A generalized class of fractal-wavelet transforms for image representation and compression

Canadian Journal of Electrical and Computer Engineering

Volumn 23, Issue 1-2, 1998, Pages 82-83

  Vrscay, Edward R ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

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EID: 24044464591     PISSN: 08408688     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. G.M. Davis, "Self-quantized wavelet subtrees: A wavelet-based theory for fractal image compression," in IEEE Data Compression Conf. Proc., J. Storer, Ed., IEEE Computer Society Press, March 1995.
2. G.M. Davis, "A wavelet-based analysis of fractal image compression," preprint, 1996.
3. B. Forte and E.R. Vrscay, "Inverse problem methods for generalized fractal transforms," in Fractal Image Encoding and Analysis, Y. Fisher, Ed., Springer-Verlag, Heidelberg, 1998.
4. H. Krupnik, D. Malah and E. Kamin, "Fractal representation of images via the discrete wavelet transform," presented at IEEE 18th Convention of Electrical Engineering in Israel, Tel-Aviv, Mar. 1995.
5. B. Simon, "Explicit link between local fractal transform and multiresolution transform," in Proc. IEEE Conf. on Image Process., Oct., 1995.
6. A. van de Walle, "Merging fractal image compression and wavelet transform methods," in Fractal Image Encoding and Analysis, Y. Fisher, Ed., Springer-Verlag, Heidelberg, 1998;
7. Relating Fractal Compression to Transform Methods, M. Math. thesis, Dept. of Applied Mathematics, University of Waterloo, Waterloo, Ont., 1995.
8. M.F. Barnsley and S. Demko, "Iterated function systems and the global construction of fractals," in Proc. Roy. Soc. London Ser. A, vol. 399, pp. 243-275, 1985.
9. M.F. Barnsley, Fractals Everywhere, New York: Academic Press, 1988.
10. J. Hutchinson, "Fractals and self-similarity," Indiana Univ. Math. J., vol. 30, pp. 713-747, 1981.
11. M.F. Barnsley and L.P. Hurd, Fractal Image Compression, Wellesley, Mass.: A.K. Peters, 1993.
12. B. Forte and E.R. Vrscay, "Theory of generalized fractal transforms," in Fractal Image Encoding and Analysis, Y. Fisher, Ed., Springer-Verlag, Heidelberg, 1998.
13. F. Mendivil and E.R. Vrscay, "Correspondence between fractal-wavelet transforms and iterated function systems," in Fractals in Engineering, From Theory to Industrial Applications, J. Lévy Véhel, E. Lutton and C. Tricot, Eds., New York: Springer-Verlag, 1997.
14. G. Oien and S. Lepsoy, "On the benefits of basis orthogonalization in fractal compression," in Fractal Image Encoding and Analysis, Y. Fisher, Ed., Springer-Verlag, Heidelberg, 1998.
15. G. Vines, "Orthogonal basis IFS," in Fractal Image Compression, Theory and Application, Y. Fisher, Ed., New York: Springer-Verlag, 1995.
16. D. Field, "Scale-invariance and self-similar "wavelet" transforms: An analysis of natural scenes and mammalian visual systems", in Wavelets, Fractals and Fourier Transforms, New Developments and New Applications, New York: Oxford Clarendon Press, 1993.
17. B. Wandell, Foundations of Vision, Sunderland, Mass.: Sinauer Associates, 1995.
18. M.F. Barnsley, S.G. Demko, J. Elton and J.S. Geronimo, "Invariant measures for Markov processes arising from Iterated Function Systems with place-dependent probabilities," Ann. Inst. H. Poincaré, vol. 24, pp. 367-394, 1988.
19. D.M. Monro, "A hybrid fractal transform," in Proc. ICASSP 5, 1993, pp. 162-172.
20. D.M. Monro and F. Dudbridge, "Fractal block coding of images," Electron. Lett., vol. 28, pp. 1053-1054, 1992.
21. A. Jacquin, "Image coding based on a fractal theory of iterated contractive image transformations," IEEE Trans. Image Process., vol. IP-1, pp. 18-30, 1992.
22. Y. Fisher, Ed., Fractal Image Compression, Theory and Application, New York: Springer-Verlag, 1995.
23. Y. Fisher, Ed., in Fractal Image Encoding and Analysis, Y. Fisher, Ed., Springer-Verlag, Heidelberg, 1998.
24. N. Lu, Fractal Imaging, New York: Academic Press, 1997.
25. I. Daubechies, Ten Lectures on Wavelets, Philadelphia: SIAM Press, 1992.
26. S.G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Analysis Machine Intell., vol. PAMI-11, no. 7, pp. 674-693, 1989.
27. G.G. Walter, Wavelets and Other Orthogonal Systems With Applications, Boca Raton, Fla.: CRC Press, 1994.
28. E.R. Vrscay, "Mathematical theory of generalized fractal transforms and associated inverse problems," in Proc. Image Tech '96 Conf. on Multimedia Imaging Technology and Applications, Atlanta, Ga., Mar. 1996.
29. P.M. Centore and E.R. Vrscay, "Continuity of attractors and invariant measures for Iterated Function Systems," Canad. Math. Bull., vol. 37, no. 3, pp. 315-329, 1994.
30. A. Said and W.P. Pearlman, "A new fast and efficient image codec based on set partitioning in hierarchical trees," IEEE Trans. Circuits and Systems for Video Tech., vol. CSVT-6, 1996.
31. S. Mallat and W.L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inform. Theory, vol. IT-38, pp. 617-643, 1992.
32. S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Pattern Analysis Machine Intell., vol. PAMI-14, pp. 710-732, 1992.
33. J. Froment and S. Mallat, "Second generation compact image coding with wavelets," in Wavelets - A Tutorial in Theory and Applications, C.K. Chui, Ed., New York: Academic Press, 1992, pp. 655-677.
34. S.G. Mallat, Wavelet Signal Processing, preprint, 1996.
35. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Process., vol. SP-41, pp. 3445-3462, 1993.
36. E.R. Vrscay, "Image processing with the fractal-wavelet transform," in preparation.
37. J. Lévy Véhel, "Fractal approaches in signal processing," preprint.
38. and "Introduction to the multifractal analysis of image," preprint.
39. K. Daoudi, Généralisations des systèmes de fonctions itérés - Applications au traitement du signal, D.Math-thesis, Université de Paris IX Dauphine, 1996.
40. K. Daoudi, J. Lévy Véhel and Y. Meyer, "Construction of continuous functions with prescribed local regularity," to appear in Constr. Approx.
41. P.D. Wakefield, D.M. Bethel and D.M. Monro, "Hybrid image compression with implicit fractal terms," in Proc. ICASSP, 1997.
42. M. Wickerhauser, Adapted Wavelet Analysis from Theory to Software, Wellesley, Mass.: A.K. Peters, 1995.