CONTRAST NORMALIZATION AND A LINEAR-MODEL FOR THE DIRECTIONAL SELECTIVITY OF SIMPLE CELLS IN CAT STRIATE CORTEX

Previous tests of the linearity of spatiotemporal summation in cat sim ple cells have compared the responses to moving sinusoidal gratings an d to gratings whose contrast was modulated sinusoidally in time. In pa rticular, since a moving grating can be expressed as a sum of modulate d gratings, the response to a moving grating should be predictable (as suming linearity) from the responses to modulated gratings. However, t hese simple linear predictions have shown varying degrees of failure ( e.g. Reid et al., 1987, 1991), depending on the directional selectivit y of the neurons (Tolhurst & Dean, 1991). We demonstrate here that the failures of these linear predictions are, in fact, explained by the c ontrast-normalization model of Heeger (1993). We concentrate on the ra tio of the measured to predicted moving grating responses. In the cont ext 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 resp onsible for directional selectivity. Hence, the contrast-normalization model can be compared quantitatively with this ratio measure, by vary ing only one free parameter. When account is taken both of the expansi ve output nonlinearity and of contrast normalization, the directional selectivity of simple cells seems to be dependent only on linear spati otemporal filtering.