The potential roles of saturating and supersaturating contrast-response functions in conjunction detection: reply to Peirce.

Peirce (2007) proposed a two-stage conjunction detection model in which the outputs of first-stage neurons selective for the conjunction components were summed to give the conjunction-detector output. He argued that a saturating (monotonic) or supersaturating (nonmonotonic) nonlinearity on the outputs of the first-stage neurons made this detector more selective for conjunctions by increasing the ratio of conjunction response to component response at the output stage, i.e., the response of the conjunction detector to a conjunction divided by its response to a single component presented in isolation. The conjunction stimulus that Peirce considered was a maximum-contrast plaid, i.e., the sum of two 0.5contrast gratings of different orientation. The equivalent single-component stimulus was a single maximumcontrast grating. Assuming no cross-orientation inhibition, if the two first-stage neurons are each selective for a different component of the plaid, with a contrastresponse function r(c), where c is component contrast, then the sum of first-stage responses to the plaid is given by rconjunction1⁄4 2r(0.5), and the sum of first-stage responses to the grating is given by rcomponent 1⁄4 r(1). Peirce defined a conjunction selectivity index (CSI), which reflects the ratio of conjunction response to component response at the output stage of his proposed conjunction detector: