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Optimization of fractal : function using genetic algorithms

Jacques Lévy Véhel 1 Evelyne Lutton 1
1 EPIDAURE - Medical imaging and robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this work, we investigate the difficult problem of the optimization of fractal functions. We first derive some relations between the local scaling exponents of the functions, the sampling rate and the accuracy of the localization of the optimum, both in the domain and the range of the functions. We then apply these ideas to the resolution of the inverse problem for iterated function system (IFS) using a genetic algorithm. In the conditions of study (2D problem for sets), the optimization process yields the optimum with a good precision and within a tractable computing time.
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Submitted on : Wednesday, May 24, 2006 - 4:11:53 PM
Last modification on : Friday, February 4, 2022 - 3:22:47 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 6:42:10 PM


  • HAL Id : inria-00074733, version 1



Jacques Lévy Véhel, Evelyne Lutton. Optimization of fractal : function using genetic algorithms. [Research Report] RR-1941, INRIA. 1993. ⟨inria-00074733⟩



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