Fully Parallel 3D Thinning Algorithms Based on Sufficient Conditions for Topology Preservation

  • Kálmán Palágyi
  • Gábor Németh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

This paper presents a family of parallel thinning algorithms for extracting medial surfaces from 3D binary pictures. The proposed algorithms are based on sufficient conditions for 3D parallel reduction operators to preserve topology for (26,6) pictures. Hence it is self-evident that our algorithms are topology preserving. Their efficient implementation on conventional sequential computers is also presented.

Keywords

Medial Surface Black Point Simple Point White Point IEEE Internat 
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.
    Arcelli, C., Sanniti di Baja, G., Serino, L.: New removal operators for surface skeletonization. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 555–566. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Bertrand, G., Aktouf, Z.: A 3D thinning algorithm using subfields. In: Proc. SPIE Conf. on Vision Geometry III, vol. 2356, pp. 113–124 (1994)Google Scholar
  3. 3.
    Bertrand, G.: A parallel thinning algorithm for medial surfaces. Pattern Recognition Letters 16, 979–986 (1995)CrossRefGoogle Scholar
  4. 4.
    Gong, W.X., Bertrand, G.: A simple parallel 3D thinning algorithm. In: Proc. 10th IEEE Internat. Conf. on Pattern Recognition, ICPR 1990, pp. 188–190 (1990)Google Scholar
  5. 5.
    Hall, R.W.: Parallel connectivity-preserving thinning algorithms. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological algorithms for digital image processing, pp. 145–179. Elsevier Science, Amsterdam (1996)CrossRefGoogle Scholar
  6. 6.
    Jonker, P.: Skeletons in N dimensions using shape primitives. Pattern Recognition Letters 23, 677–686 (2002)CrossRefMATHGoogle Scholar
  7. 7.
    Kong, T.Y.: On topology preservation in 2-d and 3-d thinning. Int. Journal of Pattern Recognition and Artificial Intelligence 9, 813–844 (1995)CrossRefGoogle Scholar
  8. 8.
    Kong, T.Y., Rosenfeld, A.: Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Processing 48, 357–393 (1989)CrossRefGoogle Scholar
  9. 9.
    Lee, T., Kashyap, R.L., Chu, C.: Building skeleton models via 3-D medial surface/axis thinning algorithms. CVGIP: Graphical Models and Image Processing 56, 462–478 (1994)Google Scholar
  10. 10.
    Ma, C.M.: On topology preservation in 3D thinning. CVGIP: Image Understanding 59, 328–339 (1994)CrossRefGoogle Scholar
  11. 11.
    Ma, C.M., Wan, S.-Y.: A medial-surface oriented 3-d two-subfield thinning algorithm. Pattern Recognition Letters 22, 1439–1446 (2001)CrossRefMATHGoogle Scholar
  12. 12.
    Malandain, G., Bertrand, G.: Fast characterization of 3D simple points. In: Proc. 11th IEEE Internat. Conf. on Pattern Recognition, pp. 232–235 (1992)Google Scholar
  13. 13.
    Manzanera, A., Bernard, T.M., Pretêux, F., Longuet, B.: Medial faces from a concise 3D thinning algorithm. In: Proc. 7th IEEE Internat. Conf. Computer Vision, ICCV 1999, pp. 337–343 (1999)Google Scholar
  14. 14.
    Palágyi, K., Kuba, A.: A parallel 3D 12-subiteration thinning algorithm. Graphical Models and Image Processing 61, 199–221 (1999)CrossRefGoogle Scholar
  15. 15.
    Palágyi, K.: A 3-Subiteration Surface-Thinning Algorithm. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 628–635. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Palágyi, K.: A Subiteration-Based Surface-Thinning Algorithm with a Period of Three. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 294–303. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Palágyi, K.: A 3D fully parallel surface-thinning algorithm. Theoretical Computer Science 406, 119–135 (2008)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Saha, P.K., Chaudhuri, B.B., Majumder, D.D.: A new shape-preserving parallel thinning algorithm for 3D digital images. Pattern Recognition 30, 1939–1955 (1997)CrossRefGoogle Scholar
  19. 19.
    Shaked, D., Bruckstein, A.: Pruning medial axes. Computer Vision Image Understanding 69, 156–169 (1998)CrossRefGoogle Scholar
  20. 20.
    Tsao, Y.F., Fu, K.S.: A parallel thinning algorithm for 3-D pictures. Computer Graphics and Image Processing 17, 315–331 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kálmán Palágyi
    • 1
  • Gábor Németh
    • 1
  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedHungary

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