Skip to main content
SpringerLink
Log in

Pose analysis using spectral geometry

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We propose a novel method to analyze a set of poses of 3D models that are represented with triangle meshes and unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectrum domain that is defined by Laplace–Beltrami operator. During this space-spectrum transform, all near-isometric deformations, mesh triangulations and Euclidean transformations are filtered away. The different spatial poses from a 3D model are represented with near-isometric deformations; therefore, they have similar behaviors in the spectral domain. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectrum domain. Semantic skeleton can be automatically built with joints detected as well. The Laplace–Beltrami operator is proved to be invariant to isometric deformations and Euclidean transformations such as translation and rotation. It also can be invariant to scaling with normalization. The discrete implementation also makes the Laplace–Beltrami operator straightforward to be applied on triangle meshes despite triangulations. Our method turns a rather difficult spatial problem into a spectral problem that is much easier to solve. The applications show that our 3D pose analysis method leads to a registration-free pose analysis and a high-level semantic part understanding of 3D shapes.

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

Access this article

Log in via an institution

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
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Au, O.K.-C., Fu, H., Tai, C.-L., Cohen-Or, D.: Handle-aware isolines for scalable shape editing. ACM Trans. Graph. 26(3), 83 (2007)

    Article  Google Scholar 

  2. Chu, H.-K., Lee, T.-Y.: Multi-resolution mean shift clustering algorithm for shape interpolation. IEEE Trans. Vis. Comput. Graph. (2009)

  3. Cornea, N.D., Silver, D., Min, P.: Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graph. 13(3), 530–548 (2007)

    Article  Google Scholar 

  4. de Aguiar, E., Theobalt, C., Thrun, S., Seidel, H.-P.: Automatic conversion of mesh animations into skeleton-based animations. Comput. Graph. Forum 27(2), 389–397 (2008)

    Article  Google Scholar 

  5. Dey, T.K., Ranjan, P., Wang, Y.: Convergence, stability, and discrete approximation of Laplace spectra. In: Proceedings of the Twenty-First Annual ACM–SIAM Symposium on Discrete Algorithms, SODA ’10, pp. 650–663. Society for Industrial and Applied Mathematics, Philadelphia (2010)

    Google Scholar 

  6. He, Y., Xiao, X., Seah, H.-S.: Harmonic 1-form based skeleton extraction from examples. Graph. Models 71(2), 49–62 (2009)

    Article  Google Scholar 

  7. Hu, J., Hua, J.: Salient spectral geometric features for shape matching and retrieval. Vis. Comput. 25(5–7), 667–675 (2009)

    Article  Google Scholar 

  8. Huang, J., Shi, X., Liu, X., Zhou, K., Wei, L.-Y., Teng, S.-H., Bao, H., Guo, B., Shum, H.-Y.: Subspace gradient domain mesh deformation. ACM Trans. Graph. 25(3), 1126–1134 (2006)

    Article  Google Scholar 

  9. James, D.L., Twigg, C.D.: Skinning mesh animations. ACM Trans. Graph. 24(3) (2005)

  10. Karni, Z., Gotsman, C.: Spectral compression of mesh geometry. In: International Conference on Computer Graphics and Interactive Techniques, pp. 279–286 (2000)

    Google Scholar 

  11. Kilian, M., Mitra, N.J., Pottmann, H.: Geometric modeling in shape space. ACM Trans. Graph. 26(3), 64 (2007)

    Article  Google Scholar 

  12. Lévy, B.: Laplace–Beltrami eigenfunctions: towards an algorithm that understand s geometry. In: IEEE International Conference on Shape Modeling and Applications (2006). Invited Talk

    Google Scholar 

  13. Lewis, J.P., Cordner, M., Fong, N.: Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation. In: SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. 165–172 (2000)

    Chapter  Google Scholar 

  14. Meyer, M., Desbrun, M., Schröder, P., Barr, A.: Discrete differential geometry operators for triangulated 2-manifolds. In: VisMath (2002)

    Google Scholar 

  15. Pascucci, V., Scorzelli, G., Bremer, P.-T., Mascarenhas, A.: Robust on-line computation of Reeb graphs: simplicity and speed. ACM Trans. Graph. 26(3), 58 (2007)

    Article  Google Scholar 

  16. Patanè, G., Spagnuolo, M., Falcidieno, B.: A minimal contouring approach to the computation of the Reeb graph. IEEE Trans. Vis. Comput. Graph. 15(4), 583–595 (2009)

    Article  Google Scholar 

  17. Reuter, M.: Hierarchical shape segmentation and registration via topological features of Laplace–Beltrami eigenfunctions. Int. J. Comput. Vis. 89(2), 287–308 (2010)

    Article  Google Scholar 

  18. Reuter, M., Wolter, F.E., Peinecke, N.: Laplace–Beltrami spectra as“Shape-DNA” of surfaces and solids. Comput. Aided Des. 38(4), 342–366 (2006)

    Article  Google Scholar 

  19. Reuter, M., Wolter, F.-E., Shenton, M., Niethammer, M.: Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis. Comput. Aided Des. 41(10), 739–755 (2009)

    Article  Google Scholar 

  20. Rustamov, R.M.: Laplace–Beltrami eigenfunctions for deformation invariant shape representation. In: SGP ’07: Proceedings of the Fifth Eurographics Symposium on Geometry Processing, pp. 225–233 (2007)

    Google Scholar 

  21. Shinagawa, Y., Kunii, T.L.: Constructing a Reeb graph automatically from cross sections. IEEE Comput. Graph. Appl. 11(6), 44–51 (1991)

    Article  Google Scholar 

  22. Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. In: SIGGRAPH ’04: ACM SIGGRAPH 2004 Papers, pp. 399–405 (2004)

    Chapter  Google Scholar 

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

    Google Scholar 

  24. Vallet, B., Lévy, B.: Spectral geometry processing with manifold harmonics. Comput. Graph. Forum (2008)

  25. Weber, O., Sorkine, O., Lipman, Y., Gotsman, C.: Context-aware skeletal shape deformation. Comput. Graph. Forum 26(3) (2007)

  26. Xu, G.: Discrete Laplace–Beltrami operator on sphere and optimal spherical triangulations. Int. J. Comput. Geom. Appl. 16(1), 75–93 (2006)

    Article  MATH  Google Scholar 

  27. Yan, H.-B., Hu, S., Martin, R.R., Yang, Y.-L.: Shape deformation using a skeleton to drive simplex transformations. IEEE Trans. Vis. Comput. Graph. 14(3), 693–706 (2008)

    Article  Google Scholar 

  28. Zou, G., Hua, J., Muzik, O.: Non-rigid surface registration using spherical thin-plate splines. In: Proceedings of International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 367–374 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Wayne State University, 5057 Woodward Ave, STE 3010, Detroit, MI, 48098, USA

    Jiaxi Hu & Jing Hua

Authors
  1. Jiaxi Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Hua
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jing Hua.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, J., Hua, J. Pose analysis using spectral geometry. Vis Comput 29, 949–958 (2013). https://doi.org/10.1007/s00371-013-0850-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-013-0850-0

Keywords

Search

Navigation