Abstract

A two-dimensional, time-dependent analysis of the mammalian retina is presented. A computer simulation of experimental data considers ganglion-cell activity as a two-dimensional process. The properties of the simulation model were examined with several input stimuli. Circular receptive fields enhance not only borders, but other spatial complexities, such as ends of lines and angles. The enhancement is remarkably insensitive to the shape of receptive fields. The processing of the input picture by on-center and off-center receptive fields is complementary but the division of labor varies with the task.

© 1975 Optical Society of America

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References

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  1. G. von Békésy, Sensory Inhibition (Princeton U. P., Princeton, New Jersey, 1967).
  2. F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, San Francisco, 1965).
  3. R. W. Rodieck, Vision Res. 5, 583 (1965).
    [Crossref] [PubMed]
  4. K. Fukushima, IEEE Trans. SSC-5, 322 (1969).
  5. K. Fukushima, Kybernetik 7, 153 (1970).
    [Crossref] [PubMed]
  6. P. Gouras, J. Physiol. 192, 747 (1967).
  7. D. H. Hubel and T. N. Wiesel, J. Physiol. 154, 572 (1960).
  8. S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
    [PubMed]
  9. H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).
  10. A. Fiorentini, in Handbook of Sensory Physiology, Vol. 7/4, Visual Psychophysics, edited by D. Jameson and L. M. Hurvich (Springer, Berlin, 1972), p. 188.
    [Crossref]
  11. E. Mach, Sitzungsberichte der mathematisch-naturwissen-schaftlichen Classe der kaiserlichen Akademie der Wissen-schaften 52, 303 (1865) (translation in Ref. 2).
  12. G. Baumgartner, J. L. Brown, and A. Schulz, J. Neurophysiol. 28, 1 (1965).
    [PubMed]
  13. G. von Békésy, J. Opt. Soc. Am. 50, 1060 (1960).
    [Crossref]
  14. G. von Békésy, J. Opt. Soc. Am. 58, 1 (1968).
    [Crossref]
  15. L. Maffei, A. Fiorentini, and L. Cervetto, J. Neurophysiol. 34, 579 (1971).
    [PubMed]
  16. R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 819 (1965).
    [PubMed]
  17. R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).
  18. D. N. Spinelli, Science 152, 1768 (1966).
    [Crossref]
  19. F. W. Campbell and R. W. Gubisch, J. Physiol. 186, 558 (1966).
  20. H. Wässle and O. D. Creutzfeldt, J. Neurophysiol. 36, 13 (1973).
  21. R. Jung, in Sensory Communication, edited by W. A. Rosenblith (MIT Press, Cambridge, Mass., 1961), pp. 627 and 796.
  22. H. B. Barlow, R. Narasimhan, and A. Rosenfeld, Science 177, 567 (1972).
    [Crossref] [PubMed]
  23. A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
    [Crossref]
  24. L. Maffei and A. Fiorentini, J. Neurophysiol. 35, 65 (1972).
    [PubMed]

1973 (1)

H. Wässle and O. D. Creutzfeldt, J. Neurophysiol. 36, 13 (1973).

1972 (2)

H. B. Barlow, R. Narasimhan, and A. Rosenfeld, Science 177, 567 (1972).
[Crossref] [PubMed]

L. Maffei and A. Fiorentini, J. Neurophysiol. 35, 65 (1972).
[PubMed]

1971 (1)

L. Maffei, A. Fiorentini, and L. Cervetto, J. Neurophysiol. 34, 579 (1971).
[PubMed]

1970 (1)

K. Fukushima, Kybernetik 7, 153 (1970).
[Crossref] [PubMed]

1969 (1)

K. Fukushima, IEEE Trans. SSC-5, 322 (1969).

1968 (2)

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[Crossref]

G. von Békésy, J. Opt. Soc. Am. 58, 1 (1968).
[Crossref]

1967 (1)

P. Gouras, J. Physiol. 192, 747 (1967).

1966 (2)

D. N. Spinelli, Science 152, 1768 (1966).
[Crossref]

F. W. Campbell and R. W. Gubisch, J. Physiol. 186, 558 (1966).

1965 (4)

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 819 (1965).
[PubMed]

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

G. Baumgartner, J. L. Brown, and A. Schulz, J. Neurophysiol. 28, 1 (1965).
[PubMed]

R. W. Rodieck, Vision Res. 5, 583 (1965).
[Crossref] [PubMed]

1960 (2)

D. H. Hubel and T. N. Wiesel, J. Physiol. 154, 572 (1960).

G. von Békésy, J. Opt. Soc. Am. 50, 1060 (1960).
[Crossref]

1957 (1)

H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

1953 (1)

S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
[PubMed]

1865 (1)

E. Mach, Sitzungsberichte der mathematisch-naturwissen-schaftlichen Classe der kaiserlichen Akademie der Wissen-schaften 52, 303 (1865) (translation in Ref. 2).

Barlow, H. B.

H. B. Barlow, R. Narasimhan, and A. Rosenfeld, Science 177, 567 (1972).
[Crossref] [PubMed]

H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

Baumgartner, G.

G. Baumgartner, J. L. Brown, and A. Schulz, J. Neurophysiol. 28, 1 (1965).
[PubMed]

Brown, J. L.

G. Baumgartner, J. L. Brown, and A. Schulz, J. Neurophysiol. 28, 1 (1965).
[PubMed]

Campbell, F. W.

F. W. Campbell and R. W. Gubisch, J. Physiol. 186, 558 (1966).

Cervetto, L.

L. Maffei, A. Fiorentini, and L. Cervetto, J. Neurophysiol. 34, 579 (1971).
[PubMed]

Creutzfeldt, O. D.

H. Wässle and O. D. Creutzfeldt, J. Neurophysiol. 36, 13 (1973).

Fiorentini, A.

L. Maffei and A. Fiorentini, J. Neurophysiol. 35, 65 (1972).
[PubMed]

L. Maffei, A. Fiorentini, and L. Cervetto, J. Neurophysiol. 34, 579 (1971).
[PubMed]

A. Fiorentini, in Handbook of Sensory Physiology, Vol. 7/4, Visual Psychophysics, edited by D. Jameson and L. M. Hurvich (Springer, Berlin, 1972), p. 188.
[Crossref]

FitzHugh, R.

H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

Fukushima, K.

K. Fukushima, Kybernetik 7, 153 (1970).
[Crossref] [PubMed]

K. Fukushima, IEEE Trans. SSC-5, 322 (1969).

Gouras, P.

P. Gouras, J. Physiol. 192, 747 (1967).

Gubisch, R. W.

F. W. Campbell and R. W. Gubisch, J. Physiol. 186, 558 (1966).

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, J. Physiol. 154, 572 (1960).

Jung, R.

R. Jung, in Sensory Communication, edited by W. A. Rosenblith (MIT Press, Cambridge, Mass., 1961), pp. 627 and 796.

Kuffler, S. W.

H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
[PubMed]

Mach, E.

E. Mach, Sitzungsberichte der mathematisch-naturwissen-schaftlichen Classe der kaiserlichen Akademie der Wissen-schaften 52, 303 (1865) (translation in Ref. 2).

Maffei, L.

L. Maffei and A. Fiorentini, J. Neurophysiol. 35, 65 (1972).
[PubMed]

L. Maffei, A. Fiorentini, and L. Cervetto, J. Neurophysiol. 34, 579 (1971).
[PubMed]

Narasimhan, R.

H. B. Barlow, R. Narasimhan, and A. Rosenfeld, Science 177, 567 (1972).
[Crossref] [PubMed]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[Crossref]

Ratliff, F.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, San Francisco, 1965).

Rodieck, R. W.

R. W. Rodieck, Vision Res. 5, 583 (1965).
[Crossref] [PubMed]

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 819 (1965).
[PubMed]

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

Rosenfeld, A.

H. B. Barlow, R. Narasimhan, and A. Rosenfeld, Science 177, 567 (1972).
[Crossref] [PubMed]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[Crossref]

Schulz, A.

G. Baumgartner, J. L. Brown, and A. Schulz, J. Neurophysiol. 28, 1 (1965).
[PubMed]

Spinelli, D. N.

D. N. Spinelli, Science 152, 1768 (1966).
[Crossref]

Stockham, T. G.

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[Crossref]

Stone, J.

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 819 (1965).
[PubMed]

von Békésy, G.

G. von Békésy, J. Opt. Soc. Am. 58, 1 (1968).
[Crossref]

G. von Békésy, J. Opt. Soc. Am. 50, 1060 (1960).
[Crossref]

G. von Békésy, Sensory Inhibition (Princeton U. P., Princeton, New Jersey, 1967).

Wässle, H.

H. Wässle and O. D. Creutzfeldt, J. Neurophysiol. 36, 13 (1973).

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, J. Physiol. 154, 572 (1960).

IEEE Trans. (1)

K. Fukushima, IEEE Trans. SSC-5, 322 (1969).

J. Neurophysiol. (7)

S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
[PubMed]

G. Baumgartner, J. L. Brown, and A. Schulz, J. Neurophysiol. 28, 1 (1965).
[PubMed]

L. Maffei, A. Fiorentini, and L. Cervetto, J. Neurophysiol. 34, 579 (1971).
[PubMed]

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 819 (1965).
[PubMed]

R. W. Rodieck and J. Stone, J. Neurophysiol. 28, 833 (1965).

H. Wässle and O. D. Creutzfeldt, J. Neurophysiol. 36, 13 (1973).

L. Maffei and A. Fiorentini, J. Neurophysiol. 35, 65 (1972).
[PubMed]

J. Opt. Soc. Am. (2)

J. Physiol. (4)

H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

P. Gouras, J. Physiol. 192, 747 (1967).

D. H. Hubel and T. N. Wiesel, J. Physiol. 154, 572 (1960).

F. W. Campbell and R. W. Gubisch, J. Physiol. 186, 558 (1966).

Kybernetik (1)

K. Fukushima, Kybernetik 7, 153 (1970).
[Crossref] [PubMed]

Proc. IEEE (1)

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[Crossref]

Science (2)

H. B. Barlow, R. Narasimhan, and A. Rosenfeld, Science 177, 567 (1972).
[Crossref] [PubMed]

D. N. Spinelli, Science 152, 1768 (1966).
[Crossref]

Sitzungsberichte der mathematisch-naturwissen-schaftlichen Classe der kaiserlichen Akademie der Wissen-schaften (1)

E. Mach, Sitzungsberichte der mathematisch-naturwissen-schaftlichen Classe der kaiserlichen Akademie der Wissen-schaften 52, 303 (1865) (translation in Ref. 2).

Vision Res. (1)

R. W. Rodieck, Vision Res. 5, 583 (1965).
[Crossref] [PubMed]

Other (4)

G. von Békésy, Sensory Inhibition (Princeton U. P., Princeton, New Jersey, 1967).

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, San Francisco, 1965).

A. Fiorentini, in Handbook of Sensory Physiology, Vol. 7/4, Visual Psychophysics, edited by D. Jameson and L. M. Hurvich (Springer, Berlin, 1972), p. 188.
[Crossref]

R. Jung, in Sensory Communication, edited by W. A. Rosenblith (MIT Press, Cambridge, Mass., 1961), pp. 627 and 796.

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Figures (6)

FIG. 1
FIG. 1

32 × 32 element input array. Receptor cells involved in one annular receptive field are crosshatched.

FIG. 2
FIG. 2

(A) Input stimulus. The border is 30° from the vertical to exploit the symmetry of the array and facilitate comparison with Fig. 3. (B) A cross section of the weighting function and a single plot across each output array, as shown by the dotted line in A. (C) The rectangular weighting function and a single plot through the array of E cells.

FIG. 3
FIG. 3

The input stimulus is shown above and the output arrays below, The top and bottom dotted lines pass through the vertex of the angles. The central dotted line is not Influenced by either angle and is thus identical to Fig. 2B. The number to the right of each dotted line is the positive peak value obtained along the line.

FIG. 4
FIG. 4

(A) The input stimulus. The points indicate active receptor cells. That is, the stimulus is a white line on a dark background. (B) A plot through the E cell output array (PE) indicated in A. (C) A picture formed by the binary matrix of suprathreshold activity (the BE matrix). The threshold TEis shown by the arrows in B.

FIG. 5
FIG. 5

The input (a white angled line on a dark background) is shown on the left, PE and PI array plots are in the center and the pictures formed by BE and BI matrices are on the right. TE is as in Fig. 4. The upper dotted line in PE and PI passes through the vertex of the angle; the lower dotted line passes through a portion uninfluenced by the angle or the end of the line. The number associated with each line in PE is the positive peak value. In PI, the left and right positive peaks are indicated by the left and right values, respectively.

FIG. 6
FIG. 6

(A) An input (a white angled line on a dark background) and output pictures formed by BE and BI matrices. TE and TI are as in Fig. 5. The weighting function is that of Fig. 2B. The vertical and horizontal line segments yield slightly different outputs because the inputs are slightly different. (B) As in A, except that the rectangular weighting function of Fig. 2C is used. TE and TI were chosen to illustrate the similarity of the output arrays.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

P j k E = i = inner A E ( ρ ) R i - i = outer A E ( ρ ) R i ,
P j k I = - i = inner A I ( ρ ) R i + i = outer A I ( ρ ) R i ;
P j k I = - P j k E when A E = A I ,
p ( x , y ) = - - a ( , ϕ ) r ( x - , y - ϕ ) d d ϕ .
B j k E = { 1 , P j k E > T E 0 , P j k E T E
B j k I = { 1 , P j k I > T I 0 , P j k I T I .