The extent of visual space inferred from perspective angles

Abstract

Retinal images are perspective projections of the visual environment. Perspective projections do not explain why we perceive perspective in 3-D space. Analysis of underlying spatial transformations shows that visual space is a perspective transformation of physical space if parallel lines in physical space vanish at finite distance in visual space. Perspective angles, i.e., the angle perceived between parallel lines in physical space, were estimated for rails of a straight railway track. Perspective angles were also estimated from pictures taken from the same point of view. Perspective angles between rails ranged from 27% to 83% of their angular size in the retinal image. Perspective angles prescribe the distance of vanishing points of visual space. All computed distances were shorter than 6 m. The shallow depth of a hypothetical space inferred from perspective angles does not match the depth of visual space, as it is perceived. Incongruity between the perceived shape of a railway line on the one hand and the experienced ratio between width and length of the line on the other hand is huge, but apparently so unobtrusive that it has remained unnoticed. The incompatibility between perspective angles and perceived distances casts doubt on evidence for a curved visual space that has been presented in the literature and was obtained from combining judgments of distances and angles with physical positions.