Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations
Inhaltsverzeichnis
Reference
A.E. Jacquin: Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations. IEEE TRANSACTIONS ON IMAGE PROCESSING. VOL. I. NO. I. JANUARY 1992.
DOI
http://dx.doi.org/10.1109/83.128028
Abstract
The author proposes an independent and novel approach to image coding, based on a fractal theory of iterated transformations. The main characteristics of this approach are that (i) it relies on the assumption that image redundancy can be efficiently exploited through self-transformability on a block-wise basis, and (ii) it approximates an original image by a fractal image. The author refers to the approach as fractal block coding. The coding-decoding system is based on the construction, for an original image to encode, of a specific image transformation-a fractal code-which, when iterated on any initial image, produces a sequence of images that converges to a fractal approximation of the original. It is shown how to design such a system for the coding of monochrome digital images at rates in the range of 0.5-1.0 b/pixel. The fractal block coder has performance comparable to state-of-the-art vector quantizers
Extended Abstract
Bibtex
Used References
M. F. Barnsley and S. Demko "Iterated function systems and the global construction of fractals", Ρroc. of Royal Soc. London, vol. A399, pp.243 -275 1985 http://dx.doi.org/10.1098/rspa.1985.0057
M. F. Barnsley Fractals Everywhere, 1988 :Academic
M. F. Barnsley , J. H. Elton and D. P. Hardin Constructive Approximation, pp.3 -31 1989 :Springer-Verlag
Î. Dunford and J. T. Schwartz Linear Operators, 1966 :Wiley
R. C. Gonzalez and P. Wintz Digital image Processing, 1977 :Addison-Wesley
R. M. Gray "Vector quantization", IEEE ASSP Mag., 1984 http://dx.doi.org/10.1109/MASSP.1984.1162229
A. E. Jacquin A fractal theory of iterated Markov operators with applications to digital image coding, 1989
A. K. Jain "Image data compression: A review", Proc. IEEE, vol. 69, 1981 http://dx.doi.org/10.1109/PROC.1981.11971
B. Mandelbrot The Fractal Geometry of Nature, 1982 :Freeman
Î. M. Nasrabadi and R. A. King "Image coding using VQ: A review", IEEE Trans. Commun., vol. 36, 1988 http://dx.doi.org/10.1109/26.3776
A. N. Netravali and B. G. Haskell Digital Pictures: Representation and Compression, 1989 :Plenum
B. Ramamurthi and A. Gersho "Classified vector quantization of images", IEEE Trans. Commun., vol. 34, 1986 http://dx.doi.org/10.1109/TCOM.1986.1096468
Links
Full Text
http://www.csee.wvu.edu/~xinl/library/papers/infor/imaging/fractal_coding.pdf