## 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.

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.

Original language | English |
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Pages (from-to) | 5-14 |

Journal | i-Perception |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - 6 Jan 2015 |

## Keywords

- Euclidean geometry
- perspective angles
- slant
- vanishing points
- visual space