Prior research has indicated that perceived depth from binocular disparity becomes increasingly compressed as viewing distance increases. One geometric consequence of this is that a symmetric 3D object should be perceived as asymmetric whenever the axis of compression is at an oblique angle to the plane of 3D symmetry. Method: To test this hypothesis, we presented binocular images of 3D polyhedra with one plane of mirror symmetry, similar to the stimuli of Li et al. (2011, doi:10.1167/11.4.11). On each trial, one of fifteen objects was rendered against a gray background on a LCD monitor. The 3D orientations of these objects were constrained so that the viewing direction (i.e., the Z-axis) formed an oblique angle with the object's symmetry plane, and at least five pairs of corresponding vertices were visible. Visible edges were all rendered in black, all occluded regions were removed, and polka-dot textures were mapped onto each visible face. Six observers looked at each polyhedron through LCD shutter glasses binocularly from a chin rest and pressed keys to stretch or compress the object along the Z dimension so as to make it appear as symmetrical as possible. Each observer performed 90 trials each from two viewing distances: "near" (100cm) and "far" (200cm). The dependent variable was the Z-scaling (S) required to make the object appear symmetrical. S=1 produced an object with perfect 3D symmetry, whereas deviations up or down from 1 produced increasing asymmetries. Results: For most observers, the adjustments were significantly larger than 1 and increased systematically with viewing distance. The group-averaged mean adjustment was S=1.24 (SE=0.07) and 1.61 (SE=0.18) at the near and far distances, respectively. This suggests that observers' inability to accurately scale binocular disparities can cause physically symmetric objects to appear asymmetric, and some asymmetric objects to appear symmetric.
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