B. Simon. Explicit link between local fractal transform and multiresolution transform. In Proc. ICIP-95 IEEE International Conference on Image Processing, Washington, D.C, 1995.
Much research are currently carried out in the field of fractal coding of images. Fractal models identify and represent self-similarity relationships within images through the use of spatial transformations of the signal associating shrinking, translation, isometries and scaling. These transformations can be interpreted frequentialy and are particulary suited to an interpretation in the multiresolution decomposition space of functions. In this paper, we study the expression of a particular fractal transform within the orthogonal multiresolution context. Conclusions drawn from the results show that the fractal transformation can be decoupled in two terms, one serves to interpolate high frequency coefficients from one resolution layer to the next while the other is a constant term containing low pass information. A fractal transformation taking these elements into account is defined and it is shown that parameters can be estimated only on the basis of multiresolution decomposition coefficients. The way to apply these results to images is then envisaged.
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@InProceedings{Simo95b,
Author = {Simon, B.},
Title = {Explicit link between local fractal transform and multiresolution transform},
BookTitle = {Proc. ICIP-95 IEEE International Conference on Image Processing},
Address = {Washington, D.C},
Year = {1995}
}