A 3D 3-Subiteration Thinning Algorithm for Medial Surfaces

  • Kálmán Palágyi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

Thinning on a binary picture is an iterative layer by layer erosion to extract a reasonable approximation to its skeleton. This paper presents an efficient 3D parallel thinning algorithm which produces medial surfaces.Three-subiteration directional strategy is proposed: each iteration step is composed of three parallel subiterations according to the three deletion directions.Th e algorithm makes easy implementation possible, since deletable points are given by matching templates containing twentyeight elements.Th e topological correctness of the algorithm for (26, 6) binary pictures is proved.

Keywords

Medial Surface Black Point Simple Point White Point Border Point 
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.
    Bertrand, G., Aktouf, Z.: A 3D thinning algorithms using subfields. In: Proc. SPIE Conference on Vision Geometry III, Vol.2356 (1994) 113–124 410Google Scholar
  2. 2.
    Bertrand, G.: A parallel thinning algorithm for medial surfaces. Pattern Recognition Letters 16 (1995) 979–986 409, 410CrossRefGoogle Scholar
  3. 3.
    Blum, H.: A transformation for extracting new descriptors of shape. Models for the Perception of Speech and Visual Form, MIT Press, (1967) 362–380 406Google Scholar
  4. 4.
    Gong, W. X., Bertrand, G.: A simple parallel 3D thinning algorithm. In: Proc. 10th International Conference on Pattern Recognition (1990) 188–190 409, 410Google Scholar
  5. 5.
    Kong, T. Y.: On topology preservation in 2-d and 3-d thinning. International Journal of Pattern Recognition and Artifical Intelligence 9 (1995) 813–844 408CrossRefGoogle Scholar
  6. 6.
    Kong, T. Y., Rosenfeld, A.: Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Processing 48 (1989) 357–393 406, 407, 408CrossRefGoogle Scholar
  7. 7.
    Lee, T., Kashyap, R. L., Chu, C.: Building skeleton models via 3-D medial surface/ axis thinning algorithms.C VGIP: Graphical Models and Image Processing 56 (1994) 462–478 409, 410CrossRefGoogle Scholar
  8. 8.
    Ma, C. M.: On topology preservation in 3D thinning. CVGIP: Image Understanding 59 (1994) 328–339 408CrossRefGoogle Scholar
  9. 9.
    Ma, C. M.: A 3D fully parallel thinning algorithm for generating medial faces. Pattern Recognition Letters 16 (1995) 83–87 409CrossRefGoogle Scholar
  10. 10.
    Ma, C. M., Sonka, M.: A fully parallel 3D thinning algorithm and its applications. Computer Vision and Image Understanding 64 (1996) 420–433 409CrossRefGoogle Scholar
  11. 11.
    Manzanera, A., Bernard, T. M., Pretêux, F., Longuet, B.: Medial faces from aconcise 3D thinning algorithm.In: Proc.7 th IEEE Int. Conf.Computer Vision, ICCV’99 (1999) 337–343 409Google Scholar
  12. 12.
    Malandain, G., Bertrand, G.: Fast characterization of 3D simple points. In: Proc.11t h IEEE International Conference on Pattern Recognition (1992) 232–235 408Google Scholar
  13. 13.
    Morgenthaler, D. G.: Three-dimensional simple points: Serial erosion, parallel thinning and skeletonization.Technical Report TR-1005, Computer Vision Laboratory, Computer Science Center, University of Maryland (1981) 407Google Scholar
  14. 14.
    Mukherjee, J., Das, P. P., Chatterjee, B. N.: On connectivity issues of ESPTA. Pattern Recognition Letters 11 (1990) 643–648 409, 410MATHCrossRefGoogle Scholar
  15. 15.
    Palágyi K., Kuba, A.: A 3D 6-subiteration thinning algorithm for extracting medial lines. Pattern Recognition Letters 19 (1998) 613–627 409, 410MATHCrossRefGoogle Scholar
  16. 16.
    Palágyi K., Kuba, A.: A hybrid thinning algorithm for 3D medical images. Journal of Computing and Information Technology-CIT 6 (1998) 149–164 410Google Scholar
  17. 17.
    Palágyi K., Kuba, A.: Directional 3D thinning using 8 subiterations. In: Proc. 8th Int.Conf. on Discrete Geometry for Computer Imagery, DGCI’99, Lecture Notes in Computer Science, Vol.1568. Springer (1999) 325–336 409Google Scholar
  18. 18.
    Palágyi K., Kuba, A.: A parallel 3D 12-subiteration thinning algorithm. Graphical Models and Image Processing 61 (1999) 199–221 409CrossRefGoogle Scholar
  19. 19.
    Saha, P.K., Chaudhuri, B.B.: Detection of 3-D simple points for topology preserving transformations with application to thinning. IEEE Transactions on Pattern Analysis and Machine Intelligence16 (1994) 1028–1032 408CrossRefGoogle Scholar
  20. 20.
    Saha, P. K., Chaudhuri, B. B., Majumder, D. D.: A new shape-preserving parallel thinning algorithm for 3D digital images. Pattern Recognition 30 (1997) 1939–1955 410CrossRefGoogle Scholar
  21. 21.
    Székely, G.: Shape characterization by local symmetries. Habilitationsschrift, ETH Zürich (1996) 406Google Scholar
  22. 22.
    Tsao, Y. F., Fu, K. S.: A parallel thinning algorithm for 3-D pictures. Computer Graphics and Image Processing 17 (1981) 315–331 409, 410CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kálmán Palágyi
    • 1
  1. 1.Department of Applied InformaticsUniversity of SzegedSzegedHungary

Personalised recommendations