Tolhurst D J, Heeger D J
Physiological Laboratory, Cambridge, U.K.
Vis Neurosci. 1997 Mar-Apr;14(2):293-309. doi: 10.1017/s0952523800011433.
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 & 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.
在几乎每一项关于猫视觉皮层简单细胞时空总和线性度的研究中，实验观测结果与线性理论的预测之间都存在系统性的不匹配。这些不匹配现象通常被解释为，初始的时空总和阶段严格呈线性，但简单细胞随后的输出阶段存在某种依赖对比度的非线性。已经提出了两种主要的输出非线性模型：阈值模型（例如Tolhurst和Dean，1987年）和对比度归一化模型（例如Heeger，1992a，b）。在本文中，将这两种模型严格拟合到各种先前发表的神经生理学数据上，以确定哪种模型能更好地解释这些数据。我们重新审视了关于在感受野不同部位呈现的两个条形刺激之间相互作用的数据；关于感受野图与空间频率调谐曲线的逆傅里叶变换之间关系的数据；关于响应幅度和相位对静止光栅空间相位的依赖性的数据；关于对移动光栅和调制光栅的响应之间关系的数据；以及关于在神经元非偏好方向移动的光栅的抑制作用的数据。在许多情况下，两种模型的预测相似，但对比度归一化模型通常比阈值模型能更好地拟合数据，并且应用归一化模型的方程更容易。更重要的是，归一化模型自然能够很好地解释刺激总对比度能量发生变化的实验结果的细节和微妙之处；其中一些现象完全超出了阈值模型的范围。对模型方程的严格应用揭示了一些两种模型都拟合得不够好的情况，因此我们必须假定，仍然存在一些有待描述的微妙非线性。
