The two-pulse experiment and cross-correlation

Abstract

Rashbass [Rashbass, C. (1970). The visibility of transient changes of luminance. Journal of Physiology, 210, 165–186] presented pairs of flashes having various contrasts separated by a delay, and found that the thresholds for detecting the pairs fell on an ellipse. He fit the data using a model that computed the filtered energy of the pulses. Although this Rashbass model is phase-insensitive, many other experimental results show that humans can perform phase-sensitive detection consistent with a template-matching mechanism. We show that an observer who uses a form of template-matching produces thresholds that fall on an ellipse, just like the Rashbass model. The results from two-pulse experiments are consistent with the idea that humans cross-correlate the stimulus (signal or noise) with a filtered version of the expected signal rather than the signal itself. In symbols, we propose that observers compute ∫ r ( t ) [ s ( t ) ∗ h ( t ) ] d t where r( t) is the received stimulus on a given trial [ s( t) + n( t) or n( t)], s( t) is the signal, h( t) is the visual filter, and ∗ is convolution.