Depth Perception
Depth Perception
Part II
1
Binocular Cues to Depth
Depth Information
Oculomotor
Accomodation
Visual
Convergence
Binocular
Monocular
Motion
Parallax
Static Cues
Perspective
Binocular Vision:
Vision with Two Eyes
Fixating an Object
Size
Interposition
Shading
Binocular cues to depth:
• Binocular cues are based on the fact that we
have two forward facing eyes that are
laterally separated
• This provides slightly displaced images in
each eye
Fovea
Fovea
• This information can be converted into a
signal about relative depth
• Based on the geometry of the images
reaching the eye
Important concepts in binocular
depth vision:
Stereopsis: Definitions
• Corresponding and non-corresponding points
• Fixation plane
• Horopter
• Retinal disparity
• Diplopia
• Stereopsis
• Stereoacuity
Our brains convert overlapping flat images projected
onto the retina of each eye into a 3-D model of the
surrounding world.
This creation of a 3-D world from the combining of
information from the two eyes is called Stereopsis from the Greek words stereos - for “solid” and opsis for
“vision” - solid vision or solid sight.
Stereopsis - is the ability to perceive depth or relative
object distance based on retinal disparity.
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Depth Perception
2
binocular stereopsis
• Because its the only aspect
of depth of which we have
some physiological
understanding
Not the most important cue for depth
Why study it?
The Early Stage of Stereopsis
When we “look” at an object with two eyes we converge
our eyes so the the image of the object falls on the fovea
of each eye - the retinal locus with the highest resolving
power.
This convergence of the eyes so that the image of the
object of interest falls on the foveas is called bifoveal
fixation and is generally considered to be the first stage
in binocular function.
The foveas can be considered to be corresponding
points on the two retinas.
Thus any object you fixate will fall on corresponding
points on the two retinas - i.e. the foveas.
• “Eavesdropping” on
binocular cells using
electrophysiology
Corresponding and noncorresponding points
• When fixating, image of target falls on fovea
of each eye
• The images of an object at the same distance
as the fixation plane will fall on the same
relative position in the two eyes
• Images that fall on
different relative
locations are said to
fall on noncorresponding points
Corresponding points and the
horopter:
• The horopter is an imaginary plane through
the fixation point that joins all corresponding
points
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Depth Perception
3
The Horopter
Points Falling on the Horopter Fall on Corresponding
Points on the Retinae
Non-corresponding Points and
Retinal Disparity
Retinal Disparity and Depth:
• There is a systematic relationship between
the amount of retinal disparity on the retina
and the distance of a target relative to the
fixation plane
• If a target is closer or more distant than the
fixation plane, its image falls on noncorresponding points in the two eyes
• If images fall on noncorresponding points, then there is
retinal disparity and the potential
for stereopsis
definition of
disparity = θR
Fusion & Panum’s Area
θL
fixating here
θL
a b
left eye view
θR
a b
right eye view
a
The process by which we merge these retinally disparate
images into a single percept is called fusion.
b
Not all images that fall on disparate points lead to double
vision-- which is also known as diplopia.
There is a narrow region on either side of the horopter
that includes all points in visual space that are fused into
single images. This region is called Panum's area - the
region where fusion occurs.
perceived depth increases with
increasing disparity (minus, closer than horopter,
plus, farther than horopter)
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Depth Perception
Locus of corresponding
retinal points - Horopter
Panum’s
fusional
space
4
Points that don't fall on the horopter fall on disparate
(non corresponding) points in the two eyes.
That is, objects located nearer or farther than the
fixated target form images in different positions on
each retina giving rise to disparity.
The difference in the location of two retinal images of
the same object is called binocular disparity.
R
L
R
L
L
Crossed disparity
R
L
Uncrossed disparity
R
L
Random Dot Stereogram
Stereoacuity
The smallest
disparity that can
be resolved =
Stereoacuity
= 10 - 20 seconds
of arc
L
R
Invented by
Bela Julesz
1956 emigre engineer
from Hungary
First innovative use of
a computer for research
in perception
R
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Depth Perception
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How a Random Dot Stereogram Works:
random black and white pixels
which are essentially the same in each eye
some, however, are shifted laterally
with respect to the others
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left eye
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right eye
RE
LE
L 1 0 1 0 1 0
R1 0 1 0 1 0
row 1
L 1 1 0 1 0 1
R 1 0 1 0 1 1
row 2
Wheatstone’s invention of the
stereoscope (c. 1836)
mirrors
Some other methods to show stereo pictures…
mirrors
top view
Polaroid glasses method
P+
Left eye image
P+
Right eye image
P-
mirrors
P-
aluminized screen
free fusion, w/o optical aids
front view
divergent
convergent
Each eye receives a separate image
How does it work?
notice that each eye receives a separate
image of just two lines having a different separation.
Brewster stereoscope
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Depth Perception
Disparity-Tuned Cell Responses
C'
C
Plane of
Fixation
B
A'
B'
Subject fixating B
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• Individual neurons were “tuned” for
different amounts and directions of
disparity
A
Stimulation Location
Cell Responses
(A,A')
(B,B')
(C,C')
Stimulation Location
"Near" cell
Cell tuned to
fixation plane
• Several different classes of neuron, some
finely tuned for small amounts of disparity,
others simply responding to “near” or “far”
"Far" cell
Autostereograms:
A Simplified Example of How
An Autostereogram Works…
• In autostereograms we use our vergence eye
movements as the stereoscope
• By converging or diverging we shift the image
in one eye relative to the other
• With the correct amount of vergence we are
now superimposing two parts of a repeating
image which has been designed to contain
disparity when viewed this way
Simplified “Magic Eye” Autostereogram
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Depth Perception
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Binocular parallax
a
b
Notice the difference in angular separation
Size constancy
Size constancy
The perception of size is closely related to
the perception of distance.
The brain is remarkably good at
compensating for changes in retinal
image size with distance in order to
keep the perceived size constant
Why does someone walking away not appear
to shrink?
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Depth Perception
Size constancy:
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The Holway-Boring experiment:
• Given the size of the image on the
retina (visual angle) and its distance, it
is possible to compute the physical size
of an object
• Size constancy is the mechanism that
makes this computation
• Holway & Boring demonstrated the
crucial importance of depth perception
in an experiment
• Observer views Test Disks located at different
distances
• Task is to adjust size of Comparison Disk to
match physical size of Test Disk
• Test disks all set
to subtend 1o of
visual angle
• Test under several
condition in which the
availability of depth
cues is varied
• Observers matched
closer to visual angle
as cues removed
Relationship between size perception
and perceived distance:
Emmert’s Law
• Generate
afterimage on
retina
• View afterimage
against surfaces at
different distances
• Note changed size
of afterimage
The perceived size of an afterimage is related to the
distance of the viewing surface from the eye
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Depth Perception
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Emmer t's l aw :
Sp = k
x
Sr x Dp
(Sp = pe rceived size; Sr = reti nal size;
Dp = pe rceived d ista nce; k = consta nt)
Ponzo Illusion
Size perception and visual illusions:
• This picture looks
odd because the
size and distance
cues are in
conflict
• A number of visual illusions may result from
the misapplication of constancy scaling
• Gregory has argued that the misjudgement of
size is because the illusory figure contains
information that activates the constancy
scaling mechanism
• Consequently, an object is seen as larger or
smaller than it should be
Muller-Lyer Illusion:
• If the arrowheads are seen as internal and
external contours, the closer, external corner
should appear bigger
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Depth Perception
The moon illusion:
• Moon (or sun) seems larger
at the horizon than at the
zenith
• Recognised in classical
times, many theories
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• Assumption: if two objects have the same retinal
image size, the one that appears closer will look
smaller
• That means horizon moon must look more distant
• Some evidence that horizon looks further away
than zenith sky
• Current most-accepted
explanation in terms of
apparent distance, although
issue is still controversial
• If zenith sky appears closer, then moon
will seem to be smaller
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