Angle Illusion in a Straight Road

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 Misperception of Orientation in Depth When Processing Multiple Pictures With Linear Perspective Cues

The leaning tower illusion suggests that combining perspective cues across multiple images can affect the perceived orientation of objects in space. We measured the accuracy of orientation perception when viewing multiple pictures. Across several experiments, 11-16 participants viewed two pictures: a sidewalk and either another sidewalk, a nature scene, or no picture. Participants adjusted an on-screen line to match the remembered orientation of one of the sidewalks. Participants also made a judgment about the parallelism of the sidewalks. Sidewalks perceived as parallel were perceived to have orientations more similar to each other than when they were paired with a nature scene or no picture. The degree of misperception can be approximately twice as large as in the leaning tower illusion, and this effect survived inversion and partially survived alternating presentation of the images. The misperception was eliminated when the participants were cued on which sidewalk they would be judging; however, when forced to process both sidewalks, the misperception reappeared. We conclude that the orientation of objects with perspective cues is misperceived when viewing multiple pictures with perspective cues and this misperception appears to be related at least in part to how parallel those objects are perceived to be.

A Cube Version of the Square-Diamond Illusion

The square-diamond illusion is often referred to as a type of size illusion. However, the 45-degree tilting of a square remarkably affects perceived corner angles when a cube version of the figure is used. This illusion is measured and discussed in relation to anisotropy in shape interpretation.

The Perspective Structure of Visual Space

Luneburg’s model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg’s model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg’s model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances.