Perceiving 3D shape constancy across changes in viewpoint is a challenging problem. We tested whether the presence of symmetry can facilitate shape discrimination for smoothly curved, solid 3D objects. Symmetric and asymmetric random shapes were generated to have the same angular power spectra, expressed as spherical harmonics. Objects were presented in three viewing conditions: shading-only, stereo-only, and combined shading and stereo. Shaded objects were illuminated by a diffused point light source, and a mirror haploscope was used to present binocular images. Objects were presented sequentially and observers judged whether the two shapes were same or different. The test objects were either the same orientation or differed by a rotation in depth of ±15°, ±30°, or ±60° relative to the standard object. In all conditions, we found that shape discrimination performance decreased with rotation in depth. Overall, shape discrimination for symmetric objects was better than for asymmetric objects. The presence of stereo information improved performance for both symmetric and asymmetric objects. The results suggest that structural constraints like symmetry are important for viewpoint invariant shape perception, and that stereo information improves shape perception even for structured 3D objects.
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