The Visual Computer

, Volume 33, Issue 3, pp 303–315 | Cite as

A meshless strategy for shape diameter analysis

  • Martin Huska
  • Serena MorigiEmail author
Original Article


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.


Shape analysis Shape diameter function Meshless surface processing Variational partitioning 


  1. 1.
    Asafi, S., Goren, A., Cohen-Or, D.: Weak convex decomposition by lines-of-sight. Comput. Graph. Forum 32(5), 23–31 (2013)CrossRefGoogle Scholar
  2. 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. 7Google Scholar
  3. 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)Google Scholar
  4. 4.
    Chen, X., Golovinskiy, A., Funkhouser, T.: A benchmark for 3d mesh segmentation. ACM Trans. Graph. 28(3), 73:1–73:12 (2009)CrossRefGoogle Scholar
  5. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 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. 129–136Google Scholar
  7. 7.
    Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. Graph. 23(3), 905–914 (2004)CrossRefGoogle Scholar
  8. 8.
    Fayolle, P.-A., Pasko, A.: Segmentation of discrete point clouds using an extensible set of templates. Vis. Comput. 29(5), 449–465 (2013)CrossRefGoogle Scholar
  9. 9.
    Heider, P., Pierre-Pierre, A., Li, R., Mueller, R., Grimm, C.: Comparing local shape descriptors. Vis. Comput. 28(9), 919–929 (2012)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)Google Scholar
  12. 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)Google Scholar
  13. 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)Google Scholar
  14. 14.
    Morigi, S., Rucci, M.: Multilevel mesh simplification. Vis. Comput. 30(5), 479–492 (2014)CrossRefGoogle Scholar
  15. 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)Google Scholar
  16. 16.
    Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2, 15–36 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Rolland-Nevière, X., Doërr, G., Alliez, P.: Robust diameter-based thickness estimation of 3d objects. Graph. Models 75(6), 279–296 (2013)CrossRefGoogle Scholar
  18. 18.
    Shamir, A.: A survey on mesh segmentation techniques. Comput. Graph. Forum 27(6), 1539–1556 (2008)CrossRefzbMATHGoogle Scholar
  19. 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)Google Scholar
  20. 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)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)Google Scholar
  23. 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly
  2. 2.Department of MathematicsUniversity of PaduaPaduaItaly

Personalised recommendations