[go: up one dir, main page]

Skip to main content
Log in

Fractal image coding - achievements and prospects

Le Codage D’image par Fractales - Bilan et Potentiel

  • Published:
Annales Des Télécommunications Aims and scope Submit manuscript

Abstract

Fractal image coding is a relatively new technique of lossy image compression which exploits the piecewise self-similarity existing in an image. In this paper we present a survey of the achievements in the field. We then focus our attention on a fundamental aspect of fractal coding - that concerning the nature of the transformations used in matching natural patterns. Through the analysis of a few models we try to suggest both the difficulties and the potential of this line of research.

Résumé

Le codage d’image par fractales est une technique relativement nouvelle de compression d’image avec perte. Cette technique exploite Vauto-similarité dans les images. Cette article présente tout d’abord un bilan des travaux effectués dans le domaine. Nous étudions par la suite plus en détail l’aspect le plus fondamental de la technique : la nature des transformations utilisées dans la mise en correspondance des éléments d’image. A travers l’analyse de quelques modèles, nous essayons enfin de mettre en évidence les difficultés et le potentiel de cette approche.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Amram (E.) andBlanc-Talon (I.) Fractal image compression : an efficient acceleration technique,Proceedings of International Conference on Imaging Science, Systems and Technology, CISST, pp. 372–378, Las Vegas, (1997).

  2. Barnsipy (M. F.):Fractals everywhere, Academic Press, New York (1988).

    Google Scholar 

  3. Barthel (K. U.), Schuttemeyer (J.), Voye (T.), Noll (P.): A new image coding technique unifying fractal and transform coding,IEEE Int. Conf. on Image Processing, Austin, Texas, (1994).

  4. Beaumont (J. M.) Image data compression using fractal techniquesBT Technol. J.,9, no. 4, pp. 93–109, (Oct 1991).

    Google Scholar 

  5. Bedford (T.), Dekking (F. M.), Keane (M. S.) Nieuw Archief voor Wiskunde, series 4,10 no. 3 (Nov. 1992) pp. 185–217, (1992).

    MATH  MathSciNet  Google Scholar 

  6. Blanc-Talon (J.) Local fractal image compression : a new approach for making real fractal compression,Proceedings of International Conference on Imaging Science, Systems and Technology, CISST’pp. 368–371, Las Vegas, (1997).

  7. Bone (D. J.) : Orthonormalfractal image encoding using overlapping blocks,Fractals, (1996).

  8. Chasserv (J-M), Davoine (F.) Bertin (E.) : Compression fractale par partitionnement de Delaunay, 14-thConference GRETSI, Juan-les-Pins, (Sept 1993).

  9. Davoine (F.), Antonini (M.), Chassery (J-M.), Barlaud (M.): Fractal image compression based on Delaunay triangulation and vector quantization,IEEE Trans IP Processing, vol. 5, no. 2, pp. 338–346, Feb. 1996).

    Article  Google Scholar 

  10. Davis (G.) : Adaptive self-quantization of wavelet subtrees : a wavelet-based theory of fractal image compression,SPIE Conference on wavelet Applications in Signal and Image Processing III, San Diego (July 1995).

  11. Fisher (Y.), Jacobs (E. W.) Boss (R. D.) Fractal image compression using iterated transforms,Image and Text Compression,J.A. storer (ed.), Kluwer Academic Publishers, (1992), pp. 35–61.

  12. Fisher (Y.) Fractal image compression - Theory and applications to digital images, (Y.) Fisher (ed.),Springer-Verlag, New York, 1994.

    Google Scholar 

  13. Frigaard (C.), Gade (J.), Hemmingsen (T.), Sand (T. S) : Image compression based on fractal theory,Technical Report, Institute for Electronic Systems, Aalborg University, Denmark, 1994.

  14. Hamzaoui (R.):, Codebook clustering by self-organising maps for Fractal image compression,Fractals, vol. 5, pp. 27–38, Supplementary Issue (April 1997).

    Article  MATH  Google Scholar 

  15. Hurtgen (B.), Hain (T), On the convergence of fractal transforms,Proceedings of ICASSP- (1994).

  16. Jacquin (A. E.) :A fractal theory of iterated Markov operators with applications to digital image coding, PhD Thesis, Georgia Institute of Technology, (August 1989).

  17. Jacquin (A. E.): Image coding based on a fractal theory of iterated contractive image transformations,IEEE Transactions on Image Processing, Vol. 1, No. 1, (Jan 1992,) pp. 18–30.

    Article  Google Scholar 

  18. Kirwan (F.):Complex algebraic curves, London Mathematical Society, Cambridge University Press, (1992).

    MATH  Google Scholar 

  19. Lepsoy (S.), Φien (G.), Ramstad (T. A.). Attractor image com- pression with a fast non-iterative decoding algorithm,ICASIP, (1993), pp. 337–340.

  20. Lepsoy (S.), Φien (G. E.), Ramstad (T. A.) : Reducing the com- plexity of a fractal-based coder,Signal Processing VI : Theories and Applications, J. Vandewalle, R. Boite, M. Moonen, A. Oos-terlink (eds.), Elsevier Science Publishers.

  21. Lepsoy (S.), Φien (G. E.), Ramstad (T. A.): An inner product space approach to image coding by contractive transformations,Pro. ICASSP-91,4, pp. 2773–2776, (1991).

    Google Scholar 

  22. Lin (H.) andVenetsantopoulos (A. N). : Fast fractal image coding using pyramids,Pro. ICIAP ’95, San Remo, (September l995) pp. 649–654.

  23. Monro (D. M.), Dudbridge (F.) Fractal block approximation of imagesElectronics Letters,28, no. 11, (May 1992).

  24. Monro (D. M.) : Generalized fractal transforms : complexity issuesPro. Data Compression Conference, (March-April 1993), IEEE Computer Soc. Press, pp. 254–261.

  25. Popescu (D. C), Yan (H.) Fractal-based method for color image compression,Journal of Electronic Imaging,4, no. 1, pp 23–30, (Jan 1995).

    Article  Google Scholar 

  26. Popescu (D. C), Dimca (A.), Yan (H.), A non-linear model for fractal image coding,IEEE Trans IP, Vol. 6 no. 3, pp. 373–382, (March 1997).

    Google Scholar 

  27. Popescu (D. C), Bone (D) : Permutation based Fractal Image Coding,Proceedings of FE97, Arcachon, (June 1997).

  28. Saupe (D.) Hamzaoui (R.) : Complexity reduction methods for fractal image compression,I.M.A. Conference Proceedings on image Processing, Mathematical Methods and Applications, Oxford University Press, (1995)

  29. Signes (J.): Geometrical interpretation of ifs based image coding,Fractals,5, pp. 133–143, Supplementary Issue (April 1997).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Portions reprinted, with permission, from IEEE Transactions on Image Processing, vol. 6, no. 3, pp. 373-382, March 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popescu, D.C. Fractal image coding - achievements and prospects. Ann. Télécommun. 53, 219–228 (1998). https://doi.org/10.1007/BF02997678

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02997678

Key words

Mots-clés

Navigation