Luminance determinants of perceived surface stratification in two-dimensional achromatic transparent patterns

Two overlapping transparent surfaces forming a two-dimensional pattern stand out in front of each other alternately. Let y denote the luminance of the region where these surfaces overlap and b the luminance of the background. In achromatic patterns, the probability that the lighter transparent surface appears to be in front of the other surface is known to increase with y and with b. The present results show that grouping by achromatic colour similarity cannot explain the effect of b. An alternative conjecture is that the luminance factors that control perceived surface segregation can explain the effects of y and b. Such an explanation predicts a new effect: the probability that one transparent surface appears to be in front increases with the absolute difference in luminance between the surface and the background. The present results confirm this prediction.