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A stochastic algorithm to compute optimal probabilities in the chaos game

Part of: Stochastic processes Communication, information

Published online by Cambridge University Press:  01 July 2016

Laura M. Morato  and
Paola Siri
Laura M. Morato*
Affiliation:
Università di Verona
Paola Siri*
Affiliation:
Università di Verona
*
∗ Postal address: Facoltà di Scienze MM.FF.NN., Ca' Vignal 2, Strada le Grazie, 37134 Verona, Italia.
∗ Postal address: Facoltà di Scienze MM.FF.NN., Ca' Vignal 2, Strada le Grazie, 37134 Verona, Italia.
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Abstract

We present a stochastic algorithm which generates optimal probabilities for the chaos game to decompress an image represented by the fixed point of an IFS operator. The algorithm can be seen as a sort of time-inhomogeneous regenerative process. We prove that optimal probabilities exist and, by martingale methods, that the algorithm converges almost surely. The method holds for IFS operators associated with any arbitrary number of possibly overlapping affine contraction maps on the pixels space.

Keywords

image decompressionstochastic algorithmmartingales

MSC classification

Primary: 94A08: Image processing (compression, reconstruction, etc.)
Secondary: 60G42: Martingales with discrete parameter
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 423 - 436
Copyright
Copyright © Applied Probability Trust 2001 

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