### Abstract

In almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mismatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by supposing that the initial spatiotemporal summation stage is strictly linear, but that the following output stage of the simple cell is subject to some contrast-dependent nonlinearity. Two main models of the output nonlinearity have been proposed: the threshold model (e.g. Tolhurst and Dean, 1987) and the contrast-normalization model (e.g. Heeger, 1992a, b). In this paper, the two models are fitted rigorously to a variety of previously published neurophysiological data, in order to determine whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in different parts of the receptive field; on the relationship between the receptive-field map and the inverse Fourier transform of the spatial-frequency tuning curve; on the dependence of response amplitude and phase on the spatial phase of stationary gratings; on the relationships between the responses to moving and modulated gratings; and on the suppressive action of gratings moving in a neuron's nonpreferred direction. In many situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better than the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is naturally able to account very well for the details and subtlety of the results in experiments where the total contrast energy of the stimuli changes; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has revealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to be characterized.

Original language | English (US) |
---|---|

Pages (from-to) | 293-309 |

Number of pages | 17 |

Journal | Visual Neuroscience |

Volume | 14 |

Issue number | 2 |

State | Published - Mar 1997 |

### Fingerprint

### Keywords

- Contrast normalization
- Directional selectivity
- Linear summation
- Nonlinear responses
- Response suppression
- Simple cells
- Thresholds
- Visual cortex

### ASJC Scopus subject areas

- Neuroscience(all)

### Cite this

*Visual Neuroscience*,

*14*(2), 293-309.

**Comparison of contrast-normalization and threshold models of the responses of simple cells in cat striate cortex.** / Tolhurst, D. J.; Heeger, D. J.

Research output: Contribution to journal › Article

*Visual Neuroscience*, vol. 14, no. 2, pp. 293-309.

}

TY - JOUR

T1 - Comparison of contrast-normalization and threshold models of the responses of simple cells in cat striate cortex

AU - Tolhurst, D. J.

AU - Heeger, D. J.

PY - 1997/3

Y1 - 1997/3

N2 - In almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mismatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by supposing that the initial spatiotemporal summation stage is strictly linear, but that the following output stage of the simple cell is subject to some contrast-dependent nonlinearity. Two main models of the output nonlinearity have been proposed: the threshold model (e.g. Tolhurst and Dean, 1987) and the contrast-normalization model (e.g. Heeger, 1992a, b). In this paper, the two models are fitted rigorously to a variety of previously published neurophysiological data, in order to determine whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in different parts of the receptive field; on the relationship between the receptive-field map and the inverse Fourier transform of the spatial-frequency tuning curve; on the dependence of response amplitude and phase on the spatial phase of stationary gratings; on the relationships between the responses to moving and modulated gratings; and on the suppressive action of gratings moving in a neuron's nonpreferred direction. In many situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better than the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is naturally able to account very well for the details and subtlety of the results in experiments where the total contrast energy of the stimuli changes; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has revealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to be characterized.

AB - In almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mismatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by supposing that the initial spatiotemporal summation stage is strictly linear, but that the following output stage of the simple cell is subject to some contrast-dependent nonlinearity. Two main models of the output nonlinearity have been proposed: the threshold model (e.g. Tolhurst and Dean, 1987) and the contrast-normalization model (e.g. Heeger, 1992a, b). In this paper, the two models are fitted rigorously to a variety of previously published neurophysiological data, in order to determine whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in different parts of the receptive field; on the relationship between the receptive-field map and the inverse Fourier transform of the spatial-frequency tuning curve; on the dependence of response amplitude and phase on the spatial phase of stationary gratings; on the relationships between the responses to moving and modulated gratings; and on the suppressive action of gratings moving in a neuron's nonpreferred direction. In many situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better than the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is naturally able to account very well for the details and subtlety of the results in experiments where the total contrast energy of the stimuli changes; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has revealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to be characterized.

KW - Contrast normalization

KW - Directional selectivity

KW - Linear summation

KW - Nonlinear responses

KW - Response suppression

KW - Simple cells

KW - Thresholds

KW - Visual cortex

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UR - http://www.scopus.com/inward/citedby.url?scp=0031104043&partnerID=8YFLogxK

M3 - Article

C2 - 9147482

AN - SCOPUS:0031104043

VL - 14

SP - 293

EP - 309

JO - Visual Neuroscience

JF - Visual Neuroscience

SN - 0952-5238

IS - 2

ER -