Chapter 5: Stereopsis

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Chapter 5 Stereopsis
Given the challenges posed by frontal eyes and a
binocular visual field, we have to wonder what
the benefits must be. The major benefit of
having binocular vision is that it provides us
with precise distance information. The
relationship between distance from the horopter
and horizontal disparity is a very orderly one,
and the brain is able to detect interocular
differences in position (HD) and converts this
into a perception of relative depth. This
process is called stereopsis.
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From this diagram, can you see that (1) HD is
directly proportional to Dd (2) decreasing PD
will decrease HD, and (3) increasing viewing
distance (d) will also decrease HD. Thus HD is
dependent upon Dd, d, and PD. Also notice that
vergence angle, theta, is inversely proportional
to vergence distance d. Thus, vergence angle
provides information about absolute distance, d,
and HD provides information about relative
distance Dd
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Quantifying the relationship between Dd, d, PD
and HD
The approximate version of this formula (the one
to remember)
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Stereopsis provides relative depth
information. How good is stereopsis?
We define stereo acuity as the minimum difference
in horizontal disparity that can be seen as a
depth difference (Dd), also known as the
disparity threshold. This can be a small as 6
seconds of arc. Knowing the equation relating HD
angles to Dd, we can calculate the smallest Dd
that can be seen as a difference in depth. As
you can see, it is very small! 28 microns (when
d25 cm)!!
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Quantifying the impact of viewing distance on
stereopsis
10000
Proximal Dd
Distall Dd
Distal Dd
Fix pt.
1000
Proximal Dd
100
10
Stereo
40
Thresholds as
of viewing
distance
1
6
0.1
0.01
By rearranging the HD equation, we see that Dd is
directly proportional to d2, that is the minimum
discriminable difference in distance, Dd
threshold, increases faster than distance, and
becomes a larger and larger proportion of the
viewing distance until eventually it equals the
viewing distance, and thus at this viewing
distance, stereopsis is useless.
0.001
0.1
1
10
100
1000
10000
Viewing distance (meters)
At a distance of about 300 meters stereopsis no
longer functions when stereoacuity is 40. It is
functional out to about 2km when stereoacuity is
6. Rule of thumb stereopsis is pretty useless
for distances over 1 km.
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Geometry of maximum distance at which stereopsis
can be used
Visual Direction Of object At infinity
d
q
Notice, that HD of object at infinity is the same
as the vergence angle. Thus, when vergence angle
approaches minimum detectable HD (e.g. 10 of
arc), even objects at infinity will generate
sub-threshold levels of HD. Thus, it is the
distance at which the vergence angle shrinks to
the HD threshold that stereopsis becomes
useless. q PD/d radians Thus d PD/ q Thus, for
a HD threshold of 10 arc seconds, this equation
becomes d PD/ q 0.064 x 1806060/10 x pi
1,320 meters
HD
Visual Axies
q vergence angle
7
Vergence as a cue to absolute distance
Evidence View through BOD (which require
convergence to re-fuse) makes things look closer,
the converse is true for BID . Also, when
viewing through BO , objects appear smaller. We
call this Convergence Micropsia. This phenomenon
is caused by convergence signaling a reduced
target distance and then size constancy forcing
the brain to interpret the retinal image size
(unaltered by the prisms) as coming from a nearer
object, and thus the object must be physically
smaller. When diverging to view Magic Eye
autostereograms, when refused they appear farther
away.
q
d
PD
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Stereo Acuity is best at the horopter. This
means that when the two targets at different
depths are near to the horopter, each will have a
small HD, and our ability to discriminate between
these is best. Once targets depart from the
region around the horopter, stereo acuity
declines (stereo thresholds increase).
DHD Stereo thresholds (arc seconds)
6
0
HD (arc minutes)
Horopter
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How does perceived depth difference vary with DHD?
YX (veridical perception)
PFA
Fused single
Perceived Depth
Diplopic
10
1
100
1000
DHD (arc minutes)
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If stereopsis is so good, how small a lateral
displacement (s) must be used to create a 10
second of arc stimulus on the virtual depth tests
such as RanDot?
OS
OD
DS
X
X
You can see from this calculations, that
generating a stereo test is not that simple if
you want to test such small disparities. Bottom
line our visual system is extremely good ad
detecting differences in monocular visual
directions.
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Clinical Stereo Acuity tests
Stereograms with R and L eye targets spatially
super-imposed but still separated such that each
is seen only by one eye.
Red/Green Anaglyphs
E.g. TNO test
Crossed Polarizers
E.g. Randot
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500
40 cm test distance, 500 to 32 arc sec range,
5AFC
200
120
75
45
Dsgt5mm HDgt2500 sec
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Ds0.97mm
HDDs/d x (180x60x60/pi) arc seconds 500
arc seconds
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40 cm test distance, 400 to 20 arc second range,
3AFC test
400
50
200
40
140
30
100
25
70
20
Ds0.78mm HD400 arc sec

• Demonstrations
• Test your partners stereo acuity with Randot,
  then place a 3D lens in front of RE (monovision
  simulation), then place 3D in front of both eye
  (bilateral blur). Which is most detrimental?
• Misconverge with pencil point. How much vergence
  error will destroy stereoacuity?

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Depth Constancy
Because the amount of HD generated by a given Dd
is not a constant (it varies with viewing
distance), some additional computation is
necessary to convert HD into a perception of
depth. Clearly, we are able to accomplish this
because objects do not appear to flatten as they
move farther away (as they would if depth
perception from stereopsis simply mirrored HD).
We call this property of human vision depth
constancy. As with all perceptual
constancies, we can not usually see them in
action. However, we can gain insight into the
depth constancy mechanism by viewing a virtual
depth target at different viewing
distances. View your clinical stereo test and
near and larger viewing distances. As the test
is moved farther from you, the HD decreases, but
what happens to the perceived depth? Why did
this happen?
Demonstration
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Demonstration
Stereo-illusions
1. Chromostereopsis
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Explanation Interocular differences in
Transverse Chromatic Aberrations.
f
f
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2. Pulfrich Effect
Decreasing retinal illuminance increases visual
latency
Eye with ND filter sees object where it was not
where it is.
Clinical application aniseikoria, optic
neuritis, unilateral cataract. Treat with ??
Demonstration
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Autostereograms Magic Eye seeing stereo
depth with a stereogram that does not have a
separate RE and LE image. Thus the name
autostereogram.
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Underconverge by one period
F
F
F
F
F
F
F
V
V
V
V
V
V
V
N
N
N
N
N
N
N
N
N
Increased period
produces
uncrossed
disparity
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Ov
erconverge by one period
F
F
F
F
F
F
F
V
V
V
V
V
V
V
N
N
N
N
N
N
N
N
N
Increased period produces
crossed disparity
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Demonstration
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Neurophysiology of Stereopsis
foveola
Visual Axis
FIX
Primary Visual Cortex
foveola
Zero HD
In order to discriminate between Horizontal
Disparities, we must have neurons that respond to
different HDs. This schematic figure shows a
binocular neuron maximally activated by zero HD
and one activated maximally by crossed HD.
xHD
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Results from single unit recording in awake
monkeys
Tuned excitatory cells
Near cells
Far cells
Response
crossed
uncrossed
0
Horizontal Disparity
The tuned excitatory cells presumably are
responsible for stereopsis, which only functions
around zero HD. The near and far cells are
thought to be used to drive disparity vergence
responses nearconvergence, and fardivergence.
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Evidence to support the role of near and far
cells in vergence control.
Targets with large (gt10 arc minute) HDs are seen
diplopically, but large crossed disparities can
be identified as near as can large uncrossed
disparities be identified as far relative to the
fixation target. Some stereo-normal subjects
were found to be unable to see diplopic crossed
disparity targets as near, and others failed to
see diplopic uncrossed disparity targets as far.
In a subsequent study, the near blind subjects
failed to initiate convergence in response to
crossed disparities, and far blind failed to
initiate divergence to large uncrossed
disparities. These results are consistent with
near and far cells being instrumental in
initiating convergence and divergence eye
movements in response to large crossed or
uncrossed HDs.