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 as a priori constraints for perceiving shape veridically. The present article provides a comprehensive review of prior studies of the perception of rectangularity and perpendicularity and it discusses their effects on 3D shape perception from both theoretical and empirical approaches. 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 of a 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 this issue, 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 some of the phenomena associated with the perception of the rectangular shape that were reported in prior studies. This finding suggests that rectangularity works for shape perception by incorporating it with some additional constraints.