Hierarchical Interpretation of Fractal Image Coding and Its Applications

The basics of a block oriented fractal image coder are reviewed. The output of the coder is an IFS (Iterated Function System), which approximates the image as a xed point of a contractive transformation. A new hierarchical interpretation of the IFS code, which relates the diierent scales of the xed point, is introduced. We prove the existence of a unique function of a continuous variable that is associated with the IFS code. It is further shown that the diierent scales of the IFS xed point are directly computable from this so called IFS embedded function. The computation of the IFS-code, depends on the sampling method, an issue that is also discussed. A matrix representation of the IFS code is described and related to the fractal dimension of the IFS embedded function. An application to a new super-resolution method, using an IFS-code, is demonstrated, and its characteristics are analyzed. Another application of the hierarchical representation to fast decoding is also presented, leading typically to an order of magnitude reduction of the computation time.