Visual contrast detection by a single channel versus probability summation among channels

It is now generally accepted that the human visual system consists of subsystems (channels) that may be activated in parallel. According to some models of detection, detection is by probability summation among channels, while in other models it is assumed that detection is by a single channel that may even be tuned specifically to the stimulus pattern (detection by a matched filter). So far, arguments in particular for the hypothesis of probbbility summation are based on plausibility considerations and on demonstrations that the data from certain detection experiments are compatible with this hypothesis. In this paper it is shown that linear contrast interrelationship functions together with a property of a large class of distribution functions (strict log-concavity or logconvexity on the relevant set of contrasts/intensities) uniquely point to detection by a single channel. In particular, models of detection by probability summation based on Quick's Model are incompatible with linear contrast interrelationship functions. Sufficient (and observable) conditions for the strict logconcavity/log-convexity of distribution functions are presented.