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By John G. Webster (Editor)

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The two most popular schemes in image coding are Huffman coding and arithmetic coding. These schemes work by different mechanisms but share the same basic idea of coding a symbol with a number of bits inversely related to the probability that it occurs. Therefore a very challenging problem for entropy coding is to generate an accurate profile for symbol probabilities. This is called the modeling problem. Modeling is done in two different ways: nonadaptive, in which the profile is determined empirically, and remains unchanged throughout coding, and adaptive, in which the profile is refined dynamically in the IMAGE AND VIDEO CODING 3 coding process by using previously coded data.

Of course, xf is usually not exactly the same as xo , but according to another theorem called the Collage Theorem (4), the closer T(xo ) is to xo the closer xf will be to xo . In other words, if the encoder can find very good matches for range blocks, the decoder can duplicate the original image very closely. However, because the decoded image is not exactly the same as the original image, fractal coding falls in the class of lossy compression methods. IMAGE AND VIDEO CODING 11 Fig. 7. A basic fractal image coding algorithm.

10. E. G. , 33: 5–53, 1972. 11. B. Hill Some aspects of a large capacity holographic memory, Appl. , 11: 182–191, 1972. 12. G. R. Knight Holographic memories, Opt. , 14: 453–459, 1975. 13. C. Gu et al. Cross-talk-limited storage capacity of volume holographic memory, J. Opt. Soc. , A9: 1978–1983, 1992. 14. H. Kogelnik Coupled wave theory for thick hologram gratings, Bell Sys. Tech. , 18: 2909–2947, 1969. 15. F. H. Mok et al. Storage of 500 high-resolution holograms in LiNbO3 crystal, Opt. , 16: 605–607, 1991.

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