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Line Geometry for 3D Shape Understanding and Reconstruction

  • Helmut Pottmann
  • Michael Hofer
  • Boris Odehnal
  • Johannes Wallner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3021)

Abstract

We understand and reconstruct special surfaces from 3D data with line geometry methods. Based on estimated surface normals we use approximation techniques in line space to recognize and reconstruct rotational, helical, developable and other surfaces, which are characterized by the configuration of locally intersecting surface normals. For the computational solution we use a modified version of the Klein model of line space. Obvious applications of these methods lie in Reverse Engineering. We have tested our algorithms on real world data obtained from objects as antique pottery, gear wheels, and a surface of the ankle joint.

Keywords

Point Cloud Spine Curve Moulding Surface Helical Gear Rotational Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Benosman, R., Kang, S.B.: Panoramic Vision: Sensors, Theory and Applications. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  2. 2.
    Chen, H.-Y., Lee, I.-K., Leopoldseder, S., Pottmann, H., Randrup, T., Wallner, J.: On surface approximation using developable surfaces. Graphical Models and Image Processing 61, 110–124 (1999)zbMATHCrossRefGoogle Scholar
  3. 3.
    Cipolla, R., Giblin, P.: Visual Motion of Curves and Surfaces. Cambridge UP, New York (2000)zbMATHGoogle Scholar
  4. 4.
    Degen, W.: Cyclides. In: Farin, G., Hoschek, J., Kim, M.-S. (eds.) Handbook of Computer Aided Geometric Design, pp. 575–601. Elsevier, Amsterdam (2002)CrossRefGoogle Scholar
  5. 5.
    De la Torre, F., Black, M.J.: Robust principal component analysis for Computer Vision. In: Proc. 8th Int. Conf. on Computer Vision, pp. 362–369 (2001)Google Scholar
  6. 6.
    Faugeras, O.: Three-dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Cambridge (1993)Google Scholar
  7. 7.
    Gupta, R., Hartley, R.: Linear pushbroom cameras. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(9), 963–975 (1997)CrossRefGoogle Scholar
  8. 8.
    Halfr, R.: Estimation of the axis of rotation of fragments of archaeological pottery. In: Proc. 21st Workshop Austrian Assoc. for Pattern Recognition, Hallstatt (1997)Google Scholar
  9. 9.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge Univ. Press, Cambridge (2000)zbMATHGoogle Scholar
  10. 10.
    Hilbert, D., Cohn-Vossen, S.: Anschauliche Geometrie. Springer, Heidelberg (1932), . Reprinted (1996), Translated as: Geometry and the Imagination, American Math. Soc. (1999)zbMATHGoogle Scholar
  11. 11.
    Illingworth, J., Kittler, J.: A survey of the Hough transform. Graphics and Image Processing 44, 87–116 (1988)CrossRefGoogle Scholar
  12. 12.
    Juttler, B., Wagner, M.: Kinematics and animation. In: Farin, G., et al. (eds.) Handbook of Computer Aided Geometric Design, pp. 723–748. Elsevier, Amsterdam (2002)CrossRefGoogle Scholar
  13. 13.
    Kos, G., Martin, R., Varady, T.: Recovery of blend surfaces in reverse engineering. Computer Aided Geometric Design 17, 127–160 (2000)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Leavers, V.: Which Hough transform? CVGIP:Image Understanding 58, 250–264 (1993)CrossRefGoogle Scholar
  15. 15.
    Mundy, J., Zissermann, A.: Geometric Invariance in Computer Vision. MIT Press, Cambridge (1992)Google Scholar
  16. 16.
    Navab, N.: Canonical representation and three view geometry of cylinders. In: Intl. Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission III, vol. XXXIV(Part 3A), pp. 218–224 (2002)Google Scholar
  17. 17.
    Pajdla, T.: Stereo geometry of non-central cameras, PhD thesis, CVUT (2002)Google Scholar
  18. 18.
    Peleg, S., Ben-Ezra, M., Pritch, Y.: Omnistereo: panoramic stereo imaging. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(3), 279–290 (2001)CrossRefGoogle Scholar
  19. 19.
    Pillow, N., Utcke, S., Zisserman, A.: Viewpoint-invariant representation of generalized cylinders using the symmetry set. Image Vision Comput. 13, 355–365 (1995)CrossRefGoogle Scholar
  20. 20.
    Pottmann, H., Randrup, T.: Rotational and helical surface reconstruction for reverse engineering. Computing 60, 307–322 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Pottmann, H., Wallner, J.: Computational Line Geometry. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  22. 22.
    Seitz, S.M.: The space of all stereo images. In: Proceedings ICCV, pp. 26–33 (2001)Google Scholar
  23. 23.
    Varady, T., Benko, T.: Reverse engineering regular objects: simple segmentation and surface fitting procedures. Int. J. Shape Modeling 4, 127–141 (1998)CrossRefGoogle Scholar
  24. 24.
    Varady, T., Martin, R.: Reverse Engineering. In: Farin, G., et al. (eds.) Handbook of Computer Aided Geometric Design, pp. 651–681. Elsevier, Amsterdam (2002)CrossRefGoogle Scholar
  25. 25.
    Willis, A., Orriols, X., Cooper, D.: Accurately Estimating Sherd 3D Surface Geometry with Application to Pot Reconstruction. In: CVPR Workshop (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Helmut Pottmann
    • 1
  • Michael Hofer
    • 1
  • Boris Odehnal
    • 1
  • Johannes Wallner
    • 1
  1. 1.Technische Universität WienWienAustria

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