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A comparison of different evolutive niching strategies for identifying a set of selfsimilar contractions for the IFS inverse problem
Keywords:
Evolutive algorithms, fractals, iterated function systems, image compressionAbstract
The key problem in fractal image compression is that of obtaining the IFS code (a set of linear transformations)which approximates a given image with a certain prescribed accuracy (inverse IFS problem).In this paper,we analyze and compare the performance of sharing and crowding niching techniques for identifying optimal selfsimilar transformations likely to represent a selfsimilar area within the image. The best results are found using the deterministic crowding method.We also present an nteractive Matlab program implementing the algorithms described in the paper.The key problem in fractal image compression is that of obtaining the IFS code (a set of linear transformations)which approximates a given image with a certain prescribed accuracy (inverse IFS problem).In this paper,we analyze and compare the performance of sharing and crowding niching techniques for identifying optimal selfsimilar transformations likely to represent a selfsimilar area within the image. The best results are found using the deterministic crowding method.We also present an nteractive Matlab program implementing the algorithms described in the paper.
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References
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[4] Evans, A.K. and Turner, M.J.: Specialization of evolutionar yalgorithms and data structures for the IFS inverse problem, in M.J. Turner editor. Proceedings of the Second IMA Conference on Image Processing: Mathematical Methods, Algorithms and Applications, 1998.
[5] Fisher, Y.: Fractal Image Compression: Theor yand Application. SpringerVerlag, 1995.
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[7] Gutiérrez, J.M., Cofiño, A.S., and Ivanissevich, M.L. An Hybrid Evolutive–Genetic Strategy for the Inverse Fractal Problem of IFS Models. in Lecture Notes in Artificial Intelligence, Springer-Verlag, in press.
[8] Gutiérrez, J.M., lglesias, A. ,Rodríguez, M.A. and Rodríguez, V.J.: Generating and Rendering Fractal Images . The Mathematica Journal 7(1), 6–14, 1997.
[9] Holland, J.H.: Adaptation in natural and artificial systems. The University o Michigan Press, 1975.
[10] Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley, 1989.
[11] Lutton, E. et al.: Mixed IFS - resolution of the inverse problem using genetic programming. INRIA Rapport 2631, 1995.
[12] Mahfoud, S.W.: Crowding and preselection revisited, in Proc. PPSN-92, Elsevier, 1992.
[13] Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, second edition, Springer-Verlag, 1994.
[14] Nettleton, D.J., Garigliano, R.: Evolutionar yalgorithms and a fractal inverse problem. Biosystems 33, 221-231, 1994.
[15] Rechenberg, I.: Evolution strategie: Optimierung technischer systeme nach prinzipien der biologischen evolution. Frommann-Holzboog Verlag, 1973.
[16] Shonkwiler, R., Mendivil, F., Deliu, A.: Genetic algorithms for the 1-D fractal inverse problem. Proceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, 495–501, 1991.
[17] Turner, M.J.andBlackledge, J.M., Andrews, P.R.: Fractal Geometr yin Digital Imaging. Academic Press, 1998.
[18] Yin, X. and Germay, N.: , A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization, Proc. I.C. Artificial Neural Nets and Genetic Algorithms, 450–457, 1993.
[2] Barnsley, M.F.: Fractals everywhere, second edition. Academic Press, 1990.
[3] Berkner, K.: A wavelet-based solution to the inverse problem for fractal interpolation functions ,inL.Vehel et al. editors. Fractals in Engineering’97. Springer Verlag,1997.
[4] Evans, A.K. and Turner, M.J.: Specialization of evolutionar yalgorithms and data structures for the IFS inverse problem, in M.J. Turner editor. Proceedings of the Second IMA Conference on Image Processing: Mathematical Methods, Algorithms and Applications, 1998.
[5] Fisher, Y.: Fractal Image Compression: Theor yand Application. SpringerVerlag, 1995.
[6] Goentzel, B.: Fractal image compression with the genetic algorithm. Complexity International 1, 111-126, 1994.
[7] Gutiérrez, J.M., Cofiño, A.S., and Ivanissevich, M.L. An Hybrid Evolutive–Genetic Strategy for the Inverse Fractal Problem of IFS Models. in Lecture Notes in Artificial Intelligence, Springer-Verlag, in press.
[8] Gutiérrez, J.M., lglesias, A. ,Rodríguez, M.A. and Rodríguez, V.J.: Generating and Rendering Fractal Images . The Mathematica Journal 7(1), 6–14, 1997.
[9] Holland, J.H.: Adaptation in natural and artificial systems. The University o Michigan Press, 1975.
[10] Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley, 1989.
[11] Lutton, E. et al.: Mixed IFS - resolution of the inverse problem using genetic programming. INRIA Rapport 2631, 1995.
[12] Mahfoud, S.W.: Crowding and preselection revisited, in Proc. PPSN-92, Elsevier, 1992.
[13] Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, second edition, Springer-Verlag, 1994.
[14] Nettleton, D.J., Garigliano, R.: Evolutionar yalgorithms and a fractal inverse problem. Biosystems 33, 221-231, 1994.
[15] Rechenberg, I.: Evolution strategie: Optimierung technischer systeme nach prinzipien der biologischen evolution. Frommann-Holzboog Verlag, 1973.
[16] Shonkwiler, R., Mendivil, F., Deliu, A.: Genetic algorithms for the 1-D fractal inverse problem. Proceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, 495–501, 1991.
[17] Turner, M.J.andBlackledge, J.M., Andrews, P.R.: Fractal Geometr yin Digital Imaging. Academic Press, 1998.
[18] Yin, X. and Germay, N.: , A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization, Proc. I.C. Artificial Neural Nets and Genetic Algorithms, 450–457, 1993.
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Published
2001-10-01
How to Cite
Gutiérrez Llorente, J. M., Ivanissevich, M. L., & Cofiño, A. S. (2001). A comparison of different evolutive niching strategies for identifying a set of selfsimilar contractions for the IFS inverse problem. Journal of Computer Science and Technology, 1(05), 12 p. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/979
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