Mixed IFS : Resolution of the Inverse Problem Using Genetic Programming

Abstract : We address here the resolution of the so-called inverse problem for IFS. This problem has already been widely considered, and some studies have been performed for affine IFS, using deterministic or stochastic methods (Simulated Annealing or Genetic Algorithm) \cite{levy-vehel88,Goertzel94}. When dealing with non affine IFS, the usual techniques do not perform well, except if some {\em a priori} hypotheses on the structure of the IFS (number and type functions) are made. In this work, a Genetic Programming method is investigated to solve the «general» inverse problem, which permits to perform at the same time a numeric and a symbolic optimization. The use of «mixed IFS», as we call them, may enlarge the scope of some applications, as for example image compression, because they allow to code a wider range of shapes.
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Evelyne Lutton, Jacques Lévy Véhel, Guillaume Cretin, Philippe Glevarec, Cédric Roll. Mixed IFS : Resolution of the Inverse Problem Using Genetic Programming. [Research Report] RR-2631, INRIA. 1995. ⟨inria-00074056⟩

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