TY - JOUR

T1 - Contrast normalization and a linear model for the directional selectivity of simple cells in cat striate cortex

AU - Tolhurst, D. J.

AU - Heeger, D. J.

N1 - Funding Information:
We thank A.F. Dean for his participation in the original experiments. This paper was written while D.J. Tolhurst was visiting Stanford. This visit was supported by an NIMH grant (MH50228) and an Alfred P. Sloan Research Fellowship to D.J. Heeger.

PY - 1997

Y1 - 1997

N2 - Previous tests of the linearity of spatiotemporal summation in cat simple cells have compared the responses to moving sinusoidal gratings and to gratings whose contrast was modulated sinusoidally in time. In particular, since a moving grating can be expressed as a sum of modulated gratings, the response to a moving grating should be predictable (assuming linearity) from the responses to modulated gratings. However, these simple linear predictions have shown varying degrees of failure (e.g. Reid et el., 1987, 1991), depending on the directional selectivity of the neurons (Tolhurst and Dean, 1991). We demonstrate here that the failures of these linear predictions are, in fact, explained by the contrast-normalization model of Heeger (1993). We concentrate on the ratio of the measured to predicted moving grating responses. In the context of the contrast-normalization model, calculating this ratio turns out to be particularly appropriate, since the ratio is independent of the precise details of the linear front-end mechanisms ultimately responsible for directional selectivity. Hence, the contrast-normalization model can be compared quantitatively with this ratio measure, by varying only one free parameter. When account is taken both of the expansive output nonlinearity and of contrast normalization, the directional selectivity of simple cells seems to be dependent only on linear spatiotemporal filtering.

AB - Previous tests of the linearity of spatiotemporal summation in cat simple cells have compared the responses to moving sinusoidal gratings and to gratings whose contrast was modulated sinusoidally in time. In particular, since a moving grating can be expressed as a sum of modulated gratings, the response to a moving grating should be predictable (assuming linearity) from the responses to modulated gratings. However, these simple linear predictions have shown varying degrees of failure (e.g. Reid et el., 1987, 1991), depending on the directional selectivity of the neurons (Tolhurst and Dean, 1991). We demonstrate here that the failures of these linear predictions are, in fact, explained by the contrast-normalization model of Heeger (1993). We concentrate on the ratio of the measured to predicted moving grating responses. In the context of the contrast-normalization model, calculating this ratio turns out to be particularly appropriate, since the ratio is independent of the precise details of the linear front-end mechanisms ultimately responsible for directional selectivity. Hence, the contrast-normalization model can be compared quantitatively with this ratio measure, by varying only one free parameter. When account is taken both of the expansive output nonlinearity and of contrast normalization, the directional selectivity of simple cells seems to be dependent only on linear spatiotemporal filtering.

KW - Contrast normalization

KW - Directional selectivity

KW - Simple cells

KW - Visual cortex

UR - http://www.scopus.com/inward/record.url?scp=0030824230&partnerID=8YFLogxK

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U2 - 10.1017/S0952523800008725

DO - 10.1017/S0952523800008725

M3 - Article

C2 - 9057265

AN - SCOPUS:0030824230

SN - 0952-5238

VL - 14

SP - 19

EP - 25

JO - Visual Neuroscience

JF - Visual Neuroscience

IS - 1

ER -