A model of human visual search is proposed. It predicts both response time (RT) and error rates (RT) as a function of image parameters such as target contrast and clutter. The model is an ideal observer, in that it optimizes the Bayes ratio of tar- get present vs target absent. The ratio is computed on the firing pattern of V1/V2 neurons, modeled by Poisson distributions. The optimal mechanism for integrat- ing information over time is shown to be a ‘soft max’ of diffusions, computed over the visual field by ‘hypercolumns’ of neurons that share the same receptive field and have different response properties to image features. An approximation of the optimal Bayesian observer, based on integrating local decisions, rather than diffusions, is also derived; it is shown experimentally to produce very similar pre- dictions. A psychophyisics experiment is proposed that may discriminate between which mechanism is used in the human brain.