Advertisement

3D Topological Thinning by Identifying Non-simple Voxels

  • Gisela Klette
  • Mian Pan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

Topological thinning includes tests for voxels to be simple or not. A point (pixel or voxel) is simple if the change of its image value does not change the topology of the image. A problem with topology preservation in 3D is that checking voxels to be simple is more complex and time consuming than in 2D. In this paper, we review some characterizations of simple voxels and we propose a new methodology for identifying non-simple points. We implemented our approach by modifying an existing 3D thinning algorithm and achieved an improved running time.

Keywords

simple points topology simple deformations thinning shape simplification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arcelli, C., Sanniti di Baja, G.: Skeletons of planar patterns. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, pp. 99–143. North-Holland, Amsterdam (1996)CrossRefGoogle Scholar
  2. 2.
    Bertrand, G., Maladain, G.: A new characterization of three-dimensional simple points. Pattern Recognition Letters 15, 169–175 (1994)zbMATHCrossRefGoogle Scholar
  3. 3.
    Bertrand, G.: Simple points, topological numbers and geodesic neighborhoods in cubic grids. Pattern Recognition Letters 15, 1003–1011 (1994)CrossRefGoogle Scholar
  4. 4.
    Fourey, S., Malgouyres, R.: A concise characterization of 3D simple points. Discrete Applied Mathematics 125, 59–80 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gau, C.J., Kong, T.Y.: 4D Minimal Non-simple Sets. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 81–91. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Hall, R.W.: Fast parallel thinning algorithms: parallel speed and connectivity preservation. Comm. ACM 32, 124–131 (1989)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hall, R.W.: Parallel connectivity-preserving thinning algorithms. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological algorithms for Digital Image Processing, pp. 145–179. North-Holland, Amsterdam (1996)CrossRefGoogle Scholar
  8. 8.
    Hilditch, C.J.: Linear skeletons from square cupboards. In: Meltzer, B., Mitchie, D. (eds.) Machine Intelligence 4, pp. 403–420. Edinburgh University Press, Edinburgh (1969)Google Scholar
  9. 9.
    Klette, G.: Characterizations of simple pixels in binary images. In: Proceedings: Image and Vision Computing New Zealand 2002, Auckland, pp. 227–232 (2002)Google Scholar
  10. 10.
    Klette, G.: A Comparative Discussion of Distance Transformations and Simple Deformations in Digital Image Processing. Machine Graphics & Vision 12, 235–256 (2003)MathSciNetGoogle Scholar
  11. 11.
    Klette, G.: Simple Points in 2D and 3D Binary Images. In: Petkov, N., Westenberg, M.A. (eds.) CAIP 2003. LNCS, vol. 2756, pp. 57–64. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Kong, T.Y.: On topology preservation in 2-D and 3-D thinning. Int. J. for Pattern Recognition and Artificial Intelligence 9, 813–844 (1995)CrossRefGoogle Scholar
  13. 13.
    Lee, C.N., Rosenfeld, A.: Simple connectivity is not locally computable for connected 3D images. Computer Vision, Graphics, and Image Processing 51, 87–95 (1990)CrossRefGoogle Scholar
  14. 14.
    Lohou, C., Bertrand, G.: A New 3D 6-Subiteration Thinning Algorithm Based on P-Simple Points. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 102–113. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Maladain, G., Bertrand, G.: Fast characterization of 3D simple points. In: Proc. 11th IAPR Int. Conf. on Pattern Recognition, The Hague, The Netherlands, vol. III, pp. 232–235 (1992)Google Scholar
  16. 16.
    Palagyi, K., Sorantin, E., Balogh, E., Kuba, A., Halmai, C., Erdohelyi, B., Hausegger, K.: A Sequential 3D Thinning Algorithm and Its Medical Applications. In: Insana, M.F., Leahy, R.M. (eds.) IPMI 2001. LNCS, vol. 2082, pp. 409–415. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Palagyi, K., Kuba, A.: Directional 3D Thinning Using 8 Subiterations. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 325–336. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Palagyi, K., Kuba, A.: A 3D 6-subiteration thinning algorithm for extracting medial lines. Pattern Recognition Letters 19, 613–627 (1998)zbMATHCrossRefGoogle Scholar
  19. 19.
    Saha, P.K., Chanda, B., Majumder, D.D.: Principles and algorithms for 2D and 3D shrinking, Tech. Rep. TR/KBCS/2/91, NCKBCS Library, Indian Statistical Institute, Calcutta, India (1991)Google Scholar
  20. 20.
    Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. Comm. ACM 13, 471–494 (1966)zbMATHGoogle Scholar
  21. 21.
    Rosenfeld, A.: Connectivity in digital pictures. Comm. ACM 17, 146–160 (1970)zbMATHMathSciNetGoogle Scholar
  22. 22.
    Rosenfeld, A., Kong, T.Y., Nakamura, A.: Topology- preserving deformations of two-valued digital pictures. Graphical Models and Image Processing 60, 24–34 (1998)CrossRefGoogle Scholar
  23. 23.
    Serra, J.: Image Analysis and Mathematical Morphology, vol. 2. Academic Press, New York (1982)zbMATHGoogle Scholar
  24. 24.
    Yokoi, S., Toriwaki, J.I., Fukumura, T.: An analysis of topological properties of digitized binary pictures using local features. Computer Graphics and Image Processing 4, 63–73 (1975)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Gisela Klette
    • 1
  • Mian Pan
    • 1
  1. 1.CITRUniversity of AucklandAucklandNew Zealand

Personalised recommendations