Noisy templates explain area summation.

The noisy template model is a variant of an ideal detector for a signal known except for contrast. The ideal detector cross-correlates the stimulus with a normalised template which is matched to the known signal pattern. The noisy template model simply adds noise to the matched template every time it is cross-correlated with the signal. This paper outlines the predictions of the noisy template model for area summation. The noisy template model explains Piper's Law, as does the ideal-observer, but it also explains critical area phenomena and the lack of area summation for contrast discrimination.