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Mixed IFS: Resolution of the inverse problem using genetic programming

  • Guillaume Cretin
  • Evelyne Lutton
  • Jacques Levy-Vehel
  • Philippe Glevarec
  • Cédric Roll
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1063)

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.

Keywords

Fractals Genetic Programming Inverse problem for IFS 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Guillaume Cretin
    • 1
  • Evelyne Lutton
    • 1
  • Jacques Levy-Vehel
    • 1
  • Philippe Glevarec
    • 1
  • Cédric Roll
    • 1
  1. 1.INRIA-RocquencourtLe Chesnay CedexFrance

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