Skip to main content

Advertisement

Springer Nature Link
Log in

Local commute-time guided MDS for 3D non-rigid object retrieval

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we propose a 3D non-rigid shape retrieval method based on canonical shape analysis. Our main idea is to transform the problem of non-rigid shape retrieval into a rigid shape retrieval problem via the well-known multidimensional scaling (MDS) approach and random walk on graphs. We first segment the non-rigid shape into local partitions based on its salient features. Then, we calculate a local MDS problem for each partition, where the local commute time distance is used as weighting function in order to preserve local shape details. Finally, we aggregate the set of local MDS problems as a global constrained problem. The constraint is formulated using the biharmonic function between local salient features. In contrast to MDS method, the proposed local MDS is computationally efficient, parameters free and gives isometry-invariant forms with minimum features distortion. Due to these advantageous properties, the proposed method achieved good retrieval accuracy on non-rigid shape benchmark datasets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Mohamed HH, Belaid S (2015) Algorithm BOSS (bag-of-salient local spectrums) for non-rigid and partial 3D object retrieval. Neurocomputing 168:790–798

    Article  Google Scholar 

  2. Pickup D et al (2015) SHREC’15 Track: canonical forms for non-rigid 3d shape retrieval. In: Eurographics Workshop on 3D Object Retrieval, EG 3DOR. https://doi.org/10.2312/3DOR.20151063

  3. Mohamed W, Hamza AB (2016) Deformable 3d shape retrieval using a spectral geometric descriptor. Appl Intell 45.2:213–229

    Article  Google Scholar 

  4. Pickup D et al (2016) Shape retrieval of non-rigid 3d human models. Int J Comput Vis 120.2:169–193

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  6. Lian Z, Godil A, Xiao J (2013) Feature-preserved 3d canonical form. Int J Comput Vis 102:221–238

    Article  Google Scholar 

  7. Pickup D, Sun X, Rosin PL, Martin RR (2015) Euclidean-distance-based canonical forms for non-rigid 3D shape retrieval. Pattern Recogn 48(8):2500–2512

    Article  Google Scholar 

  8. Bustos B et al (2014) Coulomb shapes: using electrostatic forces for deformation-invariant shape representation. In: Proceedings of the 7th eurographics workshop on 3D Object Retrieval, pp 9–15

  9. Mohamed HH, Belaid S, Naanaa W (2017) Local features-based 3d canonical form. In: Proceedings of the 6th international workshop on representations, analysis and recognition of shape and motion from imaging data, Tunisia 2016, appeared also in springer communications in computer and information science series, CCIS 684, pp 1–12. https://doi.org/10.1007/978-3-319-60654-51

  10. Borg I, Groenen P (1997) Modern multidimensional scaling-theory and applications. Springer, Berlin

    Book  MATH  Google Scholar 

  11. Faloutsos C, Lin KD (1995) A fast algorithm for indexing, data mining and visualisation of traditional and multimedia datasets. In: Proceedings of the ACM SIGMOD, pp 163–174

  12. Aflalo Y, Kimmel R (2013) Spectral multidimensional scaling. Proc Natl Acad Sci 110(45):18052–18057

  13. Shamai G, Zibulevsky M, Kimmel R (2015) Accelerating the computation of canonical forms for 3D nonrigid objects using multidimensional scaling. In: Proceedings of the 2015 eurographics workshop on 3d object retrieval. Eurographics association

  14. Xu C, Wang TY, Liu YJ, Liu L, He Y (2015) Fast wavefront propagation (FWP) for computing exact geodesic distances on meshes. IEEE Trans Vis Comput Graph 21(7):822–834

    Article  Google Scholar 

  15. Ying X, Xin S -Q (2014) He, y parallel Chen-Han (PCH) algorithm for discrete geodesics. ACM Trans Graph (TOG) 33(1):9

    Article  MATH  Google Scholar 

  16. Pickup D et al (2016) Skeleton-based canonical forms for non-rigid 3D shape retrieval. Computational Visual Media 2.3:231–243

    Article  Google Scholar 

  17. Rustamov RM (2007) Laplace-beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the fifth eurographics symposium on geometry processing. Eurographics association

  18. Kimmel R, Sethian JA (1998) Computing geodesic paths on manifolds. Proc Natl Acad Sci 95:8431–8435

    Article  MathSciNet  MATH  Google Scholar 

  19. Coifman RR et al (2005) Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc Natl Acad Sci U S A 102.21:7426–7431

    Article  Google Scholar 

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

    Article  Google Scholar 

  21. Lipman Y, Rustamov RM, Funkhouser TA (2010) Biharmonic distance. ACM Trans Graph (TOG) 29(3):27

    Article  Google Scholar 

  22. Jones PW, Maggioni M, Schul R (2008) Manifold parametrizations by eigenfunctions of the laplacian and heat kernels. Proc Natl Acad Sci 105(6):1803–1808

    Article  MathSciNet  MATH  Google Scholar 

  23. Qiu H, Hancock ER (2007) Clustering and embedding using commute times. IEEE Trans Pattern Anal Mach Intell 29:11

    Article  Google Scholar 

  24. Gȩbal K, Bærentzen JA, Aanæs H, Larsen R (2009) Shape analysis using the auto diffusion function. Computer Graphics Forum 28(5):405–1413

    Google Scholar 

  25. Crane K, Weischedel C, Wardetzky M (2013) Geodesics in heat: a new approach to computing distance based on heat flow. ACM Trans Graph 32(5):152

    Article  Google Scholar 

  26. Bronstein AM, Bronstein M, Kimmel R (2008) Numerical geometry of non-rigid shapes. Monographs in computer science. Springer

  27. Lloyd SP (1982) Least squares quantization in PCM. IEEE Trans Inf Theory IT-28:129–137

    Article  MathSciNet  MATH  Google Scholar 

  28. Lian Z, Godil A, Sun X, Xiao J (2013) CM-BOF: visual similarity-based 3d shape retrieval using clock matching and bag-of-features. Mach Vis Appl 24.8:1685–1704

  29. Siddiqi K et al (2008) Retrieving articulated 3-d models using medial surfaces. Mach Vis Appl 19.4:261–275

    Article  MATH  Google Scholar 

  30. Lian Z, Godil A, Bustos B, Daoudi M, Hermans J, Kawamura S, Kurita Y, Lavoué G, Nguyen HV, Ohbuchi R, Ohkita Y, Ohishi Y, Porikli F, Reuter M, Sipiran I, Smeets D, Suetens P, Tabia H, Vandermeulen D (2011) SHREC’11 track: shape retrieval on non-rigid 3D watertight meshes. In: Proceedings of the 4th eurographics conference on 3d object retrieval, pp 79–88

  31. Cheng Z, Lian Z, Aono M, Hamza AB, Bronstein A, Bronstein M, Bu S, Castellani U, Cheng S, Garro V, Giachetti A, Godil A, Han J, Johan H, Lai L, Li B, Li C, Li H, Litman R, Liu X, Liu Z, Lu Y, Tatsuma A, Ye J (2014) Shape retrieval of non-rigid 3D human models. In: Proceedings of the 7th eurographics workshop on 3d object retrieval, pp 101–110

  32. Lian Z, Zhang J, Choi S, ElNaghy H, El-Sana J, Furuya T, Giachetti A, Guler RA, Lai L, Li C, Li H, Limberger FA, Martin R, Nakanishi RU, Neto AP, Nonato LG, Ohbuchi R, Pevzner K, Pickup D, Rosin P, Sharf A, Sun L, Sun X, Tari S, Unal G, Wilson RC (2015) Non-rigid 3d shape retrieval. In: Proceedings of the 2015 eurographics workshop on 3d object retrieval, pp 107–120

Download references

Author information

Authors and Affiliations

  1. MARS Research Lab Higher Institute of Computer Science and Telecom (ISITCom), University of Sousse, Sousse, Tunisia

    Hela Haj Mohamed, Samir Belaid & Lotfi Ben Romdhane

  2. University of Tunis El Manar, Tunis, Tunisia

    Wady Naanaa

Authors
  1. Hela Haj Mohamed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samir Belaid
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wady Naanaa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lotfi Ben Romdhane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hela Haj Mohamed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haj Mohamed, H., Belaid, S., Naanaa, W. et al. Local commute-time guided MDS for 3D non-rigid object retrieval. Appl Intell 48, 2873–2883 (2018). https://doi.org/10.1007/s10489-017-1114-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-017-1114-x

Keywords

Search

Navigation