Complex Systems

Mixed IFS: Resolution of the Inverse Problem using Genetic Programming Download PDF

Evelyne Lutton
Jacques Levy-Vehel
Guillaume Cretin
Philippe Glevarec
Cidric Roll
INRIA - Rocquencourt;
B.P. 105, 78153 LE CHESNAY Cedex, France


We address here the resolution of the so-called inverse problem for the iterated functions system (IFS). This problem has already been widely considered, and some studies have been performed for the affine IFS, using deterministic or stochastic methods (simulated annealing or genetic algorithm). In dealing with the nonaffine IFS, the usual techniques do not perform well unless some a priori hypotheses on the structure of the IFS (number and type of functions) are made. In this work, a genetic programming method is investigated to solve the "general'' inverse problem, which allows the simultaneous performance of a numeric and a symbolic optimization. The use of a "mixed IFS'' may enlarge the scope of some applications, for example, image compression, because it allows a wider range of shapes to be coded.