Advertisement

The Visual Computer

, 25:267 | Cite as

Hierarchical aggregation for efficient shape extraction

  • Chunxia Xiao
  • Hongbo Fu
  • Chiew-Lan Tai
Original Article

Abstract

This paper presents an efficient framework which supports both automatic and interactive shape extraction from surfaces. Unlike most of the existing hierarchical shape extraction methods, which are based on computationally expensive top-down algorithms, our framework employs a fast bottom-up hierarchical method with multiscale aggregation. We introduce a geometric similarity measure, which operates at multiple scales and guarantees that a hierarchy of high-level features are automatically found through local adaptive aggregation. We also show that the aggregation process allows easy incorporation of user-specified constraints, enabling users to interactively extract features of interest. Both our automatic and the interactive shape extraction methods do not require explicit connectivity information, and thus are applicable to unorganized point sets. Additionally, with the hierarchical feature representation, we design a simple and effective method to perform partial shape matching, allowing efficient search of self-similar features across the entire surface. Experiments show that our methods robustly extract visually meaningful features and are significantly faster than related methods.

Keywords

Mesh segmentation Geometric similarity measure Shape matching Shape extraction 

References

  1. 1.
    Attene, M., Falcidieno, B., Spagnuolo, M.: Hierarchical mesh segmentation based on fitting primitives. Visual Comput. 22(3), 181–193 (2006)CrossRefGoogle Scholar
  2. 2.
    Attene, M., Katz, S., Mortara, M., Patane, G., Spagnuolo, M., Tal, A.: Mesh segmentation – a comparative study. In: International Conference on Shape Modeling and Applications (SMI’06), p. 7. IEEE Computer Society Press (2006)Google Scholar
  3. 3.
    Cohen-Steiner, D., Morvan, J.M.: Restricted Delaunay triangulations and normal cycle. In: ACM Symposium on Computational Geometry (San Diego, CA), pp. 237–246. ACM, New York, NY, San Diego, CA (2003)Google Scholar
  4. 4.
    Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of ACM SIGGRAPH 99, pp. 317–324. ACM Press/Addison-Wesley Publishing Co. (1999)Google Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Gal, R., Cohen-Or, D.: Salient geometric features for partial shape matching and similarity. ACM Trans. Graph. 25(1), 130–150 (2006)CrossRefGoogle Scholar
  7. 7.
    Garland, M., Willmott, A., Heckbert, P.S.: Hierarchical face clustering on polygonal surfaces. In: Proceedings of the 2001 Symposium on Interactive 3D Graphics (SI3D ’01), pp. 49–58. ACM (2001)Google Scholar
  8. 8.
    Gatzke, T., Grimm, C.: Feature detection using curvature maps and the min-cut/max-flow algorithm. In: Geometric Modeling and Processing, pp. 578–584. IOS Press (2006)Google Scholar
  9. 9.
    Gatzke, T., Grimm, C., Garland, M., Zelinka, S.: Curvature maps for local shape comparison. In: Shape Modeling International, pp. 244–256. IEEE Computer Society (2005)Google Scholar
  10. 10.
    Hoffman, D.D., Singh, M.: Salience of visual parts. Cognition 63(1), 29–78 (1997)CrossRefGoogle Scholar
  11. 11.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: SIGGRAPH, pp. 71–78. Academic Press Professional, Inc. (1992)Google Scholar
  12. 12.
    Ji, Z., Liu, L., Chen, Z., Wang, G.: Easy mesh cutting. Comput. Graph. Forum 25(3), 283–291 (2006)CrossRefGoogle Scholar
  13. 13.
    Katz, S., Leifman, G., Tal, A.: Mesh segmentation using feature point and core extraction. Visual Comput. 21(8–10), 649–658 (2005)CrossRefGoogle Scholar
  14. 14.
    Katz, S., Tal, A.: Hierarchical mesh decomposition using fuzzy clustering and cuts. ACM Trans. Graph. 22(3), 954–961 (2003)CrossRefGoogle Scholar
  15. 15.
    Lai, Y.K., Zhou, Q.Y., Hu, S.M., Martin, R.R.: Feature sensitive mesh segmentation. In: Solid and Physical Modeling Symposium 2006 (SPM’06), pp. 17–25. ACM (2006)Google Scholar
  16. 16.
    Lange, C., Polthier, K.: Anisotropic smoothing of point sets. Spec. Issue Comput. Aided Geom. Des. 22(7) (2005)Google Scholar
  17. 17.
    Lee, Y., Lee, S., Shamir, A., Cohen-Or, D., Seidel, H.P.: Intelligent mesh scissoring using 3D snakes. In: Pacific Graphics, pp. 279–287. IEEE Computer Society (2004)Google Scholar
  18. 18.
    Lee, Y., Lee, S., Shamir, A., Cohen-Or, D., Seidel, H.P.: Mesh scissoring with minima rule and part salience. Comput. Aided Geom. Des. 22(5), 444–465 (2005)zbMATHCrossRefGoogle Scholar
  19. 19.
    Li, X., Guskov, I.: Multi-scale features for approximate alignment of point-based surfaces. In: Symposium on Geometry Processing, pp. 217–226. Eurographics Association (2005)Google Scholar
  20. 20.
    Liu, R., Jain, V., Zhang, H.: Subsampling for efficient spectral mesh processing. Lect. Notes Comput. Sci. 4035, 172–184 (2006)CrossRefGoogle Scholar
  21. 21.
    Liu, R., Zhang, H.: Segmentation of 3D meshes through spectral clustering. In: Pacific Graphics, pp. 298–305. IEEE Computer Society (2004)Google Scholar
  22. 22.
    Liu, R., Zhang, H.: Mesh segmentation via spectral embedding and contour analysis. Comput. Graph. Forum 26(3), 385–394 (2007)CrossRefGoogle Scholar
  23. 23.
    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
  24. 24.
    Mortara, M., Patane, G., Spagnuolo, M., Falcidieno, B., Rossignac, J.: Plumber: a method for a multi-scale decomposition of 3D shapes into tubular primitives and bodies. In: Ninth ACM Symposium on Solid Modeling and Applications (SMI’04), pp. 339–344. IEEE Computer Society (2004)Google Scholar
  25. 25.
    Ohtake, Y., Belyaev, A., Seidel, H.P.: 3D scattered data approximation with adaptive compactly supported radial basis functions. In: International Conference on Shape Modeling and Applications (SMI’04), pp. 31–39. IEEE Computer Society (2004)Google Scholar
  26. 26.
    Page, D.L., Koschan, A., Abidi, M.: Perception-based 3D triangle mesh segmentation using fast marching watersheds. In: Computer Vision and Pattern Recognition, vol. 2, pp. 27–32. IEEE Computer Society (2003)Google Scholar
  27. 27.
    Pauly, M., Gross, M., Kobbelt, L.P.: Efficient simplification of point-sampled surfaces. In: Visualization, pp. 163–170. IEEE Computer Society (2002)Google Scholar
  28. 28.
    Pauly, M., Keiser, R., Gross, M.: Multi-scale feature extraction on point-sampled surfaces. In: Eurographics, pp. 281–290. Eurographics Association (2003)Google Scholar
  29. 29.
    Pfister, H., Zwicker, M., van Baar, J., Gross, M.: Surfels: surface elements as rendering primitives. In: SIGGRAPH, pp. 335–342. ACM Press/Addison-Wesley Publishing Co. (2000)Google Scholar
  30. 30.
    Shamir, A.: Segmentation and shape extraction of 3D boundary meshes. In: State-of-the-Art Report, Proceedings of Eurographics 2006, pp. 137–149. Eurographics Association (2006)Google Scholar
  31. 31.
    Sharf, A., Blumenkrants, M., Shamir, A., Cohen-Or, D.: SnapPaste: an interactive technique for easy mesh composition. Visual Comput. 22(9), 835–844 (2006)CrossRefGoogle Scholar
  32. 32.
    Sharon, E., Brandt, A., Basri, R.: Fast multiscale image segmentation. In: Computer Vision and Pattern Recognition, vol. 1, pp. 70–77. IEEE Computer Society (2000)Google Scholar
  33. 33.
    Sharon, E., Brandt, A., Basri, R.: Segmentation and boundary detection using multiscale intensity measurements. In: Computer Vision and Pattern Recognition, vol. 1, pp. 70–77. IEEE Computer Society (2001)Google Scholar
  34. 34.
    Sharon, E., Galun, M., Sharon, D., Basri, R., Brandt, A.: Hierarchy and adaptivity in segmenting visual scenes. Nature 442, 810–813 (2006)CrossRefGoogle Scholar
  35. 35.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22, 888–905 (2000)CrossRefGoogle Scholar
  36. 36.
    Vieira, M., Shimada, K.: Surface mesh segmentation and smooth surface extraction through region growing. Comput. Aided Geom. Des. 22, 771–792 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Xiao, C., Miao, Y., Liu, S., Peng, Q.: A dynamic balanced flow for filtering point-sampled geometry. Visual Comput. 22(3), 210–219 (2006)CrossRefGoogle Scholar
  38. 38.
    Yamazaki, I., Natarajan, V., Bai, Z., Hamann, B.: Segmenting point sets. In: Shape Modeling and Applications, pp. 46–51. IEEE Computer Society (2006)Google Scholar
  39. 39.
    Zelinka, S., Garland, M.: Similarity-based surface modelling using geodesic fans. In: Symposium on Geometry Processing, pp. 209–218. Eurographics Association (2004)Google Scholar
  40. 40.
    Zelinka, S., Garland, M.: Surfacing by numbers. In: Graphics Interface, pp. 107–113. Canadian Information Processing Society (2006)Google Scholar
  41. 41.
    Zhang, Y., Paik, J., Koschan, A., Abidi, M.A., Gorsich, D.: A simple and efficient algorithm for part decomposition of 3-D triangulated models based on curvature analysis. In: Proceedings of the International Conference on Image Processing, pp. 273–276. IEEE Computer Society (2002)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Computer SchoolWuhan UniversityWuhanP.R. China
  2. 2.Department of Computer Science & EngineeringHong Kong University of Science & TechnologyHong KongHong Kong

Personalised recommendations