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) [9, 12, 6]. When dealing with non affine IFS, the usual techniques do not perform well, except if some a priori hypotheses on the structure of IFS (number and type functions) are made. 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.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
M. Barnsley and S. Demko. Iterated function system and the global construction of fractals. Proceedings of the Royal Society, A 399:243–245, 1985.
M. Barnsley, V. Ervin, D. Hardin, and J. Lancaster. Solution of an inverse problem for fractals and other sets. Proc. Natl. Acad. Sci. USA, 83, 1986.
M. F. Barnsley. Fractals Everywhere. Academic Press,N Y, 1988.
G. Borgefors. Distance transformation in arbitrary dimension. Computer Vision, Graphics, and Image Processing, (27), 1984.
Y. Fisher. Fractal image compression. Siggraph 92 course notes, 1992.
B. Goertzel. Fractal image compression with the genetic algorithm. complexity International, (1), 1994.
A.E. Jacquin. Fractal image coding: a review. Proceedings of the IEEE, 81(10), October 1993.
J. R. Koza. Genetic Programming. MIT Press, 1992.
Jacques Levy-Vehel. Analyse et synthese d'objets bi-dimensionnels par des méthodes stochastiques. PhD thesis, Université de Paris Sud, Decembre 1988.
Evelyne Lutton and Patrice Martinez. A genetic algorithm for the detection of 2d geometric primitives in images. In 12-ICPR, 1994. Jerusalem, Israel, 9–13 October.
D. J. Nettleton and R. Garigliano. Evolutionary algorithms and a fractal inverse problem. Biosystems, (33):221–231, 1994. Technical note.
J. Lévy Véhel and E. Lutton. Optimization of fractal functions using genetic algorithms. In Fractal 93, 1993. London.
L. Vences and I. Rudomin. Fractal compression of single images and image sequences using genetic algorithms. The Eurographics Association, 1994.
E.W. Jacobs Y. Fisher and R.D. Boss. Fractal image compression using iterated transforms. data compression, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cretin, G., Lutton, E., Levy-Vehel, J., Glevarec, P., Roll, C. (1996). Mixed IFS: Resolution of the inverse problem using genetic programming. In: Alliot, JM., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds) Artificial Evolution. AE 1995. Lecture Notes in Computer Science, vol 1063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61108-8_42
Download citation
DOI: https://doi.org/10.1007/3-540-61108-8_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61108-0
Online ISBN: 978-3-540-49948-0
eBook Packages: Springer Book Archive