slant anisotropy and tilt-dependent variations in stereo precision
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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