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## Mixed IFS: resolution of the inverse problem using Genetic Programming (1995)

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### Other Repositories/Bibliography

Venue: | COMPLEX SYSTEMS |

Citations: | 12 - 5 self |

### Citations

10012 | Genetic Algorithms - Goldberg - 1989 |

1054 | Genetic Programming
- Koza, Poli
- 2005
(Show Context)
Citation Context ...gure 5: The domain constraint is tested on each vertex, the contractivity constraint, on each couple of vertices. 4 Genetic Programming to address the inverse problem 4.1 Introduction Since John Koza =-=[16]-=-srst proposed to extend the GA model to the space of computer programs, in order to create programs able to solve problems for which they haven't been explicitly programmed, a lot of very dierent app... |

1024 |
Fractals everywhere
- Barnsley
- 1988
(Show Context)
Citation Context ... this framework, and some solutions exist, based on deterministic or stochastic optimization methods. Most of them make some a priori restrictive hypotheses : ane IFS, with asxed number of functions =-=[5, 15, 9, 27, 17]-=-. Solutions based on Genetic Algorithms (GA) or Evolutionary Algorithms have recently been presented for ane IFS [25, 10, 24, 21]. As it will be seen in section 3, non-ane IFS provide an interesting... |

624 |
Fractals and self similarity
- Hutchinson
- 1981
(Show Context)
Citation Context ...unctions System) theory is an important topic in fractals. The geometric and measure theoretical aspects of systems of contractive maps (and associated probabilities) were worked out by J. Hutchinson =-=[14]-=-, and the existence of a unique compact invariant set was proven. These studies have provided powerful tools for the investigation of fractal sets, and the action of systems of contractive maps to pro... |

246 |
Distance transformations in arbitrary dimensions, Comput. Vision Graphics Image Process
- Borgefors
- 1984
(Show Context)
Citation Context ...n of a black & white image into a grey-level one, where the level aected to each image point is a function of its distance to the original shape. It can be easily computed by a simple algorithm (see =-=[6]-=-), based on the use of two masks (seesgure 8) : the resulting images are parameterized by d1 and d2 which represent the two elementary distances on vertical/horizontal and diagonal directions. This pa... |

213 | Iterated function systems and the global construction of fractals. Proc Roy Soc London Ser A 399:243–75 - MF, Demko - 1985 |

116 |
Fractal image coding: a review.
- Jacquin
- 1993
(Show Context)
Citation Context ... this framework, and some solutions exist, based on deterministic or stochastic optimization methods. Most of them make some a priori restrictive hypotheses : ane IFS, with asxed number of functions =-=[5, 15, 9, 27, 17]-=-. Solutions based on Genetic Algorithms (GA) or Evolutionary Algorithms have recently been presented for ane IFS [25, 10, 24, 21]. As it will be seen in section 3, non-ane IFS provide an interesting... |

69 |
Solution of an inverse problem for fractals and other sets
- Barnsley, Ervin, et al.
- 1985
(Show Context)
Citation Context ...e fractal sets has been considered by numerous authors (see for example [2, 3, 8, 12]). A major challenge of both theoretical and practical interest is the resolution of the so called inverse problem =-=[20, 26, 25, 4]-=-. An exact solution can be found in some particular cases, but in general, no exact solution is known. From a computational viewpoint this problem may be formulated as an optimization problem. A lot o... |

63 |
Fractal image compression using iterated transforms,” in Image and Text
- Fisher, Jacobs, et al.
- 1992
(Show Context)
Citation Context ... this framework, and some solutions exist, based on deterministic or stochastic optimization methods. Most of them make some a priori restrictive hypotheses : ane IFS, with asxed number of functions =-=[5, 15, 9, 27, 17]-=-. Solutions based on Genetic Algorithms (GA) or Evolutionary Algorithms have recently been presented for ane IFS [25, 10, 24, 21]. As it will be seen in section 3, non-ane IFS provide an interesting... |

62 |
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
- Barnsley, Demko, et al.
- 1988
(Show Context)
Citation Context ...dies have provided powerful tools for the investigation of fractal sets, and the action of systems of contractive maps to produce fractal sets has been considered by numerous authors (see for example =-=[2, 3, 8, 12]-=-). A major challenge of both theoretical and practical interest is the resolution of the so called inverse problem [20, 26, 25, 4]. An exact solution can be found in some particular cases, but in gene... |

53 | Genetic Algorithms and Robotics: A Heuristic Strategy for Optimization - Davidor - 1991 |

53 | Geometric primitive extraction using a genetic algorithm., - Roth, Levine - 1994 |

47 | Model-based image interpretation using genetic algorithms, Image and Vision Computing 10 (5 - Hill, Taylor - 1992 |

39 |
An ergodic theorem for iterated maps
- Elton
- 1987
(Show Context)
Citation Context ...dies have provided powerful tools for the investigation of fractal sets, and the action of systems of contractive maps to produce fractal sets has been considered by numerous authors (see for example =-=[2, 3, 8, 12]-=-). A major challenge of both theoretical and practical interest is the resolution of the so called inverse problem [20, 26, 25, 4]. An exact solution can be found in some particular cases, but in gene... |

23 | andP.Martinez, “A genetic algorithm for the detection of 2D geometric primitives in images
- Lutton
- 1994
(Show Context)
Citation Context ... then progressively tunesne details along the computation. In order to guide the research of the optimum, we use distance images. This allows to consider \smoother" functions to be optimized, as in =-=[19]-=-. A distance image is the transformation of a black & white image into a grey-level one, where the level aected to each image point is a function of its distance to the original shape. It can be easi... |

20 |
Evolutionary algorithms and a fractal inverse problem
- Nettleton, Garigliano
- 1994
(Show Context)
Citation Context ...i restrictive hypotheses : ane IFS, with asxed number of functions [5, 15, 9, 27, 17]. Solutions based on Genetic Algorithms (GA) or Evolutionary Algorithms have recently been presented for ane IFS =-=[25, 10, 24, 21]-=-. As it will be seen in section 3, non-ane IFS provide an interesting variety of shapes, whose practical interest might be large. However, in that case, the inverse problem cannot be addressed using ... |

19 |
Moment and collage methods for the inverse problem of fractal construction with iterated function systems
- Vrscay
- 1990
(Show Context)
Citation Context ...e fractal sets has been considered by numerous authors (see for example [2, 3, 8, 12]). A major challenge of both theoretical and practical interest is the resolution of the so called inverse problem =-=[20, 26, 25, 4]-=-. An exact solution can be found in some particular cases, but in general, no exact solution is known. From a computational viewpoint this problem may be formulated as an optimization problem. A lot o... |

18 |
Chaotic optimization and the construction of fractals : solution of an inverse problem, Complex Systems
- Mantica, Sloan
- 1989
(Show Context)
Citation Context ...e fractal sets has been considered by numerous authors (see for example [2, 3, 8, 12]). A major challenge of both theoretical and practical interest is the resolution of the so called inverse problem =-=[20, 26, 25, 4]-=-. An exact solution can be found in some particular cases, but in general, no exact solution is known. From a computational viewpoint this problem may be formulated as an optimization problem. A lot o... |

16 | Fractal compression of single images and image sequences using genetic algorithms. The Eurographics Association
- Vences, Rudomin
- 1994
(Show Context)
Citation Context ...i restrictive hypotheses : ane IFS, with asxed number of functions [5, 15, 9, 27, 17]. Solutions based on Genetic Algorithms (GA) or Evolutionary Algorithms have recently been presented for ane IFS =-=[25, 10, 24, 21]-=-. As it will be seen in section 3, non-ane IFS provide an interesting variety of shapes, whose practical interest might be large. However, in that case, the inverse problem cannot be addressed using ... |

10 |
Fractal image compression with the genetic algorithm
- Goertzel
- 1994
(Show Context)
Citation Context ...oblem for IFS. This problem has already been widely considered, and some studies have been performed for ane IFS, using deterministic or stochastic methods (Simulated Annealing or Genetic Algorithm) =-=[17, 10]-=-. When dealing with non ane IFS, the usual techniques do not perform well, except if some a priori hypotheses on the structure of the IFS (number and type functions) are made. In this work, a Genetic... |

8 |
Fractal image compression. Siggraph 92 course notes
- Fisher
- 1992
(Show Context)
Citation Context |

7 |
Hyperbolic Iterated Function Systems and Applications
- Hardin
- 1985
(Show Context)
Citation Context ...dies have provided powerful tools for the investigation of fractal sets, and the action of systems of contractive maps to produce fractal sets has been considered by numerous authors (see for example =-=[2, 3, 8, 12]-=-). A major challenge of both theoretical and practical interest is the resolution of the so called inverse problem [20, 26, 25, 4]. An exact solution can be found in some particular cases, but in gene... |

7 |
Optimization of fractal functions using genetic algorihms. research report INRIA
- Lutton, Levy-Vehel
- 1941
(Show Context)
Citation Context ...mixed IFS within a reasonable computation time (a few hours on Sparc 10 and Dec 5000 stations). This computation time is similar to computation times of GA applied to the inverse problem for ane IFS =-=[18]-=-, although in the case of mixed IFS the size of the search space is much more larger. This fact may be explained by the use of variable sized structures in the GP algorithm, which seems to perform a m... |

5 |
An Approach to Natural Scene Segmentation by Means of Genetic Algoritms with Fuzzy Data
- Albert, Ferri, et al.
- 1992
(Show Context)
Citation Context ...S : the w i functions have been recursively built with help of random shots in a set of basic functions, a set of terminals (x and y), and a set of constants. In our examples, the constants belong to =-=[0; 1]-=-, and the basic functions set is : + div(x; y) = x 0:0001+jyj cos sin root(x) = p jxj loga(x) = log(1 + jxj) * + 1 2 x y * + x cos Figure 3: The function ((cos(x) + 2 y) (1 + x... |

4 | Using a Genetic Algorithm to solve Constraint Satisfation Problems Generated by an Image Interpreter - Truv'e - 1991 |

4 |
Fractal Geometry and Analysis, Chapter Iterated function Systems: theory, applications and the inverse problem
- Vrscay
- 1991
(Show Context)
Citation Context |

3 |
Analyse et synth`ese d'objets bi-dimensionnels par des m'ethodes stochastiques
- V'ehel
- 1988
(Show Context)
Citation Context ...oblem for IFS. This problem has already been widely considered, and some studies have been performed for ane IFS, using deterministic or stochastic methods (Simulated Annealing or Genetic Algorithm) =-=[17, 10]-=-. When dealing with non ane IFS, the usual techniques do not perform well, except if some a priori hypotheses on the structure of the IFS (number and type functions) are made. In this work, a Genetic... |