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The Generation of N Dimensional Shape Primitives

  • Pieter P. Jonker
  • Stina Svensson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

This paper describes a method to accelerate the generation of shape primitives for N-dimensional images X N . These shape primitives can be used in conditions for topology preserving erosion or skeletonization in N-dimensional images. The method is based on the possibility to describe primitives for intrinsic dimensions \(\tilde N=N-1\) by quadratic equations of the form

\(x_N=\sum^{n=N-1}_{n=0}\left(a_nx_x+b_nx^2_n\right).\)

Keywords

N-dimensional morphology N-dimensional digital topology N-dimensional thinning 

References

  1. 1.
    Rosenfeld, A., Pfaltz, J.L.: Sequential operations in Digital Image Processing. Journal of the ACM, 471–494 (1966)Google Scholar
  2. 2.
    Coxeter, H.S.M.: Regular Polytopes, 3rd edn. Dover Publications, Inc., New York (1974) ISBN 0-486-61480-8zbMATHGoogle Scholar
  3. 3.
    Alexandroff, P.: Elementary concepts of topology. Dover Publications, Inc., New York (1961) ISDN 0-486-60747-XzbMATHGoogle Scholar
  4. 4.
    Jonker, P.P., Komen, E.R., Kraayveld, M.A.: A scalable, real-time image processing pipeline. Machine Vision Applications (8), 110–121 (1995)Google Scholar
  5. 5.
    Jonker, P.P.: Morphological Image Processing: Architecture and VLSI design (Ph.D. Thesis) Kluwer Dordrecht (1992) ISBN 90-2012766-7Google Scholar
  6. 6.
    Jonker, P.P., Vossepoel, A.M.: Connectivity in high dimensional images. In: Proc. MVA 1994, IAPR Workshop on Machine Vision Applications, IAPR, Kawasaki, Japan, December 13-15, pp. 30–33 (1994)Google Scholar
  7. 7.
    Jonker, P.P., Vermeij, O.: On skeletonization in 4D images. In: Perner, P., Rosenfeld, A., Wang, P. (eds.) SSPR 1996. LNCS, vol. 1121, pp. 79–89. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Jonker, P.P.: Skeletons in N dimensions using Shape Primitives. Pattern Recognition Letters 23, 677–686 (2002)zbMATHCrossRefGoogle Scholar
  9. 9.
    Jonker, P.P.: Morphological Operations in Recursive Neighbourhoods. Pattern Recognition Letters (2003) (to appear)Google Scholar
  10. 10.
    Serra, J.: Image analysis and mathematical morphology. Academic Press Inc., London (1982)zbMATHGoogle Scholar
  11. 11.
    Soille, P.: Morphological Image Analysis. Springer, Berlin (1999)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pieter P. Jonker
    • 1
  • Stina Svensson
    • 2
  1. 1.Pattern Recognition Group, Faculty of Applied SciencesDelft University of TechnologyDelftThe Netherlands
  2. 2.Centre for Image Analysis Lägerhyddvägen 3UppsalaSweden

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