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Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: a comparative survey

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Abstract

This paper presents a comprehensive review and analysis of recent spectral shape descriptors for nonrigid 3D shape retrieval. More specifically, we compare the latest spectral descriptors based on the Laplace–Beltrami (LB) operator, including ShapeDNA, heat kernel signature, scale invariant heat kernel signature, heat mean signature, wave kernel signature, and global point signature. We also include the eigenvalue descriptor (EVD), which is a geodesic distance-based shape signature. The global descriptors ShapeDNA and EVD are compared via the chi-squared distance, while all local descriptors are compared using the codebook model. Moreover, we investigate the ambiguity modeling of codebook for the densely distributed low-level shape descriptors. Inspired by the ability of spatial cues to improve discrimination between shapes, we also propose to adopt the isocontours of the second eigenfunction of the LB operator to perform surface partition, which can significantly ameliorate the retrieval performance of the time-scaled local descriptors. In addition, we introduce an intrinsic spatial pyramid matching approach in a bid to further enhance the retrieval accuracy. Extensive experiments are carried out on two 3D shape benchmarks to assess the performance of the spectral descriptors. Our proposed approach is shown to provide the best performance.

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References

  1. Yang, Y., Lin, H., Zhang, Y.: Content-based 3-D model retrieval: a survey. IEEE Trans. Syst. Man Cybern. Part C 37(6), 1081–1098 (2007)

    Article  Google Scholar 

  2. 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 

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

    Article  Google Scholar 

  4. Bustos, B., Keim, D.A., Saupe, D., Schreck, T., Vranic, D.V.: Feature-based similarity search in 3D object databases. ACM Comput. Surv. 37(4), 345–387 (2005)

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Macrini, D., Siddiqi, K., Dickinson, S.J.: From skeletons to bone graphs: medial abstraction for object recognition. In: Proc. CVPR, pp. 1–8 (2008)

  7. Siddiqi, K., Zhang, J., Macrini, D., Shokoufandeh, A., Bouix, S., Dickinson, S.J.: Retrieving articulated 3-D models using medial surfaces. Mach. Vis. Appl. 19(4), 261−275 (2008)

    Article  Google Scholar 

  8. Siddiqi, K., Pizer, S. (eds.): Medial representations: mathematics, algorithms and applications. Springer, Berlin (2008)

    Google Scholar 

  9. Li, C., Ben Hamza, A.: Skeleton path based approach for nonrigid 3D shape analysis and retrieval. In: Proc. IWCIA, LNCS, pp. 84–95 (2011)

  10. Mohamed, W., Ben Hamza, A.: Reeb graph path dissimilarity for 3D object matching and retrieval. V. Comput. 28(3), 305–318 (2012)

    Article  Google Scholar 

  11. Sun, J., Ovsjanikov, M., Guibas, L.J.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28(5), 1383–1392 (2009)

    Article  Google Scholar 

  12. Kokkinos, I., Bronstein, M.M., Yuille, A.: Dense scale-invariant descriptors for images and surfaces. Research Report, INRIA RR-7914 (2012)

  13. Fang, Y., Sun, M., Kim, M., Ramani, K.: Heat-mapping: a robust approach toward perceptually consistent mesh segmentation. In: Proc. CVPR, pp. 2145–2152 (2011)

  14. Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: Proceedings of computational methods for the innovative design of electrical devices, pp. 1626–1633 (2011)

  15. Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of symposium on geometry processing, pp. 225–233 (2007)

  16. Reuter, M., Wolter, F., Peinecke, N.: Laplace-Beltrami spectra as ’Shape-DNA’ of surfaces and solids. Comput. Aided Design 38(4), 342–366 (2006)

    Article  Google Scholar 

  17. Fang, Y., Sun, M., Ramani, K.: Temperature distribution descriptor for robust 3D shape retrieval. In: Proceedings of workshop on non-rigid shape analysis and deformable image alignment, CVPR (2011)

  18. EL Khoury, R., Vandeborre, J.-P., Daoudi, M.: Indexed heat curves for 3D-model retrieval. In: Proceedings of ICPR (2012)

  19. Rosenberg, S.: The Laplacian on a Riemannian manifold. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  20. Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical geometry of non-rigid shapes. Springer Berlin (2008)

    MATH  Google Scholar 

  21. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)

    Article  Google Scholar 

  22. Abdel-Hakim, A.E., Farag, A.: CSIFT: a SIFT descriptor with color invariant characteristics. In: Proceedings of CVPR, pp. 1978–1983 (2006)

  23. Bronstein, A.M., Bronstein, M.M., Guibas, L.J., Ovsjanikov, M.: Shape google: seometric words and expressions for invariant shape retrieval. ACM Trans. Graph. 30(1) (2011)

  24. Lazebnik, S., Schmid, C., Ponce, J.: Beyond bags of features: spatial pyramid matching for recognizing natural scene categories. In: Proceedings of CVPR, pp. 2169–2178 (2006)

  25. Shi, Y., Lai, R., Krishna, S., Dinov, I., Toga, A.W.: Anisotropic Laplace-Beltrami eigenmaps: bridging reeb graphs and skeletons. In: Proceedings of CVPR Workshops, pp. 1–7 (2008)

  26. Funkhouser, T.A., Min, P., Kazhdan, M.M., Chen, J., Halderman, J.A., Dobkin, D.P., Jacobs, D.P.: A search engine for 3D models. ACM Trans. Graph. 22(1), 83–105 (2003)

    Article  Google Scholar 

  27. Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)

    Article  Google Scholar 

  28. Kortgen, M., Park, G.-J., Novotni, M., Klein, R.: 3D shape matching with 3D shape contexts. In: The 7th central European seminar on computer graphics (2003)

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

    Article  Google Scholar 

  30. Kazhdan, M.M., Funkhouser, T.A., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Proceedings of symposium on geometry processing, pp. 156–165 (2003)

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

    Article  Google Scholar 

  32. Ben Hamza, A., Krim, H.: Geodesic matching of triangulated surfaces. IEEE Trans. Image Process. 15(8), 2249–2258 (2006)

    Article  Google Scholar 

  33. Jain, V., Zhang, H., Kaick, O.V.: Non-rigid spectral correspondence of triangle meshes. Int. J. Shape Model. 13(1), 101–124 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  34. Coifman, R., Lafon, S.: Diffusion maps. Appl. Comput. Harmonic Anal. 21(1), 5–30 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  35. Levy, B.: Laplace-Beltrami eigenfunctions: towards an algorithm that understands geometry. In: Proceedings of IEEE international conference on shape modeling and applications, pp. 13–20 (2006)

  36. Bronstein, M.M., Bronstein, A.M.: Shape recognition with spectral distances. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 1065–1071 (2011)

    Article  Google Scholar 

  37. Fouss, F., Pirotte, A., Renders, J., Saerens, M.: Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation. IEEE Trans. Knowl. Data Eng. 19(3), 355–369 (2007)

    Article  Google Scholar 

  38. Lipman, Y., Rustamov, RM., Funkhouser, T.A.: Biharmonic distance. ACM Trans. Graph. 29(3) (2010)

  39. Zhang, H., Kaick, O.V., Dyer, R.: Spectral mesh processing. Comput. Graph. Forum 29(6), 1865–1894 (2010)

    Article  Google Scholar 

  40. Sivic, J., Zisserman, A.: Video Google: a text retrieval approach to object matching in videos. In: Proceedings of ICCV, pp. 1470–1477 (2003)

  41. Gemert, J.V., Snoek, C.G.M., Veenman, C.J., Smeulders, A.W.M., Geusebroek, J.: Comparing compact codebooks for visual categorization. Comput. Vis. Image Underst. 114(4), 450–462 (2010)

    Article  Google Scholar 

  42. Boiman, O., Shechtman, E., Irani, M.: In defense of nearest-neighbor based image classification. In: Proceedings of CVPR, pp. 1–8 (2008)

  43. Philbin, J., Chum, O., Isard, M., Sivic, J., Zisserman, A.: Lost in quantization: improving particular object retrieval in large scale image databases. In: Proceedings of CVPR, pp. 1–8 (2008)

  44. Gemert, J.V., Veenman, C.J., Smeulders, A.W.M., Geusebroek, J.: Visual word ambiguity. IEEE Trans. Pattern Anal. Mach. Intell. 32(7), 1271–1283 (2010)

    Article  Google Scholar 

  45. Yang, J., Yu, K., Gong, Y., Huang, T.S.: Linear spatial pyramid matching using sparse coding for image classification. In: Proceedings of CVPR, pp. 1794–1801 (2009)

  46. Wang, J., Yang, J., Yu, K., Lv, F., Huang, T.S., Gong, Y.: Locality-constrained linear coding for image classification. In: Proceedings of CVPR, pp. 3360–3367 (2010)

  47. Perronnin, F., Dance, C.R.: Fisher kernels on visual vocabularies for image categorization. In: Proceedings of CVPR, pp. 1–8 (2007)

  48. Jégou, H., Douze, M., Schmid, C., Perez, P.: Aggregating local descriptors into a compact image representation. In: Proceedings of CVPR, pp. 3304–3311 (2010)

  49. Jégou, H., Perronnin, F., Douze, M., Sánchez, J., Pérez, P., Schmid, C.: Aggregating local images descriptors into compact codes. IEEE Trans. Pattern Anal. Mach. Intell. 34(9), 1704–1716 (2012)

    Article  Google Scholar 

  50. Picard, D., Gosselin, P.: Improving image similarity with vectors of locally aggregated tensors. In: Proceedings of ICIP, pp. 669–672 (2011)

  51. Bronstein, A.M., Bronstein, M.M.: Spatially-sensitive affine-invariant image descriptors. In: Proceedings of ECCV, pp. 197–208 (2010)

  52. Savarese, S., Winn, J.M., Criminisi, A.: Discriminative object class models of appearance and shape by correlatons. In: Proceedings of CVPR, pp. 2033–2040 (2006)

  53. Ling, H., Soatto, S.: Proximity distribution kernels for geometric context in category recognition. In: Proceedings of ICCV, pp. 1–8 (2007)

  54. Behmo, R., Paragios, N., Prinet, V.: Graph commute times for image representation. In: Proceedings of CVPR, pp. 1–8 (2008)

  55. Liu, D., Hua, G., Viola, P.A., Chen, T.: Integrated feature selection and higher-order spatial feature extraction for object categorization. In: Proceedings of CVPR, pp. 1–8 (2008)

  56. Grauman, K., Darrell, T.: The pyramid match kernel: Discriminative classification with sets of image features. In: Proceedings of ICCV, pp. 1458–1465 (2005)

  57. Cao, Y., Wang, C., Li, Z., Zhang, L., Zhang, L.: Spatial-bag-of-features. In: Proceedings of CVPR, pp. 3352–3359 (2010)

  58. Yang, Y., Newsam, S.: Spatial pyramid co-occurrence for image classification. In: Proceedings of ICCV, pp. 1465–1472 (2011)

  59. Zhang, Y., Jia, Z., Chen, T.: Image retrieval with geometry-preserving visual phrases. In: Proceedings of CVPR, pp. 809–816 (2011)

  60. Jia, Y., Huang, C., Darrell, T.: Beyond spatial pyramids: receptive field learning for pooled image features. In: Proceedings of CVPR, pp. 3370–3377 (2012)

  61. Krapac, J., Verbeek, J.J., Jurie, F.: Modeling spatial layout with fisher vectors for image categorization. In: Proceedings of ICCV, pp. 1487–1494 (2011)

  62. Meyer, M., Desbrun, M., Schröder, P., Barr, A.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III, Springer, Berlin, pp. 35–57 (2003)

  63. Wardetzky, M., Mathur, S., Kälberer, F., Grinspun, E.: Discrete Laplace operators: no free lunch. In: Proceedings of Eurographics symposium on geometry processing, pp. 33–37 (2008)

  64. Belkin, M., Sun, J., Wang, Y.: Discrete laplace operator on meshed surfaces. In: Proceedings of SCG, pp. 278–287 (2008)

  65. Hildebrandt, K., Polthier, K.: On approximation of the Laplace–Beltrami operator and the Willmore energy of surfaces. Comput. Gr. Forum 30(5), 1513–1520 (2011)

    Article  MathSciNet  Google Scholar 

  66. Davies, E.B., Safarov, Y. (eds.): Spectral theory and geometry. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  67. Vaxman, A., Ben-Chen, M.,, Gotsman, C.: A multi-resolution approach to heat kernels on discrete surfaces. ACM Trans. Graph. 29(4) (2010)

  68. Uhlenbeck, K.: Generic properties of eigenfunctions. Am. J. Math. 98(4), 1059–1078 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  69. Jarvelin, K., Kekalainen, J.: IR evaluation methods for retrieving highly relevant documents. In: Proceedings of SIGIR, pp. 41–48 (2000)

  70. 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: Proceedings of Eurographics/ACM SIGGRAPH Sympo. 3D Object Retrieval, pp. 101–108 (2010)

  71. Lian, Z., Godil, A., Bustos, B., Daoudi, M., Hermans, J., Kawamura, S., Kurita, Y., Lavoue, 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: Proceedings of Eurographics/ACM SIGGRAPH symposium on 3D object retrieval, pp. 79–88 (2011)

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  1. Concordia Institute for Information Systems Engineering, Concordia University, Montréal, QC, Canada

    Chunyuan Li & A. Ben Hamza

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  1. Chunyuan Li
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  2. A. Ben Hamza
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Correspondence to A. Ben Hamza.

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Communicated by P. Pala.

Appendix

Appendix

See Tables 13, 14, 15, 16, 17 and 18.

Table 13 The DCG measure of HKS based on different pairs of parameters
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Table 14 The DCG measure of SIHKS based on different pairs of parameters
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Table 15 The DCG measure of HMS based on different pairs of parameters
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Table 16 The DCG measure of WKS based on different pairs of parameters
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Table 17 Performance comparison of descriptors and their optimal parameters on SHREC 2010 dataset
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Table 18 Performance (DCG) using different codebook models of varying size based on HKS local descriptor
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Li, C., Ben Hamza, A. Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: a comparative survey. Multimedia Systems 20, 253–281 (2014). https://doi.org/10.1007/s00530-013-0318-0

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