Average increment scale-invariant heat kernel signature for 3D non-rigid shape analysis | Multimedia Tools and Applications Skip to main content
Springer Nature Link
Log in

Average increment scale-invariant heat kernel signature for 3D non-rigid shape analysis

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

Abstract

In recent years, spectral shape descriptors have attracted much attention because the Laplace-Beltrami operator(LBO) has good characteristics for non-rigid deformation shapes. The scale-invariant heat kernel signature(SIHKS) can describe the local or global information of the shape with the change of time parameters, and has scaling invariance compared with heat kernel signature(HKS). However, since the SIHKS descriptor is a feature sequence, it is impossible to balance the shape description accuracy and computational complexity when measuring shape similarity. If all feature sequences are selected for high precision description that will produce high computational complexity. Conversely, if only features under partial time parameters are selected, the accuracy will be affected and some shape features will be lost. To solve this problem, we define a more compact and efficient spectral shape descriptor, the average increment scale-invariant heat kernel signature(AISIHKS), which can effectively extract geometric and topological information by calculating the average increment of the heat kernel under all time parameters, and all the attributes of the shape can be effectively retained while reducing the feature dimension, which greatly reduces the complexity of the similarity measure. At the same time, the shape features obtained based on the increment are more discriminative than SIHKS, and can finely describe the local details of the shape. The experimental results on benchmarks show that the AISIHKS decreiptor is invariant to isometric and scale transformation, robust to topology, sampling and noise transformations, and can more accurately and robustly describe the local differences between shapes than other spectral shape descriptors, which have good performance in 3D non-rigid shape distance calculation and shape retrieval, and the more encouraging results are achieved compared with several representative approaches.

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
¥17,985 /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 (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Data Availability Statements

Data sharing not applicable to this article as no datasets were generated during the current study.

References

  1. Aubry M, Schlickewei U, Cremers D (2011) The wave kernel signature: a quantum mechanical approach to shape analysis[C]. In: Proceedings of the computer vision workshops(ICCV Workshops) , pp 1626–1633

  2. Bouttier J, Francesco P, Guitter E (2011) Geodesic distance in planar graphs[J]. Nucl Phys 663(3):535–567

    Article  MathSciNet  Google Scholar 

  3. Bronstein A, Bronstein M, Castellani U et al (2010) SHREC2010: robust large-scale shape retrieval benchmark[C]. In: Proceedings of the EUROGRAPHICS workshop on 3D object retrieval(3DOR), pp 93–100

  4. Bronstein M, Kokkinos I (2010) Scale-invariant heat kernel signatures for non-rigid shape recognition[C]. In: Proceedings of the computer vision and pattern recognition(CVPR), pp 1704–1711

  5. Bronstein A, Bronstein M, Kimmel R (2010) Numerical geometry of non-rigid shapes[J]. Comput Rev 51(4):222–223

    Google Scholar 

  6. Choukroun Y, Shtern A, Bronstein A et al (2020) Hamiltonian operator for spectral shape analysis[C]. In: Proceedings of the IEEE transactions on visualization and computer graphics, vol 26, pp 1320–1331

  7. Coifman R, Lafon S (2006) Diffusion maps[C]. In: Proceedings of the geometric structure of high-dimensional data and dimensionality reduction, pp 267–298

  8. Daras P, Zarpalas D, Tzovaras D, et al. (2006) Efficient 3-D model search and retrieval using generalized 3D radon transforms[J]. IEEE Trans Multimed 8(1):101–114

    Article  Google Scholar 

  9. Du G, Zhou M, Yin C et al (2016) A novel HKS based feature extraction algorithm[C]. In: Proceedings of the 2016 international conference on virtual reality and visualization(ICVRV), pp 144–147

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

    Article  Google Scholar 

  11. Fang Y, Xie J, Dai G et al (2015) 3D deep shape descriptor[C]. In: Proceedings of the IEEE conference on computer vision and pattern recognition(CVPR), pp 2319–2328

  12. Hammond D, Vandergheynst P, Gribonval R (2011) Wavelets on graphs via spectral graph theory[J]. Appl Comput Harmon Anal 30(2):129–150

    Article  MathSciNet  Google Scholar 

  13. Havens T, Bezdek J, Keller J et al (2008) Dunn’s cluster validity index as a contrast measure of VAT images[C]. In: Proceedings of the 19th international conference on pattern recognition, pp 1–4

  14. Hilaga M, Shinagawa Y, Komura T et al (2001) Topology matching for fully automatic similarity estimation of 3D shapes[C]. In: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp 203–212

  15. Hua J, Lai Z, Dong M et al (2008) Geodesic distance-weighted shape vector image diffusion[J]. IEEE Trans Vis Comput Graph 14(6):1643–1650

    Article  Google Scholar 

  16. Huttenlocher D, Klanderman G, Rucklidge W (1993) Comparing images using the Hausdorff distance[C]. In: Proceedings of the IEEE transactions on pattern analysis and machine intelligence, vol 15, pp 850–863

  17. Jouili S, Tabbone S (2012) Hypergraph-based image retrieval for graph-based representation[J]. Pattern Recogn 45(11):4054–4068

    Article  Google Scholar 

  18. Li C, Hamza A (2013) A multiresolution descriptor for deformable 3D shape retrieval[J]. Vis Comput 29(6–8):513–524

    Article  Google Scholar 

  19. Li C, Hamza A (2013) Intrinsic spatial pyramid matching for deformable 3D shape retrieval[J]. Int J Multimed Inform Retriev 2(4):261–271

    Article  Google Scholar 

  20. Li Z, Tang J (2015) Unsupervised feature selection via nonnegative spectral analysis and redundancy control[C]. In: Proceedings of the IEEE transactions on image processing, vol 24, pp 5343–5355

  21. Li Z, Liu J, Tang J et al (2015) Robust structured subspace learning for data representation[J]. IEEE Trans Pattern Anal Mach Intell 37(10):2085–2098

    Article  Google Scholar 

  22. Li H, Li S, Wu X et al (2018) Scale-invariant wave kernel signature for non-rigid 3D shape retrieval[c]. In: Proceedings of the 2018 IEEE international conference on big data and smart computing(BigComp), pp 448–454

  23. Lian Z, Zhang J, Choi S, Elnaghy H, Elsana J, Furuya T, Giachetti A, Guler R, Lai L, Li C (2015) SHREC’15 track: non-rigid 3D shape retrieval[C]. In: Proceedings of the Eurographics workshop on 3D object retrieval

  24. Lian Z, Godil A, Bustos B, Daoudi M, Hermans J, Kawamura S, Kurita Y, Lavoué G, Nguyen H, Ohbuchi R, Ohkita Y, Ohishi Y, Porikli F, Reuter M, Sipiran I, Smeets D, Suetens P, Tabia H, Vandermeulen D (2013) A comparison of methods for non-rigid 3D shape retrieval[J]. Pattern Recogn 46(1):449–461

    Article  Google Scholar 

  25. Marie D, Jain A (2002) A modified Hausdorff distance for object matching[C]. In: Proceedings of the 12th international conference on pattern recognition, pp 566–568

  26. Martinek M, Ferstl M, Grosso R (2012) 3D shape matching based on geodesic distance distributions[J]. The Eurographics Association, 219–220

  27. Masoumi M, Li C, Hamza A (2016) A spectral graph wavelet approach for nonrigid 3D shape retrieval[J]. Pattern Recogn Lett 83(1):339–348

    Article  Google Scholar 

  28. Mi Cl, Kayser L (2017) A remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace–Beltrami operator[J]. Semigroup Forum, 71–79

  29. Montuori A, Pugliese L, Raimondo G et al (2006) Feature selection for data driven prediction of protein model quality[C]. In: Proceedings of the 2006 IEEE international joint conference on neural network proceedings, pp 3561–3565

  30. Osada R, Funkhouser T, Chazelle B, et al. (2002) Shape distributions[J]. ACM Trans Graph 21(4):807–832

    Article  MathSciNet  Google Scholar 

  31. Ovsjanikov M, Sun J, Guibas L (2008) Global intrinsic symmetries of shapes[C]. In: Proceedings of the Computer graphics forum, vol 27, pp 1341–1348

  32. Patane G (2016) STAR-Laplacian spectral kernels and distances for geometry processing and shape analysis[J]. Comput Graph Forum, 599–624

  33. Philip S, Patrick M, Michael K, Thomas F (2004) The Princeton shape benchmark[C]. In: Proceedings of the shape modeling applications, pp 167–178

  34. Pickup D, Sun X, Rosin P et al (2015) Shrec’15 track: canonical forms for non-rigid 3d shape retrieval[C]. In: Proceedings of the 8th Eurographics conference on 3D object retrieval, pp 1–8

  35. Rabin J, Peyré G, Cohen L (2010) Geodesic shape retrieval via optimal mass transport[C]. In: Proceedings of the European conference on computer vision, pp 771–784

  36. Raviv D, Bronstein M, Bronstein A, et al. (2010) Volumetric heat kernel signatures[C]. In: Proceedings of the ACM workshop on 3D object retrieval, 3DOR, pp 39–44

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

    Article  Google Scholar 

  38. Rostami R, Bashiri F, Rostami B et al (2018) A survey on data-driven 3D shape descriptors[J]. Computer Graphics Forum, 356–393

  39. Rustamov R (2007) Laplace-Beltrami eigenfunctions for deformation invariant shape representation[C]. In: Proceedings of the fifth eurographics symposium on geometry processing, pp 225–233

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

    Article  Google Scholar 

  41. ThiruvadandamPorethi V, Godil A, Dutagaci H, Lian Z, Ohbuchi R, Furuya T (2010) SHREC’10 track: generic 3D warehouse[C]. In: Proceedings of the Eurographics workshop on 3D object retrieval

  42. Toony Z, Laurendeau D, Gagné C (2015) Describing 3D geometric primitives using the Gaussian sphere and the Gaussian accumulator[J]. 3D Res 6 (4):1–22

    Article  Google Scholar 

  43. Wang Y, Guo J, Yan D et al (2019) A robust local spectral descriptor for matching non-rigid shapes with incompatible shape structures[C]. In: Proceedings of the IEEE conference on computer vision and pattern recognition(cVPR), pp 6224–6233

  44. Wei J, Gui H, Dai Q et al (2006) Similarity-based online feature selection in content-based image retrieval[C]. In: Proceedings of the IEEE trans on image processing, vol 15, pp 702–712

  45. Wu H, Zha H (2011) Robust consistent correspondence between 3D non-rigid shapes based on Dual Shape-DNA[C]. In: Proceedings of the international conference on computer vision(ICCV), pp 587–594

  46. Xu X, Yang P, Ran B et al (2020) Long-distance deformation object recognition by integrating contour structure and scale-invariant heat kernel signature[J]. J Intell Fuzzy Syst 39(2):1–17

    Google Scholar 

  47. Yang J, Wang C (2011) Feature selection using probabilistic prediction of support vector regression[C]. In: Proceedings of the IEEE trans on neural networks, vol 22, pp 954–962

  48. Yu R, Sun J, Li H (2020) Second-order spectral transform block for 3D shape classification and retrieval[J]. IEEE Trans Image Process, 4530–4543

  49. Zeng W, Guo R, Luo F et al (2012) Discrete heat kernel determines discrete Riemannian metric[J]. Graph Model 2012(74):121–129

    Article  Google Scholar 

  50. Zhang D, Liu N, Yan Y et al (2021) Scaling invariant harmonic wave kernel signature for 3D point cloud similarity[C]. In: Proceedings of the image and graphics, pp 44–56

  51. Zhang D, Wu Z, Wang X et al (2021) 3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve. Multimed Tools Appl 80:615–640

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the reviewers for their thoughtful and constructive comments, which led to many improvements of the paper. This work was partially supported by the National Key R&D plan(No.2020YFC1523305); National Nature Science Fundation of China(No.62102213); Key R&D and transformation plan of Qinghai Province(No.2020-SF-142); Independent project fund of State Key lab of Tibetan Intelligent Information Processing and Application(Co-established by province and ministry)(Grant Nos.2022-SKL-014); Young and middle-aged scientific research fund of Qinghai Normal University(No.KJQN2021004).

Author information

Author notes

    Authors and Affiliations

    1. State Key lab of Tibetan Intelligent Information Processing and Application, Xining, 810000, China

      Yuhuan Yan, Mingquan Zhou, Dan Zhang & Shengling Geng

    2. School of Computer Science, Qinghai Normal University, Xining, 810000, China

      Yuhuan Yan, Mingquan Zhou, Dan Zhang & Shengling Geng

    3. Academy of Plateau Science and Sustainability Development, Xining, 810000, China

      Mingquan Zhou, Dan Zhang & Shengling Geng

    Authors
    1. Yuhuan Yan
      View author publications

      You can also search for this author inPubMed Google Scholar

    2. Mingquan Zhou
      View author publications

      You can also search for this author inPubMed Google Scholar

    3. Dan Zhang
      View author publications

      You can also search for this author inPubMed Google Scholar

    4. Shengling Geng
      View author publications

      You can also search for this author inPubMed Google Scholar

    Corresponding author

    Correspondence to Mingquan Zhou.

    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.

    Dan Zhang and Shengling Geng contributed equally to this work.

    About this article

    Check for updates. Verify currency and authenticity via CrossMark

    Cite this article

    Yan, Y., Zhou, M., Zhang, D. et al. Average increment scale-invariant heat kernel signature for 3D non-rigid shape analysis. Multimed Tools Appl 83, 8077–8115 (2024). https://doi.org/10.1007/s11042-023-15346-5

    Download citation

    • Received:

    • Revised:

    • Accepted:

    • Published:

    • Issue Date:

    • DOI: https://doi.org/10.1007/s11042-023-15346-5

    Keywords