The Visual Computer

, Volume 22, Issue 3, pp 181–193 | Cite as

Hierarchical mesh segmentation based on fitting primitives

  • Marco Attene
  • Bianca Falcidieno
  • Michela Spagnuolo
original article


In this paper, we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which is fitted by one of the primitives employed. Initially, each triangle represents a single cluster; at every iteration, all the pairs of adjacent clusters are considered, and the one that can be better approximated by one of the primitives forms a new single cluster. The approximation error is evaluated using the same metric for all the primitives, so that it makes sense to choose which is the most suitable primitive to approximate the set of triangles in a cluster.

Based on this approach, we have implemented a prototype that uses planes, spheres and cylinders, and have experimented that for meshes made of 100 K faces, the whole binary tree of clusters can be built in about 8 s on a standard PC.

The framework described here has natural application in reverse engineering processes, but it has also been tested for surface denoising, feature recovery and character skinning.


Clustering Denoising Sharp feature Shape abstraction Reverse engineering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alliez, P., Cohen-Steiner, D., Devillers, O., Levy, B., Desbrun, M.: Anisotropic polygonal remeshing. ACM Trans. Graph. 22(3), 485–493 (2003)Google Scholar
  2. 2.
    Attene, M., Biasotti, S., Spagnuolo, M.: Shape understanding by contour-driven retiling. Visual Comput. 19(2-3), 127–138 (2003)Google Scholar
  3. 3.
    Attene, M., Falcidieno, B., Rossignac, J., Spagnuolo, M.: Sharpen&bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling. IEEE Trans. Vis. Comput. Graph.11(2), 181–192 (2005)Google Scholar
  4. 4.
    Biasotti, S., Falcidieno, B, Spagnuolo, M.: Surface understanding based on extended reeb graph representation. In: Rana, S. (ed.) Topological Data Structures for Surfaces: An Introduction to Geographical Information Science, pp. 87–102. Wiley publishers (2004)Google Scholar
  5. 5.
    Chaperon, T., Goulette, F.: Extracting cylinders in full 3D data using a random sampling method and the Gaussian image. Proceedings of VMV 2001, held in Stuttgart, Germany, pp. 35–42 Aka GmbH (2001)Google Scholar
  6. 6.
    Cignoni, P., Rocchini, C., Scopigno, R.: Metro: measuring error on simplified surfaces. Comput. Graph. Forum 17(2) (Proceedings of Eurographics ’98), 167–174 (1998)Google Scholar
  7. 7.
    Cohen-Steiner, D., Alliez, P. and Desbrun, M.: Variational Shape Approximation. ACM Trans. Graph. 23(3), 905–914 (2004)Google Scholar
  8. 8.
    Garland, M., Willmott, A., Heckbert, P.S.: Hierarchical face clustering on polygonal surfaces. Proceedings ACM Symposium on Interactive 3D Graphics, pp. 49–58 (2001)Google Scholar
  9. 9.
    Gelfand, N., Guibas, L.J.: Shape segmentation using local slippage analysis. Proceedings Eurographics Symposium on Geometry Processing, pp. 219–228 (2004)Google Scholar
  10. 10.
    Glantz, S.A., Slinker, B.K.: Primer of Applied Regression and Analysis of Variance. McGraw-Hill Medical, ISBN 0071360867 (2000)Google Scholar
  11. 11.
    Jolliffe, I.T.: Principal Component Analysis. Springer, Berlin Heidelberg New York (1986)Google Scholar
  12. 12.
    Lewis, J. P., Cordner, M., Fong, N.: Pose space deformations: a unified approach to shape interpolation and skeleton-driven deformation. In Proceedings ACM SIGGRAPH 2000, pp. 165–172 (2000)Google Scholar
  13. 13.
    Lloyd, S.: Least square quantization on PCM. IEEE Trans. Information Theory 18, 129–137 (1982)Google Scholar
  14. 14.
    Marr, D.: Vision. Freeman Publishers, New York (1982)Google Scholar
  15. 15.
    Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential geometry operators for triangulated 2-manifolds. Visualization and Mathematics III, 35–57 (2003)Google Scholar
  16. 16.
    Mortara, M., Patanè, G., Spagnuolo, M., Falcidieno, B. and Rossignac, J.: Blowing bubbles for multi-scale analysis and decomposition of triangle meshes. Algoritmica 38(2), 227–248 (2003)Google Scholar
  17. 17.
    Petitjean, S.: A survey of methods for recovering quardics in triangle meshes. ACM Comput. Surv. 34(2), 211–262 (2002)Google Scholar
  18. 18.
    Ponce, J., Brady, J.: Toward a surface primal sketch. In: Kanade, T (ed.) Three-Dimensional Machine Vision, pp. 195–240. Kluwer, Dordrecht (1987)Google Scholar
  19. 19.
    Pottman, H., Leopoldseder, S., Hofer, M., Steiner, T., Wang, W.: Industrial geometry: recent advances and applications in CAD. Comput.-Aid. Des. 1, 513–522 (2004)Google Scholar
  20. 20.
    Pratt, V.: Direct least-squares fitting of algebraic surfaces. Computer Graphics 21(4), 145–152 (Proceedings of SIGGRAPH’87) (1987)Google Scholar
  21. 21.
    Renner, G., Várady, T., Wiess, V.: Reverse engineering of free-form features. In Proceedings of PROLAMAT 98, Trento, IFIP (1998)Google Scholar
  22. 22.
    Rössl, C., Kobbelt, L., Seidel, H.-P.: Extraction of feature lines on triangulated surfaces using morphological operators. In Proc. of Smart Graphics’00, AAAI Spring Symposium, pp. 71–75 (2000)Google Scholar
  23. 23.
    Sander, P., Wood, Z., Gortler, S.J., Snyder, J., Hoppe, H.: Multi-chart geometry images. In Proceedings of the Eurographics Symposium on Geometry Processing, pp. 146–155 (2003)Google Scholar
  24. 24.
    Sapidis, N., Besl, P.: Direct construction of polynomial surfaces from dense range images through region growing. ACM Trans. Graph. 14(2), 171–200 (1995)Google Scholar
  25. 25.
    Scales, L.E.: Introduction to Non-linear Optimization. Springer, Berlin Heidelberg New York (1985)Google Scholar
  26. 26.
    Thompson, W.B., Owen, J.C., James de St. Germain, H., Stark, S.R., Henderson, T.C.: Feature-based reverse engineering of mechanical parts. IEEE Trans. Robot. Autom. 15(1), 57–66 (1999)Google Scholar
  27. 27.
    Várady, T., Martin, R.: Reverse engineering. In Handbook of Computer Aided Geometric Design, pp. 651–681. Elsevier (2002)Google Scholar
  28. 28.
    Várady, T., Benkö, P., Kós, G.: Reverse engineering regular objects: simple segmentation and surface fitting procedures. Int. J. Shape Modeling 4(3), 127–141 (1998)Google Scholar
  29. 29.
    Vergeest, J.S.M., Horváth, I., Kuczogi, G., Opyio, E., Wiegers, T.: Reverse engineering for shape synthesis in industrial engineering. In Proceedings of the 26th International Conference on Computers in Industrial Engineering, 15–17 December, Melbourne, Australia, pp. 84–90 (1999)Google Scholar
  30. 30.
    Watanabe, K., Belyaev, A.G.: Detection of salient curvature features on polygonal surfaces. Comput. Graph. Forum 20(3), 385–392 (Proceedings of Eurographics‘01) (2001)Google Scholar
  31. 31.
    Wu, J., Kobbelt, L.: Structure recovery via hybrid variational surface approximation. Proc. Eurographics 2005, Comput. Graph. Forum 24(3), 277–284 (2005)Google Scholar
  32. 32.
    Yang, M., Lee, E.: Segmentation of measured point data using a parametric quadric surface approximation. Comput. Aid. Des. 31(7), 449–458 (1999)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Marco Attene
    • 1
  • Bianca Falcidieno
    • 1
  • Michela Spagnuolo
    • 1
  1. 1.Istituto per la Matematica Applicata e le Tecnologie InformaticheConsiglio Nazionale delle RicercheGenovaItaly

Personalised recommendations