Explicit Link between Local Fractal Transform

Much researchs are currently carried out in the eld of fractal coding of images. Fractal models try to 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 particularly 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 coeecients 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 deened and it is shown that parameters can be estimated only on the basis of multiresolution decomposition coeecients. The way to apply these results to images is then envisaged.