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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

Matched angles and computed distances of vanishing points. A. Mean perspective angles (±1 SD) between the rails matched by the three subjects. The judgments were made for physical rails (Rails), depicted rails (Picture), and for lines on a further blank screen (Lines). The black dots indicate the angles of rails and lines measured on the screen, i.e., the proximal stimulus. B. Distances of the vanishing points computed from the judged angles using the inverse relationship expressed by Equation (3) of the Appendix. The left axes indicate distances for the Rails data, the right axes distances for the Picture and Lines data. The dashed lines indicate the distance of the screen relative to the viewer.
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Figure 5: Matched angles and computed distances of vanishing points. A. Mean perspective angles (±1 SD) between the rails matched by the three subjects. The judgments were made for physical rails (Rails), depicted rails (Picture), and for lines on a further blank screen (Lines). The black dots indicate the angles of rails and lines measured on the screen, i.e., the proximal stimulus. B. Distances of the vanishing points computed from the judged angles using the inverse relationship expressed by Equation (3) of the Appendix. The left axes indicate distances for the Rails data, the right axes distances for the Picture and Lines data. The dashed lines indicate the distance of the screen relative to the viewer.

Mentions: Figure 5A shows the matched angles for each individual observer as a function of height of eye or camera. The Lines data show that the subjects judged angles between lines without perspective context with small errors. Angles between rails were judged considerably smaller than between the lines, especially between physical rails. No differences were found between binocular and monocular data. Apart from a few outliers, individual data, both binocular and monocular, differed less than 10° from the mean in each condition. Rails angles ranged from 27% to 63% of the Lines angles and Picture angles from 60% to 83%. Distances of vanishing points were computed from their relationship to the perspective angle. For physical rails, the inverse relationships are shown in Figure 3A and for depicted rails in Figure 3B. The monotonous relationships of Figure 3A gave unique solutions, the peaked relationships of Figure 3B generally gave two solutions. In the case of two solutions, the distance longer than the eye-screen distance gave the appropriate distance of the vanishing point. The computed distances were very short in relation to the length of the visible track. For physical rails, the vanishing distance ranged from just 1.02 to 5.97 m. Distance increased with eye height. For depicted rails, the vanishing distance ranged from 0.79 to 0.94 m. Since the screen was 0.57 m away from the observer, depth between the far and near ends of the rails ranged just from 0.13 to 0.27 m in the three subjects.


The extent of visual space inferred from perspective angles.

Erkelens CJ - Iperception (2015)

Matched angles and computed distances of vanishing points. A. Mean perspective angles (±1 SD) between the rails matched by the three subjects. The judgments were made for physical rails (Rails), depicted rails (Picture), and for lines on a further blank screen (Lines). The black dots indicate the angles of rails and lines measured on the screen, i.e., the proximal stimulus. B. Distances of the vanishing points computed from the judged angles using the inverse relationship expressed by Equation (3) of the Appendix. The left axes indicate distances for the Rails data, the right axes distances for the Picture and Lines data. The dashed lines indicate the distance of the screen relative to the viewer.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Figure 5: Matched angles and computed distances of vanishing points. A. Mean perspective angles (±1 SD) between the rails matched by the three subjects. The judgments were made for physical rails (Rails), depicted rails (Picture), and for lines on a further blank screen (Lines). The black dots indicate the angles of rails and lines measured on the screen, i.e., the proximal stimulus. B. Distances of the vanishing points computed from the judged angles using the inverse relationship expressed by Equation (3) of the Appendix. The left axes indicate distances for the Rails data, the right axes distances for the Picture and Lines data. The dashed lines indicate the distance of the screen relative to the viewer.
Mentions: Figure 5A shows the matched angles for each individual observer as a function of height of eye or camera. The Lines data show that the subjects judged angles between lines without perspective context with small errors. Angles between rails were judged considerably smaller than between the lines, especially between physical rails. No differences were found between binocular and monocular data. Apart from a few outliers, individual data, both binocular and monocular, differed less than 10° from the mean in each condition. Rails angles ranged from 27% to 63% of the Lines angles and Picture angles from 60% to 83%. Distances of vanishing points were computed from their relationship to the perspective angle. For physical rails, the inverse relationships are shown in Figure 3A and for depicted rails in Figure 3B. The monotonous relationships of Figure 3A gave unique solutions, the peaked relationships of Figure 3B generally gave two solutions. In the case of two solutions, the distance longer than the eye-screen distance gave the appropriate distance of the vanishing point. The computed distances were very short in relation to the length of the visible track. For physical rails, the vanishing distance ranged from just 1.02 to 5.97 m. Distance increased with eye height. For depicted rails, the vanishing distance ranged from 0.79 to 0.94 m. Since the screen was 0.57 m away from the observer, depth between the far and near ends of the rails ranged just from 0.13 to 0.27 m in the three subjects.

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