An Evolutionary Approach to Inverse Gray Level Quantization

  • Ivan Gerace
  • Marcello Mastroleo
  • Alfredo Milani
  • Simona Moraglia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4781)


The gray levels quantization technique is used to generate images which limit the number of color levels resulting in a reduction of the image size, while it preserves the quality perceived by human observers. The problem is very relevant for image storage and web distribution, as well as in the case of devices with limited bandwidth, storage and/or computational capabilities. An efficient evolutionary algorithm for the inverse gray level quantization problem, based on a technique of dynamical local fitness evaluation, is presented. A population of blur operators is evolved with a fitness given by the energy function to be minimized. In order to avoid the unfeasible computational overhead due to the fitness evaluation calculated on the entire image, an innovative technique of dynamical local fitness evaluation has been designed and integrated in the evolutionary scheme. The sub–image evaluation area is dynamically changed during evolution of the population, and the evolutionary scheme operates a form of machine learning while exploring subarea which are significatively representative of the global image. The experimental results confirm the adequacy of such a method.


evolutionary algorithms image compression machine learning 


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  1. 1.
    Bedini, L., Gerace, I., Salerno, E., Tonazzini, A.: Models and Algorithms for Edge-Preserving Image Reconstruction. Advances in Imaging and Electron Physics 97, 86–189 (1996)Google Scholar
  2. 2.
    Bedini, L., Gerace, I., Tonazzini, A.: A Deterministic Algorithm for Reconstruction Images with Interacting Discontinuities. CVGIP: Graphical Models Image Process 56, 109–123 (1994)CrossRefGoogle Scholar
  3. 3.
    Blake, A.: Comparison of the Efficiency of Deterministic and Stochastic Algorithms for Visual Reconstruction. IEEE Trans. Pattern Anal. Machine Intell. 11, 2–12 (1989)zbMATHCrossRefGoogle Scholar
  4. 4.
    Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge, MA (1987)Google Scholar
  5. 5.
    Gerace, I., Martinelli, F., Sanchini, G.: Estimation of the free parameters in th problem of edge-preserving image reconstraction by a shooting method. In: SMMSP 2006. The 2006 International TICSP Workshopo on Spectral Methods and Multirate Signal Processing, Florence, Italy, pp. 205–212 (2006)Google Scholar
  6. 6.
    Gerace, I., Pandolfi, R., Pucci, P.: A new GNC Algorithm for Spatial Dithering. In: SMMSP2003. proceedings of the 2003 International Workshop on Spectral Methods and Multirate Signal Processing, pp. 109–114 (2003)Google Scholar
  7. 7.
    Gerace, I., Pandolfi, R., Pucci, P.: A new estimation of blur in the blind restoration problem. In: ICIP 2003. proceeding of IEEE International Conference on Image Processing, p. 4. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar
  8. 8.
    Geman, D., Reynolds, G.: Constrained Restoration and the Recovery of Discontinuities. IEEE Trans. Pattern Anal. Machine Intell. 14, 367–383 (1992)CrossRefGoogle Scholar
  9. 9.
    Goldberg, D., Debb, K.: A comparative analysis of selection schemes used in Genetic Algorithms. In: Rawlins, G.J.E. (ed.) Foundation of genetic Algorithms, Morgan Kaufman, San Francisco (1991)Google Scholar
  10. 10.
    Hansen, C.: Analysis of Discrete Ill-Posed Problems By Means of the L-Curve. SIAM Review 34, 561–580 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Holland, S.H.: Adaptation in natural and artificial systems. The University of Michigan press, Ann Arbor, MI (1975)Google Scholar
  12. 12.
    Li, S.Z.: Roof-Edge Preserving Image Smoothing Based on MRFs. IEEE Trans. Image Process 9, 1134–1138 (2000)CrossRefGoogle Scholar
  13. 13.
    Nikolova, M.: Markovian Reconstruction Using a GNC Approach. IEEE Trans. Image Process 8, 1204–1220 (1999)CrossRefGoogle Scholar
  14. 14.
    Reginska, T.: A Regularization Parameter in Discrete Ill-Posed Problems. SIAM J. Sci. Comput. 17, 740–749 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sokolov, A., Whitley, D.: Unbiased tournament selection. In: Proceeding of GECCO 2005, Washington, DC, USA, pp. 1131–1138 (2005)Google Scholar
  16. 16.
    Stevenson, R.L.: Inverse Halftoning via MAP Estimation. IEEE Trans. Image Process 6, 574–583 (1997)CrossRefGoogle Scholar
  17. 17.
    Tonazzini, A.: Blur Identification Analysis in Blind Image Deconvolution Using Markov Random Fields. Pattern Recogn. and Image Analysis 11, 669–710 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ivan Gerace
    • 1
  • Marcello Mastroleo
    • 1
  • Alfredo Milani
    • 1
  • Simona Moraglia
    • 2
  1. 1.Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, I-06123 PGItaly
  2. 2.Dipartimento di Ingegneria Industriale, Università degli Studi di Perugia, via Duranti 67, I-06125 PerugiaItaly

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