A Multi - Resolution Framework for FractalImage
نویسندگان
چکیده
The starting point of this paper is the basic fractal coder suggested by Jacquin. The coder nds and encodes the parameters of a partitioned iterated function system (PIFS), which approximates the signal as a xed-point of a contractive transformation. The work presented here can be divided into two parts. The rst part begins with a presentation of the hierarchical structure of the PIFS code. This structure relates the code and its xed-point in diierent resolutions. It is shown that there exists a function of a continuous variable which is directly related to the PIFS. It is shown that by properly manipulating this function, called the PIFS embedded-function, one can compute the xed-points related to the code in any desired resolution. We end the rst part with a brief description of several applications, such as a fast non-iterative decoder, a method for fractal interpolation of the signal via its PIFS code, and an improved collage-bound. 1 The hierarchical representation of the IFS code establishs a link to mul-tiresolution analysis of the code. In the second part of the work we present a method for mapping similar regions within an image in the wavelet domain. We rst show a new formulation by which mappings, which are identical to conventional IFS mappings, are found in the Haar wavelet transform domain. We then propose to use diierent mother-wavelet than Haar. The use of other wavelets than Haar results in the overlap of mapped regions, thus avoiding the typical blockiness associated with conventional blockwise IFS. By Using mappings between the wavelet coeecients we can enrich the family of transformations. This leads to a new fractal-wavelet image coder that reduces blockiness, and improves the PSNR of the reconstructed image.
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