slant anisotropy and tilt-dependent variations in stereo precision
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Slant Anisotropy and Tilt-dependent Variations in Stereo
Precision
Tandra GhoseVision Science Program
UC Berkeley
http://john.berkeley.edu
James M. HillisDept. of Psychology
Univ. of Pennsylvania
Simon J. WattVision Science Program
UC Berkeley
Michael S. LandyDept. of Psychology
NYU
Martin S. BanksVision Science Program,Optometry & Psychology
UC BerkeleySupported by NIH, NSF
Slant Anisotropy
Tilt 0
Tilt 90
Slant Anisotropy
Less slant perceived in stereograms for slant about vertical axis (tilt = 0) than for slant about horizontal axis (tilt = 90)
Why?
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 horopterGarding et al (1995)Frisby et al (1999)
• Cue conflict between disparity & other slant cues
o
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
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 horopterGarding et al (1995)Frisby et al (1999)
• Cue conflict between disparity & other slant cues
o
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 horopterGarding et al (1995)Frisby et al (1999)
• Cue conflict between disparity & other slant cues
o
Cue Combination
Multiple depth cues are used to estimate 3D shape
Cue Combination
Estimates can be combined by a weighted average
ˆ ˆ ˆD D T TS w S w S ˆ
ˆD
T
S
S
2
2 2
1
1 1D
D
D T
w
2
2 2
1
1 1T
T
D T
w
: slant estimate from disparity
: slant estimate from texture
If the cues have uncorrelated noises, weighted average has minimal variance if:
Cue Combination
Estimates can be combined by a weighted average
ˆ ˆ ˆD D T TS w S w S
Combined estimate is shifted toward single-cue estimate of lower variance
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
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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ 0TS
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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ ˆD DS w S 1Dw
ˆ 0TS
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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ ˆD DS w S 1Dw
ˆ 0TS
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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ ˆD DS w S 1Dw
ˆ 0TS
Cue Combination & Slant Anisotropy
ˆ ˆT DS SWith 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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ ˆT DS SWith 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
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ ˆT DS SWith real surfaces:
so
Thus, we expect variation in wD to have little or no effect on perceived slant.
Cue Combination & Slant Anisotropy
To test the idea that slant anisotropy results from cue conflicts and lower disparity weight with tilt 0, we …..
1. Measured slant discrimination with single cues (disparity & texture) at tilt 0 and 90
2. Used those measurements to predict weights for two-cue experiment at tilt 0 and 90
3. Measured slant discrimination in two-cue experiment at tilt 0 and 90
4. Compared the predicted and observed weights
Cue Combination & Slant Anisotropy
To test the idea that slant anisotropy results from cue conflicts and lower disparity weight with tilt 0, we …..
1. Measured slant discrimination with single cues (disparity & texture) at tilt 0 and 90
2. Used those measurements to predict weights for two-cue experiment at tilt 0 and 90
3. Measured slant discrimination in two-cue experiment at tilt 0 and 90
4. Compared the predicted and observed weights
Cue Combination & Slant Anisotropy
To test the idea that slant anisotropy results from cue conflicts and lower disparity weight with tilt 0, we …..
1. Measured slant discrimination with single cues (disparity & texture) at tilt 0 and 90
2. Used those measurements to predict weights for disparity and texture at tilt 0 and 90
3. Measured slant discrimination in two-cue experiment at tilt 0 and 90
4. Compared the predicted and observed weights
Cue Combination & Slant Anisotropy
To test the idea that slant anisotropy results from cue conflicts and lower disparity weight with tilt 0, we …..
1. Measured slant discrimination with single cues (disparity & texture) at tilt 0 and 90
2. Used those measurements to predict weights for disparity and texture at tilt 0 and 90
3. Measured slant discrimination in two-cue experiment at tilt 0 and 90
4. Compared the predicted and observed weights
Cue Combination & Slant Anisotropy
To test the idea that slant anisotropy results from cue conflicts and lower disparity weight with tilt 0, we …..
1. Measured slant discrimination with single cues (disparity & texture) at tilt 0 and 90
2. Used those measurements to predict weights for disparity and texture at tilt 0 and 90
3. Measured slant discrimination in two-cue experiment at tilt 0 and 90
4. Compared the predicted and observed weights
Single-cue Experiment
• 2-IFC: choose interval which has more positive slantno feedback
• Standard S = –60,-30,0,30 or 60 degS controlled by 2-down,1-up staircases
• Discrimination thresholds measured for tilts 0 and 90
• Measured for texture alone & for disparity aloneused for estimating D
2 and T
2
and from that we can derive predicted weights wD and wT
Texture threshold
Monocular viewing
Stimulus
Disparity Threshold
Binocular viewing
Stimulus
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
S of no-conflict stimulus controlled by 2-down,1-up and 1- down,2-up staircases
Two-cue Experiment
No-conflict stimulusDisparityTexture
specified slant
Conflict stimulusDisparityTexture
specified slant
For each conflict stimulus, we find the value of the no-conflict stimulus that has the same perceived slant (PSE).
Texture Dominance
SD varied
Sfixed
Svaried in Conflict Stimulus (deg)
PSE
(deg
)ST varied
wT = 1wD = 0
Disparity Dominance
SD varied
Sfixed
Svaried in Conflict Stimulus (deg)
PSE
(deg
)ST varied
wT = 0wD = 1
Two-cue Results
50 60conflict (deg)
Base Slant = 60
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
50 60 70
PS
E
50 60 70
50
60
70
50
60
70
Svaried in Conflict Stimulus (deg)
SD variedST varied
Predictions
50 60conflict (deg)
Base Slant = 60
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
50 60 70
PS
E
50 60 70
50
60
70
50
60
70
Svaried in Conflict Stimulus (deg)
SD variedST varied
Two-cue Results
50 60conflict (deg)
Base Slant = 30
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
20 30 4020 30 40
20
30
40
20
30
40
Svaried in Conflict Stimulus (deg)
Predictions
50 60conflict (deg)
Base Slant = 30
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
20 30 4020 30 40
20
30
40
20
30
40
Svaried in Conflict Stimulus (deg)
Two-cue Results
50 60conflict (deg)
Base Slant = 0
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
-10 0 10
PS
E
-10 0 10
-10
0
10
-10
0
10
Svaried in Conflict Stimulus (deg)
Predictions
50 60conflict (deg)
Base Slant = 0
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
-10 0 10
PS
E
-10 0 10
-10
0
10
-10
0
10
Svaried in Conflict Stimulus (deg)
Two-cue Results
50 60conflict (deg)
Base Slant = -30
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
-40 -30 -20 -40 -30 -20
-40
-30
-20
-40
-30
-20
Svaried in Conflict Stimulus (deg)
Predictions
50 60conflict (deg)
Base Slant = -30
50 60conflict (deg)
SJW
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
-40 -30 -20 -40 -30 -20
-40
-30
-20
-40
-30
-20
Svaried in Conflict Stimulus (deg)
Two-cue Results
50 60 70conflict (deg)-70 -60 -50
-70
-60
-50
Base Slant = -60
50 60 70conflict (deg)-70 -60 -50
-70
-60
-50
SJW
tilt 0 tilt 90
Svaried in Conflict Stimulus (deg)
PSE
(deg
)
Sfixed Sfixed
Predictions
50 60 70conflict (deg)-70 -60 -50
-70
-60
-50
Base Slant = -60
50 60 70conflict (deg)-70 -60 -50
-70
-60
-50
SJW
tilt 0 tilt 90
Svaried in Conflict Stimulus (deg)
PSE
(deg
)
Sfixed Sfixed
Predictions
50 60 70conflict (deg)-70 -60 -50
-70
-60
-50
Base Slant = -60
50 60 70conflict (deg)-70 -60 -50
-70
-60
-50
RM
tilt 0 tilt 90
Svaried in Conflict Stimulus (deg)
PSE
(deg
)
Sfixed Sfixed
Predictions
50 60conflict (deg)
Base Slant = -30
50 60conflict (deg)
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
-40 -30 -20 -40 -30 -20
-40
-30
-20
-40
-30
-20
Svaried in Conflict Stimulus (deg)
RM
Predictions
50 60conflict (deg)
Base Slant = 0
50 60conflict (deg)
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
-10 0 10
PS
E
-10 0 10
-10
0
10
-10
0
10
Svaried in Conflict Stimulus (deg)
RM
Predictions
50 60conflict (deg)
Base Slant = 30
50 60conflict (deg)
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
20 30 4020 30 40
20
30
40
20
30
40
Svaried in Conflict Stimulus (deg)
RM
Predictions
50 60conflict (deg)
Base Slant = 60
50 60conflict (deg)
tilt 0 tilt 90
PSE
(deg
)
Sfixed Sfixed
50 60 70
PS
E
50 60 70
50
60
70
50
60
70
Svaried in Conflict Stimulus (deg)
RM
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 that’s 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.
Single-cue Experiment
The thresholds were used to determine the variances of the disparity and texture estimators at different tilts and base slants.
2
2 2T
DD T
Tw
T T
2
2 2D
TD T
Tw
T T
2 2
2 2D T T
T D D
w Tw T
Empirical weightsSingle cue thresholds
% “
mor
e sl
ant”
50%
75%
threshold
slant difference
Single-Cue data
Disparity threshold Texture threshold
Base-Slant (deg)
Log(
thre
shol
d)
Tilt=0Tilt=90
Single-Cue data
Disparity threshold Texture threshold
Base-Slant (deg)
Log(
thre
shol
d)
Tilt=0Tilt=90
With real surfaces:
so
Thus, we expect variation in wD to have little or no effect on perceived slant.
S = wD*SD + (1-wD)*ST
S = ST
Cue Combination & Slant Anisotropy
ˆ ˆ ˆD D T TS w S w S
ˆ ˆT DS S
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