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The Perspective Structure of Visual Space

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ABSTRACT

Luneburg’s model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg’s model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg’s model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances.

No MeSH data available.


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Effect of vanishing distance and fixation direction on perspective space. Panels show physical stimuli (blue dots and lines) and their equivalents in perspective space (red dots and lines). Gray dots indicate the positions of the eyes. Panels (a) show the panels of Figure 1 but now for the conditions that the vanishing point is at half the distance. Panels (b) show the panels of Figure 1 for a fixation direction of about 10° to the left side.
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fig3-2041669515613672: Effect of vanishing distance and fixation direction on perspective space. Panels show physical stimuli (blue dots and lines) and their equivalents in perspective space (red dots and lines). Gray dots indicate the positions of the eyes. Panels (a) show the panels of Figure 1 but now for the conditions that the vanishing point is at half the distance. Panels (b) show the panels of Figure 1 for a fixation direction of about 10° to the left side.

Mentions: Perspective space as introduced in the previous section contains two parameters, that is, distance of vanishing point and fixation direction. It is obvious that the parameters may vary across observers and conditions. Distance of vanishing point may depend on context as was recently shown in judgments of perspective angles between rails (Erkelens, 2015a). Distances were about 5 m for judgments made in a full-cue, natural environment and about 0.3 m for judgments made from pictures of the same scene. Fixation direction is fixed in some psychophysical experiments but not in others and certainly not under natural viewing conditions. It is relevant to know how the two parameters affect the positions of objects in perspective space. Figure 3 shows the positions of points in perspective space for a short distance of the vanishing point (Figure 3(a)) and an oblique direction of fixation (Figure 3(b)).Figure 3.


The Perspective Structure of Visual Space
Effect of vanishing distance and fixation direction on perspective space. Panels show physical stimuli (blue dots and lines) and their equivalents in perspective space (red dots and lines). Gray dots indicate the positions of the eyes. Panels (a) show the panels of Figure 1 but now for the conditions that the vanishing point is at half the distance. Panels (b) show the panels of Figure 1 for a fixation direction of about 10° to the left side.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License 1 - License 2 - License 3
Show All Figures
getmorefigures.php?uid=PMC5016827&req=5

fig3-2041669515613672: Effect of vanishing distance and fixation direction on perspective space. Panels show physical stimuli (blue dots and lines) and their equivalents in perspective space (red dots and lines). Gray dots indicate the positions of the eyes. Panels (a) show the panels of Figure 1 but now for the conditions that the vanishing point is at half the distance. Panels (b) show the panels of Figure 1 for a fixation direction of about 10° to the left side.
Mentions: Perspective space as introduced in the previous section contains two parameters, that is, distance of vanishing point and fixation direction. It is obvious that the parameters may vary across observers and conditions. Distance of vanishing point may depend on context as was recently shown in judgments of perspective angles between rails (Erkelens, 2015a). Distances were about 5 m for judgments made in a full-cue, natural environment and about 0.3 m for judgments made from pictures of the same scene. Fixation direction is fixed in some psychophysical experiments but not in others and certainly not under natural viewing conditions. It is relevant to know how the two parameters affect the positions of objects in perspective space. Figure 3 shows the positions of points in perspective space for a short distance of the vanishing point (Figure 3(a)) and an oblique direction of fixation (Figure 3(b)).Figure 3.

View Article: PubMed Central - PubMed

ABSTRACT

Luneburg’s model has been the reference for experimental studies of visual space for almost seventy years. His claim for a curved visual space has been a source of inspiration for visual scientists as well as philosophers. The conclusion of many experimental studies has been that Luneburg’s model does not describe visual space in various tasks and conditions. Remarkably, no alternative model has been suggested. The current study explores perspective transformations of Euclidean space as a model for visual space. Computations show that the geometry of perspective spaces is considerably different from that of Euclidean space. Collinearity but not parallelism is preserved in perspective space and angles are not invariant under translation and rotation. Similar relationships have shown to be properties of visual space. Alley experiments performed early in the nineteenth century have been instrumental in hypothesizing curved visual spaces. Alleys were computed in perspective space and compared with reconstructed alleys of Blumenfeld. Parallel alleys were accurately described by perspective geometry. Accurate distance alleys were derived from parallel alleys by adjusting the interstimulus distances according to the size-distance invariance hypothesis. Agreement between computed and experimental alleys and accommodation of experimental results that rejected Luneburg’s model show that perspective space is an appropriate model for how we perceive orientations and angles. The model is also appropriate for perceived distance ratios between stimuli but fails to predict perceived distances.

No MeSH data available.


Related in: MedlinePlus