Solving an ill-posed inverse problem of three-dimensional (3D) vision
Conventional approaches to vision (i) either assumed that explicit 3D visual representations are not needed, (ii) or they tried to produce 3D reconstructions by combining visual cues (shading, texture, motion, binocular). All these approaches failed because they minimized, or eliminated altogether, the role of a priori constraints (aka priors). The human visual system solves the 3D recovery problem remarkably well, and it does it all the time. So, why not learn from it? I will present a theory that explains how the human visual system recovers 3D shapes and scenes from 2D retinal images. The visual system solves this problem by choosing the most symmetrical 3D interpretations of 2D images. Using 3D symmetry as an a priori constraint makes sense because all natural objects are symmetrical, or nearly so. This is true with animal bodies, plants, as well as man-made objects. Symmetry proves to be very effective computationally because it represents 3D abstract characteristics of objects, rather than the objects themselves. Using an abstract constraint allows the visual system to recover both familiar and unfamiliar 3D shapes and scenes. Note that because symmetry is a mathematical concept, the human visual system does not have to learn it from experience; we may simply be born with it.