Abstract
We propose a model for the first stage of the cortical transformation of the visual image based on the principle that the cortex encodes the information with the minimum number of channels mathematically needed. We restrict our model to be consistent with the data on size adaptation, the known relationships of acuity and the inverse of magnification factor with eccentricity, and the electrophysiological findings on the physiological uniformity of the striate cortex. Assuming that each hypercolumn analyzes a limited spatial domain, we apply the sampling theorem to show that only 16 channels, composed of 4 sizes, are needed for one dimension. The extension to 2 dimensions leads to a possible scheme for the number, spacing, and orientational disposition of the elements, together with predictions about the number of inputs from the eyes and the total number of hypercolumns. Since all these predictions are consistent with physical and neural estimates, we conclude that the cortex may analyze the image along the lines we suggest.
Similar content being viewed by others
References
Barlow, H.B.: The physical limits of visual discrimination. In: Photophysiology, Vol. 2. New York: Academic Press, Inc. 1964
Barlow, H.B.: Optic nerve impulses and Weber's law. Cold Spring Harbor Symposia on Quantitative Biology 30, 539–546 (1965)
Barlow, H.B.: Retinal and central factors in human vision limited by noise. In: Photoreception in vertebrates, Barlow, H.B., Fatt, P. (eds.) pp. 337–358. London: Academic Press 1977
Barlow, H.B.: The Ferrier lecture: Critical limiting factors in the design of the eye and visual cortex. Proc. R. Soc. Lond. B (1981) (in press)
Blakemore, C., Campbell, F.W.: On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images. J. Physiol. 203, 237–260 (1969)
Bracewell, R.M.: Strip integration in radio astronomy. Aust. J. Phys. 9, 198–217 (1956)
Bracewell, R.N.: The Fourier transform and its applications. New York: McGraw-Hill Book Co. 1965
Campbell, F.W., Robson, J.G.: Applications of Fourier analysis to the visibility of gratings. J. Physiol. 197, 551–566 (1968)
Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. 1. New York: Interscience Publishers 1937
Cowan, J.D.: Some remarks on channel bandwidths for visual contrast detection. In: Neurosciences research program bulletin, Vol. 5, pp. 492–515. Poppel, Ernst, Held, Richards, Dowling (eds.) 1977
Cowey, A., Rolls, E.T.: Human cortical magnification factor and its relation to visual acuity. Exp. Brain Res. 21, 447–454 (1974)
Daniel, P.M., Whitteridge, D.: The representation of the visual field on the cerebral cortex in monkeys. J. Physiol. 159, 203–221 (1961)
DeValois, R.L., Morgan, H., Snodderly, D.M.: Psychophysical studies of monkey vision. III. Spatial luminance contrast sensitivity tests of Macaque and human observers. Vision Res. 14, 75–81 (1974)
DeValois, R.L., Albrecht, D.G., Thorell, L.G.: Cortical cells: Bar and edge detectors or spatial frequency filters? In: Frontiers in visual science, Cool, S.J., Smith, III, E.L. (eds.) pp. 544–556. Berlin, Heidelberg, New York: Springer 1978
DeValois, R.L., DeValois, K.K.: Spatial vision. Ann. Rev. Psychol. 31, 309–341 (1980)
Drasdo, N.: The neural representation of visual space. Nature 266, 554–556 (1977)
Enroth-Cugell, C., Robson, J.G.: The contrast sensitivity of retinal ganglion cells of the cat. J. Physiol. 187, 517–552 (1966)
Gabor, D.: Theory of communication. J. Inst. Electr. Eng. Part 3, 93, 429–457 (1946)
Gottfried, Kurt: Quantum mechanics. Reading, Mass. W.A. Benjamin, Inc. 1966
Hecht, S., Shlaer, S., Pirenne, N.H.: Energy, quanta, and vision. J. Gen. Physiol. 25, 819–840 (1942)
Hubel, David H., Wiesel, Torsten N.: Sequence regularity and geometry of orientation columns in the monkey striate cortex. J. Comp. Neurol. 158, 267–294 (1974a)
Hubel, David H., Wiesel, Torsten N.: Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor. J. Comp. Neurol. 158, 295–305 (1974b)
Hubel, David H., Wiesel, Torsten N., Stryker, N.P.: Anatomical demonstration of orientation columns in macaque monkey. J. Comp. Neurol. 177, 361–380 (1978)
Koenderink, J.J., Bouman, M.A., Bueno de Mesquita, A.E., Slappendel, S.: Perimetry of contrast detection thresholds of moving spatial sine wave patterns. III. The target extent as a sensitivity controlling parameter. J. Opt. Soc. Am. 68, 854–860 (1978a)
Koenderink, J.J., Doorn, van A.J.: Visual detection of spatial contrast; influence of location in the visual field, target extent and illuminance level. Biol. Cybern. 30, 157–167 (1978b)
Marr, D.: Early processing of visual information. Philos. Trans. R. Soc. (London) 275, 483–524 (1976)
Movshon, J.A., Thompson, I.D., Tolhurst, D.J.: Spatial summation in the receptive fields of simple cells in the cat's striate cortex. J. Physiol. 283, 53–77 (1978a)
Movshon, J.A., Thompson, I.D., Tolhurst, D.J.: Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat's visual cortex. J. Physiol. 283, 101–120 (1978b)
Pollen, Daniel A., Lee, James R., Taylor, Joseph H.: How does the striate cortex begin the reconstruction of the visual world? Science 173, 74–77 (1971)
Polyak, Stephen: The vertebrate visual system. Chicago: The University of Chicago Press 1957
Potts, A.M., Hodges, D., Shelman, C.B., Fritz, K.J., Levy, N.S., Mangnall, Y.: Morphology of the primate optic nerve: I. Method and total fiber count. Invest. Ophthal. 11, 980–998 (1972)
Richards, Whitman: Experiments in texture perception. Final report, Air Force Office of Scientific Research, Contract No. F44620-74-C-0076 (1978)
Robson, J.G.: Receptive fields: Neural representation of the spatial and intensive attributes of the visual image. In: Handbook of perception, Carterette, E.C., Friedman, M.P. (eds.), Vol. V., pp. 81–116 New York: Academic Press 1975
Robson, J.G.: Neutral images: The physiological basis of spatial vision. In: Visual coding and adaptability, Harris, L.S., Erlbaum, L., and associates. (eds.). New Jersey: Hillsborough 1980
Robson, J.G., Graham, N.: Probability summation and regional variation in contrast sensitivity across the visual field. Vision Res. (1981) (in press)
Rovamo, J., Virsu, V., Nasanen, R.: Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision. Nature 271, 54–56 (1978)
Sakitt, B.: Counting every quantum. J. Physiol. 223, 131–150 (1972)
Sakitt, B.: Why the cortical magnification factor in rhesus cannot be isotropic. Vision Res. (1981) (in press)
Sakitt, B., Barlow, H.B.: An economical encoding for size and position information. Psychonomic Society Abstracts (1977)
Schwartz, E.L.: Spatial mapping in the primate sensory projection: Analytic structure and relevance to perception. Biol. Cybern. 25, 181–194 (1977)
Shlaer, Simon: The relation between visual acuity and illumination. J. Gen. Physiol. 22, 165–188 (1937)
Sholl, D.A.: The organization of the cerebral cortex. (Chap. III. The general quantitative history of the cerebral cortex.) London: Methuen: New York: Wiley 1956 (New York: Reprinted by Hafner 1967)
Van Buren, J.M.: The retinal ganglion cell layer. Springfield, Illinois: Charles C. Thomas 1963
Westheimer, G.: Pupil size and visual resolution. Vision Res. 4, 39–45 (1964)
Weymouth, Frank W.: Visual sensory units and the minimal angle of resolution. Am. J. Opthal. Ser. 3 46, Part. II, 102–113 (1958)
Wilson, Hugh R., Bergen, James R.: A four mechanism model for threshold spatial vision. Vision Res. 19, 19–32 (1979)
Author information
Authors and Affiliations
Additional information
Supported by NIH grants EY 03412 and EY 02621
Rights and permissions
About this article
Cite this article
Sakitt, B., Barlow, H.B. A model for the economical encoding of the visual image in cerebral cortex. Biol. Cybern. 43, 97–108 (1982). https://doi.org/10.1007/BF00336972
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00336972