Skip to main content
SpringerLink
Log in

A Network Analysis for Correspondence Learning via Linearly-Embedded Functions

  • Conference paper
  • First Online:
Pattern Recognition (DAGM GCPR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14264))

Included in the following conference series:

  • 194 Accesses

Abstract

Calculating correspondences between non-rigidly deformed shapes is the backbone of many applications in 3D computer vision and graphics. The functional map approach offers an efficient solution to this problem and has been very popular in learning frameworks due to its low-dimensional and continuous nature. However, most methods rely on the eigenfunctions of the Laplace-Beltrami operator as a basis for the underlying function spaces. While these have many advantages, they are also sensitive to non-isometric deformations and noise. Recently a method to learn the basis functions along with suitable descriptors has been proposed by Marin et al.. We do an in-depth analysis of the architecture proposed, including a new training scheme to increase robustness against sampling inconsistencies and an extension to unsupervised training which still obtains results on-par with the supervised approach.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: International Conference on Computer Vision (ICCV) (2011)

    Google Scholar 

  2. Aygün, M., Lähner, Z., Cremers, D.: Unsupervised dense shape correspondence using heat kernels. In: Conference on 3D Vision (3DV) (2020)

    Google Scholar 

  3. Bogo, F., Romero, J., Loper, M., Black, M.J.: FAUST: dataset and evaluation for 3D mesh registration. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2014)

    Google Scholar 

  4. Burghard, O., Klein, R.: Efficient lifted relaxations of the quadratic assignment problem. In: Vision, Modeling & Visualization (VMV) (2017)

    Google Scholar 

  5. Cao, D., Roetzer, P., Bernard, F.: Unsupervised learning of robust spectral shape matching. In: Transactions on Graphics (Proceedings of SIGGRAPH) (2023)

    Google Scholar 

  6. Colombo, M., Boracchi, G., Melzi, S.: PC-GAU: PCA basis of scattered gaussians for shape matching via functional maps. In: Smart Tools and Applications in Graphics (STAG) (2022)

    Google Scholar 

  7. Eisenberger, M., Lähner, Z., Cremers, D.: Divergence-free shape correspondence by deformation. Comput. Graph. Forum (CGF) 38(5) (2019)

    Google Scholar 

  8. Eisenberger, M., Lähner, Z., Cremers, D.: Smooth shells: multi-scale shape registration with functional maps. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2020)

    Google Scholar 

  9. Eisenberger, M., Toker, A., Leal-Taixé, L., Cremers, D.: Deep shells: unsupervised shape correspondence with optimal transport. In: 34th Conference on Neural Information Processing Systems (NeurIPS) (2020)

    Google Scholar 

  10. Ezuz, D., Heeren, B., Azencot, O., Rumpf, M., Ben-Chen, M.: Elastic correspondence between triangle meshes. Comput. Graph. Forum (CGF) (2019)

    Google Scholar 

  11. Halimi, O., Litany, O., Rodolà, E., Bronstein, A.M., Kimmel, R.: Unsupervised learning of dense shape correspondence. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    Google Scholar 

  12. Holzschuh, B., Lähner, Z., Cremers, D.: Simulated annealing for 3D shape correspondence. In: Conference on 3D Vision (3DV) (2020)

    Google Scholar 

  13. Kezurer, I., Kovalsky, S.Z., Basri, R., Lipman, Y.: Tight relaxation of quadratic matching. In: Computer Graphics Forum (CGF), vol. 34 (2015)

    Google Scholar 

  14. Litany, O., Remez, T., Rodolà, E., Bronstein, A., Bronstein, M.: Deep functional maps: Structured prediction for dense shape correspondence. In: International Conference on Computer Vision (ICCV) (2017)

    Google Scholar 

  15. Liu, S., Xu, H., Yan, D.M., Hu, L., Liu, X., Li, Q.: WTFM layer: an effective map extractor for unsupervised shape correspondence. Comput. Graph. Forum 41(7), 51–61 (2022)

    Article  Google Scholar 

  16. Loper, M., Mahmood, N., Romero, J., Pons-Moll, G., Black, M.J.: SMPL: a skinned multi-person linear model. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 34(6), 248:1–248:16 (2015)

    Google Scholar 

  17. Marin, R., Rakotosaona, M.J., Melzi, S., Ovsjanikov, M.: Correspondence learning via linearly-invariant embedding. In: Conference on Neural Information Processing Systems (NeurIPS) (2020)

    Google Scholar 

  18. Melzi, S., Rodolà, E., Castellani, U., Bronstein, M.M.: Localized manifold harmonics for spectral shape analysis. Comput. Graph. Forum (CGF) 37(6) (2018)

    Google Scholar 

  19. Melzi, S., Ren, J., Rodolà, E., Sharma, A., Wonka, P., Ovsjanikov, M.: Zoomout: spectral upsampling for efficient shape correspondence. Comput. Graph. Forum (CGF) (2019)

    Google Scholar 

  20. Monji-Azad, S., Hesser, J., Löw, N.: A review of non-rigid transformations and learning-based 3D point cloud registration methods. ISPRS J. Photogrammetry Remote Sens. (2023)

    Google Scholar 

  21. Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.: Functional maps: a flexible representation of maps between shapes. ACM Trans. Graph. (ToG) (Proc. SIGGRAPH) (2012)

    Google Scholar 

  22. Pai, G., Ren, J., Melzi, S., Wonka, P., Ovsjanikov, M.: Fast sinkhorn filters: using matrix scaling for non-rigid shape correspondence with funcitonal maps. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2021)

    Google Scholar 

  23. Panine, M., Kirgo, M., Ovsjanikov, M.: Non-isometric shape matching via functional maps on landmark-adapted bases. Comput. Graph. Forum (CGF) (2022)

    Google Scholar 

  24. Qi, C.R., Su, H., Mo, K., Guibas, L.J.: Pointnet: deep learning on point sets for 3D classification and segmentation. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2017)

    Google Scholar 

  25. Qi, C.R., Yi, L., Su, H., Guibas, L.J.: PointNet++: deep hierarchical feature learning on point sets in a metric space. In: Neural Information Processing Systems (NeurIPS) (2017)

    Google Scholar 

  26. Rodolà, E., Bronstein, A., Albarelli, A., Bergamasco, F., Torsello, A.: A game-theoretic approach to deformable shape matching. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2012)

    Google Scholar 

  27. Roufosse, J.M., Sharma, A., Ovsjanikov, M.: Unsupervised deep learning for structured shape matching. In: International Conference on Computer Vision (ICCV) (2019)

    Google Scholar 

  28. Sahillioǧlu, Y.: Recent advances in shape correspondence. Vis. Comput. (2020)

    Google Scholar 

  29. Sharp, N., Attaiki, S., Crane, K., Ovsjanikov, M.: DiffusionNet: discretization agnostic learning on surfaces. Trans. Graph. (ToG) (2022)

    Google Scholar 

  30. Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. In: Symposium on Geometry Processing (SGP) (2009)

    Google Scholar 

  31. Tombari, F., Salti, S., Di Stefano, L.: Unique signatures of histograms for local surface description. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6313, pp. 356–369. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15558-1_26

    Chapter  Google Scholar 

  32. Varol, G., et al.: Learning from synthetic humans. In: CVPR (2017)

    Google Scholar 

  33. Vestner, M., et al.: Efficient deformable shape correspondence via kernel matching. In: International Conference on 3D Vision (3DV) (2017)

    Google Scholar 

  34. Windheuser, T., Schlickewei, U., Schmidt, F.R., Cremers, D.: Large-scale integer linear programming for orientation-preserving 3D shape matching. Comput. Graph. Forum (CGF) 30(5) (2011)

    Google Scholar 

Download references

Acknowledgements

Zorah Lähner is supported by a KI-Starter grant of the Ministry of Culture and Science of the State of North Rhine-Westphalia.

Author information

Authors and Affiliations

  1. University of Siegen, Hölderlinstr. 3, 57076, Siegen, Germany

    Sharik Siddiqi & Zorah Lähner

  2. IAB – Institut für Angewandte Bauforschung, Über der Nonnenwiese 1, 99428, Weimar, Germany

    Sharik Siddiqi

Authors
  1. Sharik Siddiqi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zorah Lähner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zorah Lähner .

Editor information

Editors and Affiliations

  1. IWR, Heidelberg University, Heidelberg, Germany

    Ullrich Köthe

  2. IWR, Heidelberg University, Heidelberg, Germany

    Carsten Rother

1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 154 KB)

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Siddiqi, S., Lähner, Z. (2024). A Network Analysis for Correspondence Learning via Linearly-Embedded Functions. In: Köthe, U., Rother, C. (eds) Pattern Recognition. DAGM GCPR 2023. Lecture Notes in Computer Science, vol 14264. Springer, Cham. https://doi.org/10.1007/978-3-031-54605-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-54605-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-54604-4

  • Online ISBN: 978-3-031-54605-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation