The two-pulse experiment and cross-correlation.

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 integral r(t)[s(t) *h(t)]dt 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.