The Visual Computer

, Volume 21, Issue 8–10, pp 659–668 | Cite as

Mesh segmentation driven by Gaussian curvature

  • Hitoshi Yamauchi
  • Stefan Gumhold
  • Rhaleb Zayer
  • Hans-Peter Seidel
original article

Abstract

Mesh parameterization is a fundamental problem in computer graphics as it allows for texture mapping and facilitates many mesh processing tasks. Although there exists a variety of good parameterization methods for meshes that are topologically equivalent to a disk, the segmentation into nicely parameterizable charts of higher genus meshes has been studied less. In this paper we propose a new segmentation method for the generation of charts that can be flattened efficiently. The integrated Gaussian curvature is used to measure the developability of a chart, and a robust and simple scheme is proposed to integrate the Gaussian curvature. The segmentation approach evenly distributes Gaussian curvature over the charts and automatically ensures a disklike topology of each chart. For numerical stability, we use an area on the Gauss map to represent Gaussian curvature. The resulting parameterization shows that charts generated in this way have less distortion compared to charts generated by other methods.

Keywords

Mesh segmentation Gauss map Gaussian curvature Parameterization Developability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benkő, P., Várady, T.: Direct segmentation of smooth, multiple point regions. In: Proceedings of Geometric Modeling and Processing Theory and Applications (GMP ’02), pp. 169–178. IEEE Press, New York (2002)Google Scholar
  2. 2.
    Cohen–Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. Graph. 23(3), 905–914 (2004)Google Scholar
  3. 3.
    Cohen–Steiner, D., Morvan, J.M.: Restricted delaunay triangulations and normal cycle. In: Proceedings of the 19th Symposium on Computational Geometry, pp. 312–321 (2003)Google Scholar
  4. 4.
    Desbrun, M., Meyer, M., Alliez, P.: Intrinsic parameterizations of surface meshes. In: Proceedings of Eurographics, 21(3), 209–218 (2002)Google Scholar
  5. 5.
    Dey, T.K., Giesen, J., Goswami, S.: Shape segmentation and matching with flow discretization. In: Proceedings of the Workshop on Algorithms Data Structures (WADS 03). Lecture notes in computer science, vol 2748, pp. 25–36 (2003)Google Scholar
  6. 6.
    Elber, G.: Model fabrication using surface layout projection. Comput.-Aided Des. 27(4), 283–291 (1995)Google Scholar
  7. 7.
    Erickson, J., Har-Peled, S.: Optimally cutting a surface into a disk. In: Workshop of the 18th ACM Symposum on Computational Geometry, pp. 244–253 (2002)Google Scholar
  8. 8.
    Funkhouser, T., Kazhdan, M., Shilane, P., Min, P., Kiefer, W., Tal, A., Rusinkiewicz, S., Dobkin, D.: Modeling by example. ACM Trans. Graph. 23(3), 652–663 (2004)Google Scholar
  9. 9.
    Garland, M., Willmott, A., Heckbert, P.: Hierarchical face clustering on polygonal surfaces. In: Workshop of the ACM Symposium on Interactive 3D Graphics, pp. 49–58 (2001)Google Scholar
  10. 10.
    Gelfand, N., Guibas, L.J.: Shape segmentation using local slippage analysis. In: Workshop of the Eurographics Symposium on Geometry Processing (SGP-04), pp. 219–228 (2004)Google Scholar
  11. 11.
    Hoschek, J.: Approximation of surfaces of revolution by developable surfaces. Comput.-Aided Des. 30(10), 757–763 (1998)Google Scholar
  12. 12.
    Inoue, K., Itoh, T., Yamada, A., Furuhata, T., Shimada, K.: Clustering large number of faces for 2-dimensional mesh generation. In: Proceedings of the 8th International Meshing Roundtable, pp. 281–292 (1999)Google Scholar
  13. 13.
    Julius, D., Kraevoy, V., Shaffer, A.: D-charts: Quasi-developable mesh segmentation. In: Proceedings of Eurographics (2005) (in press)Google Scholar
  14. 14.
    Kalvin, A.D., Taylor, R.H.: Superfaces: polygonal mesh simplification with bounded error. IEEE Comput. Graph. Appl. 16(3), 64–77 (1996)Google Scholar
  15. 15.
    Katz, S., Tal, A.: Hierarchical mesh decomposition using fuzzy clustering and cuts. ACM Trans. Graph. 22(3), 954–961 (2003)Google Scholar
  16. 16.
    Lee, A.W.F., Sweldens, W., Schröder, P., L. Cowsar, L., Dobkin, D.: MAPS: Multiresolution adaptive parameterization of surfaces. In: Proceedings of SIGGRAPH, pp. 95–104 (1998)Google Scholar
  17. 17.
    Lévy, B., Petitjean, S., Ray, N., Maillot, J.: Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21(3), 362–371 (2002)Google Scholar
  18. 18.
    Liu, R., Zhang, H.: Segmentation of 3D meshes through spectral clustering. In: Pacific Graphics, pp. 298–305 (2004)Google Scholar
  19. 19.
    Maillot, J., Yahia, H., Verroust, A.: Interactive texture mapping. In: Proceedings of SIGGRAPH, pp. 27–34 (1993)Google Scholar
  20. 20.
    Mangan, A.P., Whitaker, R.T.: Partitioning 3D surface meshes using watershed segmentation. IEEE Trans. Visual. Comput. Graph. 5(4), 308–321 (1999)Google Scholar
  21. 21.
    Max, N.: Weights for computing vertex normals from facet normals. J. Graph. Tools 4(2), 1–6 (1999)Google Scholar
  22. 22.
    Mitani, J., Suzuki, H.: Making papercraft toys from meshes using strip-based approximate unfolding. ACM Trans. Graph. 23(3), 259–263 (2004)Google Scholar
  23. 23.
    Page, D.L., Koschan, A., Abidi, M.: Perception-based 3d triangle mesh segmentation using fast marching watersheds. In: Proceedings of the International Conference on Computer Vision and Pattern Recognition, 2, 27–32 (2003)Google Scholar
  24. 24.
    Pottmann, H., Farin, G.E.: Developable rational bézier and b-spline surfaces. Comput. Aided Geom. Des. 12(5), 513–531 (1995)Google Scholar
  25. 25.
    Sander, P.V., Snyder, J., Gortler, S.J., Hoppe, H.: Texture mapping progressive meshes. In: Proceedings of SIGGRAPH, pp. 409–416 (2001)Google Scholar
  26. 26.
    Sander, P.V., Wood, Z.J., Gortler, S.J., Snyder, J., Hoppe, H.: Multi-chart geometry images. In: Proceedings of the Eurographics Symposium on Geometry Processing (SGP-03), pp. 146–155 (2003)Google Scholar
  27. 27.
    Shamir, A.: A formulation of boundary mesh segmentation. In: 3DPVT, pp. 82–89 (2004)Google Scholar
  28. 28.
    Shlafman, S., Tal, A., Katz, S.: Metamorphosis of polyhedral surfaces using decomposition. Comput. Graph. Forum 21(3), 219–228 (2002)Google Scholar
  29. 29.
    Sorkine, O., Cohen-Or, D., Goldenthal, R., Lischinski, D.: Bounded-distortion piecewise mesh parameterization. In: IEEE Visualization, pp. 355–362 (2002)Google Scholar
  30. 30.
    Welch, W., Witkin, A.: Free-form shape design using triangulated surfaces. In: Proceedings of SIGGRAPH, pp. 247–256 (1994)Google Scholar
  31. 31.
    Zhou, K., Snyder, J., Guo, B., Shum, H.Y.: Iso-charts: stretch-driven mesh parameterization using spectral analysis. In: Proceedings of the Eurographics Symposium on Geometry Processing (SGP-04), pp. 47–56 (2004)Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Hitoshi Yamauchi
    • 1
  • Stefan Gumhold
    • 1
  • Rhaleb Zayer
    • 1
  • Hans-Peter Seidel
    • 1
  1. 1.MPI InformatikSaarbrückenGermany

Personalised recommendations