Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns

  • Kenneth D. Miller
Part of the Physics of Neural Networks book series (NEURAL NETWORKS)


The formation of ocular dominance and orientation columns in the mammalian visual cortex is briefly reviewed. Correlation-based models for their development are then discussed, beginning with the models of Von der Malsburg. For the case of semilinear models, model behavior is well understood: correlations determine receptive field structure, intracortical interactions determine projective field structure, and the “knitting together” of the two determines the cortical map. This provides a basis for simple but powerful models of ocular dominance and orientation column formation: ocular dominance columns form through a correlation-based competition between left-eye and right-eye inputs, while orientation columns can form through a competition between ON-center and OFF-center inputs. These models account well for receptive field structure but are not completely adequate to account for the details of cortical map structure. Alternative approaches to map structure, including the self-organizing feature map of Kohonen, are discussed. Finally, theories of the computational function of correlation-based and self-organizing rules are discussed.


Visual Cortex Receptive Field Cortical Cell Input Pattern Orientation Selectivity 
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. [1]
    K. Albus, W. Wolf (1984) Early post-natal development of neuronal function in the kitten’s visual cortex: A laminar analysis. J. Physiol. 348:153–185Google Scholar
  2. [2]
    J.J. Atick (1992) Could information theory provide an ecological theory of sensory processing? In: Princeton Lectures on Biophysics, W. Bialek (Ed.) (World Scientific, Singapore), pp. 223–289Google Scholar
  3. [3]
    H.B. Barlow (1989) Unsupervised learning. Neural Comp. 1:295–311CrossRefGoogle Scholar
  4. [4]
    B.O. Braastad, P. Heggelund (1985) Development of spatial receptive-field organization and orientation selectivity in kitten striate cortex. J. Neurophysiol. 53:1158–1178Google Scholar
  5. [5]
    E.M. Callaway, L.C. Katz (1990) Emergence and refinement of clustered horizontal connections in cat striate cortex. J. Neurosci. 10:1134–1153Google Scholar
  6. [6]
    B. Chapman, M.P. Stryker (1993) Development of orientation selectivity in ferret visual cortex and effects of deprivation. J. Neurosci. 13:5251–5262Google Scholar
  7. [7]
    M. Constantine-Paton, H.T. Cline, E. Debski (1990) Patterned activity, synaptic convergence and the NMDA receptor in developing visual pathways. Ann. Rev. Neurosci. 13:129–154CrossRefGoogle Scholar
  8. [8]
    R. Durbin, G. Mitchison (1990) A dimension reduction framework for understanding cortical maps. Nature 343:644–647ADSCrossRefGoogle Scholar
  9. [9]
    E. Erwin, K. Obermayer, K. Schulten (1995) Models of orientation and ocular dominance columns in the visual cortex: A critical comparison. Neural Comp. 7:425–468CrossRefGoogle Scholar
  10. [10]
    P. Foldiak (1989) Adaptive network for optimal linear feature extraction. In: Proceedings, IEEE/INNS International Joint Conference on Neural Networks, Vol. 1 (IEEE Press, New York), pp. 401–405CrossRefGoogle Scholar
  11. [11]
    Y. Fregnac, M. Imbert (1984) Development of neuronal selectivity in the primary visual cortex of the cat. Physiol. Rev. 64:325–434Google Scholar
  12. [12]
    G.J. Goodhill (1993) Topography and ocular dominance: A model exploring positive correlations. Biol. Cybern. 69:109–118CrossRefGoogle Scholar
  13. [13]
    G.J. Goodhill, D.J. Willshaw (1990) Application of the elastic net algorithm to the formation of ocular dominance stripes. Network 1:41–59MathSciNetCrossRefGoogle Scholar
  14. [14]
    C.S. Goodman, C.J. Shatz (1993) Developmental mechanisms that generate precise patterns of neuronal connectivity. Cell 72(Suppl):77–98CrossRefGoogle Scholar
  15. [15]
    R.W. Guillery (1972) Binocular competition in the control of geniculate cell growth. J. Comp. Neurol. 144:117–130CrossRefGoogle Scholar
  16. [16]
    R.W. Guillery, D.J. Stelzner (1970) The differential effects of unilateral lid closure upon the monocular and binocular segments of the dorsal lateral geniculate nucleus in the cat. J. Comp. Neurol. 139:413–422CrossRefGoogle Scholar
  17. [17]
    J.A. Hertz, A.S. Krogh, R.G. Palmer (1991) Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, MA)Google Scholar
  18. [18]
    J. J. Hopfield (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79Google Scholar
  19. [19]
    J.J. Hopfield (1984) Neurons with graded responses have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 81Google Scholar
  20. [20]
    D.H. Hubel, T.N. Wiesel (1963) Receptive fields of cells in striate cortex of very young, visually inexperienced kittens. J. Neurophysiol. 26:994–1002Google Scholar
  21. [21]
    M. Idiart, B. Berk, L.F. Abbott (1995) Reduced representation by neural networks with restricted receptive fields. Neural Comp. 7:507–517CrossRefGoogle Scholar
  22. [22]
    N. Intrator (1992) Feature extraction using an unsupervised neural network. Neural Computation 4:98–107CrossRefGoogle Scholar
  23. [23]
    N. Intrator, L.N. Cooper (1992) Objective function formulation of the BCM theory of visual cortical plasticity: Statistical connections, stability conditions. Neural Networks 5:3–17CrossRefGoogle Scholar
  24. [24]
    T. Kohonen (1989) Self-Organization and Associative Memory, 3rd ed. (Springer-Verlag, Berlin)CrossRefGoogle Scholar
  25. [25]
    S. LeVay, T.N. Wiesel, D.H. Hubel (1980) The development of ocular dominance columns in normal and visually deprived monkeys. J. Comp. Neurol. 191:1–51CrossRefGoogle Scholar
  26. [26]
    Z. Li, J.J. Atick (1994) Efficient stereo coding in the multiscale representation. Network 5:157–174MATHCrossRefGoogle Scholar
  27. [27]
    R. Linsker (1986) From basic network principles to neural architecture: Emergence of spatial-opponent cells. Proc. Natl. Acad. Sci. USA 83:7508–7512ADSCrossRefGoogle Scholar
  28. [28]
    R. Linsker (1986) Prom basic network principles to neural architecture: Emergence of orientation-selective cells. Proc. Natl. Acad. Sci. USA 83:8390–8394ADSCrossRefGoogle Scholar
  29. [29]
    R. Linsker (1986) From basic network principles to neural architecture: Emergence of orientation columns. Proc. Natl. Acad. Sci. USA 83:8779–8783ADSCrossRefGoogle Scholar
  30. [30]
    R. Linsker (1988) Self-organization in a perceptual network. Computer 21:105–117CrossRefGoogle Scholar
  31. [31]
    R. Linsker (1992) Local synaptic learning rules suffice to maximize mutual information in a linear network. Neural Comput. 4:691–702CrossRefGoogle Scholar
  32. [32]
    S. Löwel, W. Singer (1993) Strabismus changes the spacing of ocular dominance columns in the visual cortex of cats. Soc. Neuro. Abs. 19:867Google Scholar
  33. [33]
    S. Luttrell (1994) A Bayesian analysis of self-organizing maps. Neural Comp. 6:767–794MATHCrossRefGoogle Scholar
  34. [34]
    D. J.C. MacKay, K.D. Miller (1990) Analysis of Linsker’s applications of Hebbian rules to linear networks. Network 1:257–298MathSciNetMATHCrossRefGoogle Scholar
  35. [35]
    D.J.C. MacKay, K.D. Miller (1990) Analysis of Linsker’s simulations of Hebbian rules. Neural Comput. 2:173–187CrossRefGoogle Scholar
  36. [36]
    L. Maffei, L. Galli-Resta (1990) Correlation in the discharges of neighboring rat retinal ganglion cells during prenatal life. Proc. Nat. Acad. Sci. USA 87:2861–2864ADSCrossRefGoogle Scholar
  37. [37]
    D.N. Mastronarde (1989) Correlated firing of retinal ganglion cells. Trends Neu-rosci. 12:75–80CrossRefGoogle Scholar
  38. [38]
    M. Meister, R.O.L. Wong, D.A. Baylor, C.J. Shatz (1991) Synchronous bursts of action-potentials in ganglion cells of the developing mammalian retina. Science 252:939–943ADSCrossRefGoogle Scholar
  39. [39]
    K.D. Miller (1990) Correlation-based models of neural development. In: Neuro-science and Connectionist Theory, M.A. Gluck, D.E. Rumelhart, (Eds.) (Lawrence Erlbaum, Hillsdale, NJ), pp. 267–353Google Scholar
  40. [40]
    K.D. Miller (1990) Derivation of linear Hebbian equations from a nonlinear Hebbian model of synaptic plasticity. Neural Comput. 2:321–333CrossRefGoogle Scholar
  41. [41]
    K.D. Miller (1994) A model for the development of simple cell receptive fields and the ordered arrangement of orientation columns through activity-dependent competition between ON-and OFF-center inputs. J. Neurosci. 14:409–441Google Scholar
  42. [42]
    K.D. Miller, J.B. Keller, M.P. Stryker (1989) Ocular dominance column development: Analysis and simulation. Science 245:605–615ADSCrossRefGoogle Scholar
  43. [43]
    K.D. Miller, D.J.C. MacKay (1994) The role of constraints in Hebbian learning. Neural Comput. 6:100–126CrossRefGoogle Scholar
  44. [44]
    K.D. Miller, M.P. Stryker (1990) The development of ocular dominance columns: Mechanisms and models. In: Connectionist Modeling and Brain Function: The Developing Interface, S.J. Hanson, C.R. Olson (Eds.) (MIT Press/Bradford, Cambridge, MA), pp. 255–350Google Scholar
  45. [45]
    M. Miyashita, S. Tanaka (1992) A mathematical model for the self-organization of orientation columns in visual cortex. NeuroReport 3:69–72CrossRefGoogle Scholar
  46. [46]
    K. Obermayer, G.G. Blasdel, K. Schulten (1992) A statistical mechanical analysis of self-organization and pattern formation during the development of visual maps. Phys. Rev. A 45:7568–7589ADSCrossRefGoogle Scholar
  47. [47]
    E. Oja (1982) A simplified neuron model as a principal component analyzer. J. Math. Biol. 15:267–273MathSciNetMATHCrossRefGoogle Scholar
  48. [48]
    H. Ritter, T. Martinetz, K. Schulten (1992) Neural Computation and Self-Organizing Maps: An Introduction (Addison-Wesley, Reading, MA)MATHGoogle Scholar
  49. [49]
    J. Rubner, K. Schulten (1990) Development of feature detectors by selforganization. Biol. Cybern. 62:193–199CrossRefGoogle Scholar
  50. [50]
    T.D. Sanger (1989) An optimality principle for unsupervised learning. In: Advances in Neural Information Processing Systems, Vol. 1, D. Touretzky (Ed.) (Morgan Kaufmann, San Mateo, CA), pp. 11–19Google Scholar
  51. [51]
    C.J. Shatz (1992) The developing brain. Scientific Am. 267:60–67CrossRefGoogle Scholar
  52. [52]
    C.J. Shatz, M.P. Stryker (1978) Ocular dominance in layer IV of the cat’s visual cortex and the effects of monocular deprivation. J. Physiol. 281:267–283Google Scholar
  53. [53]
    J. Sirosh, R. Mikkulainen (1995) A unified neural network model for the selforganization of topographic receptive fields and lateral interactions. Neural Cornput (to appear)Google Scholar
  54. [54]
    M.P. Stryker, S.L. Strickland (1984) Physiological segregation of ocular dominance columns depends on the pattern of afferent electrical activity. Inv. Opthal. Supp. 25:278Google Scholar
  55. [55]
    N.V. Swindale (1992) A model for the coordinated development of columnar systems in primate striate cortex. Biol. Cyb. 66:217–230CrossRefGoogle Scholar
  56. [56]
    S. Tanaka (1991) Theory of ocular dominance column formation: Mathematical basis and computer simulation. Biol. Cybern. 64:263–272CrossRefGoogle Scholar
  57. [57]
    C. von der Malsburg (1973) Self-organization of orientation selective cells in the striate cortex. Kybernetik 14:85–100CrossRefGoogle Scholar
  58. [58]
    C. von der Malsburg (1993) Network self-organization in the ontogenesis of the mammalian visual system. Internal Report 93-06, Ruhr-Universität Bochum, Institut für Neuroinformatik, 44780 Bochum, GermanyGoogle Scholar
  59. [59]
    C. von der Malsburg, D. J. Willshaw (1976) A mechanism for producing continuous neural mappings: ocularity dominance stripes and ordered retino-tectal projections. Exp. Brain Res. (Supp.) 1:463–469Google Scholar
  60. [60]
    T.N. Wiesel, D.H. Hubel (1965) Comparison of the effects of unilateral and bilateral eye closure on cortical unit responses in kittens. J. Neurophysiol. 28:1029–1040Google Scholar
  61. [61]
    T.N. Wiesel, D.H. Hubel (1974) Ordered arrangement of orientation columns in monkeys lacking visual experience. J. Comp. Neurol. 158:307–318CrossRefGoogle Scholar
  62. [62]
    F. Wolf, H-U. Bauer, T. Geisel (1994) Formation of field discontinuities and islands in visual cortical maps. Biol. Cyb. 70:525–531MATHCrossRefGoogle Scholar
  63. [63]
    F. Wolf, K. Pawelzik, T. Geisel, D.S. Kim, T. Bonhoeffer (1994) Optimal smoothness of orientation preference maps. In: Computation in Neurons and Neural Systems (Kluwer, Boston), pp. 97–102CrossRefGoogle Scholar
  64. [64]
    R.O. Wong, M. Meister, C.J. Shatz (1993) Transient period of correlated bursting activity during development of the mammalian retina. Neuron 11:923–938CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Kenneth D. Miller
    • 1
  1. 1.Departments of Physiology and Otolaryngology, W.M. Keck Center for Integrative Neuroscience, and Sloan Center for Theoretical NeurobiologyUniversity of CaliforniaSan FranciscoUSA

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