape retrieval contest 2007: watertight models track. In: Veltkamp, R.C., ter Haar, F.B (eds.) SHREC 2007: 3D Shape Retrieval Contest. Technical Report UU-CS-2007-015, pp. 5–10. Utrecht University, Utrecht (2007)

    Google Scholar 

  19. Hamza, A.B., Krim, H.: Geodesic object representation and recognition. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 2886, pp. 378–387. Springer, Berlin/Heidelberg (2003)

    Chapter  Google Scholar 

  20. Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.L.: Topology matching for fully automatic similarity estimation of 3D shapes. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’01, pp. 203–212. ACM Press, New York (2001)

    Chapter  Google Scholar 

  21. Jain, V., Zhang, H.: A spectral approach to shape-based retrieval of articulated 3D models. Comput. Aided Des. 39, 398–407 (2007)

    Article  Google Scholar 

  22. Järvelin, K., Kekäläinen, J.: Cumulated gain-based evaluation of ir techniques. ACM Trans. Inf. Syst. 20, 2002 (2002)

    Article  Google Scholar 

  23. Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: SGP’03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 156–164. Eurographics Association, Aire-la-Ville (2003)

    Google Scholar 

  24. Kim, D., Park, I., Yun, I., Lee, S.: A new mpeg-7 standard: perceptual 3-d shape descriptor. In: Aizawa, K., Nakamura, Y., Satoh, S. (eds.) Advances in Multimedia Information Processing—PCM 2004. Lecture Notes in Computer Science, vol. 3332, pp. 238–245. Springer, Berlin/Heidelberg (2005)

    Chapter  Google Scholar 

  25. Kuhn, H.W.: The Hungarian method for the assignment problem. In: J’únger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008, pp. 29–47. Springer, Berlin/Heidelberg (2010)

    Chapter  Google Scholar 

  26. Lian, Z., Godil, A., Fabry, T., Furuya, T., Hermans, J., Ohbuchi, R., Shu, C., Smeets, D., Suetens, P., Vandermeulen, D., Wuhrer, S.: SHREC’10 track: non-rigid 3D shape retrieval. In: Daoudi, M., Schreck, T., Spagnuolo, M., Pratikakis, I., Veltkamp, R.C., Theoharis, T. (eds.) 3DOR, pp. 101–108. Eurographics Association, Aire-la-Ville (2010)

    Google Scholar 

  27. Lian, Z., Godil, A., Bustos, B., Daoudi, M., Hermans, J., Kawamura, S., Kurita, Y., Lavoué, G., Nguyen, H.V., Ohbuchi, R., Ohkita, Y., Ohishi, Y., Reuter, F.P.M., Sipiran, I., Smeets, D., Suetens, P., Tabia, H., Vandermeulen, D.: SHREC’11 track: shape retrieval on non-rigid 3D watertight meshes. In: 3DOR’11, pp. 79–88 (2011)

    Google Scholar 

  28. Mademlis, A., Daras, P., Tzovaras, D., Strintzis, M.G.: 3D object retrieval using the 3D shape impact descriptor. Pattern Recognit. 42, 2447–2459 (2009)

    Article  MATH  Google Scholar 

  29. Meyer, M., Desbrun, M., Schroder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. Math. Vis. 3, 1–26 (2002)

    Google Scholar 

  30. Papadakis, P., Pratikakis, I., Perantonis, S., Theoharis, T.: 3D object retrieval using an efficient and compact hybrid shape descriptor. In: Eurographics Workshop on 3D Object Retrieval, pp. 9–16 (2008)

    Google Scholar 

  31. Papadakis, P., Pratikakis, I., Theoharis, T., Perantonis, S.: PANORAMA: a 3D shape descriptor based on panoramic views for unsupervised 3D object retrieval. Int. J. Comput. Vis. 89, 177–192 (2009). doi:10.1007/s11263-009-0281-6

    Article  Google Scholar 

  32. Peyré, G., Cohen, L.D.: Geodesic remeshing using front propagation. Int. J. Comput. Vis. 69, 145–156 (2006). doi:10.1007/s11263-006-6859-3

    Article  Google Scholar 

  33. Reuter, M., Wolter, F.E., Peinecke, N.: Laplace-beltrami spectra as ‘shape-dna’ of surfaces and solids. Comput.-Aided Des. 38, 342–366 (2006). doi:10.1016/j.cad.2005.10.011. Symposium on Solid and Physical Modeling 2005

    Article  Google Scholar 

  34. Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the fifth Eurographics Symposium on Geometry Processing, pp. 225–233. Eurographics Association, Aire-la-Ville (2007). http://portal.acm.org/citation.cfm?id=1281991.1282022

    Google Scholar 

  35. Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing shock graphs. In: IEEE International Conference on Computer Vision, pp. 755–762 (2001)

    Google Scholar 

  36. Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics. Computer Vision, and Materials Science, vol. 11. Cambridge University Press, Cambridge (1999). http://www.amazon.com/Level-Methods-Fast-Marching-Computational/dp/0521645573

    MATH  Google Scholar 

  37. Sfikas, K., Theoharis, T., Pratikakis, I.: ROSy+: 3D object pose normalization based on pca and reflective object symmetry with application in 3D object retrieval. Int. J. Comput. Vis. 91, 262–279 (2010). doi:10.1007/s11263-010-0395-x

    Article  Google Scholar 

  38. Sfikas, K., Pratikakis, I., Theoharis, T.: ConTopo: non-rigid 3D object retrieval using topological information guided by conformal factors. In: 3DOR’11, pp. 25–32 (2011)

    Google Scholar 

  39. Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton shape benchmark. In: Shape Modeling and Applications, pp. 167–178 (2004)

    Chapter  Google Scholar 

  40. Shinagawa, Y., Kunii, T.L., Kergosien, Y.L.: Surface coding based on Morse theory. IEEE Comput. Graph. Appl. 11, 66–78 (1991)

    Article  Google Scholar 

  41. Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock graphs and shape matching. Int. J. Comput. Vis. 35, 13–32 (1999). doi:10.1023/A:1008102926703. http://dl.acm.org/citation.cfm?id=335600.335602

    Article  Google Scholar 

  42. Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton based shape matching and retrieval. In: Shape Modeling International, pp. 130–139 (2003). doi:10.1109/SMI.2003.1199609

    Chapter  Google Scholar 

  43. Takahashi, S., Shinagawa, Y., Kunii, T.L.: A feature-based approach for smooth surfaces. In: Proceedings of the Fourth ACM Symposium on Solid Modeling and Applications, SMA’97, pp. 97–110. ACM Press, New York (1997)

    Chapter  Google Scholar 

  44. Tangelder, J., Veltkamp, R.: A survey of content based 3D shape retrieval methods. Multimed. Tools Appl. 39, 441–471 (2008)

    Article  Google Scholar 

  45. Tarasov, S.P., Vyalyi, M.N.: Construction of contour trees in 3D in o(nlogn) steps. In: Proceedings of the Fourteenth Annual Symposium on Computational Geometry, SCG’98, pp. 68–75. ACM Press, New York (1998)

    Chapter  Google Scholar 

  46. Tierny, J., Vandeborre, J.P., Daoudi, M.: Partial 3D shape retrieval by reeb pattern unfolding. Comput. Graph. Forum 28(1), 41–55 (2009)

    Article  Google Scholar 

  47. Tung, T., Schmitt, F.: The augmented multiresolution reeb graph approach for content-based retrieval of 3D shapes. Int. J. Shape Model. 11(1), 91–120 (2005)

    Article  Google Scholar 

  48. Wang, S., Wang, Y., Jin, M., Gu, X., Samaras, D.: 3D surface matching and recognition using conformal geometry. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2006)

    Google Scholar 

  49. Xiang, P., Hua, C., Gang, F., Chuan, Z.: Pose insensitive 3D retrieval by Poisson shape histogram. In: Shi, Y., van Albada, G., Dongarra, J., Sloot, P. (eds.) Computational Science—ICCS 2007. Lecture Notes in Computer Science, vol. 4488, pp. 25–32. Springer, Berlin/Heidelberg (2007)

    Chapter  Google Scholar 

  50. Zaharia, T., Preteux, F.J.: 3d-shape-based retrieval within the Mpeg-7 framework, pp. 133–145. SPIE (2001). doi:10.1117/12.424969. http://link.aip.org/link/?PSI/4304/133/1

  51. Zhang, J., Siddiqi, K., Macrini, D., Shokoufandeh, A., Dickinson, S.: Retrieving articulated 3-d models using medial surfaces and their graph spectra. In: Rangarajan, A., Vemuri, B., Yuille, A. (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, vol. 3757, pp. 285–300. Springer, Berlin/Heidelberg (2005)

    Chapter  Google Scholar 

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Acknowledgements

This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: THALIS.

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Authors and Affiliations

  1. Computer Graphics Laboratory, Department of Informatics and Telecommunications, University of Athens, Athens, Greece

    Konstantinos Sfikas & Theoharis Theoharis

  2. IDI, NTNU, Trondheim, Norway

    Theoharis Theoharis

  3. Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    Ioannis Pratikakis

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  1. Konstantinos Sfikas
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  3. Ioannis Pratikakis
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Correspondence to Konstantinos Sfikas.

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Sfikas, K., Theoharis, T. & Pratikakis, I. Non-rigid 3D object retrieval using topological information guided by conformal factors. Vis Comput 28, 943–955 (2012). https://doi.org/10.1007/s00371-012-0714-z

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