Effects of contrast and length on vernier acuity explained with noisy templates

Vernier acuity depends on the integration of information from multiple photoreceptors. For this reason, vernier acuity thresholds ought to exhibit effects of stimulus size and contrast analogous to those that occur in area summation experiments. In this paper, we consider some area and contrast effects found in vernier acuity experiments, and explain them with a model of detection and discrimination which we call the Noisy Template model. The Noisy Template model assumes that psychophysical tasks are performed (or can be approximated) by cross-correlation of the stimulus with a decision template which is optimal for the task at hand. The Noisy Template model crucially adds the assumption that the template contains noise. This yields inefficiency in the decision process which increases with stimulus size and contrast. Predictions of the Noisy Template model are derived for the case of vernier acuity, and compared with existing experiments.