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.

Highlights

  • Visual space is the space that we perceive as the consequence of instantaneous visual stimulation of the eyes

  • If the inferred visual space would be congruent to physical space, i.e., Euclidean space, we would have expected perspective angles close to zero degree

  • If perspective angles would be unrelated to visual space, we would have expected to measure perspective angles similar to the angles between rails and lines in the proximal stimulus

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Summary

Introduction

Visual space is the space that we perceive as the consequence of instantaneous visual stimulation of the eyes. The structure of visual space has been the subject of many experimental, theoretical, and philosophical studies (Blank, 1961; Blumenfeld, 1913; Cuijpers, Kappers & Koenderink, 2000; Foley, 1972; Hatfield, 2003; Higashiyama, 1984; Hillebrand, 1902; Indow, 1991; Koenderink, van Doorn, & Lappin, 2000; Luneburg, 1950; Musatov, 1976; Suppes, 1977; Todd, Oomes, Koenderink, & Kappers, 2001; Wagner, 1985). Most studies have been concerned with the near-binocular space. The properties of a richly structured visual space beyond near distance have received less attention. Recent studies have shown that properties of the ground surface in the real world can significantly affect distance perception (Sinai, Ooi, & He, 1998; Wu, Ooi, & He, 2004). Distance estimation was found to be very accurate for flat and continuous surfaces up to 20 m (Sinai et al, 1998)

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