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

Spatial transformations. Left figures: Parallel lines and planes in physical space run from a screen (light blue) in front of an eye to infinity (just a finite part is shown). Center figures: Projections of the lines and planes on the frontal screen represent the proximal stimulus. Right figures: Visual space is postulated to be the 3-D expansion of the proximal stimulus in depth limited to a finite vanishing point. The vanishing point is in the straight-ahead direction in the top figures and in a rightward direction in the bottom figures. The light-red vertical plane indicates the sagittal plane.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Spatial transformations. Left figures: Parallel lines and planes in physical space run from a screen (light blue) in front of an eye to infinity (just a finite part is shown). Center figures: Projections of the lines and planes on the frontal screen represent the proximal stimulus. Right figures: Visual space is postulated to be the 3-D expansion of the proximal stimulus in depth limited to a finite vanishing point. The vanishing point is in the straight-ahead direction in the top figures and in a rightward direction in the bottom figures. The light-red vertical plane indicates the sagittal plane.

Mentions: In vision, two processes may have a significant impact on the representation of the physical space. One process is optical and the other neural of nature. In Figure 1, sets of lines and planes are drawn to show how the two processes retain and change specific spatial properties. The first process is the optical transformation from 3-D to 2-D space and occurs in the eye where light reflected from objects in physical space is projected onto the retina. In Figure 1, the retinal projection, i.e., proximal stimulus, is imaged as a pattern on a screen placed in front of the eye perpendicular to the straight-ahead direction. The projection on the screen is a planar representation of the retinal stimulus. The proximal stimulus is inevitably a perspective projection of physical space because the eye collects spatial information from a single vantage point. A consequence of linear perspective is that straight lines in the proximal stimulus are projections of straight lines in physical space (Tyler, 2014). Another consequence of linear perspective is that projections of lines of one orientation in physical space (1 in Figure 1) converge to a single point in the proximal stimulus (2 in Figure 1). Lines of different orientation (4 in Figure 1) have a different point of convergence (5 in Figure 1).


The extent of visual space inferred from perspective angles.

Erkelens CJ - Iperception (2015)

Spatial transformations. Left figures: Parallel lines and planes in physical space run from a screen (light blue) in front of an eye to infinity (just a finite part is shown). Center figures: Projections of the lines and planes on the frontal screen represent the proximal stimulus. Right figures: Visual space is postulated to be the 3-D expansion of the proximal stimulus in depth limited to a finite vanishing point. The vanishing point is in the straight-ahead direction in the top figures and in a rightward direction in the bottom figures. The light-red vertical plane indicates the sagittal plane.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Spatial transformations. Left figures: Parallel lines and planes in physical space run from a screen (light blue) in front of an eye to infinity (just a finite part is shown). Center figures: Projections of the lines and planes on the frontal screen represent the proximal stimulus. Right figures: Visual space is postulated to be the 3-D expansion of the proximal stimulus in depth limited to a finite vanishing point. The vanishing point is in the straight-ahead direction in the top figures and in a rightward direction in the bottom figures. The light-red vertical plane indicates the sagittal plane.
Mentions: In vision, two processes may have a significant impact on the representation of the physical space. One process is optical and the other neural of nature. In Figure 1, sets of lines and planes are drawn to show how the two processes retain and change specific spatial properties. The first process is the optical transformation from 3-D to 2-D space and occurs in the eye where light reflected from objects in physical space is projected onto the retina. In Figure 1, the retinal projection, i.e., proximal stimulus, is imaged as a pattern on a screen placed in front of the eye perpendicular to the straight-ahead direction. The projection on the screen is a planar representation of the retinal stimulus. The proximal stimulus is inevitably a perspective projection of physical space because the eye collects spatial information from a single vantage point. A consequence of linear perspective is that straight lines in the proximal stimulus are projections of straight lines in physical space (Tyler, 2014). Another consequence of linear perspective is that projections of lines of one orientation in physical space (1 in Figure 1) converge to a single point in the proximal stimulus (2 in Figure 1). Lines of different orientation (4 in Figure 1) have a different point of convergence (5 in Figure 1).

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