Letter | Published:

Network model of shape-from-shading: neural function arises from both receptive and projective fields

Naturevolume 333pages452454 (1988) | Download Citation



It is not known how the visual system is organized to extract information about shape from the continuous gradations of light and dark found on shaded surfaces of three-dimensional objects1,2. To investigate this question3,4, we used a learning algorithm to construct a neural network model which determines surface curvatures from images of simple geometrical surfaces. The receptive fields developed by units in the network were surprisingly similar to the actual receptive fields of neurons observed in the visual cortex5,6 which are commonly believed to be 'edge' or 'bar' detectors, but have never previously been associated with shading. Thus, our study illustrates the difficulty of trying to deduce neuronal function solely from determination of their receptive fields. It is also important to consider the connections a neuron makes with other neurons in subsequent stages of processing, which we call its 'projective field'.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1

    Ramachandran, V. S. Nature 331, 163–166 (1988).

  2. 2

    Mingolla, E. & Todd, J. T. Biol. Cyber. 53, 137–151 (1986).

  3. 3

    Ikeuchi, K. & Horn, B. K. P. Art. Intell. 17, 141–184 (1981).

  4. 4

    Pentland, A. P. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 170–187 (1984).

  5. 5

    Hubel, D. H. & Wiesel, T. N. J. Physiol., Lond. 160, 106–154 (1962).

  6. 6

    Hubel, D. H. & Wiesel, T. N. J. Neurophysiol. 28, 229–289 (1965).

  7. 7

    Rumelhart, D. E., Hinton, G. E. & Williams, R. J. in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. 1 (eds Rumelhart, D. E. & McClelland, J. L.) 318–362 (MIT Press, Cambridge, 1986).

  8. 8

    Mullikan, W. H., Jones, J. P. & Palmer, L. A. J. Neurophysiol. 52, 372–387 (1984).

Download references

Author information


  1. Department of Biophysics, Johns Hopkins University, Baltimore, Maryland, 21218, USA

    • Sidney R. Lehky
    •  & Terrence J. Sejnowski


  1. Search for Sidney R. Lehky in:

  2. Search for Terrence J. Sejnowski in:

About this article

Publication history



Issue Date



Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.