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Partial Fractal Model for Hybird Image Coding

  • David Zhang
  • Xiaobo Li
  • Zhiyong Liu
Part of the The International Series on Asian Studies in Computer and Information Science book series (ASIS, volume 11)

Abstract

The fractal image compression technique models a natural image using a contractive mapping called fractal mapping in the image space. In this chapter, we first introduce the concept of fractal mapping and some useful definitions. In Section 5.2, we demonstrate that the fractal image coding algorithm is compatible with other image coding methods. A new mapping in the image space, called partial fractal mapping is proposed in Section 5.3. A general framework of fractal-based hybrid image coding encoding/decoding systems is presented in Section 5.4. Section 5.5 proposes a new hybrid image coding scheme, which non-fractal coded regions are used to help the encoding of fractal coded regions. Experiments in Section 5.6 show that the proposed system performs better than the quadtree-based fractal image coding algorithm and the JPEG image compression standard at high compression ratios larger than 30.

Keywords

Hybrid System Compression Ratio Iterate Function System Image Code Fractal Mapping 
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]
    B.B. MandelbrotThe Fractal Geometry of NatureSan Francisco: W.H. Freeman, 1983.Google Scholar
  2. [2]
    M.F. BarnsleyFractals Everywhere, New York: Academic Press, 1988.Google Scholar
  3. [3]
    A.E. Jacquin, “Image coding based on a fractal theory of iterated contraceptive image transformations”IEEE Trans. Image Process.1(1): 18–30, Jan. 1992.CrossRefGoogle Scholar
  4. [4]
    A.E. Jacquin, “Fractal image coding: a review”Proceedings of the IEEE81(10):1451–1465, Oct. 1993.CrossRefGoogle Scholar
  5. [5]
    Y. Fisher, ed.Fractal Image Compression: Theory and ApplicationNew York: Springer-Verlag, 1994.MATHGoogle Scholar
  6. [6]
    Y. Linde, A. Buzo, and R.M. Gray“ An algorithm for vector quantizer design”IEEE Trans. Commun.COM-28:84–95, Jan. 1980.CrossRefGoogle Scholar
  7. [7]
    T. Laurencot and A.E. Jacquin, “Hybrid image block coders incorporating fractal coding and vector quantization, with a robust classification scheme”AT&T Tech. Memo. Feb. 1992.Google Scholar
  8. [8]
    G.E. Oien, and S. Lepsoy, “Fractal image coding with fast decoder convergence”Signal Processing40:105–117, 1994.CrossRefGoogle Scholar
  9. [9]
    Y. Fisher, “Fractal image compression with quadtrees”, inFractal Image Compression: Theory and Applications to Digital ImagesY. Fisher, ed., New York: Springer-Verlag, 1994.Google Scholar
  10. [10]
    Z. Wang and Y.L. Yu, “Fractal block coding in residue domain,”China Journal of Electronics, 14(3):236–240, 1997.CrossRefGoogle Scholar
  11. [11]
    X.K. Zhou, ed.Practical Microcomputer Image ProcessingBeijing: Beijing Univ. of Aeronautics and Astronautics Press, 1994.Google Scholar
  12. [12]
    I.H. Witten, R.M. Neal, and J.G. Cleary, “Arithmetic coding for data compression”Communications of the ACM30(6):520–540, Jun. 1987.CrossRefGoogle Scholar
  13. [13]
    G.K. Wallace, The JPEG Still Picture Compression StandardCommunications of the ACM34(4):30–44, April 1991.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • David Zhang
    • 1
  • Xiaobo Li
    • 2
  • Zhiyong Liu
    • 3
  1. 1.Hong Kong Polytechnic UniversityHong Kong
  2. 2.University of AlbertaCanada
  3. 3.National Natural Science Foundation of ChinaChina

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