Large Systematic Deviations in Visual Parallelism

Abstract

The visual environment is distorted with respect to the physical environment. Luneburg [1947, Mathematical Analysis of Binocular Vision (Princeton, NJ: Princeton University Press)] assumed that visual space could be described by a Riemannian space of constant curvature. Such a space is described by a metric which defines the distance between any two points. It is uncertain, however, whether such a metric description is valid. Two experiments are reported in which subjects were asked to set two bars parallel to each other in a horizontal plane. The backdrop consisted of wrinkled black plastic sheeting, and the floor and ceiling were hidden by means of a horizontal aperture restricting the visual field of the subject vertically to 10 deg. We found that large deviations (of up to 40 degrees) occur and that the deviations are proportional to the separation angle: on average, the proportion is 30%. These deviations occur for 30 degrees, 60 degrees, 120 degrees, and 150 degrees reference orientations, but not for 0 degree and 90 degrees reference orientations; there the deviation is approximately 0 degree for most subjects. A Riemannian space of constant curvature, therefore, cannot be an adequate description. If it were, then the deviation between the orientation of the test and the reference bar would be independent of the reference orientation. Furthermore, we found that the results are independent of the distance of the bars from the subject, which suggests either that visual space has a zero mean curvature, or that the parallelity task is essentially a monocular task. The fact that the deviations vanish for a 0 degree and 90 degrees orientation is reminiscent of the oblique effect reported in the literature. However, the 'oblique effect' reported here takes place in a horizontal plane at eye height, not in a frontoparallel plane.

Effects of Context on a Visual 3-D Pointing Task

“…For example, Darling and Bartelt (2005) found that an internally specified gravity reference is important for orienting objects visually. Cuijpers et al (2000b) also found an oblique effect in research with a parallelity task in which the observers had to put a bar parallel to a reference bar. The oblique effect that Cuijpers et al found is different from the former oblique effects.…”

Matching perceived depth from disparity and from velocity: Modeling and psychophysics

“…Some of these experiments have been conducted in the laboratory with computer-generated displays Brenner & Landy, 1999;Brenner & van Damme, 1999;Collett, Schwarz, & Sobel, 1991;Johnston, 1991;Johnston, Cumming, & Landy, 1994;Norman & Todd, 1998;Todd, Oomes, Koenderink, & Kappers, 2001;Tittle, Todd, Perotti, & Norman, 1995), whereas other studies have been carried out by using real objects in fully illuminated natural environments (Baird & Biersdorf, 1967;Battro, Netto, & Rozestraten, 1976;Bradshaw, Parton, & Glennerster, 2000;Cuijpers, Kappers, & Koenderink, 2000a, Cuijpers, Kappers, & Koenderink, 2000bGilinsky, 1951;Harway, 1963;Koenderink, van Doorn, Kappers, & Todd, 2002;Koenderink, van Doorn, & Lappin, 2000;Loomis, Da Silva, Fujita, & Fukusima, 1992;Loomis & Philbeck, 1999;Norman, Crabtree, Clayton, & Norman, 2005;Norman, Lappin, & Norman, 2000;Norman, Todd, Perotti, & Tittle, 1996 -see their Experiment 4). In most of the cases, however, the psychophysical literature suggests that human observers do not estimate the viewing distance correctly.…”

Visual space under free viewing conditions

“…Recently, Cuijpers, Kappers, and Koenderink (2000a, 2000b, 2001 did indoor experiments in a room where most pictorial depth cues were eliminated from the visual field by means of wrinkled plastic that prevented observers from seeing the walls. The floor and ceiling of the room were not visible because the observer was seated in a cabin that restricted the vertical field of view.…”

“…For the parallelity task, we also had a third parameter-namely, the orientation of the reference rod. Relative distance and separation angle were chosen as parameters because, together, they can quite naturally give an indication of the positions of the objects with respect to the observer, and also because they were the major parameters in the experiments of Cuijpers et al (2000aCuijpers et al ( , 2000bCuijpers et al ( , 2002). Since we want to test whether a room full of depth information will change the structure of visual space, it is important to be able to use Cuijpers et al's data as a baseline for our measurements.…”