Depth Perception 223of that information: Familiar size may determine perceived
size, which, in agreement with the size-distance invariance
hypothesis, may determine perceived distance (Ittelson,
1960).
The hypothesis that familiar size may determine apparent
size (or apparent distance) has been denied by the theory of
off-sized perceptions(Gogel & Da Silva, 1987). According to
this theory, the distance of a familiar object under impover-
ished viewing conditions is determined by the egocentric ref-
erence distance, which in turn determines the size of the
object according to the size-distance invariance hypothesis.
Direct Perception
Epstein (1982) summarizes the main ideas of Gibson’s (1979)
account of size perception as follows: “(a) there is no percep-
tual representation of size correlated with the retinal size of
the object; (b) perceived size and perceived distance are in-
dependent direct functions of information in stimulation;
(c) perceived size and perceived distance are not causally
linked, nor is the perception of size mediated by operations
combining information about retinal size and perceived dis-
tance. The correlation between perceived size and perceived
distance is attributed to the correlation between the specific
variables of stimulation which govern these percepts in the
particular situation” (p. 78).
Surprisingly little research on size perception has been
conducted within the direct-perception perspective. How-
ever, the available empirical evidence, consistent with this
perspective, suggests that perceived size might be affected by
the ground texture gradients (Bingham, 1993; Sinai, Ooi, &
He, 1998) and the horizon ratio (Carello, Grosofsky, Reichel,
Solomon, & Turvey, 1989).
Size in Pictures Versus Size in the World
It is sometimes assumed that illusions, especially geometrical
ones, are artifacts of picture perception. This assumption is
false, at least with respect to the anisotropy between vertical
and horizontal extents. The perceptual bias to see vertical ex-
tents as greater than equivalent horizontal extents is even
greater when viewing large objects in the world than when
viewing pictures (Chapanis & Mankin, 1967; Higashiyama,
1996; Yang, Dixon, & Proffitt, 1999).
Yang et al. (1999) compared the magnitude of the vertical-
horizontal illusion for scenes viewed in pictures, in the real
world, and in virtual environments viewed in a head-mounted
display. They found that pictures evoke a bias averaging
about 6%, whereas viewing the same scenes in real or virtual
worlds results in an overestimation of the vertical averaging
about 12%.Geographical Slant PerceptionThe perceptual bias to overestimate vertical extents pales in
comparison to that seen in the perception of geographical
slant. Perceived topography grossly exaggerates the geometri-
cal properties of the world in which we live (Bhalla &
Proffitt, 1999; Kammann, 1967; Ross, 1974; Proffitt, Bhalla,
Gossweiler, & Midgett, 1995).
Proffitt et al. (1995; Bhalla & Proffitt, 1999) obtained two
measures of explicit geographical slant perception from
observers who stood at either the tops or bottoms of hills in
either real or virtual worlds. Observers provided verbal judg-
ments and also adjusted the size of a pie-shape segment of a
disk so as to make it correspond to the cross-section of the
hills they were observing. These two measures were nearly
equivalent and revealed huge overestimations. Five-degree
hills, for example, were judged to be about 20 , and 10 hills
were judged to be about 30. These huge overestimations
seem odd for at least two reasons. First, people know what
angles look like. Proffitt et al. (1995) asked participants to set
cross-sections with the disk to a variety of angles and found
that they were quite accurate in doing so. Second, when
viewing a hill in cross-section, the disk could be accurately
adjusted by lining up the two edges of the pie section to lines
in the visual scene; however, the overestimations found for
people viewing hills in cross-section do not differ from judg-
ments taken when the hills are viewed head-on (Proffitt,
Creem, & Zosh, 2001).
Proffitt and colleagues have argued that the conscious
overestimation of slant is adaptive and reflective of psy-
chophysical response compression (Bhalla & Proffitt, 1999;
Proffitt et al., 2001; Proffitt et al., 1995). Psychophysical re-
sponse compression means that participants’ response sensi-
tivities decline with increases in the magnitude of the stimulus.
Expressed as a power function, the exponent is less than 1. Re-
sponse compression promotes sensitivity to small changes in
slant within the range of small slants that are of behavioral rel-
evance for people. Overestimation necessarily results from a
response compression function that is anchored at 0 and 90.
People are accurate at 0 —they can tell whether the ground is
going up or down—and for similar reasons of discontinuity,
they are also accurate at 90.
All of Proffitt’s and his colleagues’ studies utilized a third
dependent measure, which was a visually guided action in
which participants adjusted the incline of a tilt board without
looking at their hands. These action-based estimates of slant
were far more accurate than were the explicit judgments.