On Convergence of Discrete and Selective Fractal Operators
It is proved that any iterative sequence for a fractal operator which is contractive in l1 norm with contractivity c *, after clamping and rounding to integer levels, is perceptually convergent at the threshold т ≥ 1=(1 — c *): Eventual contractivity is a sufficient condition for the convergence of iterations of a fractal operator. This paper shows that it is also necessary if the averaging operation in the definition of the fractal operator is replaced by the selection operation.
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- 1.M. F. Barnsley, Fractals everywhere Addison Wesley, 1988.Google Scholar
- 3.J. Dugundi and A. Granas, Fixed point theory, Polish Scientic Publishers, Warszawa, 1982.Google Scholar
- 4.Y. Fisher ed., Fractal image compression, Theory and Application, Springer Verlag, New York, 1995.Google Scholar
- 6.W. Skarbek, On convergence of affine fractal operators, Image Processing and Communications, 1(1), 1995.Google Scholar