Abstract
A picture is a powerful and convenient medium for inducing the illusion that one perceives a three-dimensional scene. The relative invariance of picture perception across viewing positions has aroused the interest of painters, photographers, and visual scientists. This study explores variables that may underlie the invariance. It presents a computational analysis of distances and directions in sets of two photographs of perspective scenes taken from different camera positions. Focal lengths of the lens and picture sizes are chosen such that the sizes of one of the familiar objects are equally large in both photographs. The selected object is perceived at the same distance in both photographs, independent of viewing distance, showing that pictorial distance is fully determined by angular size of the object. Pictorial distance is independent of camera position, focal length of the lens, and picture size. Distances and directions of pictorial objects are computed as a function of viewing distance, and compared with distances and directions of the physical objects as a function of camera position. The computations show that ratios between pictorial distances, directions, and angular sizes of objects in a photograph are constant, as a function of viewing distance. The constant ratios are proposed as the reason for invariance of picture perception over a range of viewing distances. Reanalysis of distance judgments obtained from the literature shows that perspective space, previously proposed as the model for visual space, is also a good model for pictorial space. The geometry of pictorial space contradicts some conceptions about picture perception.
Highlights
Pictures are images on flat surfaces, in which human subjects can see objects at a distance and in depth
To further test the hypothesis that the geometries of pictorial and visual space are similar, this study presents computations made on sets of two photographs of a perspective scene containing familiar objects
The current study shows that angular size determines the pictorial distance of familiar objects
Summary
Pictures are images on flat surfaces, in which human subjects can see objects at a distance (i.e., relative to the viewer) and in depth (i.e., relative to other objects). Two conclusions relevant for the current study were that (1) familiar shape and size are powerful cues for slant and distance perception, and (2) apart from a stronger underestimation of slant and distance, there was no reason to assume a different geometry for pictorial space. To further test the hypothesis that the geometries of pictorial and visual space are similar, this study presents computations made on sets of two photographs of a perspective scene containing familiar objects. The computations of perceived distances and directions in this study are based on the following hypothesis: “When looking at a picture, viewers perceive the distance of a depicted object (the physical distal stimulus) as the distance of an imaginary physical object (the pictorial distal stimulus) that produces the same retinal image (the proximal stimulus)”. The hypothesis proved to be successful in describing perceived slant of obliquely viewed grid figures as functions of depicted slant and slant of the picture [51,52]
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