Brightness as an indicator to distance: relative brightness per se or contrast with the background?

A black and a white target are displayed, in five different conditions, on five grey backgrounds having different degrees of brightness (from very bright to very dark). The results show that the target having the higher contrast with its background is perceived as the nearer. With the off-white background, e.g., the black target appears as the nearer to the observer. This contradicts the well-known concept according to which the brighter target should in any case be perceived as the nearer ("relative brightness" cue). The conclusion is that the frame of reference must be taken into consideration: study of the indicators to distance in an empty space and per se is not sufficient.