Two authors (TS and ZP) were tested in two control sessions (50 trials per session). In the first session, stereoscopic images of 3D symmetrical polyhedra were generated for a 2-m viewing distance but shown to the subjects from a 50-cm viewing distance. For this viewing condition, the perceived depth intervals, as predicted from
Equation 1, were compressed by a factor of 4 compared to the simulated intervals. If the subject's percept is affected by binocular metric information, the perceived 3D shapes would be thinner, as compared to the simulated 3D shapes. Furthermore, the compression of a 3D shape along the depth direction might destroy the 3D mirror symmetry of the perceived shape. In the second session, stereoscopic images of the 3D shapes were generated for a 50-cm viewing distance and shown to the subjects from a 2-m viewing distance. For this viewing condition, the perceived depth intervals, as predicted from
Equation 1, were stretched by a factor of 4 compared to the simulated intervals. If the subject's percept is affected by binocular metric information, the perceived 3D shapes would be stretched in depth, as compared to the simulated 3D shapes, and their 3D symmetry might be destroyed. The remaining aspects of the procedure and the apparatus were the same as those in
Experiment 1. Results of this control experiment are shown in
Figure 10. The graphs on the left show performance in the non-conflict situation, and the graphs on the right show performance in the conflict situation (TS's performance in the non-conflict situation was replotted from
Figure 4). It can be seen that performance is different in these two situations and the change of performance is in the direction predicted by
Equation 1. However, the magnitude of the change is much smaller than what would be predicted by
Equation 1. Specifically, the maximal difference in observed shape recovery errors in the conflict situations, when the ratio of the actual to simulated viewing distance changed by a factor of 16 (from 4:1 to 1:4), is only about 2.5. So, there is some effect of binocular metric information, but this effect is rather small. Both subjects reported that on several trials in the conflict sessions the 3D shapes did not look exactly symmetric. The distortion of symmetry was expected if the binocular shape percept is affected by binocular metric information. What is interesting is that on most trials in the conflict situation the 3D shapes
did look symmetric. This again suggests that the effect of binocular metric information is small and not systematic. Perhaps, in real life, this effect is observed only when the viewing direction is degenerate: parallel or orthogonal to the symmetry plane. Recall that, for such viewing directions, both the symmetry prior and the depth order information are much less effective. However, objects in our natural environment are almost never viewed from degenerate viewing directions, and if they are, the observer can usually move her head in order to view the object from another direction. Therefore, it is possible that binocular metric information is not used too often, at least when the task is to recover shapes of natural objects.