Skip to main content
SpringerLink
Log in

New methods for image generation and compression

  • Conference paper
  • First Online:
New Results and New Trends in Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 555))

  • 192 Accesses

Abstract

We survey new methods in “Computational Fractal Geometry.” We start with M. Barnsley's pioneering Iterative Function Systems and our extension of this method, in particular Mutually Recursive Function Systems. Further we discuss (Probabilistic) Finite Generators, L-systems and other methods as used for image generations.

This research was supported by the National Sciences Foundation under Grant No. CCR-8702752.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.F.Barnsley, Fractals Everywhere, Academic Press, 1988.

    Google Scholar 

  2. M.F.Barnsley, R.L.Devaney, B.B.Mandelbrot, H-O.Peitgen, D.Saupe and R.S.Voss, The Science of Fractal Images, Springer-Verlag, 1988.

    Google Scholar 

  3. J. Berstel and A. Nait Abdallah, Quadtrees Generated by Finite Automata. AFCET 61–62, 167–175 (1989).

    Google Scholar 

  4. J.Berstel and M.Morcrette, Compact Representation of Pattern by Finite Automata, Res.Rep. 89–66, Institut de Programmation, Université Paris 7 (1989).

    Google Scholar 

  5. L. Boasson and M. Nivat, Adherences of Languages, JCSS 20, 285–309 (1980).

    Google Scholar 

  6. G.J. Chaitin, Algorithmic Information Theory, IBM Journal of Research and Development 21, 350–359 (1977).

    Google Scholar 

  7. K. Culik II and S. Dube, Affine Automata and Related Techniques for Generation of Complex Images, Technical Report TR 90009, Dept. of Computer Science, Univ. of S. Carolina. Preliminary version in Proc. of MFCS'1990. Lecture Notes in Computer Science 452, Springer-Verlag 1990, pp. 224–231.

    Google Scholar 

  8. K. Culik II and S. Dube, Rational and Affine Expressions for Image Synthesis. Preliminary version in Proc. of FST-TCS'1990. Lecture Notes in Computer Science 472, Springer-Verlag 1990, pp. 76–90. To appear in Discrete Applied Mathematics.

    Google Scholar 

  9. K. Culik II and S. Dube, Balancing Order and Chaos in Image Generation, Technical Report TR 9103, Dept. of Computer Science, Univ. of S. Carolina. Preliminary version to appear in the Proc. of ICALP'91, Madrid, Spain.

    Google Scholar 

  10. K. Culik II and S. Dube, Encoding Images as Words and Languages, Proc. of the International Colloquium on Words, Languages and Combinatorics, Kyoto Sangyo University, Japan, August 1990.

    Google Scholar 

  11. K. Culik II and J. Kari, Image Compression Using Weighted Finite Automata, manuscript.

    Google Scholar 

  12. K. Culik II and J. Kari, Finite Automata Computing Real Functions, manuscript.

    Google Scholar 

  13. F.M. Dekking, Recurrent Sets, Advances in Mathematics 44, 78–104 (1982).

    Google Scholar 

  14. S. Dube, Using Fractal Geometry for Analysis of Divide-and-Conquer Algorithms, manuscript.

    Google Scholar 

  15. S. Even, Rational Numbers and Regular Events, IEEE Transactions on Electronic Computers, EC-13, No. 6, 740–741 (1964).

    Google Scholar 

  16. J.Gleick, Chaos-Making a New Science, Penguin Books, 1988.

    Google Scholar 

  17. J. Hartmanis and R.E. Stearns, Sets of Numbers Defined By Finite Automata, American Mathematical Monthly 74, 539–542 (1967).

    Google Scholar 

  18. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, (1982).

    Google Scholar 

  19. P. Prusinkiewicz, Applications of L-systems to Computer Imagery, in H. Ehrig, M. Nagl, A. Rosenfeld, and G. Rozenberg, editors, Graph Grammars and Their Application to Computer Science; Third International Workshop, pp.534–548, Springer-Verlag, Berlin, 1987. Lecture Notes in Computer Science 291.

    Google Scholar 

  20. A.R. Smith, Plants, Fractals, and Formal Languages, Computer Graphics 18, 1–10 (1984).

    Google Scholar 

  21. L.Staiger, Quadtrees and the Hausdorff Dimension of Pictures, Workshop on Geometrical Problems of Image Processing, Georgenthal GDR, 173–178 (1989).

    Google Scholar 

  22. Not Just a Pretty Face: Compressing Pictures with Fractals. Scientific American, p. 77, March 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, Uriversity of South Carolina, 29208, Columbia, SC, USA

    Karel Culik II & Simant Dube

Authors
  1. Karel Culik II
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Simant Dube
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hermann Maurer

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Culik, K., Dube, S. (1991). New methods for image generation and compression. In: Maurer, H. (eds) New Results and New Trends in Computer Science. Lecture Notes in Computer Science, vol 555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0038183

Download citation

  • DOI: https://doi.org/10.1007/BFb0038183

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54869-0

  • Online ISBN: 978-3-540-46457-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation