A. Pentland, B. Horowitz. A practical approach to fractal-based image compression. In Proceedings from SPIE Visual Communications and Image Processing, Volume 1605, Pages 467-474, 1991.
Fractal techniques for image compression have recently attracted a great deal of attention. Unfortunately, little in the way of practical algorithms or techniques have published. We present a technique for image compression that is based on a very simple type of iterative fractal. In our algorithm a wavelet transform (quadrature mirror filter pyramid) is used to decompose an image into bands containing information from different scales (spatial frequencies) and orientations. The conditional probabilities between these different scale bands are then determined, and used as the basis for a predictive coder. We find that the wavelet transform's various scale and orientation bands have a great deal of redundant, self-similar structure. This redundant structure is, however, in the form of multi-modal conditional probabilities, so that linear predictors perform poorly. Our algorithm uses a simple histogram method to determine the multi-modal conditional probabilities between scales. The resulting predictive coder is easily integrated into existing subband coding schemes. Comparison of this fractal-based scheme with our standard wavelet vector coder on 256 x 256 grea-level imagery shows up to a two-fold gain in coding efficiency with no loss in image quality, and up to a four-fold gain with small loss in image quality. Coding and decoding are implemented by small table lookups, making real-time application feasible.
@InProceedings{PeHo91,
Author = {Pentland, A. and Horowitz, B.},
Title = {A practical approach to fractal-based image compression},
BookTitle = {Proceedings from SPIE Visual Communications and Image Processing},
Volume = {1605},
Pages = {467--474},
Year = {1991}
}