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A new class of markov processes for image encoding

Published online by Cambridge University Press:  01 July 2016

Michael F. Barnsley  and
John H. Elton
Michael F. Barnsley*
Affiliation:
Georgia Institute of Technology
John H. Elton*
Affiliation:
Georgia Institute of Technology
*
Postal address for both authors: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
Postal address for both authors: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

A new class of iterated function systems is introduced, which allows for the computation of non-compactly supported invariant measures, which may represent, for example, greytone images of infinite extent. Conditions for the existence and attractiveness of invariant measures for this new class of randomly iterated maps, which are not necessarily contractions, in metric spaces such as , are established. Estimates for moments of these measures are obtained.

Special conditions are given for existence of the invariant measure in the interesting case of affine maps on . For non-singular affine maps on , the support of the measure is shown to be an infinite interval, but Fourier transform analysis shows that the measure can be purely singular even though its distribution function is strictly increasing.

Keywords

RANDOM MAPSFRACTALS
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 1 , March 1988 , pp. 14 - 32
Copyright
Copyright © Applied Probability Trust 1988 

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