A role of rectangularity in perceiving a 3D shape of an object

Rectangularity and perpendicularity of contours are important properties of 3D shape for the visual system and the visual system can use them asa prioriconstraints for perceivingshape veridically. The presentarticle provides a comprehensive review ofpriorstudiesofthe perception of rectangularity and perpendicularity anditdiscussestheir effects on3D shape perception from both theoretical and empiricalapproaches. It has been shown that the visual system is biased to perceive a rectangular 3D shape from a 2D image. We thought that this bias might be attributable to the likelihood of a rectangular interpretation but this hypothesis is not supported by the results of our psychophysical experiment. Note that the perception ofa rectangular shape cannot be explained solely on the basis of geometry. A rectangular shape is perceived from an image that is inconsistent with a rectangular interpretation. To address thisissue, we developed a computational model that can recover a rectangular shape from an image of a parallelopiped. The model allows the recovered shape to be slightly inconsistent so that the recovered shape satisfies the a priori constraints of maximum compactness and minimal surface area. This model captures someof thephenomenaassociated withthe perception of the rectangular shape that were reported inpriorstudies. This finding suggests that rectangularity works for shape perception by incorporatingitwith someadditionalconstraints.

The Concept of Symmetry and the Theory of Perception

Perceptual constancy refers to the fact that the perceived geometrical and physical characteristics of objects remain constant despite transformations of the objects such as rigid motion. Perceptual constancy is essential in everything we do, like recognition of familiar objects and scenes, planning and executing visual navigation, visuomotor coordination, and many more. Perceptual constancy would not exist without the geometrical and physical permanence of objects: their shape, size, and weight. Formally, perceptual constancy and permanence of objects are invariants, also known in mathematics and physics as symmetries. Symmetries of the Laws of Physics received a central status due to mathematical theorems of Emmy Noether formulated and proved over 100 years ago. These theorems connected symmetries of the physical laws to conservation laws through the least-action principle. We show how Noether's theorem is applied to mirror-symmetrical objects and establishes mental shape representation (perceptual conservation) through the application of a simplicity (least-action) principle. This way, the formalism of Noether's theorem provides a computational explanation of the relation between the physical world and its mental representation.