Skip to main content
SpringerLink
Log in

A meshless strategy for shape diameter analysis

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

Abstract

An approach to computing an intuitive local thickness from surface meshes was introduced with the shape diameter function (SDF) in Shapira et al. (Vis Comput 24(4):249–259, 2008). In this paper, we present a new dynamic approach to the computation of the SDF for a cloud of points on the boundary of a volumetric object. We employ a particle flow driven by a simple collision test. The resulting SDF scalar field can be naturally exploited as a shape property for the volume-oriented object decomposition. Experimental results show the effectiveness and efficiency of our proposals.

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. Asafi, S., Goren, A., Cohen-Or, D.: Weak convex decomposition by lines-of-sight. Comput. Graph. Forum 32(5), 23–31 (2013)

    Article  Google Scholar 

  2. Attene M., Katz S., Mortara M., Patane G., Spagnuolo M., Tal A.: Mesh segmentation—a comparative study. In: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006, Washington, DC, USA, 2006, SMI’06, IEEE Computer Society, p. 7

  3. Au, O.K.-C., Zheng, Y., Chen, M., Xu, P., Tai, C.-L.: Mesh segmentation with concavity-aware fields. In: IEEE Transactions on Visualization and Computer Graphics, vol. 18, pp. 1125–1134 (2012)

  4. Chen, X., Golovinskiy, A., Funkhouser, T.: A benchmark for 3d mesh segmentation. ACM Trans. Graph. 28(3), 73:1–73:12 (2009)

    Article  Google Scholar 

  5. Casciola, G., Lazzaro, D., Montefusco, L.B., Morigi, S.: Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants. Comput. Math. Appl. 51(8), 1185–1198 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cignoni P., M.Callieri, Corsini M., Dellepiane M., Ganovelli F., G.Ranzuglia: MeshLab an open-source mesh processing tool. In: Sixth Eurographics Italian Chapter (2008), pp. 129–136

  7. Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. Graph. 23(3), 905–914 (2004)

    Article  Google Scholar 

  8. Fayolle, P.-A., Pasko, A.: Segmentation of discrete point clouds using an extensible set of templates. Vis. Comput. 29(5), 449–465 (2013)

    Article  Google Scholar 

  9. Heider, P., Pierre-Pierre, A., Li, R., Mueller, R., Grimm, C.: Comparing local shape descriptors. Vis. Comput. 28(9), 919–929 (2012)

    Article  Google Scholar 

  10. Kaick, O.V., Fish, N., Kleiman, Y., Asafi, S., Cohen-Or, D.: Shape segmentation by approximate convexity analysis. ACM Trans. Graph. 34(1), 4:1–4:11 (2014)

    Article  Google Scholar 

  11. Kovacic M., Guggeri F., Marras S., Scateni R.: Fast approximation of the shape diameter function. In: Proceedings Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) (2010)

  12. Desbrun M., Meyer M., Schröder P., Barr A.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege H.-C., Polthier K. (eds.) Visualization and Mathematics III. Mathematics and Visualization, pp. 35–57. Springer, Berlin (2003)

  13. Ming Lien J., Amato N. M.: Approximate convex decomposition of polyhedra. Tech. rep. In: Proceeding of ACM Symposium on Solid and Physical Modeling (2007)

  14. Morigi, S., Rucci, M.: Multilevel mesh simplification. Vis. Comput. 30(5), 479–492 (2014)

    Article  Google Scholar 

  15. Morigi S., Rucci M., Sgallari F.: Nonlocal surface fairing. In: Bruckstein A., Haar Romeny B., Bronstein A., Bronstein M. (eds.) Scale Space and Variational Methods in Computer Vision, vol. 6667 of Lecture Notes in Computer Science, pp. 38–49. Springer, Berlin (2012)

  16. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2, 15–36 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  17. Rolland-Nevière, X., Doërr, G., Alliez, P.: Robust diameter-based thickness estimation of 3d objects. Graph. Models 75(6), 279–296 (2013)

    Article  Google Scholar 

  18. Shamir, A.: A survey on mesh segmentation techniques. Comput. Graph. Forum 27(6), 1539–1556 (2008)

    Article  MATH  Google Scholar 

  19. Staten, M., Owen, S., Shontz, S., Salinger, A., Coffey, T.: A comparison of mesh morphing methods for 3d shape optimization. In: Quadros, W. (ed.) Proceedings of the 20th International Meshing Roundtable, pp. 293–311. Springer, Berlin (2012)

  20. Shapira, L., Shamir, A., Cohen-Or, D.: Consistent mesh partitioning and skeletonisation using the shape diameter function. Vis. Comput. 24(4), 249–259 (2008)

    Article  Google Scholar 

  21. Shapira, L., Shalom, S., Shamir, A., Cohen-Or, D., Zhang, H.: Contextual part analogies in 3d objects. Int. J. Comput. Vis. 89(2–3), 309–326 (2010)

    Article  Google Scholar 

  22. Unger M., Pock T., Trobin W., Cremers D., Bischof H.: TVSeg—interactive total variation based image segmentation. In: British Machine Vision Conference BMVC (2008)

  23. Yan, D.-M., Wang, W., Liu, Y., Yang, Z.: Variational mesh segmentation via quadric surface fitting. Comput. Aided Des. 44(11), 1072–1082 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bologna, P.zza Porta San Donato 5, Bologna, Italy

    Martin Huska & Serena Morigi

  2. Department of Mathematics, University of Padua, Via Trieste, 63, Padua, Italy

    Martin Huska

Authors
  1. Martin Huska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Serena Morigi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Serena Morigi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huska, M., Morigi, S. A meshless strategy for shape diameter analysis. Vis Comput 33, 303–315 (2017). https://doi.org/10.1007/s00371-015-1198-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-015-1198-4

Keywords

Search

Navigation