We have developed generalized ideal observer models relating human performance in detection tasks to physical properties of medical imaging systems, such as spatial resolution and noise power spectrum. Our approach treats detection as a special case of amplitude estimation, with certain other aspects of the signal, e.g., size or location, considered additional unknown parameters. The models are based on the Barankin lower bound on the precision with which the quantities of interest can be determined. We have found the Barankin bound to be particularly promising in predicting human performance in detection with location uncertainty. Its predictions differ from those of other proposed models in two respects. First, our results suggest that the degradation in performance due to location uncertainty depends on resolution. Second, we have shown analytically that for a given search area, the ratio of ideal observer performance when location is unknown to performance when location is known is nearly independent of signal size. This differs from previously proposed models which predict that the effect of location uncertainty depends on the ratio of signal size to search area, but agrees with the results of reported perceptual experiments testing this question.