The Visual Computer

, Volume 26, Issue 12, pp 1421–1433 | Cite as

Segmenting point-sampled surfaces

  • Ichitaro Yamazaki
  • Vijay Natarajan
  • Zhaojun Bai
  • Bernd Hamann
Original Article

Abstract

Extracting features from point-based representations of geometric surface models is becoming increasingly important for purposes such as model classification, matching, and exploration. In an earlier paper, we proposed a multiphase segmentation process to identify elongated features in point-sampled surface models without the explicit construction of a mesh or other surface representation. The preliminary results demonstrated the strength and potential of the segmentation process, but the resulting segmentations were still of low quality, and the segmentation process could be slow. In this paper, we describe several algorithmic improvements to overcome the shortcomings of the segmentation process. To demonstrate the improved quality of the segmentation and the superior time efficiency of the new segmentation process, we present segmentation results obtained for various point-sampled surface models. We also discuss an application of our segmentation process to extract ridge-separated features in point-sampled surfaces of CAD models.

Keywords

Point sets Sampling Features Geodesic distance Normalized cut Topological methods Spectral analysis Multiphase segmentation Hierarchical segmentation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M.: Shape modeling with point-sampled geometry. In: SIGGRAPH ’03: ACM SIGGRAPH 2003 Papers, pp. 641–650. ACM Press, New York (2003) CrossRefGoogle Scholar
  2. 2.
    Zwicker, M., Pauly, M., Knoll, O., Gross, M.: Pointshop 3D: an interactive system for point-based surface editing. In: SIGGRAPH ’02: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, pp. 322–329. ACM Press, New York (2002) CrossRefGoogle Scholar
  3. 3.
    Pfister, H., Gross, M.: Point-based computer graphics. IEEE Comput. Graph. Appl. 24(4), 22–23 (2004) CrossRefGoogle Scholar
  4. 4.
    Gross, M.H.: Getting to the point…? IEEE Comput. Graph. Appl. 26(5), 96–99 (2006) CrossRefGoogle Scholar
  5. 5.
    Sainz, M., Pajarola, R., Lario, R.: Points reloaded: point-based rendering revisited. In: Proceedings Symposium on Point-Based Graphics, Eurographics Association, pp. 121–128, 2004 Google Scholar
  6. 6.
    Tenebaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 190(5500), 2319–2323 (2000) CrossRefGoogle Scholar
  7. 7.
    Yamazaki, I., Natarajan, V., Bai, Z., Hamann, B.: Segmenting point sets. In: SMI ’06: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006 (SMI’06), pp. 4–13. IEEE Computer Society, Washington (2006) Google Scholar
  8. 8.
    Funkhouser, T., Kazhdan, M., Shilane, P., Min, P., Kiefer, W., Tal, A., Rusinkiewicz, S., Dobkin, D.: Modeling by example. In: SIGGRAPH ’04: ACM SIGGRAPH 2004 Papers, pp. 652–663. ACM Press, New York (2004) CrossRefGoogle Scholar
  9. 9.
    Gregory, A., State, A., Lin, M., Manocha, D., Livingston, M.: Interactive surface decomposition for polyhedral morphing. Vis. Comput. 15(9), 453–470 (1999) CrossRefGoogle Scholar
  10. 10.
    Zockler, M., Stalling, D., Hege, H.-C.: Fast and intuitive generation of geometric shape transitions. Vis. Comput. 16(5), 241–253 (2004) CrossRefGoogle Scholar
  11. 11.
    Karni, Z., Gotsman, C.: Spectral compression of mesh geometry. In: SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. 279–286. ACM Press/Addison-Wesley, New York (2000) CrossRefGoogle Scholar
  12. 12.
    Cohen-Steiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. In: SIGGRAPH ’04: ACM SIGGRAPH 2004 Papers, pp. 905–914. ACM Press, New York (2004) CrossRefGoogle Scholar
  13. 13.
    Attene, M., Falcidieno, B., Spagnuolo, M.: Hierarchical mesh segmentation based on fitting primitives. Vis. Comput. 22(3), 181–193 (2006) CrossRefGoogle Scholar
  14. 14.
    Zuckerberger, E., Tal, A., Shlafman, S.: Polyhedral surface decomposition with applications. Comput. Graph. 25(5), 733–743 (2002) CrossRefGoogle Scholar
  15. 15.
    Li, X., Toon, T., Tan, T., Huang, Z.: Decomposing polygon meshes for interactive applications. In: I3D ’01: Proceedings of the 2001 Symposium on Interactive 3D Graphics, pp. 35–42. ACM Press, New York (2001) CrossRefGoogle Scholar
  16. 16.
    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) CrossRefGoogle Scholar
  17. 17.
    Biasotti, S., Marini, S., Mortara, M., Patané, G.: An overview on properties and efficacy of topological skeletons in shape modelling. In: SMI ’03: Proceedings of the Shape Modeling International 2003, p. 245. IEEE Computer Society, Washington (2003) CrossRefGoogle Scholar
  18. 18.
    Katz, S., Tal, A.: Hierarchical mesh decomposition using fuzzy clustering and cuts. In: SIGGRAPH ’03: ACM SIGGRAPH 2003 Papers, pp. 954–961. ACM Press, New York (2003) CrossRefGoogle Scholar
  19. 19.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000) CrossRefGoogle Scholar
  20. 20.
    Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high performance scientific simulations. In: Sourcebook of Parallel Computing, pp. 491–541. Morgan Kaufmann, San Francisco (2003) Google Scholar
  21. 21.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999) CrossRefGoogle Scholar
  22. 22.
    Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995) MATHGoogle Scholar
  23. 23.
    Shamir, A.: A formulation of boundary mesh segmentation. In: 3DPVT ’04: Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium, pp. 82–89. IEEE Computer Society, Washington (2004) CrossRefGoogle Scholar
  24. 24.
    Garland, M., Willmott, A., Heckbert, P.S.: Hierarchical face clustering on polygonal surfaces. In: I3D ’01: Proceedings of the 2001 symposium on Interactive 3D Graphics, pp. 49–58. ACM Press, New York (2001) CrossRefGoogle Scholar
  25. 25.
    Sander, P., Snyder, J., Gortler, S., Hoppe, H.: Texture mapping progressive meshes. In: SIGGRAPH ’01: Proceedings of the 28th annual conference on Computer Graphics and Interactive Techniques, pp. 409–416. ACM Press, New York (2001) CrossRefGoogle Scholar
  26. 26.
    Zhou, K., Synder, J., Guo, B., Shum, H.-Y.: Iso-charts: stretch-driven mesh parameterization using spectral analysis. In: SGP ’04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 45–54. ACM Press, New York (2004) CrossRefGoogle Scholar
  27. 27.
    Katz, S., Leifman, G., Tal, A.: Mesh segmentation using feature points and core extraction. Vis. Comput. 21(8–10), 649–658 (2005) CrossRefGoogle Scholar
  28. 28.
    Lee, Y., Lee, S., Shamir, A., Cohen-Or, D., Seidel, H.P.: Intelligent mesh scissoring using 3D snakes. In: PG ’04: Proceedings of the Computer Graphics and Applications, 12th Pacific Conference on (PG’04), pp. 279–287. IEEE Computer Society, Washington (2004) Google Scholar
  29. 29.
    Liu, R., Zhang, H.: Segmentation of 3D meshes through spectral clustering. In: PG ’04: Proceedings of the Computer Graphics and Applications, 12th Pacific Conference (PG’04), pp. 298–305. IEEE Computer Society, Washington (2004) Google Scholar
  30. 30.
    Mangan, A.P., Whitaker, R.T.: Partitioning 3D surface meshes using watershed segmentation. IEEE Trans. Vis. Comput. Graph. 5(4), 308–321 (1999) CrossRefGoogle Scholar
  31. 31.
    Patane, G., Spagnuolo, M., Falcidieno, B.: Para-Graph: graph-based parameterization of triangle meshes with arbitrary genus. Comput. Graph. Forum 23(4), 783–797 (2004) CrossRefGoogle Scholar
  32. 32.
    Shalfman, S., Tal, A., Katz, S.: Metamorphosis of polyhedral surfaces using decomposition. Proc. Eurograph. 21(3), 219–228 (2002) Google Scholar
  33. 33.
    Zhang, E., Mischaikow, K., Turk, G.: Feature-based surface parameterization and texture mapping. ACM Trans. Graph. 24(1), 1–27 (2005) CrossRefGoogle Scholar
  34. 34.
    Zhou, Y., Huang, Z.: Decomposing polygon meshes by means of critical points. In: MMM ’04: Proceedings of the 10th International Multimedia Modelling Conference, p. 187. IEEE Computer Society, Washington (2004) CrossRefGoogle Scholar
  35. 35.
    Sander, P., Wood, Z., Gortler, S., Snyder, J., Hoppe, H.: Multi-chart geometry images. In: SGP ’03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry Processing, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, pp. 146–155, 2003 Google Scholar
  36. 36.
    Yamauchi, H., Lee, S., Lee, Y., Ohtake, Y., Belyaev, A., Seidel, H.P.: Feature sensitive mesh segmentation with mean shift. In: SMI ’05: Proceedings of the International Conference on Shape Modeling and Applications 2005 (SMI’ 05), pp. 238–245. IEEE Computer Society, Washington (2005) Google Scholar
  37. 37.
    Page, D.L., Koschan, A., Abidi, M.A.: Perception-based 3D triangle mesh segmentation using fast marching watersheds. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 27–32, 2003 Google Scholar
  38. 38.
    Dey, T.K., Giesen, J., Goswami, S.: Shape segmentation and matching with flow discretization. In: Proc. Workshop on Algorithms and Data Structure, pp. 25–36, 2003 Google Scholar
  39. 39.
    Gotsman, C.: On graph partitioning, spectral analysis, and digital mesh processing. In: SMI ’03: Proceedings of the International Conference on Shape Modeling and Applications 2003 (SMI’ 03), p. 165. IEEE Computer Society, Washington (2003) Google Scholar
  40. 40.
    Attene, M., Katz, S., Mortara, M., Patane, G., Spagnuolo, M., Tal, A.: Mesh segmentation—a comparative study. In: SMI ’06: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006 (SMI’06), pp. 14–25. IEEE Computer Society, Washington (2006) Google Scholar
  41. 41.
    Fiduccia, C.M., Mattheyses, R.M.: A linear time heuristic for improving network partitions. In: DAC ’82: Proceedings of the 19th Conference on Design Automation, pp. 175–181. IEEE Press, Piscataway (1982) Google Scholar
  42. 42.
    Kernighan, B., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 291–307 (1970) Google Scholar
  43. 43.
    Matsumoto, Y.: An Introduction to Morse Theory, Amer. Math. Soc., 2002, translated from Japanese by K. Hudson and M. Saito Google Scholar
  44. 44.
    Milnor, J.: Morse Theory. Princeton University Press, Princeton (1963) MATHGoogle Scholar
  45. 45.
    Bremer, P.T., Edelsbrunner, H., Hamann, B., Pascucci, V.: A topological hierarchy for functions on triangulated surfaces. IEEE Trans. Vis. Comput. Graph. 10(4), 385–396 (2004) CrossRefGoogle Scholar
  46. 46.
    Gyulassy, A., Natarajan, V., Pascucci, V., Bremer, P.T., Hamann, B.: A topological approach to simplification of three-dimensional scalar fields. IEEE Trans. Vis. Comput. Graph. 12(4), 474–484 (2006) CrossRefGoogle Scholar
  47. 47.
    Natarajan, V., Pascucci, V.: Volumetric data analysis using Morse–Smale complexes. In: SMI ’05: Proceedings of the International Conference on Shape Modeling and Applications 2005 (SMI’ 05), pp. 322–327. IEEE Computer Society, Washington (2005) Google Scholar
  48. 48.
    Edelsbrunner, H., Morozov, D., Pascucci, V.: Persistence-sensitive simplification of functions on 2-manifolds. In: SCG ’06: Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, pp. 127–134. ACM Press, New York (2006) CrossRefGoogle Scholar
  49. 49.
    Freeman, L.C.: Centrality in social networks: conceptual classification. Soc. Netw. 1(3), 215–239 (1979) CrossRefGoogle Scholar
  50. 50.
    Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, New York (1994) Google Scholar
  51. 51.
    Hilaga, M., Shinagawa, Y., Komura, T., Kunii, T.L.: Topology matching for fully automatic similarity estimation of 3D shapes. In: SIGGRAPH ’01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 203–212. ACM Press, New York (2001) CrossRefGoogle Scholar
  52. 52.
    Mount, D.M., ANN, S. Arya: A library for approximate nearest neighbor searching, http://www.cs.umd.edu/~mount/ANN/ (2010)
  53. 53.
    Roger, P., Bohr, H.: A new family of global protein shape descriptors. ACM Comput. Surv. 182(2), 167–181 (2003) Google Scholar
  54. 54.
    AIM@SHAPE, http://www.aimatshape.net/ (2010)
  55. 55.
    Level of detail for 3D graphics, http://www.lodbook.com/models/ (2010)
  56. 56.
    Garland, M.: QSlim simplification software, http://www.graphics.cs.uiuc.edu/~garland/software/qslim.html (2010)

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Ichitaro Yamazaki
    • 1
  • Vijay Natarajan
    • 3
  • Zhaojun Bai
    • 1
  • Bernd Hamann
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaDavisUSA
  2. 2.Department of Computer ScienceInstitute for Data Analysis and Visualization (IDAV)DavisUSA
  3. 3.Department of Computer Science and Automation, Supercomputer Education and Research CentreIndian Institute of ScienceBangaloreIndia

Personalised recommendations