Dobbins A, Zucker S W, Cynader M S
Computer Vision and Robotics Laboratory, McGill Research Centre for Intelligent Machines, McGill University, Montréal, Québec, Canada.
Nature. 1987;329(6138):438-41. doi: 10.1038/329438a0.
Neurons in the visual cortex typically respond selectively to the orientation, and velocity and direction of movement, of moving-bar stimuli. These responses are generally thought to provide information about the orientation and position of lines and edges in the visual field. Some cells are also endstopped, that is selective for bars of specific lengths. Hubel and Wiesel first observed that endstopped hypercomplex cells could respond to curved stimuli and suggested they might be involved in detection of curvature, but the exact relationship between endstopping and curvature has never been determined. We present here a mathematical model relating endstopping to curvature in which the difference in response of two simple cells gives rise to endstopping and varies in proportion to curvature. We also provide physiological evidence that endstopped cells in area 17 of the cat visual cortex are selective for curvature, whereas non-endstopped cells are not, and that some are selective for the sign of curvature. The prevailing view of edge and curve determination is that orientations are selected locally by the class of simple cortical cells and then integrated to form global curves. We have developed a computational theory of orientation selection which shows that measurements of orientation obtained by simple cells are not sufficient because there will be strong, incorrect responses from cells whose receptive fields (RFs) span distinct curves (Fig. 1). If estimates of curvature are available, however, these inappropriate responses can be eliminated. Curvature provides the key to structuring the network that underlies our theory and distinguishes it from previous lateral inhibition schemes.
视觉皮层中的神经元通常对移动光条刺激的方向、速度和运动方向具有选择性反应。这些反应一般被认为能提供有关视野中线条和边缘的方向及位置的信息。一些细胞也是终端抑制型的，即对特定长度的光条具有选择性。休伯尔和威塞尔首先观察到终端抑制型超复杂细胞能够对弯曲刺激做出反应，并提出它们可能参与曲率检测，但终端抑制与曲率的确切关系从未确定。我们在此提出一个将终端抑制与曲率相关联的数学模型，其中两个简单细胞反应的差异产生了终端抑制，且与曲率成比例变化。我们还提供了生理学证据，表明猫视觉皮层17区的终端抑制型细胞对曲率具有选择性，而非终端抑制型细胞则不然，并且有些细胞对曲率的正负具有选择性。关于边缘和曲线判定的主流观点是，方向由简单皮层细胞类型在局部进行选择，然后整合形成全局曲线。我们已经开发出一种方向选择的计算理论，该理论表明简单细胞获得的方向测量是不够的，因为其感受野跨越不同曲线的细胞会有强烈的错误反应（图1）。然而，如果有曲率估计值，这些不适当的反应就可以消除。曲率为构建我们理论基础的网络提供了关键，并使其有别于先前的侧向抑制方案。
