Abstract
Optimal fractal image compression is an NP-hard combinatorial optimization problem where the domain of feasible solutions is a large finite set T of contractive affine mappings, and the cost function is \( ||{f^{*}} - {f_{T}}||_{2}^{2} \) where f* is the original image, and f T is the fixed point of T G T. In contrast, traditional fractal coders are based on a greedy algorithm known as collage coding, which minimizes \( ||{f^{*}} - T\left( {{f^{*}}} \right)||_{2}^{2} \). We describe a local search algorithm that rapidly improves the solution obtained by collage coding. In particular, we show how the successive computations of the cost function can be efficiently done by combining a Gauss-Scidel like iterative method and a graph algorithm.
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Hamzaoui, R., Saupe, D. (2002). Fractal Image Compression with Fast Local Search. In: Barnsley, M.F., Saupe, D., Vrscay, E.R. (eds) Fractals in Multimedia. The IMA Volumes in Mathematics and its Application, vol 132. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9244-6_5
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DOI: https://doi.org/10.1007/978-1-4684-9244-6_5
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