Biological Cybernetics

, Volume 68, Issue 5, pp 465–476 | Cite as

Emergence of orientation selective simple cells simulated in deterministic and stochastic neural networks

  • M. Stetter
  • E. W. Lang
  • A. Müller


The processing of visual data in area 17 of the mammalian cortex is mainly performed by cells with receptive fields which are tuned to different orientations of input stimuli. The mechanisms underlying the emergence of receptive field properties of orientation selective cells are not well understood up to now. Recently, some models for the prenatal development of the receptive fields of orientation selective simple cells have been proposed, which emerge in neural networks trained by Hebb type unsupervised learning rules. These models, however, use different network architectures and are restricted to the case of identical input neurons. In this work, a biologically motivated neural network model with a general architecture is presented. It is trained with a Hebb type updating rule and with uncorrelated input. The input neurons are identified with retinal ganglion cells and exhibit mature Mexican hat type receptive fields. If the receptive fields of the input neurons have identical properties (deterministic model), a set of parameter domains is found, which characterize different kinds of receptive field maturation behaviour of the network. Results obtained by other authors with similar models are contained in this description as special cases. In addition, the more general and rarely investigated stochastic model, where random variations of the parameters describing the receptive fields of the input neurons occur, is investigated. A high sensitivity of the network against these random variations is obtained. In case of large variations of receptive field parameters of the ganglion cells, a qualitatively new kind of maturation behaviour appears. A significant part of the synaptic connections from ganglion cells to the cortical cell is removed and small simple cell receptive fields with only few lobes emerge. The stochastic model is found to provide a better description of the size, scatter and structure of receptive fields present in biological systems, than the deterministic model.


Ganglion Cell Receptive Field Retinal Ganglion Cell Deterministic Model Input Neuron 
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.


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  1. Brown TH, Kairiss EW, Keenan CL (1990) Hebbian synapses: Biophysical mechanisms and algorithms. Annu Rev Neurosci 13:475–511Google Scholar
  2. Daughman JG (1985) Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. J Opt Soc Am A 2:1160–1169Google Scholar
  3. Hebb DO (1949) The organization of behaviour. Wiley, New YorkGoogle Scholar
  4. Hubel DH, Wiesel TN (1959) Receptive fields of single neurones in the cat's striate cortex. J Physiol (London) 148:574–591Google Scholar
  5. Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J Physiol (London) 160:106–154Google Scholar
  6. Hubel DH, Wiesel TN (1968) Receptive fields and functional architecture of monkey striate cortex. J Physiol (London) 195:215–243Google Scholar
  7. Hubel DH, Wiesel TN (1974) Uniformity of monkey striate cortex: A parallel relationship between field size, scatter, and magnification factor. J Comp Neurol 158:295–306Google Scholar
  8. Hubel DH, Wiesel TN (1977) Functional architecture of macaque monkey visual cortex. Proc R Soc London Ser B 198:1–59Google Scholar
  9. Humphrey AL, Sur M, Uhlrich DJ, Sherman SM (1985) Projection patterns of individual X- and Y-cell axons from the lateral geniculate nucleus to cortical area 17 in the cat. J Comp Neurol 233:159–189Google Scholar
  10. Kammen DM, Yuille AL (1988) Spontaneous symmetry-breaking energy functions and the emergence of orientation selective cortical cells. Biol Cybern 59:23–31Google Scholar
  11. Levick WR, Thibos LN (1980) Orientation bias of cat retinal ganglion cells. Nature 286:389–390Google Scholar
  12. Linsker R (1986a) From basic network principles to neural architecture: Emergence of spatial-opponent cells. Proc Natl Acad Sci USA 83:7508–7512Google Scholar
  13. Linsker R (1986b) From basic network principles to neural architecture: Emergence of orientation-selective cells. Proc Natl Acad Sci USA 83:8390–8394Google Scholar
  14. Linsker R (1990a) Designing a sensory processing system: What can be learned from principal component analysis. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN), (Washington, DC, 16–19 January 1990)Google Scholar
  15. Linsker R (1990b) Perceptual neural organization: Some approaches based on network models and information theory. Annu Rev Neurosci 13:257–281Google Scholar
  16. Lund JS (1988) Anatomical organization of macaque monkey striate visual cortex. Annu Rev Neurosci 11:253–288Google Scholar
  17. Marcelja S (1980) Mathematical description of the responses of simple cortical cells. J Opt Soc Am 70:1297–1300Google Scholar
  18. Mumford D (1991) On the computational architecture of the neocortex. I. The role of the thalamo-cortical loop. Biol Cybern 65:135–145Google Scholar
  19. Oja E (1982) A simplified neuron model as a principal component analyzer. J Math Biol 15:267–273Google Scholar
  20. Rockel AJ, Hiorns RW, Powell TPS (1980) The basic uniformity in structure of the neocortex. Brain 103:221–244Google Scholar
  21. Schiller PH, Finlay BL, Volman SF (1976a) Quantitative studies of single-cell properties in monkey striate cortex. I. Spatiotemporal organization of receptive fields. J Neurophysiol 39:1288–1319Google Scholar
  22. Schiller PH, Finlay BL, Volman SF (1976b) Quantitative studies of single-cell properties in monkey striate cortex. II. Orientation specificity and ocular dominance. J Neurophysiol 39:1320–1333Google Scholar
  23. Shou T, Leventhal, AG (1989) Organized arrangement of orientation-sensitive relay cells in the cat's dorsal lateral geniculate nucleus. J Neurosci 9:4287–4302Google Scholar
  24. Wiesel TN, Hubel DH (1974) Ordered arrangement of orientation columns in monkeys lacking visual experience. J Comp Neurol 158:307–318Google Scholar
  25. Wörgötter F, Koch C (1991) A detailed model of the primary visual athway in the cat: Comparison of afferent excitatory and intracortical inhibitory connection schemes for orientation selectivity. J Neurosci 11:1959–1979Google Scholar
  26. Yuille AL, Kammen DM, Cohen DS (1989) Quadrature and the development of orientation selective cortical cells by Hebb rules. Biol Cybern 61:183–194Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. Stetter
    • 1
  • E. W. Lang
    • 1
  • A. Müller
    • 1
  1. 1.Institut für Biophysik und physikalische BiochemieUniversität RegensburgRegensburgGermany

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