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22.3. Spatial Vision 579
distant, occluded surface. Comparisons of the motion of surface texture to either
side of a boundary can also be used to infer ordinal depth, even in the absence
of accretion or deletion of the texture. Discontinuities in optic flow and accre-
tion/deletion of surface texture are referred to as dynamic occlusion cues and are
another powerful source of visual information about the spatial structure of the
environment.
The speed that a viewer is traveling relative to points in the world cannot be
determined from visual motion alone (see Section 22.4.3). Despite this limitation,
it is possible to use visual information to determine the time it will take to reach a
visible point in the world even when speed cannot be determined. When velocity
is constant, time-to-contact (often referred to as time-to-collision)isgivenbythe
retinal size of an entity towards which the observer is moving, divided by the rate
at which that image size is increasing.
5
In the biological vision literature, this is
often called the τ function (Lee & Reddish, 1981). If distance information to the
structure in the world on which the time-to-collision estimate is based is available,
then this can be used to determine speed.
22.3.5 Pictorial Cues
An image can contain much information about the spatial structure of the world
from which it arose, even in the absence of binocular stereo or motion. As evi-
dence for this, note that the world still appears three-dimensional even if we close
one eye, hold our head stationary, and nothing moves in the environment. (As
discussed in Section 22.5, the situation is more complicated in the case of pho-
tographs and other displayed images.) There are three classes of such pictorial
depth cues. The best known of these involve linear perspective.Therearealso
Figure 22.24. The
classical linear perspective
effects include object size
scaled by distance, the con-
vergence of parallel lines,
the ground plane extending
to a visible horizon, and po-
sition on the ground plane
relative to the horizon.
Im-
age courtesy Sam Pullara.
a number of occlusion cues that provide information about ordinal depth even in
the absence of perspective. Finally, illumination cues involving shading, shadows
and interreflections, and aerial perspective also provide visual information about
spatial layout.
The term linear perspective is often used to refer to properties of images in-
volving object size in the image scaled by distance, the convergence of parallel
lines, the ground plane extending to a visible horizon, and the relationship be-
tween the distance to objects on the ground plane and the image location of those
objects relative to the horizon (Figure 22.24). More formally, linear perspective
cues are those visual cues which exploit the fact that under perspective projection,
the image location onto which points in the world are projected is scaled by
1
z
,
5
The terms time-to-collision and time-to-contact are misleading, since contact will only occur if
the viewer’s trajectory actually passes through or near the entity under view.