An hybrid evolutive-genetic strategy for the inverse fractal problem of IFS models

Abstract

Iterated Function Systems are popular techniques for generating selfsimilar fractals. An important practical problem in this field is that of obtaining the IFS code which approximates a given image with a certain prescribed accuracy (inverse IFS problem). In this paper we present an hybrid evolutive-genetic algorithm to solve the inverse IFS problem in two steps: First, an Evolutive Strategy (ES) is applied to identify a set of affine transformations associated with selfsimilar structures within the image. Then, the best adapted transformations are combined forming an initial population of IFS models and a Genetic Algorithm (GA) is used to find the optimal IFS model. We show that this hybrid algorithm performs significantly better than one-step global evolutive or genetic algorithms which have been recently reported in the literature. © Springer-Verlag 2000.