Visual Form pp 517-525 | Cite as

On Symmetric Forms of Discrete Sets of Points and Digital Curves

  • Fridrich Sloboda

Abstract

Geometrical properties of subsets of digital pictures play an important role in image analysis. Mathematical morphology is an approach to image processing which consists in transformations of subsets of digital pictures to facilitate subsequent processing [1,4,7,9,10,11,15,16,17]. In this paper a linear operator represented by a boolean circulant Toeplitz matrix, which transforms an ordered discrete even set of n points into its symmetric form with the common centroid is described.

Keywords

Symmetric Form Mathematical Morphology Toeplitz Matrice Moment Invariant Digital Picture 
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.

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References

  1. [1]
    A. Arcelli and G. Massorati, “Regular arcs in digital contours”, CGIP, no. 4, pp. 339-360, 1975.Google Scholar
  2. [2]
    L. Berezin and N. Zhidkoy, Computing methods, Oxford: Pergamon Press, 1965.MATHGoogle Scholar
  3. [3]
    P. Davies, Circulant matrices, New York: Wiley, 1979.Google Scholar
  4. [4]
    I. Hargittai, Symmetry, New York: Pergamon Press, 1986.MATHGoogle Scholar
  5. [5]
    H. Freeman, “Computer processing of line-drawing images”, Computing Surveys, no.6, pp.57-97, 1974.Google Scholar
  6. [6]
    M.K. Hu, “Visual pattern recognition by moment invariants”, IRE Trans. on Infor. Theory, no.8, pp. 1-12, 1962.Google Scholar
  7. [7]
    R. Klette, “The m-dimensional grid point space”, CGIP, vol. 30, pp. 1–12, 1985.MATHGoogle Scholar
  8. [8]
    S. Maitra, “Moment invariants”, Proc. IEEE, vol. 64, pp. 697–699, 1979.CrossRefGoogle Scholar
  9. [9]
    A. Rosenfeld and J. LPfaltz, “Distance functions on digital pictures”, Pattern Recognition, vol. 1, pp. 35–51, 1968.CrossRefGoogle Scholar
  10. [10]
    A. Rosenfeld, “Arcs and curves in digital pictures”, JACM, 1, pp. 146–160, 1973.Google Scholar
  11. [11]
    A. Rosenfeld, “Adjency in digital pictures”, Inform. Control, vol. 26, pp. 1264–1269, 1974.MathSciNetCrossRefGoogle Scholar
  12. [12]
    A. Rosenfeld and A. C. Kak, Digital picture processing, New York: Academic Press, 1976.CrossRefGoogle Scholar
  13. [13]
    A. Rosenfeld, Picture languages, New York: Academic Press, 1979.MATHGoogle Scholar
  14. [14]
    F. Sloboda, “Toeplitz matrices, homothety and least squares approximation”, in Parallel Computing: Methods, Algorithms and Applications, D.J. Evans and C. Sutti, Eds., Bristol: Adam Hilger, 1989.Google Scholar
  15. [15]
    J. Sklansky and V. Gonzales, “Fast polygonal approximation of digitized curves”, Pattern recognition, no.12, pp.327-331, 1980.Google Scholar
  16. [16]
    J. Sklansky, R.L. Chazin and B.J. Hansen, “Minimum perimeter polygon of digitized silhouettes”, IEEE Trans. on Comp., no.3, pp.260-268, 1972.Google Scholar
  17. [17]
    G.T. Toussaint, Computational morphology, Amsterdam: North Holland, 1988.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Fridrich Sloboda
    • 1
  1. 1.Institute of Technical CyberneticsBratislavaCzechoslovakia

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