Slant%20Anisotropy%20and%20Tilt-dependent%20Variations%20in%20Stereo%20Precision

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Slant Anisotropy and Tilt-dependent Variations in
Stereo Precision
James M. Hillis Dept. of Psychology Univ. of
Pennsylvania Simon J. Watt Vision Science
Program UC Berkeley Michael S. Landy Dept. of
Psychology NYU Martin S. Banks Vision Science
Program, Optometry Psychology UC Berkeley
Tandra Ghose Vision Science Program UC Berkeley
http//john.berkeley.edu
Supported by NIH, NSF
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Slant Anisotropy

• Tilt 0

Tilt 90
3
Slant Anisotropy
Less slant perceived in stereograms for slant
about vertical axis (tilt 0) than for slant
about horizontal axis (tilt 90) Why?
4
Theories of Slant Anisotropy

• Orientation disparity tilt
• Cagenello Rogers (1988, 1993)
• Size and shear disparity processed differently
  Mitcheson McKee (1990)
• Mitcheson Westheimer (1990)
• Gillam et al (1991, 1992)
• Banks, Hooge, Backus (2001)
• Straightening the curved horizontal horopter
• Garding et al (1995)
• Frisby et al (1999)
• Cue conflict between disparity other slant
  cues

o
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Real Surfaces Slant Anisotropy
Bradshaw et al (2002) examined slant anisotropy
for virtual real surfaces found no slant
anisotropy with real surfaces.conflict crucial to
the effect
Random-dot virtual surfaces
Real surfaces
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Theories of Slant Anisotropy

• Orientation disparity tilt
• Cagenello Rogers (1988, 1993)
• Size and shear disparity processed differently
  Mitcheson McKee (1990)
• Mitcheson Westheimer (1990)
• Gillam et al (1991, 1992)
• Banks, Hooge, Backus (2001)
• Straightening the curved horizontal horopter
• Garding et al (1995)
• Frisby et al (1999)
• Cue conflict between disparity other slant
  cues

o
7
Theories of Slant Anisotropy

• Orientation disparity tilt
• Cagnello Rogers (1988, 1993)
• Size and shear disparity processed differently
  Mitcheson McKee (1990)
• Mitcheson Westheimer (1990)
• Gillam et al (1991, 1992)
• Banks, Hooge, Backus (2001)
• Straightening the curved horizontal horopter
• Garding et al (1995)
• Frisby et al (1999)
• Cue conflict between disparity other slant
  cues

o
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Cue Combination
Multiple depth cues are used to estimate 3D shape
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Cue Combination
Estimates can be combined by a weighted average
slant estimate from disparity
slant estimate from texture
If the cues have uncorrelated noises, weighted
average has minimal variance if
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Cue Combination
Estimates can be combined by a weighted average
Combined estimate is shifted toward single-cue
estimate of lower variance
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Cue Combination Slant Anisotropy
The relevant cues in the phenomenon are slant
from disparity slant from texture So we
have In random-element stereograms so
where Thus, we expect less perceived slant
when wD is small We propose that wD less for
tilt 0 than for tilt 90
12
Cue Combination Slant Anisotropy
The relevant cues in the phenomenon are slant
from disparity slant from texture So we
have In random-element stereograms so
where Thus, we expect less perceived slant
when wD is small We propose that wD less for
tilt 0 than for tilt 90
13
Cue Combination Slant Anisotropy
The relevant cues in the phenomenon are slant
from disparity slant from texture So we
have In random-element stereograms so
where Thus, we expect less perceived slant
when wD is small We propose that wD less for
tilt 0 than for tilt 90
14
Cue Combination Slant Anisotropy
The relevant cues in the phenomenon are slant
from disparity slant from texture So we
have In random-element stereograms so
where Thus, we expect less perceived slant
when wD is small We propose that wD less for
tilt 0 than for tilt 90
15
Cue Combination Slant Anisotropy
The relevant cues in the phenomenon are slant
from disparity slant from texture So we
have In random-element stereograms so
where Thus, we expect less perceived slant
when wD is small We propose that wD less for
tilt 0 than for tilt 90
16
Cue Combination Slant Anisotropy
The relevant cues in the phenomenon are slant
from disparity slant from texture So we
have In random-element stereograms so
where Thus, we expect less perceived slant
when wD is small We propose that wD is less for
tilt 0 than for tilt 90
17
Cue Combination Slant Anisotropy
With real surfaces so Thus, we expect
variation in wD to have little or no effect on
perceived slant because the weights presumably
add to 1
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Cue Combination Slant Anisotropy
With real surfaces so Thus, we expect
variation in wD to have little or no effect on
perceived slant because the weights presumably
add to 1
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Cue Combination Slant Anisotropy
With real surfaces so Thus, we expect
variation in wD to have little or no effect on
perceived slant.
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Cue Combination Slant Anisotropy
To test the idea that slant anisotropy results
from cue conflicts and lower disparity weight
with tilt 0, we ..

• Measured slant discrimination with single cues
  (disparity texture) at tilt 0 and 90
• Used those measurements to predict weights for
  two-cue experiment at tilt 0 and 90
• Measured slant discrimination in two-cue
  experiment at tilt 0 and 90
• Compared the predicted and observed weights

21
Cue Combination Slant Anisotropy
To test the idea that slant anisotropy results
from cue conflicts and lower disparity weight
with tilt 0, we ..

• Measured slant discrimination with single cues
  (disparity texture) at tilt 0 and 90
• Used those measurements to predict weights for
  two-cue experiment at tilt 0 and 90
• Measured slant discrimination in two-cue
  experiment at tilt 0 and 90
• Compared the predicted and observed weights

22
Cue Combination Slant Anisotropy
To test the idea that slant anisotropy results
from cue conflicts and lower disparity weight
with tilt 0, we ..

• Measured slant discrimination with single cues
  (disparity texture) at tilt 0 and 90
• Used those measurements to predict weights for
  disparity and texture at tilt 0 and 90
• Measured slant discrimination in two-cue
  experiment at tilt 0 and 90
• Compared the predicted and observed weights

23
Cue Combination Slant Anisotropy
To test the idea that slant anisotropy results
from cue conflicts and lower disparity weight
with tilt 0, we ..

• Measured slant discrimination with single cues
  (disparity texture) at tilt 0 and 90
• Used those measurements to predict weights for
  disparity and texture at tilt 0 and 90
• Measured slant discrimination in two-cue
  experiment at tilt 0 and 90
• Compared the predicted and observed weights

24
Cue Combination Slant Anisotropy
To test the idea that slant anisotropy results
from cue conflicts and lower disparity weight
with tilt 0, we ..

• Measured slant discrimination with single cues
  (disparity texture) at tilt 0 and 90
• Used those measurements to predict weights for
  disparity and texture at tilt 0 and 90
• Measured slant discrimination in two-cue
  experiment at tilt 0 and 90
• Compared the predicted and observed weights

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Single-cue Experiment

• 2-IFC choose interval which has more positive
  slant
• no feedback
• Standard S 60,-30,0,30 or 60 deg
• DS controlled by 2-down,1-up staircases
• Discrimination thresholds measured for tilts 0
  and 90
• Measured for texture alone for disparity alone
• used for estimating sD2 and sT2
• and from that we can derive predicted weights
  wD and wT

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Texture threshold
Monocular viewing
Stimulus
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Disparity Threshold
Binocular viewing
Stimulus
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Two-cue Experiment

• 2-IFC which interval has more positive slant?
• 2 conflict conditions ST or SD fixed at -60,
  -30, 0, 30 or 60 deg for two tilts (0 and 90 deg)
  the other one varied
• Conflict (difference between fixed and varied
  cue) -10, -5, 0, 5 10 deg
• DS of no-conflict stimulus controlled by
  2-down,1-up and 1- down,2-up staircases

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Two-cue Experiment
Conflict stimulus
Disparity
Texture
specified slant
For each conflict stimulus, we find the value of
the no-conflict stimulus that has the same
perceived slant (PSE).
No-conflict stimulus
Disparity
Texture
specified slant
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Texture Dominance
wT 1 wD 0
SD varied
ST varied
PSE (deg)
Sfixed
Svaried in Conflict Stimulus (deg)
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Disparity Dominance
wT 0 wD 1
SD varied
ST varied
PSE (deg)
Sfixed
Svaried in Conflict Stimulus (deg)
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Two-cue Results
Base Slant 60
tilt 0
tilt 90
70
60
PSE (deg)
PSE
Sfixed
Sfixed
SD varied
50
SJW
ST varied
50
60
50
60
50
60
70
50
60
70
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
33
Predictions
Base Slant 60
tilt 0
tilt 90
70
60
PSE (deg)
PSE
Sfixed
Sfixed
SD varied
50
SJW
ST varied
50
60
50
60
50
60
70
50
60
70
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Two-cue Results
Base Slant 30
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
SJW
50
60
50
60
20
30
40
20
30
40
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Predictions
Base Slant 30
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
SJW
50
60
50
60
20
30
40
20
30
40
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
36
Two-cue Results
Base Slant 0
tilt 0
tilt 90
PSE (deg)
PSE
Sfixed
Sfixed
SJW
50
60
50
60
-10
0
10
-10
0
10
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Predictions
Base Slant 0
tilt 0
tilt 90
PSE (deg)
PSE
Sfixed
Sfixed
SJW
50
60
50
60
-10
0
10
-10
0
10
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
38
Two-cue Results
Base Slant -30
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
SJW
50
60
50
60
-40
-30
-20
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Predictions
Base Slant -30
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
SJW
50
60
50
60
-40
-30
-20
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
40
Two-cue Results
Base Slant -60
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
SJW
50
60
70
50
60
70
-70
-60
-50
-70
-60
-50
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Predictions
Base Slant -60
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
SJW
50
60
70
50
60
70
-70
-60
-50
-70
-60
-50
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Predictions
Base Slant -60
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
RM
50
60
70
50
60
70
-70
-60
-50
-70
-60
-50
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
43
Predictions
Base Slant -30
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
RM
50
60
50
60
-40
-30
-20
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Predictions
Base Slant 0
tilt 0
tilt 90
PSE (deg)
PSE
Sfixed
Sfixed
RM
50
60
50
60
-10
0
10
-10
0
10
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
45
Predictions
Base Slant 30
tilt 0
tilt 90
PSE (deg)
Sfixed
Sfixed
RM
50
60
50
60
20
30
40
20
30
40
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
46
Predictions
Base Slant 60
tilt 0
tilt 90
70
60
PSE (deg)
PSE
Sfixed
Sfixed
50
RM
50
60
50
60
50
60
70
50
60
70
conflict (deg)
conflict (deg)
Svaried in Conflict Stimulus (deg)
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Conclusions

1. In the single-cue experiment, disparity
   thresholds were slightly, but consistently, lower
   with tilt 90 than with tilt 0.
2. Therefore, we predicted that with tilt 0 deg,
   weight given to disparity is relatively less than
   with tilt 90, and thats what we found.
3. Slant anisotropy is thus a byproduct of cue
   conflict between disparity- and texture-specified
   slants.
4. However, the cause of poorer disparity thresholds
   at tilt 0 remains mysterious.

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Single-cue Experiment
The thresholds were used to determine the
variances of the disparity and texture estimators
at different tilts and base slants.
Empirical weights
Single cue thresholds
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Single-Cue data
Disparity threshold
Texture threshold
Log(threshold)
Base-Slant (deg)
Tilt0
Tilt90
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Single-Cue data
Disparity threshold
Texture threshold
Log(threshold)
Base-Slant (deg)
Tilt0
Tilt90
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Cue Combination Slant Anisotropy
With real surfaces so Thus, we expect
variation in wD to have little or no effect on
perceived slant. S wDSD (1-wD)ST S ST