Handbook of Psychology, Volume 4: Experimental Psychology

Depth Perception215

Figure 8.1F=fixation point, I=interocular separation, =depth dif-
ference between FandG, =binocular parallax of F, and =binocular
parallax of G. The relative disparity, , between FandGis – .

D





I

G

F



whereis the angular binocular disparity,Dis the viewing
distance,is the depth, andIis the interocular distance.
The angles and distances of stereo geometry are specified in
Figure 8.1. From disparity, therefore, the depth magnitudes
can be recovered as

 

The previous equation reveals that there is a nonlinear rela-
tionship between horizontal disparity () and depth () that
varies with the interocular separation (I) and the viewing
distance (D). This means that disparity information by itself
is not sufficient for specifying depth magnitudes, because
different combinations of interocular separation, depth, and
distance can generate the same disparity. In order to provide
an estimate about depth, disparity must be scaled, so to speak,
by some other source of information specifying the interocu-
lar separation and the viewing distance. This is the traditional
stereoscopic depth-constancy problem(Ono & Comerford,
1977).
One proposal is that this scaling of disparity is accom-
plished on the basis of extraretinal sources. According to this
approach, failures of veridical depth perception from stereop-
sis have been attributed to the misperception of the viewing
distance. Johnston (1991), for example, showed random-dot
stereograms to observers who decided whether they were
seeing simulated cylinders that were flattened or elongated
along the depth axis with respect to a circular cylinder.
Johnston found that depth was overestimated at small dis-
tances (with physically circular cylinders appearing as elon-
gated in depth) and underestimated at larger distances (with
physically circular cylinders appearing as flattened). These
depth distortions have been attributed to the hypothesis that

D^2



ID

observers scaled the horizontal disparities with an incorrect

measure of physical distance, entailing an overestimation of

close distances and an underestimation of far distances. A

second proposal is that disparity is scaled on the basis of

purely visual information. Mayhew and Longuet-Higgins

(1982), for example, proposed that full metric depth con-

stancy could be achieved by the global computation of verti-

cal disparities. The psychophysical findings, however, do not

support this hypothesis. It has been found, in fact, that human

performance is very poor in tasks involving the estimation of

metric structure from binocular disparities, especially if com-

pared with the precision demonstrated by performance in

stereo acuity tasks involving ordinal-depth discriminations,

with thresholds as low as 2 s arc (Ogle, 1952).

Koenderink and van Doorn (1976) proposed a second

purely visual model of stereo-depth. This model does not try

to account for the recovery of absolute depth, but only for the

recovery of the affine (i.e., ordinal) structure from a combina-

tion of the horizontal and vertical local disparity gradient. This

model, however, is inconsistent with the psychophysical data.

It predicts that the local manipulation of either horizontal or

vertical disparity should have the same effects on perceived

shape; however, it has been shown that the manipulation of the

local horizontal disparities has reliable consequences on per-

ceived depth, whereas the manipulation of the local vertical

disparities does not (Cumming, Johnston, & Parker, 1991).

Moreover, several studies have shown that vertical disparity

processing is not local, but rather is performed by pooling over

a large area (Rogers & Bradshaw, 1993).

In conclusion, binocular disparity in isolation gives rise to

the most compelling impression of depth, and for relatively

short distances provides a reliable source of relative-, but not

of absolute-depth information. Although the geometric rela-

tionship between binocular disparity and depth is well under-

stood, a plausible psychological model of stereopsis has yet

to be provided.

Pictorial

Pictorial depth cues consist of those depth-relevant regulari-

ties that are manifested in pictures. There is a long list of

these cues, and although we have attempted to describe the

most important ones, our list is not exhaustive.

Aerial Perspective. Aerial perspectiverefers to the re-

duction of contrast that occurs when an object is viewed from

great distances. Aerial perspective is the product of the scat-

tering of light by particles in the atmosphere. The contrast

reduction by aerial perspective is a function of both distance

and the attenuation coefficient of the atmosphere. Under hazy