Limit to the detection of Glass patterns in the presence of noise

A method is developed for quantifying the strength of the moiré effects known as Glass patterns. Unpaired randomly placed dots are added to the pattern while the discriminability d' of the degraded pattern is determined in a yes-no test. For a given discriminability the number of pairs required increases in direct proportion to the number of random dots. A model is developed based on the ideal discrimination of an excess of oriented pairs. Results conforming to Weber's law are predicted; the dependence of d' on the amount of noise and the number of point pairs is also predicted. A numerical constant derived from the model provides a measure of the strength of the moiré effect of a chosen pattern. Note that, for this task, statistical considerations predict Weber's law, not the square-root law, as a limit, and this result holds whenever second-order structure is detected in the image.