Phase-dependent asymmetry of pattern masking in natural images explained by intrinsic position uncertainty

A number of recent studies have been directed at measuring and modeling detection of targets at specific locations in natural backgrounds, a key subtask of visual search in natural environments. A useful approach is to bin natural background patches into joint histograms with bins along specific background dimensions. By measuring psychometric functions in a sparse subset of these bins, it is possible to estimate how the included dimensions jointly affect detectability over the whole space of natural backgrounds. In previous studies, we found that threshold is proportional to the product of the background luminance, contrast, and similarity; a result predicted by a simple template-matching observer with divisive normalization along each of the dimensions. The measure of similarity was the cosine similarity of the amplitude spectra of the target and background (S(A))—a phase-invariant measure. Here, we investigated the effect of the cosine similarity of the target and background images (S(I|A))—a phase-dependent measure. We found that threshold decreases monotonically with S(I|A) in agreement with a recent study (Rideaux et al., 2022). In contrast, the template-matching observer predicts threshold to be a U-shaped function of S(I|A) reaching a minimum when the target and background are orthogonal (S(I|A) = 0). Surprisingly, when the template-matching observer includes a small amount of intrinsic position uncertainty (measured in a separate experiment) the pattern of thresholds is explained.