Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-19T02:36:35.212Z Has data issue: false hasContentIssue false
  • English
  • Français

Half-squaring in responses of cat striate cells

Published online by Cambridge University Press:  02 June 2009

David J. Heeger
David J. Heeger
Affiliation:
NASA-Ames Research Center, Moffett Field and Department of Psychology, Stanford University, Stanford
Get access Rights & Permissions [Opens in a new window]

Abstract

Simple cells in striate cortex have been depicted as rectified linear operators, and complex cells have been depicted as energy mechanisms (constructed from the squared sums of linear operator outputs). This paper discusses two essential hypotheses of the linear/energy model: (1) that a cell's selectivity is due to an underlying (spatiotemporal and binocular) linear stage; and (2) that a cell's firing rate depends on the squared output of the underlying linear stage. This paper reviews physiological measurements of cat striate cell responses, and concludes that both of these hypotheses are supported by the data.

Keywords

Striate (primary visual) cortexSimple cellsComplex cellsSpatiotemporal linear operatorsEnergy mechanismsSquaringDirection selectivity
Type
Research Articles
Information
Visual Neuroscience , Volume 9 , Issue 5 , November 1992 , pp. 427 - 443
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adelson, E.H. & Bergen, J.R. (1985). Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America A 2, 284–299.CrossRefGoogle ScholarPubMed
Albrecht, D.G. & Geisler, W.S. (1991). Motion sensitivity and the contrast-response function of simple cells in the visual cortex. Visual Neuroscience 7, 531–546.Google Scholar
Andrews, B.W. & Pollen, D.A. (1979). Relationship between spatial frequency selectivity and receptive field profile of simple cells. Journal of Physiology (London) 287, 163–176.CrossRefGoogle ScholarPubMed
Baker, C.L. (1988). Spatial and temporal determinants of directionally selective velocity preference in cat striate cortex. Journal ofNeurophysiology 59, 1557–1574.CrossRefGoogle ScholarPubMed
Baker, C.L. (1990). Spatial- and temporal-frequency selectivity as a basis for velocity preference in cat striate cortex neurons. Visual Neuroscience 4, 101–113.CrossRefGoogle ScholarPubMed
Baker, C.L. & Cynader, M.S. (1986). Spatial receptive-field properties of direction-selective neurons in cat striate cortex. Journal of Neurophysiology 55, 1136–1152.CrossRefGoogle ScholarPubMed
Berardi, N., Bisti, S., Cattaneo, A., Fiorentini, A. & Maffei, L. (1982). Correlation between the preferred orientation and spatial frequency of neurones in visual areas 17 and 18 of the cat. Journal of Physiology (London) 323, 603–618.Google Scholar
Bonds, A.B. (1989). Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex. Visual Neuroscience 2, 41–55.CrossRefGoogle ScholarPubMed
Campbell, F.W., Cleland, B.G., Cooper, G.F. & Enroth-Cugell, C. (1968). The angular selectivity of visual cortical cells to moving gratings. Journal of Physiology (London) 198, 237–250.CrossRefGoogle ScholarPubMed
Campbell, F.W., Cooper, G.F. & Enroth-Cugell, C. (1969). The spatial selectivity of visual cells of the cat. Journal of Physiology (London) 203, 223–235.Google Scholar
Citron, M.C. & Emerson, R.C. (1983). White noise analysis of cortical directional selectivity in cat. Brain Research 279, 271–277.Google Scholar
Dean, A.F. & Tolhurst, D.J. (1983). On the distinctiveness of simple and complex cells in the visual cortex of the cat. Journal of Physiology (London) 344, 305–325.CrossRefGoogle ScholarPubMed
Dean, A.F. & Tolhurst, D.J. (1986). Factors influencing the temporal phase of response to bar and grating stimuli for simple cells in the cat striate cortex. Experimental Brain Research 62, 143–151.CrossRefGoogle ScholarPubMed
Derrington, A.M. & Lennie, P. (1984). Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque. Journal of Physiology (London) 357, 219–240.Google Scholar
Devalois, K. & Tootell, R. (1983). Spatial-frequency-specific inhibition in cat striate cortex cells. Journal of Physiology (London) 336, 359–376.CrossRefGoogle Scholar
Devalois, K.K., Devalois, R.L. & Yund, E.W. (1979). Responses of striate cortex cells to grating and checkerboard patterns. Journal of Physiology (London) 291, 483–505.CrossRefGoogle Scholar
Devalois, R.L., Yund, E.W. & Hepler, N. (1982). The orientation and direction selectivity of cells in macaque visual cortex. Vision Research 22, 531–544.CrossRefGoogle Scholar
Emerson, R.C. (1988). A linear model for symmetric receptive fields: Implications for classification test with flashed and moving images. Spatial Vision 3, 159–177.CrossRefGoogle ScholarPubMed
Emerson, R.C., Bergen, J.R. & Adelson, E.H. (1992 a). Directionally selective complex cells and the computation of motion energy in cat visual cortex. Vision Research 32, 203–218.CrossRefGoogle ScholarPubMed
Emerson, R.C. & Citron, M.C. (1989). Linear and nonlinear mechanisms of motion selectivity in single neurons of the cat's visual cortex. In Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, ed. Kleinman, D.L., pp. 448–453.CrossRefGoogle Scholar
Emerson, R.C., Citron, M.C., Vaughn, W.J. & Klein, S.A. (1987). Nonlinear directionally selective subunits in complex cells of cat striate cortex. Journal of Neurophysiology 58, 33–65.Google Scholar
Emerson, R.C. & Gerstein, G.L. (1977). Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity. Journal of Neurophysiology 40, 136–155.CrossRefGoogle ScholarPubMed
Emerson, R.C., Korenberg, M.J. & Citron, M.C. (1989). Identification of intensive nonlinearities in cascade models of visual cortex and its relation to cell classification. In Advanced Methods of Physiological System Modeling, ed. Marmarelis, V.Z., pp. 97–111. New York: Plenum.Google Scholar
Emerson, R.C., Korenberg, M.J. & Citron, M.C. (1992 b). Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex. Biological Cybernetics 66, 291–300.Google Scholar
Enroth-Cugell, C. & Robson, J.G. (1966). The contrast sensitivity of retinal ganglion cells of the cat. Journal of Physiology (London) 187, 517–552.CrossRefGoogle ScholarPubMed
Enroth-Cugell, C., Robson, J.G., Schweitzer-Tong, D.E. & Watson, A.B. (1983). Spatio-temporal interactions in cat retinal ganglion cells showing linear spatial summation. Journal of Physiology (London) 341, 279–307.Google Scholar
Fahle, M. & Poggio, T. (1981). Visual hyperacuity: Spatiotemporal interpolation in human vision. Proceedings of the Royal Society B (London) 213, 451–477.Google ScholarPubMed
Field, D.J. & Tolhurst, D.J. (1986). The structure and symmetry of simple-cell receptive field profiles in the cat's visual cortex. Proceedings of the Royal Society B (London) 228, 379–400.Google ScholarPubMed
Foster, K.H., Gaska, J.P., Marcelja, S. & Pollen, D.A. (1983). Phase relationships between adjacent simple cells in the feline visual cortex. Journal of Physiology (London) 345, 22P.Google Scholar
Foster, K.H., Gaska, J.P., Nagler, M. & Pollen, D.A. (1985). Spatial and temporal frequency selectivity of neurons in visual cortical areas V1 and V2 of the macaque monkey. Journal of Physiology (London) 365, 331–363.Google Scholar
Freeman, R.D. & Ohzawa, I. (1990). On the neurophysiological organization of binocular vision. Vision Research 30, 1661–1676.CrossRefGoogle ScholarPubMed
Ganz, L. & Felder, R. (1984). Mechanism of directional selectivity in simple neurons of the cat's visual cortex analyzed with stationary flash sequences. Journal of Neurophysiology 51, 294–324.CrossRefGoogle ScholarPubMed
Glezer, V.D., Tscherbach, T.A., Gauselman, V.E. & Bondarko, V.E. (1980). Linear and nonlinear properties of simple and complex receptive fields in area 17 of the cat visual cortex. Biological Cybernetics 37, 195–208.CrossRefGoogle ScholarPubMed
Glezer, V.D., Tscherbach, T.A., Gauselman, V.E. & Bondarko, V.E. (1982). Spatio-temporal organization of receptive fields of the cat striate cortex. Biological Cybernetics 43, 35–49.CrossRefGoogle ScholarPubMed
Goodwin, A.W., Henry, G.H. & Bishop, P.O. (1975). Direction selectivity of simple cells: Properties and mechanisms. Journal of Neurophysiology 38, 1500–1523.CrossRefGoogle Scholar
Hamilton, D.B., Albrecht, D.G. & Geisler, W.S. (1989). Visual cortical receptive fields in monkey and cat: Spatial and temporal phase transfer function. Vision Research 29, 1285–1308.CrossRefGoogle ScholarPubMed
Hammond, P. & Pomfrett, C.J.D. (1990). Influence of spatial frequency on tuning and bias for orientation and direction in the cat's striate cortex. Vision Research 30, 359–369.Google Scholar
Heeger, D.J. (1990). Nonlinear model of cat striate physiology. Society for Neuroscience Abstracts 16, 229.Google Scholar
Heeger, D.J. (1991). Nonlinear model of neural responses in cat visual cortex. In Computational Models of Visual Processing, ed. Landy, M. & Movshon, J.A. pp. 119–133. Cambridge, Massachusetts: MIT Press.Google Scholar
Heeger, D.J. (1992 a). Normalization of cell responses in cat striate cortex. Visual Neuroscience 9, 181–197.CrossRefGoogle ScholarPubMed
Heeger, D.J. (1992 b). Modeling simple cell direction selectivity with normalized, half-squared, linear operators. Investigative Ophthalmology and Visual Science (Suppl.) 33, 953.Google Scholar
Heeger, D.J. & Adelson, E.H. (1989). Nonlinear model of cat striate cortex. Optics News, 15, A-42.Google Scholar
Heggelund, P. (1981 a). Receptive-field organization of simple cells in cat striate cortex. Experimental Brain Research 42, 89–98.Google ScholarPubMed
Heggelund, P. (1981 b). Receptive-field organization of complex cells in cat striate cortex. Experimental Brain Research 42, 99–107.Google ScholarPubMed
Heggelund, P. (1986). Quantitative studies of the discharge fields of single cells in cat striate cortex. Journal of Physiology (London) 373, 277–292.CrossRefGoogle ScholarPubMed
Henry, G.H., Bishop, P.O. & Dreher, B. (1974 a). Orientation axis and direction as stimulus parameters for striate cells. Vision Research 14, 767–777.Google Scholar
Henry, G.H., Dreher, B. & Bishop, P.O. (1974 b). Orientation specificity of cells in cat striate cortex. Journal of Neurophysiology 37, 1394–1409.CrossRefGoogle ScholarPubMed
Henry, G.H., Goodwin, A.W. & Bishop, P.O. (1978). Spatial summation of responses in receptive fields of single cells in cat striate cortex. Experimental Brain Research 32, 245–266.Google Scholar
Holub, R.A. & Morton-Gibson, M. (1981). Response of visual cortical neurons of the cat to moving sinusoidal gratings: Response-contrast functions and spatiotemporal integration. Journal of Neurophysiology 46, 1244–1259.Google Scholar
Hubel, D. & Wiesel, T. (1962). Receptive fields, binocular interaction, and functional architecture in the cat's visual cortex. Journal of Physiology (London) 160, 106–154.CrossRefGoogle ScholarPubMed
Ikeda, H. & Wright, M.J. (1975 a). Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat's visual cortex. Experimental Brain Research 22, 363–383.Google Scholar
Ikeda, H. & Wright, M.J. (1975 b). Retinotopic distribution, visual latency and orientation tuning of “sustained” and “transient” cortical neurones in area 17 of the cat. Experimental Brain Research 22, 385–398.CrossRefGoogle Scholar
Jones, J.P. & Palmer, L.A. (1987 a). The two-dimensional spatial structure of simple receptive fields in cat striate cortex. Journal of Neurophysiology 58, 1187–1211.CrossRefGoogle ScholarPubMed
Jones, J.P. & Palmer, L.A. (1987 b). An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. Journal of Neurophysiology 58, 1233–1258.Google Scholar
Jones, J.P., Stepnoski, A. & Palmer, L.A. (1987). The two-dimensional spectral structure of simple receptive fields in cat striate cortex. Journal of Neurophysiology 58, 1212–1232.CrossRefGoogle ScholarPubMed
Kulikowski, J.J. & Bishop, P.O. (1981 a). Linear analysis of the response of simple cells in the cat visual cortex. Experimental Brain Research 44, 386–400.Google Scholar
Kulikowski, J.J. & Bishop, P.O. (1981 b). Fourier analysis and spatial representation in the visual cortex. Experimentia 37, 160–163.CrossRefGoogle ScholarPubMed
Kulikowski, J.J. & Bishop, P.O. (1982). Silent periodic cells in the cat striate cortex. Vision Research 22, 191–200.CrossRefGoogle ScholarPubMed
Kulikowski, J.J., Bishop, P.O. & Kato, H. (1981). Spatial arrangement of responses by cells in the cat visual cortex to light and dark bars and edges. Experimental Brain Research 44, 371–385.Google Scholar
Kulikowski, J.J. & Vidyasagar, T.R. (1986). Space and spatial frequency: Analysis and representation in the macaque striate cortex. Experimental Brain Research 64, 5–18.CrossRefGoogle ScholarPubMed
Maffei, L. & Fiorentini, A. (1973). The visual cortex as a spatial frequency analyzer. Vision Research, 13, 1255–1267.CrossRefGoogle Scholar
Maffei, L., Morrone, C., Pirchio, M. & Sandini, G. (1979). Responses of visual cortical cells to periodic and nonperiodic stimuli. Journal of Physiology (London) 296, 27–47.CrossRefGoogle ScholarPubMed
Mancini, M., Madden, M.C. & Emerson, R.C. (1990). White noise analysis of temporal properties in simple receptive fields of cat cortex. Biological Cybernetics 63, 209–219.Google Scholar
Mclean, J. & Palmer, L.A. (1989). Contribution of linear spatiotemporal receptive field structure to velocity selectivity of simple cells in area 17 of cat. Vision Research 29, 675–679.Google Scholar
Movshon, J.A., Thompson, I.D. & Tolhurst, D.J. (1978 a). Spatial summation in the receptive fields of simple cells in the cat's striate cortex. Journal of Physiology (London) 283, 53–77.CrossRefGoogle ScholarPubMed
Movshon, J.A., Thompson, I.D. & Tolhurst, D.J. (1978 b). Receptive-field organization of complex cells in the cat's striate cortex. Journal of Physiology (London) 283, 79–99.Google Scholar
Movshon, J.A., Thompson, I.D. & Tolhurst, D.J. (1978 c). Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat's visual cortex. Journal of Physiology (London) 283, 101–120.Google Scholar
Ohzawa, I., Deangelis, G.C. & Freeman, R.D. (1990). Stereoscopic depth discrimination in the visual cortex: Neurons ideally suited as disparity detectors. Science 249, 1037–1041.CrossRefGoogle ScholarPubMed
Ohzawa, I. & Freeman, R.D. (1986 a). The binocular organization of simple cells in the cat's visual cortex. Journal of Neurophysiology 56, 221–242.Google Scholar
Ohzawa, I. & Freeman, R.D. (1986 b). The binocular organization of complex cells in the cat's visual cortex. Journal of Neurophysiology 56, 243–259.CrossRefGoogle ScholarPubMed
Ohzawa, I., Sclar, G. & Freeman, R.D. (1985). Contrast gain control in the cat's visual system. Journal of Neurophysiology 54, 651–667.Google Scholar
Palmer, L.A. & Davis, T.L. (1981). Receptive-field structure in cat striate cortex. Journal of Neurophysiology 46, 260–276.CrossRefGoogle ScholarPubMed
Pettigrew, J.D., Nikara, T. & Bishop, P.O. (1968). Responses to moving slits by single units in cat striate cortex. Experimental Brain Research 6, 373–390.Google Scholar
Pollen, D. & Ronner, S. (1981). Phase relationships between adjacent simple cells in the visual cortex. Science 212, 1409–1411.CrossRefGoogle ScholarPubMed
Pollen, D. & Ronner, S. (1982). Spatial computation performed by simple and complex cells in the visual cortex of the cat. Vision Research 22, 101–118.CrossRefGoogle ScholarPubMed
Pollen, D. & Ronner, S. (1983). Visual cortical neurons as localized spatial-frequency filters. IEEE Transactions on Systems, Man, and Cybernetics 13, 907–916.Google Scholar
Pollen, D.A., Andrews, B.W. & Feldon, S.E. (1978). Spatial-frequency selectivity of periodic complex cells in the visual cortex of the cat. Vision Research 18, 665–682.CrossRefGoogle ScholarPubMed
Pollen, D.A., Gaska, J.P. & Jacobson, L.D. (1988). Responses of simple and complex cells to compound sine-wave gratings. Vision Research 28, 25–39.Google Scholar
Reid, R.C., Soodak, R.E. & Shapley, R.M. (1987). Linear mechanisms of directional selectivity in simple cells of cat striate cortex. Proceedings of the National Academy of Sciences of the U.S.A. 84, 8740–8744.CrossRefGoogle ScholarPubMed
Reid, R.C., Soodak, R.E. & Shapley, R.M. (1991). Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex. Journal of Neurophysiology 66, 505–529.Google Scholar
Robson, J.G. (1988). Linear and nonlinear operations in the visual system. Investigative Ophthalmology and Visual Science (Suppl.) 29, 117.Google Scholar
Robson, J.G., Tolhurst, D.J., Freeman, R.D. & Ohzawa, I. (1988). Simple cells in the visual cortex of the cat can be narrowly tuned for spatial frequency. Visual Neuroscience 1, 415–419.CrossRefGoogle ScholarPubMed
Rose, D. & Blakemore, C. (1974). An analysis of orientation selectivity in the cat's visual cortex. Experimental Brain Research 20, 1–17.Google Scholar
Rybicki, C.B., Tracy, D.M. & Pollen, D.A. (1972). Complex cell response depends on interslit spacing. Nature New Biology 240, 77–78.CrossRefGoogle ScholarPubMed
Schiller, P.H., Finlay, B.L. & Volman, S.F. (1976). Quantitative studies of single-cell properties in monkey striate cortex. II. Orientation specificity and ocular dominance. Journal of Neurophysiology 39, 1320–1333.CrossRefGoogle ScholarPubMed
Shapley, R., Kaplan, E. & Soodak, R. (1981). Spatial summation and contrast sensitivity of X and Y cells in the lateral geniculate nucleus of the macaque. Nature 292, 543–545.CrossRefGoogle ScholarPubMed
Shapley, R., Reid, R.C. & Soodak, R. (1991). Spatiotemporal receptive fields and direction selectivity. In Computational Models of Visual Processing, ed. Landy, M. & Movshon, J.A. pp. 109–118. Cambridge, Massachusetts: MIT Press.Google Scholar
Sillito, A.M. (1977). Inhibitory processes underlying the directional specificity of simple, complex, and hypercomplex cells in the cat's visual cortex. Journal of Physiology (London) 271, 699–720.CrossRefGoogle ScholarPubMed
Spekreuse, H. & Van Den Bero, T.J.T.P. (1971). Interaction between colour and spatial coded processes converging to retinal ganglion cells in goldfish. Journal of Physiology (London) 215, 679–692.CrossRefGoogle Scholar
Spitzer, H. & Hochstein, S. (1985 a). Simpleand complex-cell response dependences on stimulation parameters. Journal of Neurophysiology 53, 1244–1265.Google Scholar
Spitzer, H. & Hochstein, S. (1985 b). A complex-cell receptive-field model. Journal of Neurophysiology 53, 1266–1286.Google Scholar
Suarez, H. & Koch, C. (1989). Linking linear threshold units with quadratic models of motion perception. Neural Computation 1, 318–320.CrossRefGoogle Scholar
Szulborski, R.G. & Palmer, L.A. (1990). The two-dimensional spatial structure of nonlinear subunits in the receptive fields of complex cells. Vision Research 30, 249–254.CrossRefGoogle ScholarPubMed
Szulborski, R.G. & Palmer, L.A. (1991). Linear behavior of complex cell subunits in cat striate cortex. Investigative Ophthalmology and Visual Science (Suppl.) 32, 1253.Google Scholar
Tadmor, Y. & Tolhurst, D.J. (1989). The effect of threshold on the relationship between the receptive-field profile and the spatial-frequency tuning curve in simple cells of the cat's striate cortex. Visual Neuroscience 3, 445–454.CrossRefGoogle ScholarPubMed
Tolhurst, D.J. & Dean, A.F. (1987). Spatial summation by simple cells in the striate cortex of the cat. Experimental Brain Research 66, 607–620.Google Scholar
Tolhurst, D.J. & Dean, A.F. (1991). Evaluation of a linear model of directional selectivity in simple cells of the cat's striate cortex. Visual Neuroscience 6, 421–428.CrossRefGoogle ScholarPubMed
Tolhurst, D.J. & Movshon, J.A. (1975). Spatial and temporal contrast sensitivity of striate cortical neurons. Nature 257, 674–675.CrossRefGoogle Scholar
Tolhurst, D.J. & Thompson, I.D. (1981). On the variety of spatial frequency selectivities shown by neurons in area 17 of the cat. Proceedings of the Royal Society B (London) 213, 183–199.Google Scholar
Troy, J.B. (1983). Spatial contrast sensitivities of X and Y type neurones in the cat's dorsal lateral geniculate nucleus. Journal of Physiology (London) 344, 399–417.Google Scholar
Van Santen, J.P.H. & Sperling, G. (1985). Elaborated Reichardt detectors. Journal of the Optical Society of America A 2, 300–321.Google Scholar
Watson, A.B. & Ahumada, A.J. (1983). A look at motion in the frequency domain. In Motion: Perception and representation, ed. Tsotsos, J.K., pp. 1–10. New York: Association for Computing Machinery.Google Scholar
Watson, A.B. & Ahumada, A.J. (1985). Model of human visual-motion sensing. Journal of the Optical Society of America A 2, 322–342.Google Scholar
Webster, M.A. & Devalois, R.L. (1985). Relationship between spatial-frequency and orientation tuning of striate-cortex cells. Journal of the Optical Society of America A 2, 1124–1132.CrossRefGoogle ScholarPubMed
Wolbarsht, M.L., Wacner, H.G. & Macnichol, E.F. (1961). The origin of on and off responses of retinal ganglion cells. In The Visual System: Neurophysiology and Psychophysics, ed. Jung, & Kornhuber, , pp. 163–170. Berlin: Springer.Google Scholar