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chapter summary from 6-11 and short answer questions with answers!

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Matthias Niemeier

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Chapter summaries 6
1. Reconstructing a three-dimensional world from two, non-Euclidean, curved, two-
dimensional retinal images is one basic problem faced by the brain.
2.Having two eyes has a number of advantages, some of which have to do with depth
perception. However, it is important to remember that it is possible to reconstruct the
three-dimensional world from a single two-dimensional image. Two eyes have other
advantages over just one: expanding the visual field, permitting binocular summation,
and providing redundancy if one eye is damaged.
3.A number of monocular cues provide information about three-dimensional space.
These include occlusion, various size and position cues, aerial perspective, linear
perspective, motion cues, and accommodation.
4.Having two laterally separated eyes connected to a single brain also provides us with
important information about depth through the geometry of the small differences
between the images in each eye. These differences, known as binocular disparities,
give rise to stereoscopic depth perception.
5.Random dot stereograms show that you don't need to know what you are seeing
before you see it in stereoscopic depth. Binocular disparity alone can support shape
6.The difficulty of matching an image element in one eye with the correct element in the
other eye is known as the correspondence problem. The brain uses several tricks
to solve the problem. For example, it reduces the initial complexity of the problem by
matching large blobs in the low-spatial-frequency information before trying to
match every high-frequency detail.
7.Single neurons in primary visual cortex and beyond have receptivefields that cover a
region in three-dimensional space, not just the two-dimensional image plane. Some
neurons respond to a wide range of depths (e.g., stimuli beyond the current distance
of fixation). Others have more precise receptive fields.
8.When the stimuli on corresponding loci in the two eyes are different, we experience a
continuous perceptual competition between the two eyes known as
binocular rivalry.
9.All of these various monocular and binocular depth cues are combined
(unconsciously) according to what prior knowledge tells us about the probability of
the current event. Making the wrong guess about the cause of visual input can lead
to illusions.
Study questions:
What is the advantage in binocular summation?
The advantage in binocular summation is that detecting a stimulus can be done with two
eyes, as opposed to just one, and so this yields more information about the stimulus.
Explain the difference between a monocular depth cue and a binocular depth cue.
A monocular depth cue is available when the world is viewed with one eye alone. A binocular depth
cue relies on information from both eyes.

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What is the idea behind positivism?
Positivism is a philosophical position arguing that all you really have to go on is the evidence of your
senses, so the world might be nothing more than an elaborate hallucination.
Monocular Cues to Three-Dimensional Space
Name three monocular cues.
1) Occlusion 2) Relative size cue 3) Texture gradient.
Explain what is meant by texture gradient.
Texture gradient is a depth cue based on the geometric fact that items of the same size form smaller
images when they are farther away. Thus, an array of items that change in size across the image will
appear to form a surface in depth.
What kind of information does an aerial perspective provide about the stimulus?
An aerial perspective is a depth cue that is based on the implicit understanding that light is scattered
by the atmosphere. More light is scattered when you look through more atmosphere. Thus, more
distant objects are subject to more scatter and appear fainter, bluer, and less distinct. An aerial
perspective provides information about the relative distance of objects from the observer
What is a vanishing point?
A vanishing point is the apparent point at which parallel lines receding in depth converge.
What kind of movement does the motion parallax depend on? Explain.
Motion parallax depends on the viewer's head movement. The geometric information obtained from
an eye in two different positions at two different times is similar to the information from two eyes in
two different positions in the head at the same time.
What is a pictorial depth cue?
A pictorial depth cue is a cue to distance or depth used by artists to depict three-dimensional depth
in two-dimensional pictures.
How are convergence and divergence important to depth perception?
Convergence and divergence are important to depth perception because they are used to place the
two images of a feature in the world on corresponding locations in the two retinal images (typically on
the fovea of each eye). They both reduce the disparity of that feature to zero, or nearly zero.
Binocular Vision and Stereopsis
Explain the concept of corresponding retinal points.
Corresponding retinal points are points on the retina of each eye where the monocular retinal images
of a single object are formed at the same distance from the fovea in each eye. The two foveas are
also corresponding points.

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Explain the concept of the Vieth-Müller circle, and how it is related to the horopter.
The Vieth-Müller circle refers to the location of objects whose images fall on geometrically
corresponding points in the two retinas. If the two eyes are looking at one spot, then there will be a
surface of zero disparity running through that spot (known as the horopter).
What is the difference between crossed disparity and uncrossed disparity?
Crossed disparity is the sign of disparity created by objects in front of the plane of fixation (the
horopter). Images of objects that are located in front of the horopter will appear to be displaced to the
left in the right eye, and to the right in the left eye. Uncrossed disparity is the sign of disparity created
by objects behind the plane of fixation. Images of objects that are located behind the horopter will
appear to be displaced to the right in the right eye, and to the left in the left eye
What is a stereoscope?
A stereoscope is a device for presenting one image to one eye and another image to the other eye,
thereby creating a single three-dimensional image.
When is free fusion used?
Free fusion is a technique of converging, or crossing the eyes in order to view a stereogram without a
What does stereoblindness often result from?
Stereoblindness, or the inability to make use of binocular disparity as a depth cue often results from
a childhood visual disorder such as a strabismus, in which the two eyes are misaligned.
What is a random dot stereogram?
A random dot stereogram is a stereogram made of a large number or randomly placed dots. The
random dot stereogram contains no monocular cues to depth.
When does one view cyclopean stimuli?
One views cyclopean stimuli when looking at random dot stereograms. These are stimuli that are
defined by binocular disparity alone.
Define the correspondence problem.
The correspondence problem is the problem of figuring out which bit of the image in the left eye
should be matched with which bit in the right eye.
Name two ways of solving the correspondence problem.
1) Blurring the image to result in lower spatial frequency, so that there are not that many dots to
analyze and 2) using the uniqueness constraint, in which a feature in the world will be represented
exactly once in each retinal image.
What is binocular rivalry?
Binocular rivalry is the competition between the two eyes for control of visual perception, which is
evident when completely different stimuli are presented to the two eyes.
Combining Depth Cues
In what way does the Bayesian approach take into account past experience? Explain.
The Bayesian approach is a statistical model which states that prior knowledge could influence one's
estimates of the probability of a current event. In the case of vision, since the retinal images formed
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