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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.


Parallel and distance alleys as measured by Blumenfeld (1913). Panels show the stimuli at their initial locations (blue dots) and the mean settings of four subjects under the instructions of parallelism (red dots) and equidistance (green dots). The panel labeled Means shows the settings averaged across the four subjects. Gray dots indicate the positions of the eyes.
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fig4-2041669515613672: Parallel and distance alleys as measured by Blumenfeld (1913). Panels show the stimuli at their initial locations (blue dots) and the mean settings of four subjects under the instructions of parallelism (red dots) and equidistance (green dots). The panel labeled Means shows the settings averaged across the four subjects. Gray dots indicate the positions of the eyes.

Mentions: A critical test for the perspective space model is being able to describe the parallel and distance alleys of Blumenfeld (1913) because on the basis of these alleys Luneburg (1947, 1950) concluded that visual space had to be a Riemannian space of constant curvature. To make the alley results accessible to computation, Blumenfeld’s data were reanalyzed and rearranged. Blumenfeld (1913) reported the parallel and distance alleys in an extensive paper of 160 pages including 73 tables, written in the German language. Each table lists the settings made by one subject under one (parallel or equidistant) instruction. Four subjects produced complete sets of data in both types of alley experiments. Blumenfeld (1913) did not provide an oversight of these data. Therefore, parallel and distance alleys were constructed from Blumenfeld’s tables for these four subjects (Figure 4). Mean settings were computed of all settings made by individual subjects. No distinction was made between measurements in which stimuli were presented simultaneously or in succession.Figure 4.


The Perspective Structure of Visual Space
Parallel and distance alleys as measured by Blumenfeld (1913). Panels show the stimuli at their initial locations (blue dots) and the mean settings of four subjects under the instructions of parallelism (red dots) and equidistance (green dots). The panel labeled Means shows the settings averaged across the four subjects. Gray dots indicate the positions of the eyes.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

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

fig4-2041669515613672: Parallel and distance alleys as measured by Blumenfeld (1913). Panels show the stimuli at their initial locations (blue dots) and the mean settings of four subjects under the instructions of parallelism (red dots) and equidistance (green dots). The panel labeled Means shows the settings averaged across the four subjects. Gray dots indicate the positions of the eyes.
Mentions: A critical test for the perspective space model is being able to describe the parallel and distance alleys of Blumenfeld (1913) because on the basis of these alleys Luneburg (1947, 1950) concluded that visual space had to be a Riemannian space of constant curvature. To make the alley results accessible to computation, Blumenfeld’s data were reanalyzed and rearranged. Blumenfeld (1913) reported the parallel and distance alleys in an extensive paper of 160 pages including 73 tables, written in the German language. Each table lists the settings made by one subject under one (parallel or equidistant) instruction. Four subjects produced complete sets of data in both types of alley experiments. Blumenfeld (1913) did not provide an oversight of these data. Therefore, parallel and distance alleys were constructed from Blumenfeld’s tables for these four subjects (Figure 4). Mean settings were computed of all settings made by individual subjects. No distinction was made between measurements in which stimuli were presented simultaneously or in succession.Figure 4.

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.