A simple photometric factor in perceived depth order of bistable transparency patterns

Previous studies on perceptual transparency defined the photometric condition in which perceived depth ordering between two surfaces becomes ambiguous. Even under this bistable transparency condition, it is known that depth-order perceptions are often biased toward one specific interpretation (Beck, Prazdny, & Ivry, 1984; Delogu, Fedorov, Belardinelli, & van Leeuwen, 2010; Kitaoka, 2005; Oyama & Nakahara, 1960). In this study, we examined what determines the perceived depth ordering for bistable transparency patterns using stimuli that simulated two partially overlapping disks resulting in four regions: a (background), b (portion of right disk), p (portion of left disk), and q (shared region). In contrast to the previous theory that proposed contributions of contrast against the background region (i.e., contrast at contour b/a and contrast at contour p/a) to perceived depth order in bistable transparency patterns, the present study demonstrated that contrast against the background region has little influence on perceived depth order compared with contrast against the shared region (i.e., contrast at contour b/q and contrast at contour p/q). In addition, we found that the perceived depth ordering is well predicted by a simpler model that takes into consideration only relative size of lightness difference against the shared region. Specifically, the probability that the left disk is perceived as being in front is proportional to (|b - q| - |p - q|) / (|b - q| + |p - q|) calculated based on lightness.