i
i
i
i
i
i
i
i
22.3. Spatial Vision 573
partially because of the different sorts of information available from different vi-
sual cues and partly because of the different purposes to which the information
is put (Klatzky, 1998). Egocentric representations are defined with respect to the
viewer’s body. They can be subdivided into coordinate systems fixed to the eyes,
head, or body. Allocentric representations, also called exocentric representations,
are defined with respect to something external to the viewer. Allocentric frames
of reference can be local to some configuration of objects in the environment or
can be globally defined in terms of distinctive locations, gravity, or geographic
properties.
The distance from the viewer to a particular visible location in the environ-
ment, expressed in an egocentric representation, is often referred to as depth in
the perception literature. Surface orientation can be represented in either egocen-
tric or allocentric coordinates. In egocentric representations of orientation, the
term slant is used to refer to the angle between the line of sight to the point and
the surface normal at the point, while the term tilt refers to the orientation of the
projection of the surface normal onto a plane perpendicular to the line of sight.
Distance and orientation can be expressed in a variety of measurement scales.
Absolute descriptions are specified using a standard that is not part of the sensed
information itself. These can be culturally defined standards (e.g, meters), or
standards relative to the viewer’s body (e.g., eye height, the width of one’s shoul-
ders). Relative descriptions relate one perceived geometric property to another
(e.g., point a is twice as far away as point b). Ordinal descriptions are a special
Cue
a r o
Requirements for absolute depth
Accommodation x x x very limited range
Binocular convergence x x x limited range
Binocular disparity - x x limited range
Linear perspective, height x x x requires viewpoint height
in picture, horizon ratio
Familiar size x x x
Relative size - x x
Aerial perspective ? x x adaptation to local conditions
Absolute motion parallax ? x x requires viewpoint velocity
Relative motion parallax - - x
Texture gradients - x -
Shading - x -
Occlusion - - x
Figure 22.17. Common visual cues for absolute (a), relative (r), and ordinal (o) depth.
i
i
i
i
i
i
i
i
574 22. Visual Perception
case of relative measure in which the sign, but not the magnitude, of the relation
is all that is represented. Figure 22.17 provides a list of the most commonly con-
sidered visual cues, along with a characterization of the sorts of information they
can potentially provide.
22.3.2 Ocularmotor Cues
Ocularmotor information about depth results directly from the muscular control
of the eyes. There are two distinct types of ocularmotor information. Accommo-
dation is the process by which the eye optically focuses at a particular distance.
Convergence (often referred to as vergence) is the process by which the two eyes
are pointed towards the same point in three-dimensional space. Both accommo-
dation and convergence have the potential to provide absolute information about
depth.
Physiologically, focusing in the human eye is accomplished by distorting the
shape of the lens at the front of the eye. The vision system can infer depth from
the amount of this distortion. Accommodation is a relatively weak cue to distance
and is ineffective beyond about 2 m. Most people have increasing difficultly in
focusing over a range of distances as they get beyond about 45 years old. For
them, accommodation becomes even less effective.
Those not familiar with the specifics of visual perception sometimes confuse
depth estimation from accommodation with depth information arising out of the
Figure 22.18. Does the central square appear in front of the pattern of circles or is it seen
as appearing through a square hole in the pattern of circles? The only difference in the two
images is the sharpness of the edge between the line and circle patterns (Marshall et al.
(1999), used by permission
).
i
i
i
i
i
i
i
i
22.3. Spatial Vision 575
θ
ipd
z
Figure 22.19. The
vergence
of the two eyes provides information about the distance to the
point on which the eyes are fixated.
blur associated with limited depth-of-field in the eye. The accommodation depth
cue provides information about the distance to that portion of the visual field that
it is in focus. It does not depend on the degree to which other portionsof the visual
field are out of focus, other than that blur is used by the visual system to adjust
focus. Depth-of-field does seem to provide a degree of ordinal depth information
(Figure 22.18), though this effect has received only limited investigation.
If two eyes fixate on the same point in space, trigonometry can be used to
determine the distance from the viewer to the viewed location (Figure 22.19). For
the simplest case, in which the point of interest is directly in front of the viewer,
z =
ipd/2
tan θ
, (22.5)
where z is the distance to a point in the world, ipd is the interpupillary distance
indicating the distance between the eyes, and θ is the vergence angle indicating
the orientation of the eyes relative to straight ahead. For small θ, which is the case
for the geometric configuration of human eyes, tan θ ≈ θ when θ is expressed in
radians. Thus, differences in vergence angle specify differences in depth by the
following relationship:
Δθ ≈
ipd
2
·
1
Δz
. (22.6)
As θ → 0 in uniform steps, Δz gets increasingly larger. This means that stereo
vision is less sensitive to changes in depth as the overall depth increases. Conver-
gence in fact only provides information on absolute depth for distances out to a
few meters. Beyond that, changes in distance produce changes in vergence angle
that are too small to be useful.
There is an interaction between accommodation and convergence in the hu-
man visual system: accommodation is used to help determine the appropriate
i
i
i
i
i
i
i
i
576 22. Visual Perception
vergence angle, while vergence angle is used to help set the focus distance. Nor-
mally, this helps the visual system when there is uncertainty is setting either ac-
commodation or vergence. However, stereographic computer displays break the
relationship between focus and convergence that occurs in the real world, leading
to a number of perceptual difficulties (Wann et al., 1995).
22.3.3 Binocular Disparity
The vergence angle of the eyes when fixated on a common point in space is only
one of the ways that the visual system is able to determine depth from binocular
stereo. A second mechanism involves a comparison of the retinal images in the
two eyes and does not require information about where the eyes are pointed. A
simple example demonstrates the effect. Hold your arm straight out in front of
you, with your thumb pointed up. Stare at your thumb and then close one eye.
Now, simultaneously open the closed eye and close the open eye. Your thumb will
appear to be more or less stationary, while the more distant surfaces seen behind
your thumb will appear to move from side to side (Figure 22.20). The change
in retinal position of points in the scene between the left and right eyes is called
disparity.
The binocular disparity cue requires that the vision system be able to match
the image of points in the world in one eye with the imaged locations of those
points in the other eye, a process referred to as the correspondence problem.This
is a relatively complicated process and is only partially understood. Once cor-
respondences have been established, the relative positions on which particular
(left eye image) (right eye image)
Figure 22.20. Binocular disparity. The view from the left and right eyes shows an offset for
surface points at depths different from the point of fixation.
Images courtesy Peter Shirley.
i
i
i
i
i
i
i
i
22.3. Spatial Vision 577
uncrossed
disparity
crossed
disparity
fixation point
more distant point
nearer point
Figure 22.21. Near the line of sight, surface points nearer than the fixation point produce
disparities in the opposite direction from those associated with surface points more distant
than the fixation point.
points in the world project onto the left and right retinas indicate whether the
points are closer than or farther away than the point of fixation. Crossed disparity
occurs when the corresponding points are displaced outward relative to the fovea
and indicates that the surface point is closer than the point of fixation. Uncrossed
disparity occurs when the corresponding points are displaced inward relative to
the fovea and indicates that the surface point is farther away than the point of
fixation (Figure 22.21).
4
Binocular disparity is a relative depth cue, but it can
provide information about absolute depth when scaled by convergence. Equation
(22.5) applies to binocular disparity as well as binocular convergence. As with
convergence, the sensitivity of binocular disparity to changes in depth decreases
with depth.
22.3.4 Motion Cues
Relative motion between the eyes and visible surfaces will produce changes in the
image of those surfaces on the retina. Three-dimensional relative motion between
the eye and a surface point produces two-dimensional motion of the projection of
the surface point on the retina. This retinal motion is given the name optic flow.
Optic flow serves as the basis for several types of depth cues. In addition, optic
flow can be used to determine information about how a person is moving in the
world and whether or not a collision is imminent (Section 22.4.3).
If a person moves to the side while continuing to fixate on some surface point,
then optic flow provides information about depth similar to stereo disparity. This
4
Technically, crossed and uncrossed disparities indicate that the surface point generating the dis-
parity is closer to or farther away from the horopter. The horopter is not a fixed distance away from
the eyes but rather it is a curved surface passing through the point of fixation.
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.