A neural model is constructed based on the structure of a visual orientation hypercolumn in mammalian striate cortex. It is then assumed that the perceived orientation of visual contours is determined by the pattern of neuronal activity across orientation columns. Using statistical estimation theory, limits on the precision of orientation estimation and discrimination are calculated. These limits are functions of single unit response properties such as orientation tuning width, response amplitude and response variability, as well as the degree of organization in the neural network. It is shown that a network of modest size, consisting of broadly orientation selective units, can reliably discriminate orientation with a precision equivalent to human performance. Of the various network parameters, the discrimination threshold depends most critically on the number of cells in the hypercolumn. The form of the dependence on cell number correctly predicts the results of psychophysical studies of orientation discrimination. The model system's performance is also consistent with psychophysical data in two situations in which human performance is not optimal. First, interference with orientation discrimination occurs when multiple stimuli activate cells in the same hypercolumn. Second, systematic errors in the estimation of orientation can occur when a stimulus is composed of intersecting lines. The results demonstrate that it is possible to relate neural activity to visual performance by an examination of the pattern of activity across orientation columns. This provides support for the hypothesis that perceived orientation is determined by the distributed pattern of neural activity. The results also encourage the view that limits on visual discrimination are determined by the responses of many neurons rather than the sensitivity of individual cells.