On Convergence of Discrete and Selective Fractal Operators

  • Authors:

  • Wladyslaw Skarbek

  • Affiliations:

  • -

  • Venue:
  • CAIP '99 Proceedings of the 8th International Conference on Computer Analysis of Images and Patterns
  • Year:
  • 1999

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Abstract

It is proved that any iterative sequence for a fractal operator which is contractive in l∞ norm with contractivity c*, after clamping and rounding to integer levels, is perceptually convergent at the threshold Τ ≥ 1/(1 - c*): Eventual contractivity is a suffcient 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.