Multi-valued and Universal Binary Neurons: Learning Algorithms, Application to Image Processing and Recognition

  • Igor N. Aizenberg
  • Naum N. Aizenberg
  • Georgy A. Krivosheev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1715)


Multi-valued and universal binary neurons (MVN and UBN) are the neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partial-defined multiple-valued function on the single MVN and an arbitrary mapping described by partial-defined or fully-defined Boolean function (which can be not threshold) on the single UBN. The fast-converged learning algorithms are existing for both types of neurons. Such features of the MVN and UBN may be used for solution of the different kinds of problems. One of the most successful applications of the MVN and UBN is their usage as basic neurons in the Cellular Neural Networks (CNN) for solution of the image processing and image analysis problems. Another effective application of the MVN is their use as the basic neurons in the neural networks oriented to the image recognition.


Boolean Function Learning Rule Image Recognition Cellular Neural Network Spectral Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chua L. O. and Yang L., “Cellular neural networks: Theory”, IEEE Transactions on Circuits and Systems. Vol. 35, No 10 (1988), 1257–1290zbMATHCrossRefGoogle Scholar
  2. 2.
    Proc. of the First IEEE International Workshop on Cellular neural networks and their applications (CNNA-90)” Budapest (1990).Google Scholar
  3. 3.
    Lee C. ­. and. Pineda de Gyvez J “Color Image Processing in a Cellular Neural-Network Environment”, IEEE Trans. On Neural Networks, vol.7, No 5, (1996), 1086–1088.CrossRefGoogle Scholar
  4. 4.
    Roska T. and Chua L.O. “The CNN Universal Machine: An Analogic Array Computer”, IEEE Transactions on Circuits and Syst.-II, vol.40. (1993), 163–173.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Harrer H. and Nossek J. A. “Discrete-time cellular neural networks”,International Journal of Circuit Theory and Applications, Vol.20, (1992), 453–467.CrossRefGoogle Scholar
  6. 6.
    Aizenberg N. N., Aizenberg I. N “CNN based on multi-valued neuron as a model of associative memory for gray-scale images”, Proc. of the 2-d IEEE International Workshop on Cellular Neural Networks and their Applications, Munich, October 12–14 (1992), 36–41.Google Scholar
  7. 7.
    Aizenberg I. N. “Processing of noisy and small-detailed gray-scale images using cellular neural networks” Journal of Electronic Imaging, vol.6, No 3, (1997), 272–285.CrossRefGoogle Scholar
  8. 8.
    Aizenberg N. N., Ivaskiv Yu.L Multiple-Valued Threshold Logic. Naukova Dumka, Kiev, (1977) (in Russian)Google Scholar
  9. 9.
    Aizenberg N. N., Aizenberg I. N. “Fast Convergenced Learning Algorithms for Multi-Level and Universal Binary Neurons and Solving of the some Image Processing Problems”, Lecture Notes in Computer Science, Ed.-J. Mira, J. Cabestany, A. Prieto, Vol.686, Springer-Verlag, Berlin-Heidelberg(1993), 230–236.Google Scholar
  10. 10.
    Aizenberg N. N., Aizenberg I. N.. Krivosheev G.A. “Multi-Valued Neurons: Learning, Networks, Application to Image Recognition and Extrapolation of Temporal Series”, Lecture Notes in Computer Science, Vol.930, (J. Mira, F. Sandoval ­ Eds.), Springer-Verlag, (1995), 389–395.Google Scholar
  11. 11.
    Aizenberg N.N., Aizenberg I.N., Krivosheev G.A. “Multi-Valued Neurons: Mathematical model, Networks, Application to Pattern Recognition”, Proc. of the 13 Int.Conf. on Pattern Recognition, Vienna, August 25-30,1996,Track D, IEEE Computer Soc. Press, (1996), 185–189.Google Scholar
  12. 12.
    Jankowski S., Lozowski A., Zurada M. “Complex-Valued Multistate Neural Associative Memory”, IEEE Trans. on Neural Networks, Vol. 7, (1996), 1491–1496.CrossRefGoogle Scholar
  13. 13.
    Petkov N., Kruizinga P., Lourens T. “Motivated Approach to Face Recognition”, Lecture Notes in Computer Science, Vol. 686, (J. Mira, F. Sandoval ­ Eds.), Springer-Verlag, (1993), 68–77.Google Scholar
  14. 14.
    Lawrence S., Lee Giles C., Ah Chung Tsoi and Back A. D.“Face Recognition:A Convolutional Neural-Network Approach”, IEEE Trans. on Neural Networks, Vol.8, (1997), pp. 98–113.CrossRefGoogle Scholar
  15. 15.
    Foltyniewicz R. “Automatic Face Recognition via Wavelets and Mathematical Morphology”, Proc. of the 13 Int. Conf. on Pattern Recognition, Vienna, August 25-30, 1996, Track B, IEEE Computer Soc. Press, (1996), 13–17.Google Scholar
  16. 16.
    N. Ahmed, K.R. Rao “Orthogonal Transforms for Digital Signal Processing”, Springer Verlag (1975).Google Scholar
  17. 17.
    Haykin S. Neural Networks. A Comprehensive Foundation. Macmillan College Publishing Company, New York, 1994.Google Scholar
  18. 18.
    Oppenheim A.V. and. Lim S.J“The importance of phase in signals”, Proc. IEEE, Vol.69, (1981), pp. 529–541.CrossRefGoogle Scholar
  19. 19.
    Turk M. and Petland A. “Eigenfaces for Recognition”, Journal of Cognitive Neuroscience, Vol.3, (1991).Google Scholar
  20. 20.
    Aizenberg I.N., Aizenberg N.N., Agaian S., Astola J., Egiazarian K. “Nonlinear cellular neural filtering for noise reduction and extraction of image details”, SPIE Proceedings, Vol. 3646, 1999, pp.100–111.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Igor N. Aizenberg
    • 1
  • Naum N. Aizenberg
    • 1
  • Georgy A. Krivosheev
    • 2
  1. 1.Minaiskaya 28UzhgorodUkraine
  2. 2.Paustovskogo 3MoscowRussia

Personalised recommendations