Fractals everywhere
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Fractal image compression: theory and application
Fractal image compression: theory and application
Fractal Imaging
Fractal Image Encoding and Analysis
Fractal Image Encoding and Analysis
A wavelet-based analysis of fractal image compression
IEEE Transactions on Image Processing
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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.