Advertisement

On Convergence of Discrete and Selective Fractal Operators

  • Władysław Skarbek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1689)

Abstract

It is proved that any iterative sequence for a fractal operator which is contractive in l1 norm with contractivity c *, after clamping and rounding to integer levels, is perceptually convergent at the threshold т ≥ 1=(1 — c *): Eventual contractivity is a sufficient condition for the convergence of iterations of a fractal operator. This paper shows that it is also necessary if the averaging operation in the definition of the fractal operator is replaced by the selection operation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. F. Barnsley, Fractals everywhere Addison Wesley, 1988.Google Scholar
  2. 2.
    M. F. Barnsley and L. P. Hurd, Fractal image compression, AK Peters. Ltd, Wellesley, MA, 1993.zbMATHGoogle Scholar
  3. 3.
    J. Dugundi and A. Granas, Fixed point theory, Polish Scientic Publishers, Warszawa, 1982.Google Scholar
  4. 4.
    Y. Fisher ed., Fractal image compression, Theory and Application, Springer Verlag, New York, 1995.Google Scholar
  5. 5.
    A. E. Jacquin, “Image coding based on a fractal theory of iterated contractive image transformations”, IEEE Trans. on Image Processing, vol. 1,no. 1, pp. 18–30, 1992.CrossRefGoogle Scholar
  6. 6.
    W. Skarbek, On convergence of affine fractal operators, Image Processing and Communications, 1(1), 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Władysław Skarbek
    • 1
  1. 1.Multimedia Laboratory Department of Electronics and Information TechnologyWarsaw University of TechnologyWarsaw

Personalised recommendations