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Summary 2.4. Problem 6: The third dimension
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This is a detailed summary of problem 6 of course 2.4 Perception.
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Chapter 3. Spatial vision
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Problem 6Case a Coordinator Questions
1. Which cues influence the perception of 1. Describe monocular cues used to see depth.
depth 2. What are accommodation and convergence?
2. What influences the perception of depth
How do these cues work?
in two dimensions?
3. What binocular cues do we use to see
Kw: Linear perspective
depth?
Case b
1. How do the combined visual inputs 4. How might depth cues contribute to size
create depth? illusions?
2. How does splitting images create
depth?
Case c
1. What is the Ponzo illusions & what
Source: Wolfe, 2nd ed, chapter 6, pp 149-178
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.
The geometry of the real world= Euclidean, the geometry of retinal images of that world
is decidedly non-Euclidean. The geometry becomes non-Euclidean when the three-
dimensional world is projected onto the curved, two-dimensional surface of the retina.
e.g. parallel lines in the world do not necessarily remain parallel in the retinal image etc.
if we want to appreciate the Euclidean world, we have to reconstruct it from non-Euclidean
input.
- We reconstruct the world from two non-Euclidean inputs: the two distinct retinal
images. The retinal images we get from each eye are different from each other
because the two retinas are in slightly different places.
- Having two eyes might confer to some evolutionary advantage as having two lungs,
two brain hemispheres etc. If you lose one eye you will still be able to see. Another
advantage is that doubling the eyes allows us to see more of the world. rabbit
visual fields extends to full 360 degrees.
- Our visual field is limited to about 190 degrees from left to right, 110 degreed of
which is covered by both eyes. The field is more restricted vertically, with about 60
degrees up from the center gaze and 80 degrees down.
- Binocular: with two eyes, Monocular: with one eye.
- Overlapping, binocular visual fields give predator animals such as humans a better
chance to spot small, fast-moving objects in front of them that might provide dinner.
(e.g., those rabbits, whose dome-shaped visual fields are adapted to avoid being
caught).
- 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.
, - Binocular disparity: the differences between the two retinal images of the same
world. Disparity is the basis for stereopsis, a vivid perception of the three-
dimensionality of the world that is not available with monocular vision.
- Stereopsis: the ability to use binocular disparity as a cue to depth. It is not a
necessary condition for depth perception or space perception. It adds richness to
perception of the three-dimensional world.
Depth cues: information about the third dimension (depth) of visual space. Depth cues may
be molecular or binocular.
Molecular 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.
Monocular Cues to Three-Dimensional Space
Occlusion: a cue to relative depth order in which, one object obstructs the view of part of
another object. E.g. a circle in front of a square in front of a triangle. Occlusion is a
nonmetrical depth cue; it just gives relative orderings of occluders and occludees, but no
depth magnitude e.g. nose in front of face.
Metrical depth cue: a depth cue that provides quantitative information about distance in
the third dimension.
Size and Position Cues
The image on the retina formed by an object out in the world gets
smaller as the object gets farther away.
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. E.g. parallel lines do not converge in the real world,
but they do in the two-dimensional projection of that world.
the visual system knows that, all else being equal, smaller things
are/look father away. Relative size: a comparison of size between items
without knowing the absolute size of either one.
Figure 6.7: even though all of these plasticine balls are resting on the
same surface, the small ones appear to be farther away. Some portion
of the visual system assumes that all of these items are the same. If one
balls projects a smaller image on the retina and if the balls really are the
same size, then the smaller one must be farther away. This is the cue of
relative size.
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