iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/s11042-020-09420-5
3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve | Multimedia Tools and Applications Skip to main content
Springer Nature Link
Log in

3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

3D non-rigid shape similarity is a meaningful and challenging task in deformable shape analysis. In this paper, we present a 3D non-rigid shape similarity measure framework based on Laplace-Beltrami operator which achieves the state-of-the-art performance in shape analysis tasks. The presented framework is used to measure 3D non-rigid shape similarity by calculating the Fréchet distance between the shape spectral distances distribution curves extracting geometry and topology information of shapes. Here, the wave diffusion distance within shape spectral distances is selected because it can describe the shape with high accuracy and does not depend on the time parameter. In addition, our framework is more flexible and computationally efficient: it can be generalized to any distance distribution curves and different distances between the shape distances distribution curves. Experiment results show that the proposed framework can measure 3D non-rigid shape similarity accurately and robustly on benchmarks and have good performance in 3D non-rigid shape retrieval.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

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

Similar content being viewed by others

References

  1. Alt H, Knauer C, Wenk C (2001) Matching polygonal curves with respect to the fréchet distance. In: Symposium on theoretical aspects of computer science, pp 63–74

  2. Andriy M, Xubo S (2010) Point set registration: coherent point drift. IEEE Trans Patt Anal Mach Intel 32(12):2262–2275

    Article  Google Scholar 

  3. Anguelov D, Srinivasan P, Koller D, Thrun S, Rodgers J, Davis J (2005) SCAPE: Shape completion and animation of people. ACM Trans Graph 24(3):408–416

    Article  Google Scholar 

  4. Aspert N, Santa-Cruz D, Ebrahimi T (2002) MESH: Measuring errors between surfaces using the hausdorff distance. In: IEEE international conference on multimedia and expo, vol 1, pp 705–708

  5. Aubry M, Schlickewei U, Cremers D (2011) The wave kernel signature: A quantum mechanical approach to shape analysis. In: IEEE international conference on computer vision workshops, pp 1626–1633

  6. Axenopoulos A, Rafailidis D, Papadopoulos G, Houstis EN, Daras P (2016) Similarity search of flexible 3d molecules combining local and global shape descriptors. IEEE/ACM Trans Comput Bio Bioinforma 13(5):954–970

    Article  Google Scholar 

  7. Belongie S, Malik J, Puzicha J (2010) Shape matching and object recognition using shape contexts. In: IEEE international conference on computer science and information technology, pp 483–507

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

    Article  Google Scholar 

  9. Besl PJ, Mckay ND (1992) A method for registration of 3-D shapes. IEEE Trans Patt Anal Mach Intel 14(2):239–256

    Article  Google Scholar 

  10. Biasotti S, Cerri A, Bronstein A, Bronstein M (2016) Recent trends, applications, and perspectives in 3D shape similarity assessment. Computer Graphics Forum 35(6):87–119

    Article  Google Scholar 

  11. Bronstein MM, Bronstein AM (2011) Shape recognition with spectral distances. IEEE Trans Patt Anal Mach Intel 33(5):1065

    Article  Google Scholar 

  12. Bronstein MM, Kokkinos I (2010) Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Computer vision and pattern recognition, pp 1704–1711

  13. Bronstein AM, Bronstein MM, Kimmel R (2009) Monographs in computer science, Numerical geometry of non-rigid shapes. Multidimensional Scaling[J] (Chapter 7):137–167, https://doi.org/10.1007/978-0-387-73301-2

  14. Castellani U, Cristani M, Fantoni S, Murino V (2010) Sparse points matching by combining 3D mesh saliency with statistical descriptors. Computer Graphics Forum 27(2):643–652

    Article  Google Scholar 

  15. Chui H, Rangarajan A (2003) A new point matching algorithm for non-rigid registration. Comput Vis Image Underst 89(2):114–141

    Article  MATH  Google Scholar 

  16. Eiter T, Mannila H (1994) Computing discrete fréchet distance. Tech. rep., Citeseer

  17. Fang Y, Liu YS, Ramani K (2009) Three dimensional shape comparison of flexible proteins using the local-diameter descriptor. Bmc Structural Bio 9(1):29–29

    Article  Google Scholar 

  18. Ghorpade VK, Checchin P, Malaterre L, Trassoudaine L (2017) 3D Shape representation with spatial probabilistic distribution of intrinsic shape keypoints. Eurasip J Advances Signal Process 2017(1):52

    Article  Google Scholar 

  19. Hamza AB (2016) A graph-theoretic approach to 3d shape classification. Neurocomputing 211:11–21

    Article  Google Scholar 

  20. Havens TC, Bezdek JC, Keller JM, Popescu M (2009) Dunn’s cluster validity index as a contrast measure of vat images. In: International conference on pattern recognition, pp 1–4

  21. He S, Choi YK, Guo Y, Guo X, Wang W (2015) A 3D shape descriptor based on spectral analysis of medial axis. Computer Aided Geometric Design 39 (C):50–66

    Article  MathSciNet  MATH  Google Scholar 

  22. Ion A, Artner NM, Peyre G, Marmol SBL (2009) 3D shape matching by geodesic eccentricity. In: IEEE computer society conference on computer vision and pattern recognition workshops, pp 1–8

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

  24. Lian Z, Godil A, Bustos B, Daoudi Mea (2011) SHREC’11 track: shape retrieval on non-rigid 3d watertight meshes. In: Proceedings of the 4th Eurographics conference on 3D object retrieval, EG 3DOR’11, Eurographics Association, pp 79–88

  25. 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

    Article  Google Scholar 

  26. Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Patt Anal Mach Intel 29(2):286

    Article  Google Scholar 

  27. Ling H, Okada K (2006) Diffusion distance for histogram comparison. In: IEEE computer society conference on computer vision and pattern recognition, pp 246–253

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

    Article  Google Scholar 

  29. Lowe DG (1999) Object recognition from local scale-invariant features. In: IEEE international conference on computer vision, pp 1150

  30. Mahmoudi M, Sapiro G (2009) Three-dimensional point cloud recognition via distributions of geometric distances. Graph Model 71(1):22–31

    Article  Google Scholar 

  31. Marcolin F, Vezzetti E (2017) Novel descriptors for geometrical 3d face analysis. Multimedia Tools and Applications 76(12):13805–13834

    Article  Google Scholar 

  32. Osada R, Funkhouser TA, Chazelle B, Dobkin DP (2002) Shape distributions. ACM Trans Graph 21(4):807–832

    Article  MathSciNet  MATH  Google Scholar 

  33. Ovsjanikov M, Sun J, Guibas L (2008) Global intrinsic symmetries of shapes. In: Computer graphics forum, vol 27, pp 1341–1348

  34. Patané G, Barsky BA (2017) An introduction to Laplacian spectral distances and kernels: Theory, computation, and applications. In: ACM SIGGRAPH, pp 3

  35. Pickup D, Sun Xea (2015) Canonical forms for non-rigid 3d shape retrieval. In: Eurographics workshop on 3d object retrieval

  36. Pickup D, Sun X, Rosin PL, Martin RRea (2014) SHREC’14 track: Shape retrieval of non-rigid 3d human models. In: Proceedings of the 7th eurographics workshop on 3D object retrieval, EG 3DOR’14, Eurographics Association

  37. Pickup D, Sun X, Rosin PL, Martin RR (2016) Skeleton-based canonical forms for non-rigid 3d shape retrieval. Comput Vis Med 2(3):231–243

    Article  Google Scholar 

  38. Roman-Rangel E, Wang C, Marchand-Maillet S (2016) Simmap: Similarity maps for scale invariant local shape descriptors. Neurocomputing 175:888–898

    Article  Google Scholar 

  39. Rustamov RM (2007) Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics symposium on geometry processing, pp 225–233

  40. Shinagawa Y, Kunii TL (1991) Constructing a reeb graph automatically from cross sections. IEEE Comput Graph Appl 11(6):44–51

    Article  Google Scholar 

  41. Smeets D, Hermans J, Vandermeulen D, Suetens P (2012) Isometric deformation invariant 3D shape recognition. Pattern Recogn 45 (7):2817–2831

    Article  Google Scholar 

  42. Sun J, Ovsjanikov M, Guibas L (2009) A concise and provably informative multi-scale signature based on heat diffusion. In: Computer fraphics forum, vol 28, pp 1383–1392

  43. Sundar H, Silver D, Gagvani N, Dickinson S (2003) Skeleton based shape matching and retrieval. In: Shape modeling international, pp 130–139

  44. Tatsuma A, Koyanagi H, Aono M (2012) A large-scale shape benchmark for 3d object retrieval: Toyohashi shape benchmark

  45. Tierny J, Vandeborre JP, Daoudi M (2010) Partial 3D shape retrieval by reeb pattern unfolding. Computer Graphics Forum 28(1):41–55

    Article  Google Scholar 

  46. Vezzetti E, Marcolin F, Tornincasa S, Ulrich L, Dagnes N (2018) 3D geometry-based automatic landmark localization in presence of facial occlusions. Multimedia Tools and Applications 77(11):14177–14205

    Article  Google Scholar 

  47. Wang H, Li Y, Jin H, Yin C, Su X, Chen W (2003) Three-dimensional visualization of shape measurement data based on a computer generated hologram. J Opt A Pure Appl Opt 5(5):S195—S199

    Google Scholar 

  48. Xu G (2004) Discrete laplace–beltrami operators and their convergence. Computer Aided Geometric Design 21(8):767–784

    Article  MathSciNet  MATH  Google Scholar 

  49. Yao B, Li Z, Ding M, Chen M (2016) Three-dimensional protein model similarity analysis based on salient shape index. BMC Bioinforma 17 (1):131–131

    Article  Google Scholar 

  50. ÇeliktutanBerk GökberkBülent SankurLale Akarun ASAD (2008) Bosphorus database for 3d face analysis. Biomet Ident Manage 1:47–56

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments. This research was partially supported by the National Key Cooperation between the BRICS of China(No.2017YFE0100500), National Key R&D Program of China (No. 2017YFB1002604) and Beijing Natural Science Foundation of China (No.4172033).

Author information

Authors and Affiliations

  1. School of Artificial Intelligence, Beijing Normal University, Beijing, China

    Dan Zhang, Zhongke Wu, Xingce Wang, Chenlei Lv & Mingquan Zhou

  2. Engineering Research Center of Virtual Reality and Applications, Ministry of Education, Beijing Key Laboratory of Digital Preservation and Virtual Reality for Cultural Heritage, Beijing Normal University, Beijing, 100875, China

    Dan Zhang, Zhongke Wu, Xingce Wang, Chenlei Lv & Mingquan Zhou

Authors
  1. Dan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongke Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xingce Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chenlei Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mingquan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xingce Wang.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, D., Wu, Z., Wang, X. et al. 3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve. Multimed Tools Appl 80, 615–640 (2021). https://doi.org/10.1007/s11042-020-09420-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09420-5

Keywords

Search

Navigation