Convexity theorem for subthreshold stimuli in linear models of visual contrast detection

Under the general assumption that visual contrast detection occurs by a parallel array of linear detectors, either without probability summation or with probability summation of a commonly assumed type, it is shown that the set of functions representing subthreshold stimuli must be convex. Thus, for example, a planar plot of the threshold locus using multiples of any two functions as axes, must be convex (cannot bulge inward). If experimental evidence to the contrary were discovered, it would rule out detection by parallel linear detectors of the above type. One possible kind of such evidence would be an inward cusp of the threshold locus corresponding to one of a special class of stimuli to which the visual system might be specifically sensitive.