Hostname: page-component-6b88cc9666-zbq8r Total loading time: 0 Render date: 2026-02-16T00:39:39.399Z 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
Affiliation:
NASA-Ames Research Center, Moffett Field and Department of Psychology, Stanford University, Stanford

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 thesquared 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.

Information

Type
Research Articles
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.)

Article purchase

Temporarily unavailable

References

Adelson,E.H. &Bergen,J.R. (1985).Spatiotemporal energy models for the perception of motion.Journal of the Optical Society of America A2,284–299.CrossRefGoogle ScholarPubMed
Albrecht,D.G. &Geisler,W.S. (1991).Motion sensitivity and the contrast-response function of simple cells in the visual cortex.Visual Neuroscience7,531–546.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 ofNeurophysiology59,1557–1574.CrossRefGoogle ScholarPubMed
Baker,C.L. (1990).Spatial- and temporal-frequency selectivity as a basis for velocity preference in cat striate cortex neurons.Visual Neuroscience4,101–113.CrossRefGoogle ScholarPubMed
Baker,C.L. &Cynader,M.S. (1986).Spatial receptive-field properties of direction-selective neurons in cat striate cortex.Journal of Neurophysiology55,1136–1152.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 Neuroscience2,41–55.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 Research279,271–277.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 Research62,143–151.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 Research22,531–544.CrossRefGoogle Scholar
Emerson,R.C. (1988).A linear model for symmetric receptive fields: Implications for classification test with flashed and moving images.Spatial Vision3,159–177.CrossRefGoogle ScholarPubMed
Emerson,R.C.,Bergen,J.R. &Adelson,E.H. (1992a).Directionally selective complex cells and the computation of motion energy in cat visual cortex.Vision Research32,203–218.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. InProceedings 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 Neurophysiology58,33–65.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 Neurophysiology40,136–155.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. InAdvanced 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. (1992b).Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex.Biological Cybernetics66,291–300.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 Research30,1661–1676.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 Neurophysiology51,294–324.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 Cybernetics37,195–208.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 Cybernetics43,35–49.CrossRefGoogle ScholarPubMed
Goodwin,A.W.,Henry,G.H. &Bishop,P.O. (1975).Direction selectivity of simple cells: Properties and mechanisms.Journal of Neurophysiology38,1500–1523.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 Research29,1285–1308.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 Research30,359–369.Google Scholar
Heeger,D.J. (1990).Nonlinear model of cat striate physiology.Society for Neuroscience Abstracts16,229.Google Scholar
Heeger,D.J. (1991). Nonlinear model of neural responses in cat visual cortex. InComputational Models of Visual Processing, ed.Landy,M. &Movshon,J.A. pp.119–133.Cambridge, Massachusetts:MIT Press.Google Scholar
Heeger,D.J. (1992a).Normalization of cell responses in cat striate cortex.Visual Neuroscience9,181–197.CrossRefGoogle ScholarPubMed
Heeger,D.J. (1992b).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. (1981a).Receptive-field organization of simple cells in cat striate cortex.Experimental Brain Research42,89–98.Google ScholarPubMed
Heggelund,P. (1981b).Receptive-field organization of complex cells in cat striate cortex.Experimental Brain Research42,99–107.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. (1974a).Orientation axis and direction as stimulus parameters for striate cells.Vision Research14,767–777.Google Scholar
Henry,G.H.,Dreher,B. &Bishop,P.O. (1974b).Orientation specificity of cells in cat striate cortex.Journal of Neurophysiology37,1394–1409.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 Research32,245–266.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 Neurophysiology46,1244–1259.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. (1975a).Spatial and temporal properties of ‘sustained’ and ‘transient’ neurones in area 17 of the cat's visual cortex.Experimental Brain Research22,363–383.Google Scholar
Ikeda,H. &Wright,M.J. (1975b).Retinotopic distribution, visual latency and orientation tuning of “sustained” and “transient” cortical neurones in area 17 of the cat.Experimental Brain Research22,385–398.CrossRefGoogle Scholar
Jones,J.P. &Palmer,L.A. (1987a).The two-dimensional spatial structure of simple receptive fields in cat striate cortex.Journal of Neurophysiology58,1187–1211.CrossRefGoogle ScholarPubMed
Jones,J.P. &Palmer,L.A. (1987b).An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex.Journal of Neurophysiology58,1233–1258.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 Neurophysiology58,1212–1232.CrossRefGoogle ScholarPubMed
Kulikowski,J.J. &Bishop,P.O. (1981a).Linear analysis of the response of simple cells in the cat visual cortex.Experimental Brain Research44,386–400.Google Scholar
Kulikowski,J.J. &Bishop,P.O. (1981b).Fourier analysis and spatial representation in the visual cortex.Experimentia37,160–163.CrossRefGoogle ScholarPubMed
Kulikowski,J.J. &Bishop,P.O. (1982).Silent periodic cells in the cat striate cortex.Vision Research22,191–200.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 Research44,371–385.Google Scholar
Kulikowski,J.J. &Vidyasagar,T.R. (1986).Space and spatial frequency: Analysis and representation in the macaque striate cortex.Experimental Brain Research64,5–18.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 Cybernetics63,209–219.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 Research29,675–679.Google Scholar
Movshon,J.A.,Thompson,I.D. &Tolhurst,D.J. (1978a).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. (1978b).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. (1978c).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.Science249,1037–1041.CrossRefGoogle ScholarPubMed
Ohzawa,I. &Freeman,R.D. (1986a).The binocular organization of simple cells in the cat's visual cortex.Journal of Neurophysiology56,221–242.Google Scholar
Ohzawa,I. &Freeman,R.D. (1986b).The binocular organization of complex cells in the cat's visual cortex.Journal of Neurophysiology56,243–259.CrossRefGoogle ScholarPubMed
Ohzawa,I.,Sclar,G. &Freeman,R.D. (1985).Contrast gain control in the cat's visual system.Journal of Neurophysiology54,651–667.Google Scholar
Palmer,L.A. &Davis,T.L. (1981).Receptive-field structure in cat striate cortex.Journal of Neurophysiology46,260–276.CrossRefGoogle ScholarPubMed
Pettigrew,J.D.,Nikara,T. &Bishop,P.O. (1968).Responses to moving slits by single units in cat striate cortex.Experimental Brain Research6,373–390.Google Scholar
Pollen,D. &Ronner,S. (1981).Phase relationships between adjacent simple cells in the visual cortex.Science212,1409–1411.CrossRefGoogle ScholarPubMed
Pollen,D. &Ronner,S. (1982).Spatial computation performed by simple and complex cells in the visual cortex of the cat.Vision Research22,101–118.CrossRefGoogle ScholarPubMed
Pollen,D. &Ronner,S. (1983).Visual cortical neurons as localized spatial-frequency filters.IEEE Transactions on Systems, Man, and Cybernetics13,907–916.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 Research18,665–682.CrossRefGoogle ScholarPubMed
Pollen,D.A.,Gaska,J.P. &Jacobson,L.D. (1988).Responses of simple and complex cells to compound sine-wave gratings.Vision Research28,25–39.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 Neurophysiology66,505–529.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 Neuroscience1,415–419.CrossRefGoogle ScholarPubMed
Rose,D. &Blakemore,C. (1974).An analysis of orientation selectivity in the cat's visual cortex.Experimental Brain Research20,1–17.Google Scholar
Rybicki,C.B.,Tracy,D.M. &Pollen,D.A. (1972).Complex cell response depends on interslit spacing.Nature New Biology240,77–78.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 Neurophysiology39,1320–1333.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.Nature292,543–545.CrossRefGoogle ScholarPubMed
Shapley,R.,Reid,R.C. &Soodak,R. (1991). Spatiotemporal receptive fields and direction selectivity. InComputational 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. (1985a).Simpleand complex-cell response dependences on stimulation parameters.Journal of Neurophysiology53,1244–1265.Google Scholar
Spitzer,H. &Hochstein,S. (1985b).A complex-cell receptive-field model.Journal of Neurophysiology53,1266–1286.Google Scholar
Suarez,H. &Koch,C. (1989).Linking linear threshold units with quadratic models of motion perception.Neural Computation1,318–320.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 Research30,249–254.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 Neuroscience3,445–454.CrossRefGoogle ScholarPubMed
Tolhurst,D.J. &Dean,A.F. (1987).Spatial summation by simple cells in the striate cortex of the cat.Experimental Brain Research66,607–620.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 Neuroscience6,421–428.CrossRefGoogle ScholarPubMed
Tolhurst,D.J. &Movshon,J.A. (1975).Spatial and temporal contrast sensitivity of striate cortical neurons.Nature257,674–675.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 A2,300–321.Google Scholar
Watson,A.B. &Ahumada,A.J. (1983). A look at motion in the frequency domain. InMotion: 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 A2,322–342.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 A2,1124–1132.CrossRefGoogle ScholarPubMed
Wolbarsht,M.L.,Wacner,H.G. &Macnichol,E.F. (1961). The origin of on and off responses of retinal ganglion cells. InThe Visual System: Neurophysiology and Psychophysics, ed.Jung, &Kornhuber,, pp.163–170.Berlin:Springer.Google Scholar