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Chapter 6

PSYB51H3 Chapter 6: Chapter 6

Course Code
Matthias Niemeier

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Chapter 6: Space Perception and Binocular Vision
The ability to perceive and interact with the structure of space is one of the fundamental goals of the
visual system
Realism: a philosophical position arguing that there is a real world to sense
Positivism: a philosophical position arguing that all we really have to go on is the evidence of the
senses, so the world might be nothing more than an elaborate hallucination
Euclidean: referring to the geometry of the world, so named in honour of Euclid, the ancient Greek
geometer of the third century BCE. In Euclidean geometry, parallel lines remain parallel as they are
extended in space, objects maintain the same size and shape as they move around in space, the
internal angles of a triangle always add to 180 degrees, and so forth
Although the real world is Euclidean, the geometry of retinal images of that world is decidedly non-
The geometry becomes non-Euclidean when the three-dimensional world is projected onto the
curved, two-dimensional surface of the retina
Parallel lines in the world do not necessarily remain parallel in the retinal image, the angles of a
triangle don’t always add up to 180 degrees, and the retinal area occupied by an object gets
smaller as the object moves farther away from the eyeball
Generally, we reconstruct the world from two non-Euclidean inputs: the two distinct retinal images.
Because the retinas are in slightly different places, they always differ. Your two eyes see somewhat
different views of the world
Why have two eyes?
One advantage of having two eyes is that if you lose one, you still have the other
Secondly, having two eyes allows you to see more of the world
Our visual field is limited to about 190 degrees from left to right, 110 degrees of which is covered by
both eyes
The field is more restricted vertically: about 60 degrees up from the center of gaze and 80 degrees
down—limited by the anatomy of cheeks and eyebrows
Binocular: with two eyes
Overlapping binocular visual fields give predator animals a better chance to spot small, fast-moving
objects in front of them
Binocular summation: the combination (or “summation”) of signals from each eye in ways that make
performance on many tasks better with both eyes than with either eye alone
This principle may have provided the evolutionary pressure that first moved eyes to the front of
some birds’ and mammals’ faces
Once the eyes moved to the front, evolution found an additional use for overlapping visual fields:
binocular disparity: the differences between the two retinal images of the same scene. Disparity is the
basis for stereopsis, a vivid perception of the three-dimensionality of the world that is not available with
monocular vision
Monocular: with one eye
Stereopsis: the ability to use binocular disparity as a cue to depth
Stereopsis is not a necessary condition for depth perception or space perception
Painters and movie directors manage to convey realistic impressions of depth on flat canvases and
movie screens
Stereopsis adds a richness to perception of the three-dimensional world
Depth cues: information about the third dimension (depth) of visual space. Depth cues may be
monocular or binocular
Monocular depth cue: a depth cue that is available even when the world is viewed with one eye alone
Binocular depth cue: a depth cue that relies on information from both eyes. Stereopsis is the primary
example in humans, but convergence and the ability of two eyes to see more of an object than one eye
sees are also binocular depth cues

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Monocular Cues to Three-Dimensional Space
It is geometrically impossible for the visual system to create a perfectly faithful reconstruction of
Euclidean space, given the non-Euclidean input we receive through our eyes
The best we can do is to use depth cues to infer aspects of the three-dimensional world from our two-
dimensional retinal images
Occlusion: a cue to relative depth order in which, for example, one object obstructs the view of part of
another object
As a depth cue, occlusion gives information about the relative position of objects
Occlusion is present in almost every visual scene, and many researchers argue that it is the most
reliable of all the depth cues
It is wrong only in the case of “accidental viewpoints”, with a careful placement of the objects and the
Occlusion is a nonmetrical depth cue—a depth cue that provides information about the depth order
(relative depth) but not depth magnitude (e.g., his nose is in front of his face)—it just gives us the
relative orderings of occluders and occludes
Metrical depth cue: a depth cue that provides quantitative information about distance in the third
Size and Position Cues
Projective geometry: for purposes of studying perception of the three-dimensional world, the geometry
that describes the transformations that occur when the three-dimensional world is projected onto a two-
dimensional surface. For example, parallel lines do not converge in the real world, but they do in the
two-dimensional projection of that world
The image on the retina formed by an object out in the world gets smaller as the object gets farther
Projective geometry describes how the world is projected onto a surface
Relative size: a comparison of size between items without knowing the absolute size of either one
The visual system knows that, all else being equal, smaller things are farther away
Texture gradient: a depth cue based on the geometric fact that items of the same size form smaller
images when they are farther away. An array of items that change in size smoothly across the image
will appear to form a surface titled in depth
Relative height: as a depth cue, the observation that objects at different distances from the viewer on
the ground plane will form images at different heights in the retinal image. Objects farther away will be
seen as higher in the image
Texture fields that provide an impression of three-dimensionality are really combinations of relative size
and relative height cues
In Figure 6.11 page 155, the rabbit in the top centre is the same size as the rabbit in the right bottom.
But the one on the bottom right seems smaller. This is because we infer, on the basis of relative height,
that the rabbit at the bottom must be closer. If it is closer and it forms an image of the same size as the
rabbit at the top centre, it follows that the rabbit at the bottom must be smaller
Familiar size: a depth cue based on knowledge of the typical size of objects, such as humans or
Recall that occlusion is a nonmetrical cue, providing only depth order. The relative size and relative
height cues, especially taken together, provide some metrical information
Relative metrical depth cue: a depth cue that could specify, for example, that object A is twice as far
away as object B without providing information about the absolute distance to either A or B
Relative size and height do not tell us the exact distance to an object or between objects
Absolute metrical depth cue: a depth cue that provides quantifiable information about distance in the
third dimension (e.g., his nose sticks out 4 centimeters in front of his face)
Familiar size could be an absolute metrical depth cue
If your visual system knew the actual size of an object and the visual angle of the object’s projection
on the retina, it could (at least in theory) calculate the exact distance from object to eye

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In practice, however, even if you know that your friend is 5’10 tall, the visual system does not seem
to know that fact with a precision that would let you know he’s standing exactly 12 feet away
Aerial Perspective
Fainter objects may appear to be farther away than darker ones
Aerial perspective (or haze): a depth cue based on the implicit understanding that light is scattered by
the atmosphere. More light is scattered when we look through more atmosphere. Thus, more distant
objects are subject to more scatter and appear fainter, bluer, and less distinct
Figure 6.15: short wavelengths (blue) are scattered more than medium and long wavelengths. This is
why the sky looks blue and why objects farther away look not only hazy, but bluish
Scattering of light by the atmosphere makes more distant features appear hazy and blue
Linear Perspective
Linear perspective: a depth cue based on the fact that lines that are parallel in the three-dimensional
world will appear to converge in a two-dimensional image
Except when the parallel lines lie in a plane that is parallel to the plane of the two-dimensional
For example, standing in front of a closed door, the parallel sides of that door would remain parallel
in the retinal image. If we opened the door onto a hallway, the parallel lines from the walls, floor,
and ceiling would converge in the two-dimensional retinal image as they receded into the distance
in the three-dimensional world
Indeed, if the hall went back far enough, the walls, floor, and ceiling would seem to meet at a point
called the vanishing point—the apparent point at which parallel lines receding in depth converge
Like the relative size and height cues, linear perspective provides relative, but not absolute, metrical
depth information
Pictorial Depth Cues and Pictures
As a group, the depth cues discussed so far are known as pictorial depth cues—cues to distance or
depth used by artists to depict three-dimensional depth in two-dimensional pictures
To correctly interpret the shape of three-dimensional objects from two-dimensional pictures, people take
the orientation of the flat surface of the image into account. This allows them to understand that the
picture is, in fact, a picture and not the real thing; and at the same time they can calculate an accurate
impression of the thing that is portrayed
Anamorphosis (or anamorphic projection): use of the rules of linear perspective to create a two-
dimensional image so distorted that it looks correct only when viewed from a specific angle or with a
mirror that counters the distortion
This technique illustrates that the ability to cope with distortion is limited. In anamorphic projection,
the rules of linear perspective are pushed to an extreme in which the projection of three dimensions
into two creates a picture that is recognizable only from an unusual vantage point (or sometimes
with a curved mirror)
Motion Cues
Beyond the pictorial depth cues, a number of additional sources of information are available to our
visual system when we view real-world scenes that cannot be reproduced in a static two-dimensional
The first non-pictorial depth cue we will discuss is motion parallax—an important depth cue that is
based on head movement. The geometric information obtained from an eye in two different positions at
two different times (motion parallax) is similar to the information from two eyes in different positions in
the head at the same time (stereopsis)
As you look out the window of a moving train, objects closer to you shift position more quickly than
do objects farther away from one moment to the next. This regularity can be exploited as a depth
Laying under a tree and gazing up at the branches and leaves with one eye covered and your head
stationary, you will notice that the leaves and branches form a relatively flat texture. You will see all
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