The perception of a 3D shape must be excluded from Hoffman et al.'s "interface theory" primarily because shape is characterized by its symmetries. When these symmetries are used as a priori constraints, 3D shapes are always recovered from 2D retinal images veridically. These facts make it clear that 3D shape perception is completely different from, as well as more important than, all other perceptions because the veridicality of our perception of 3D shapes (and 3D scenes) accounts for our successful adaptation to the natural environment.
Keywords: Shape; Vision; symmetry.