New methods for image generation and compression

  • Karel CulikII
  • Simant Dube
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 555)

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.

Keywords

Hausdorff Distance Affine Transformation Finite Automaton Systolic Array Iterate Function System 
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]
    M.F.Barnsley, Fractals Everywhere, Academic Press, 1988.Google Scholar
  2. [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. [3]
    J. Berstel and A. Nait Abdallah, Quadtrees Generated by Finite Automata. AFCET 61–62, 167–175 (1989).Google Scholar
  4. [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. [5]
    L. Boasson and M. Nivat, Adherences of Languages, JCSS 20, 285–309 (1980).Google Scholar
  6. [6]
    G.J. Chaitin, Algorithmic Information Theory, IBM Journal of Research and Development 21, 350–359 (1977).Google Scholar
  7. [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. [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. [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. [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. [11]
    K. Culik II and J. Kari, Image Compression Using Weighted Finite Automata, manuscript.Google Scholar
  12. [12]
    K. Culik II and J. Kari, Finite Automata Computing Real Functions, manuscript.Google Scholar
  13. [13]
    F.M. Dekking, Recurrent Sets, Advances in Mathematics 44, 78–104 (1982).Google Scholar
  14. [14]
    S. Dube, Using Fractal Geometry for Analysis of Divide-and-Conquer Algorithms, manuscript.Google Scholar
  15. [15]
    S. Even, Rational Numbers and Regular Events, IEEE Transactions on Electronic Computers, EC-13, No. 6, 740–741 (1964).Google Scholar
  16. [16]
    J.Gleick, Chaos-Making a New Science, Penguin Books, 1988.Google Scholar
  17. [17]
    J. Hartmanis and R.E. Stearns, Sets of Numbers Defined By Finite Automata, American Mathematical Monthly 74, 539–542 (1967).Google Scholar
  18. [18]
    B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, (1982).Google Scholar
  19. [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. [20]
    A.R. Smith, Plants, Fractals, and Formal Languages, Computer Graphics 18, 1–10 (1984).Google Scholar
  21. [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. [22]
    Not Just a Pretty Face: Compressing Pictures with Fractals. Scientific American, p. 77, March 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Karel CulikII
    • 1
  • Simant Dube
    • 1
  1. 1.Dept. of Computer ScienceUriversity of South CarolinaColumbiaUSA

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