An image-driven model for pattern detection, resistant to Birdsall linearisation

If detection were governed by an isolated (and possibly nonlinear) transducer, then a linearisation of the psychometric function (d-prime vs target amplitude) must accompany any threshold elevation due to the addition of external noise. This is the Birdsall theorem. From the fact that noise can elevate threshold without linearising the psychometric function, we can safely infer that detection is not governed by an isolated transducer. Heretofore, image-driven models, which accept images or numerical descriptions thereof as input, have proven incompatible with this failure of Birdsall linearisation, unless they incorporate the principle of intrinsic uncertainty, which asserts that detection is governed by the maximum activity in several independent (noisy) sensors. One image-driven model incompatible with the failure of Birdsall linearisation is Watson and Solomon's (J. Opt. Soc. Am. A, 14 (1997), 2379) model of visual contrast gain control and pattern masking. Here I report a simple modification - pooling sensor outputs before, instead of after the comparison of input images - allowing that model to predict curved psychometric functions, even when external noise elevates threshold by more than 20 dB, without any detrimental effect to the quality of its fit to pattern-masking thresholds in the absence of noise. The failure of Birdsall linearisation, therefore, does not necessarily imply independent samples of performance-limiting noise in multiple visual sensors. Instead, performance-limiting noise may arise after the visual system combines output from mutually inhibitory sensors.