Mixed IFS: Resolution of the Inverse Problem Using Genetic Programming

We address here th e 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 determin ist ic or stochast ic methods (simulated annealing or genetic algorithm). In dealing with the nonaffine IFS, the usual techniques do not perform well unless some a priori hypoth eses on th e structure of the IFS (number and typ e of funct ions) are made. In this work, a genetic programming method is investigated to solve the "general" inverse problem, which allows the simultaneous perform ance of a numeric and a symbolic optimization . The use of a "mixed IFS" may enlarge th e scope of some applications, for example, image compression, because it allows a wider range of shapes to be coded.