An Interpolative Scheme for Fractal Image Compression in the Wavelet Domain
Standard fractal image coding methods seek to find a contractive fractal transform operator T that best scales and copies subsets of a target image I (its domain blocks) onto smaller subsets (its range blocks). The fixed point of this operator is an approximation to the image I and can be generated by iteration of T. Although generally good fidelity is achieved at significant compression rates, the method can suffer from blockiness artifacts. This inspired the introduction of fractal-wavelet transforms which operate on the wavelet representations of functions: Wavelet coefficient subtrees are scaled and copied onto lower subtrees. We propose a simple adaptive and unrestricted fractal-wavelet scheme that adopts a dynamic partitioning of the wavelet decomposition tree, resulting in intermediate representations between the various dyadic levels. In this way, one may (i) generate a continuous and relatively smooth rate distortion curve and (ii) encode images at a pre-defined bit rate or representation tolerance error.
KeywordsFractal image compression fractal-wavelet compression IFS
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