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A Necessary and Sufficient Contractivity Condition for the Fractal Transform Operator

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Abstract

This paper revisits the concept of fractal image coding and the contractivity conditions of the fractal transform operator. All such existing conditions are only sufficient. This paper formulates a necessary and sufficient condition for the contractivity of the fractal transform operator associated to a fractal code. Furthermore, analytical results on the convergence of the fractal image decoding will be derived.

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Authors and Affiliations

  1. Department of Medical Biophysics, University of Toronto, Imaging Research, Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada

    Mehran Ebrahimi

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  1. Mehran Ebrahimi
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Correspondence to Mehran Ebrahimi.

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Ebrahimi, M. A Necessary and Sufficient Contractivity Condition for the Fractal Transform Operator. J Math Imaging Vis 35, 186–192 (2009). https://doi.org/10.1007/s10851-009-0164-z

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  • DOI: https://doi.org/10.1007/s10851-009-0164-z

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