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The theory of signal detectability (TSD) predicts that uncertainty of the spatial location of a luminance-increment stimulus should influence the detectability of the stimulus. If d′ is the detectability, E is the increment luminance, N2 is the variance of the noise that obscures the signal, and M is the number of equally likely non-overlapping stimuli, TSD predicts (d′) 2 = loge1–1/M + 1/M exp (E2/N2). TSD also predicts that the slope of the ROC curve on probability paper should decrease in the presence of stimulus-position uncertainty. Both predictions were confirmed in psychophysical tests of human observers for foveally viewed stimuli.
Cohn et al. (Sun,) studied this question.