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Multi-Fourier spectra descriptor and augmentation with spectral clustering for 3D shape retrieval

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Abstract

We propose a new method of similarity search for 3D shape models, given an arbitrary 3D shape as a query. The method features the high search performance enabled in part by our unique feature vector called Multi-Fourier Spectra Descriptor (MFSD), and in part by augmenting the feature vector with spectral clustering. The MFSD is composed of four independent Fourier spectra with periphery enhancement. It allows us to faithfully capture the inherent characteristics of an arbitrary 3D shape object regardless of the dimension, orientation, and original location of the object when it is first defined. Given a 3D shape database, the augmentation with spectral clustering is done first by computing the p-minimum spanning tree of the whole data set, where p is a number usually much less than m, the size of the whole 3D shape data set. We then define the affinity matrix, which is a square matrix of size m by m, where each element of the matrix denotes the distance between two shape objects. The distance is computed in advance by traversing the p-minimum spanning tree. The eigenvalue decomposition is then applied to the affinity matrix to reduce dimensionality of the matrix, followed by grouping into k clusters. The cluster information is kept for augmenting the search performance when a query is given. With a series of benchmark data sets, we will demonstrate that our approach outperforms previously known methods for 3D shape retrieval.

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References

  1. Baeza-Yates, R., Ribeiro-Neto, B.: Modern Information Retrieval. Addison-Wesley, Reading (1999)

    Google Scholar 

  2. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)

    Article  MATH  Google Scholar 

  3. Bengio, Y., Delalleau, O., Roux, N.L., Paiement, J.F., Vincent, P., Ouimet, M.: Learning eigenfunctions links spectral embedding and kernel PCA. Neural Comput. 16(10), 2197–2219 (2004)

    Article  MATH  Google Scholar 

  4. Bengio, Y., Delalleau, O., Le Roux, N., Paiement, J.-F., Vincent, P., Ouimet, M.: Spectral clustering and kernel PCA are learning eigenfunctions. Tech. Report, No. 1239, Département d’informatique er recherche opérationnelle, Université de Montreal

  5. Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Size functions for comparing 3D models. Pattern Recognit. 41(9), 2855–2873 (2008)

    Article  MATH  Google Scholar 

  6. Bratley, P., Fox, B.L., Niederreiter, H.: Algorithm 738: Programs to generate Niederreiter’s low-discrepancy sequences

  7. Bustos, B., Keim, D., Saupe, D., Chreck, T.S., Vranić, D.: Using entropy impurity for improved 3D object similarity search. In: Proc. IEEE ICME 2004, pp. 1303–1306 (2004)

  8. Bustos, B., Keim, D., Saupe, D., Chreck, T.S., Vranić, D.: Automatic selection and combination of descriptors for effective 3D similarity search. In: Proc. IEEE MCBAR ’04, pp. 514–521 (2004)

  9. Bustos, B., Keim, D., Saupe, D., Chreck, T.S., Vranić, D.: Feature-based similarity search in 3D object databases. ACM Comput. Surv. (CSUR) 37(4), 345–387 (2005)

    Article  Google Scholar 

  10. Chen, D.-Y., Tian, X.-P., Shen, Y.-T., Ouhyoung, M.: On visual similarity based 3D model retrieval. Comput. Graph. Forum 22(3), 223–232 (2003). NTU data available at 3d.csie.ntu.edu.tw

    Article  Google Scholar 

  11. Daras, P., Tzovaras, D. et al.: 3D search and retrieval using Krawtchouk moments. In: SHREC2006, pp. 17–21 (2006)

  12. Deerwester, S., et al.: Indexing by latent semantic analysis. J. Am. Soc. Inf. Sci. 41(16), 391–407 (1990)

    Article  Google Scholar 

  13. Del Bimbo, A., Pala, P.: Content-based retrieval of 3D models. ACM Trans. Multimedia Comput. Commun. Appl. 2(1), 20–43 (2006)

    Article  Google Scholar 

  14. Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1285–1295 (2003)

    Article  Google Scholar 

  15. Gotsman, C., Karni, Z.: Spectral compression of mesh geometry. In: Proc. ACM SIGGRAPH, pp. 279–286 (2000)

  16. He, X., Ma, W.-Y., Zhang, H.-J.: Learning an image manifold for retrieval. In: Proc. ACM Multimedia 2004, pp. 17–23 (2004)

  17. Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.L.: Topology matching for fully automatic similarity estimation of 3D shapes. In: ACM Proc. SIGGRAPH 2001, pp. 203–212 (2001)

  18. Jain, V., Zhang, H.: A spectral approach to shape-based retrieval of articulated 3D models. Comput. Aided Des. 39(5), 398–407 (2007)

    Article  Google Scholar 

  19. Jayanti, S., Kalyanaraman, Y., Iyer, N., Ramani, K.: Developing an engineering shape benchmark for cad models. Comput. Aided Des. 38(9), 939–953 (2006)

    Article  Google Scholar 

  20. Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Proc. Eurographics/ACM SIGGRAPH Symp. on Geometric Processing, pp. 156–164 (2003)

  21. Leifman, G., Meir, R., Tal, A.: Semantic-oriented 3d shape retrieval using relevance feedback. Vis. Comput. (Pac. Graph.) 21(8–10), 865–875 (2005)

    Article  Google Scholar 

  22. Levina, E., Bickel, P.J.: Maximum likelihood estimation of intrinsic dimension. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems, vol. 17. MIT Press, Cambridge (2005)

    Google Scholar 

  23. Liu, R., Zhang, H.: Segmentation of 3D meshes through spectral clustering. In: Pacific Conference on Computer Graphics and Applications 2004, pp. 298–305 (2004)

  24. Makadia, A., Daniilidis, K.: Light field similarity for model retrieval. In: SHREC2006, pp. 32–35 (2006)

  25. Min, P.: A 3D model search engine. Ph.D. Thesis, Princeton University (2004)

  26. MPEG-7 Video Group: Description of Core Experiments for Motion and Shape. ISO/IEC N3397, MPEG-7, Geneva, June 2000

  27. Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems, vol. 14 (2001)

  28. Novotni, M., Klein, R.: 3D Zernike descriptors for content based shape retrieval. In: Proc. the Eighth ACM Symposium on Solid Modeling and Applications, pp. 216–225 (2003)

  29. Ohbuchi, R., Kobayashi, J.: Unsupervised learning from a corpus for shape-based 3D model retrieval, poster paper. In: Proc. ACM MIR 2006, Santa Barbara, CA, Oct. 26–27, 2006

  30. Ohbuchi, R., Mukaiyama, A., Takahashi, S.: A frequency-domain approach to watermarking 3D shapes. Comput. Graph. Forum 21(3), 373–382 (2002)

    Article  Google Scholar 

  31. Ohbuchi, R., Otagiri, T., Ibato, M., Takei, T.: Shape-similarity search of three-dimensional models using parameterized statistics. In: Proc. Pacific Graphics 2002, pp. 265–274 (2002)

  32. Ohbuchi, R., Nakazawa, M., Takei, T.: Retrieving 3D shape based on their appearance. In: Proc. 5th ACM SIGMM Workshop on Multimedia Information Retrieval (MIR 2003), Berkeley, 2003

  33. Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. ACM Trans. Graph. 21(4), 807–832 (2002)

    Article  Google Scholar 

  34. Papadakis, P., Pratikakis, I., Perantonis, S., Theoharis, T.: Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation. Pattern Recognit. 40(9), 2437–2452 (2007)

    Article  MATH  Google Scholar 

  35. Pu, J., Lou, K., Ramani, K.: A 2D sketch-based user interface for 3D CAD model retrieval. J. Comput. Aided Des. Appl. 2(6), 717–727 (2005)

    Google Scholar 

  36. Reuter, M., Wolter, F.-E., Peinecke, N.: Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids. Comput. Aided Des. 38, 342–366 (2006)

    Article  Google Scholar 

  37. Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton shape benchmark. In: Proc. SMI ’04, pp. 167–178 (2004)

  38. Sundar, H., Silver, D., Gagvani, N., Dickenson, S.: Skeleton based shape matching and retrieval. In: Proceedings of the Shape Modeling International (SMI ’03), pp. 130–142. IEEE Computer Society, Washington (2003)

    Chapter  Google Scholar 

  39. Tangelder, J.W.H., Veltkamp, R.C.: A survey of content based 3D shape retrieval methods. In: Proc. SMI ’04, pp. 145–156 (2004)

  40. Veltkamp, R.C., ter Haar, F.B.: SHREC2007 3D shape retrieval contest. Technical Report UU-CS-2007-015, http://give-lab.cs.uu.nl/SHREC/shrec2007/ (2007)

  41. Veltkamp, R.C., Ruijsenaars, R., Spagnuolo, M., Zwol, R.V., ter Harr, F.B.: SHREC2006 3D shape retrieval contest. Utrecht University Dept. Information and Computing Sciences. Technical Report UU-CS-2006-030 (ISSN:0924-3275), http://give-lab.cs.uu.nl/shrec/shrec2006/ (2006)

  42. von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)

    Article  MathSciNet  Google Scholar 

  43. Vranić, D.V.: 3D model retrieval. Ph.D. Thesis, University of Leipzig (2004)

  44. Vranić, D.V.: DESIRE: a composite 3D-shape descriptor. In: ICME, pp. 962–965. IEEE, New York (2005)

    Google Scholar 

  45. Vranić, D.V., Saupe, D.: 3D shape descriptors based on 3D Fourier transform. In: Proc. EURASIP Conference on Digital Signal Processing for Multimedia Communications and Services (ECMCS 2001), Budapest, Hungary, pp. 271–274 (2001)

  46. Vranić, D.V., Saupe, D., Richter, J.: Tools for 3D-object retrieval: Karhunen–Loeve transform and spherical harmonics. In: Proc. IEEE 4th Workshop on Multimedia Signal Processing, pp. 293–298 (2001)

  47. Yang, L.: Building k-edge connected neighborhood graph for geodesic distance estimation and nonlinear data projection, Pattern Recognit. Lett. 26 (2005)

  48. Zhang, H., van Kaick, O., Dyer, R.: Spectral method for mesh processing and analysis. In: Proc. of Eurographics 2007 State of the Art Report, pp. 1–22 (2007)

  49. Zhang, J., Siddiqi, K., Macrini, D., Shokoufandeh, A., Dickinson, S.J.: Retrieving articulated 3-D models using medial surfaces and their graph spectra. In: EMMCVPR. Lecture Notes in Computer Science, vol. 3757, pp. 285–300. Springer, New York (2005)

    Google Scholar 

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  1. Toyohashi University of Technology, 1-1 Tempakucho, Hibarigaoka, Toyohashi, Aichi, Japan

    Atsushi Tatsuma & Masaki Aono

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  1. Atsushi Tatsuma
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  2. Masaki Aono
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Correspondence to Masaki Aono.

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Tatsuma, A., Aono, M. Multi-Fourier spectra descriptor and augmentation with spectral clustering for 3D shape retrieval. Vis Comput 25, 785–804 (2009). https://doi.org/10.1007/s00371-008-0304-2

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