The perception of length on curved and flat surfaces

Abstract

In three experiments, observers judged the apparent extents of spatial intervals along the surface of a curved cylinder or a flat plane that was binocularly viewed in a natural, indoor environment. The observers' judgments of surface lengths were precise and reliable but were also inaccurate and subject to relatively large constant errors. These distortions differed among the observers, but they tended to perceive lengths oriented along the curved dimension of the cylinder as being longer than physically equivalent lengths in the noncurved dimension. This phenomenon did not occur when the observers judged curved and noncurved paths on the flat surface. In addition, some observers' judgments of length were affected by changes in the distance to the cylinder, whereas others were affected by the cylinder's orientation in space. These results demonstrate that the perception of length on surfaces is highly dependent on the particular context in which the length occurs.Vision is primarily a system for perceiving spatial relations in the observer's environment. Its effectiveness is sufficient enough that most observers never question how it is achieved. Scientific investigations of spatial vision were begun more than 160 years ago, but many ofits basic characteristics remain poorly understood. The perception oflength is a good example.Pioneering psychophysical studies of the perception of length were conducted by Weber in the 1830s. Weber found that observers could precisely discriminate small differences in the two-dimensional (2-D) lengths of line segments, with discrimination thresholds on the order of 1%-5% (Weber, 1834(Weber, /1978. Not long afterward, Fechner studied discriminations of lengths between endpoints of compasses, Volkmann examined perceived distances between parallel threads, and both verified Weber's findings about the precision oflength discriminations (reported in Fechner, 1860(reported in Fechner, /1966. Weber, Fechner, and other 19th-century investigators also discovered that the perception of length is relative: A just discriminable inWe thank Myron Braunstein, Hal Sedgwick, and G. John Andersen for their helpful comments and suggestions regarding these experiments. We especially thank Myron Braunstein and John Andersen for suggesting a number of the manipulations included in Experiment 3, which allowed us to separate the relative effects of changes in curvature and depth on the perception oflength on real surfaces. Correspondence concerning this article should be addressed to 1.

Aging and the perception of slant from optical texture, motion parallax, and binocular disparity

“…However, the older observers' judgments were more variable and less precise than those of the younger observers (see Figures 6 and 7). Given that the observers made their judgments of slant manually, purely perceptual judgments of distance in depth, they are typically inaccurate (e.g., Lappin, Shelton, & Rieser, 2006;Loomis, Da Silva, Fujita, & Fukusima, 1992;Loomis & Philbeck, 1999;Norman, Crabtree, Clayton, & Norman, 2005;Norman, Lappin, & Norman, 2000;Norman, Todd, Perotti, & Tittle, 1996). However, when observers make their judgments of distance motorically using blindfolded walking, they are typically accurate (e.g., Loomis et al, 1992;Rieser, Ashmead, Talor, & Youngquist, 1990;Steenhuis & Goodale, 1988;Thomson, 1983).…”

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.…”

Environmental context influences visually perceived distance

“…The common intuition that perceived space is Euclideanthat is, invariant with changes in the observer's viewing position-has been repeatedly contradicted by experimental evidence (e.g., Foley, 1972;Foley et al, 2004;Koenderink, 2001;Koenderink, van Doorn, & Lappin, 2000;Loomis et al, 1996;Norman & Todd, 1993;Norman, Lappin, & Norman, 2000;Norman et al, 1996;Todd & Norman, 2003;Toye, 1986;Wagner, 1985). In Wagner and in Loomis et al (1992), for example, perceived relative distances between objects in an open field were compared, and both studies showed that separations in the sagittal plane appeared to be only about 50%-70% as large as physically equal separations in the frontal plane.…”