Limits...
The extent of visual space inferred from perspective angles.

Erkelens CJ - Iperception (2015)

Bottom Line: Perspective projections do not explain why we perceive perspective in 3-D space.The shallow depth of a hypothetical space inferred from perspective angles does not match the depth of visual space, as it is perceived.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.

View Article: PubMed Central - PubMed

Affiliation: Helmholtz Institute, Utrecht University, Utrecht, The Netherlands; e-mail: c.j.erkelens@uu.nl.

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.

No MeSH data available.


Related in: MedlinePlus

Stimulus geometry. (a) The subject viewed (E represents the position of the eyes) physical rails (thick black lines) from a central position between the rails. The rails seemed to converge to vanishing point V. (b) The subject viewed rails depicted on the vertical screen (blue). The relationship between perspective angle φ at V and distance of the vanishing point (r) was computed from the geometry of the isosceles triangle (red) with base b and height h, and eye height e. The proximal stimuli (projections in the blue planes) are identical in (a) and (b). For reasons of clarity the examples (a) and (b) are fictitious and are drawn at different scales.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4441024&req=5

Figure 6: Stimulus geometry. (a) The subject viewed (E represents the position of the eyes) physical rails (thick black lines) from a central position between the rails. The rails seemed to converge to vanishing point V. (b) The subject viewed rails depicted on the vertical screen (blue). The relationship between perspective angle φ at V and distance of the vanishing point (r) was computed from the geometry of the isosceles triangle (red) with base b and height h, and eye height e. The proximal stimuli (projections in the blue planes) are identical in (a) and (b). For reasons of clarity the examples (a) and (b) are fictitious and are drawn at different scales.

Mentions: The relationship between perspective angle (φ) and distance between viewer and vanishing point (r) is illustrated in Figure 6 for viewing disappearing rails of a real railway line (a) and for viewing the same rails in a picture (b). The relationship is determined by two equations. Trigonometry of the red isosceles triangle of Figure 6a provides one equation, namely,(1)ϕ=2arctan⁡(b2h)and the Pythagorean theorem provides the other,(2)e2+r2=h2.Elimination of h from equations 1 and 2 gives(3)ϕ=2arctan⁡(b2e2+r2).


The extent of visual space inferred from perspective angles.

Erkelens CJ - Iperception (2015)

Stimulus geometry. (a) The subject viewed (E represents the position of the eyes) physical rails (thick black lines) from a central position between the rails. The rails seemed to converge to vanishing point V. (b) The subject viewed rails depicted on the vertical screen (blue). The relationship between perspective angle φ at V and distance of the vanishing point (r) was computed from the geometry of the isosceles triangle (red) with base b and height h, and eye height e. The proximal stimuli (projections in the blue planes) are identical in (a) and (b). For reasons of clarity the examples (a) and (b) are fictitious and are drawn at different scales.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4441024&req=5

Figure 6: Stimulus geometry. (a) The subject viewed (E represents the position of the eyes) physical rails (thick black lines) from a central position between the rails. The rails seemed to converge to vanishing point V. (b) The subject viewed rails depicted on the vertical screen (blue). The relationship between perspective angle φ at V and distance of the vanishing point (r) was computed from the geometry of the isosceles triangle (red) with base b and height h, and eye height e. The proximal stimuli (projections in the blue planes) are identical in (a) and (b). For reasons of clarity the examples (a) and (b) are fictitious and are drawn at different scales.
Mentions: The relationship between perspective angle (φ) and distance between viewer and vanishing point (r) is illustrated in Figure 6 for viewing disappearing rails of a real railway line (a) and for viewing the same rails in a picture (b). The relationship is determined by two equations. Trigonometry of the red isosceles triangle of Figure 6a provides one equation, namely,(1)ϕ=2arctan⁡(b2h)and the Pythagorean theorem provides the other,(2)e2+r2=h2.Elimination of h from equations 1 and 2 gives(3)ϕ=2arctan⁡(b2e2+r2).

Bottom Line: Perspective projections do not explain why we perceive perspective in 3-D space.The shallow depth of a hypothetical space inferred from perspective angles does not match the depth of visual space, as it is perceived.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.

View Article: PubMed Central - PubMed

Affiliation: Helmholtz Institute, Utrecht University, Utrecht, The Netherlands; e-mail: c.j.erkelens@uu.nl.

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.

No MeSH data available.


Related in: MedlinePlus