Effects of target-amplitude and background-contrast uncertainty predicted by a normalized template-matching observer

When detecting targets under natural conditions, the visual system almost always faces multiple, simultaneous, dimensions of extrinsic uncertainty. This study focused on the simultaneous uncertainty about target amplitude and background contrast. These dimensions have a large effect on detection and vary greatly in natural scenes. We measured the human performance for detecting a sine-wave target in white noise and natural-scene backgrounds for two levels of prior probability of the target being present. We derived and tested the ideal observer for white-noise backgrounds, a special case of a template-matching observer that dynamically moves its criterion with the background contrast (the DTM observer) and two simpler models with a fixed criterion: the template-matching (TM) observer and the normalized template-matching (NTM) observer that normalizes template response by background contrast. Simulations show that, when the target prior is low, the performance of the NTM observer is near optimal and the TM observer is near chance, suggesting that manipulating the target prior is valuable for distinguishing among models. Surprisingly, we found that the NTM and DTM observers better explain human performance than the TM observer for both target priors in both background types. We argue that the visual system most likely exploits contrast normalization, rather than dynamic criterion adjustment, to deal with simultaneous background contrast and target amplitude uncertainty. Finally, our findings show that the data collected under high levels of uncertainty have a rich structure capable of discriminating between models, providing an alternative approach for studying high dimensions of uncertainty.