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.