Slant Anisotropy and Tilt- dependent Variations in Stereo Precision Tandra Ghose Vision Science...

Slant Anisotropy and Tilt-dependent Variations in Stereo

Precision

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


• Orientation disparity & tilt Cagenello & Rogers (1988, 1993)





o


• Orientation disparity & tilt Cagnello & Rogers (1988, 1993)





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


So we have:


so where






So we have:


so where





ˆ 0TS


So we have:


so where





ˆ ˆD DS w S 1Dw

ˆ 0TS


So we have:


so where


We propose that wD is less for tilt 0 than for tilt 90



ˆ ˆD DS w S 1Dw

ˆ 0TS


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




so


no effect on perceived slant because the weights presumably add to 1




so


no effect on perceived slant.


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


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)

PS

E (

deg

)ST varied

wT = 1

wD = 0

Disparity Dominance

SD varied

Sfixed


PS

E (

deg

)ST varied

wT = 0

wD = 1

Two-cue Results

50 60conflict (deg)

Base Slant = 60

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

50 60 70

PS

E

50 60 70

50

60

70

50

60

70


SD variedST varied

Predictions

50 60conflict (deg)

Base Slant = 60

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

50 60 70

PS

E

50 60 70

50

60

70

50

60

70


SD variedST varied

Two-cue Results

50 60conflict (deg)

Base Slant = 30

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

20 30 4020 30 40

20

30

40

20

30

40


Predictions

50 60conflict (deg)

Base Slant = 30

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

20 30 4020 30 40

20

30

40

20

30

40


Two-cue Results

50 60conflict (deg)

Base Slant = 0

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

-10 0 10

PS

E

-10 0 10

-10

0

10

-10

0

10


Predictions

50 60conflict (deg)

Base Slant = 0

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

-10 0 10

PS

E

-10 0 10

-10

0

10

-10

0

10


Two-cue Results

50 60conflict (deg)

Base Slant = -30

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

-40 -30 -20 -40 -30 -20

-40

-30

-20

-40

-30

-20


Predictions

50 60conflict (deg)

Base Slant = -30

50 60conflict (deg)

SJW

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

-40 -30 -20 -40 -30 -20

-40

-30

-20

-40

-30

-20


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


PS

E (

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


PS

E (

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


PS

E (

deg

)

Sfixed Sfixed

Predictions

50 60conflict (deg)

Base Slant = -30

50 60conflict (deg)

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

-40 -30 -20 -40 -30 -20

-40

-30

-20

-40

-30

-20


RM

Predictions

50 60conflict (deg)

Base Slant = 0

50 60conflict (deg)

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

-10 0 10

PS

E

-10 0 10

-10

0

10

-10

0

10


RM

Predictions

50 60conflict (deg)

Base Slant = 30

50 60conflict (deg)

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

20 30 4020 30 40

20

30

40

20

30

40


RM

Predictions

50 60conflict (deg)

Base Slant = 60

50 60conflict (deg)

tilt 0 tilt 90

PS

E (

deg

)

Sfixed Sfixed

50 60 70

PS

E

50 60 70

50

60

70

50

60

70


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 T

w T

Empirical weightsSingle cue thresholds

% “

mo

re s

lan

t”

50%

75%

threshold

slant difference

Single-Cue data

Disparity threshold Texture threshold

Base-Slant (deg)

Log(

thre

shol

d)

Tilt=0

Tilt=90

With real surfaces:

so


no effect on perceived slant.

S = wD*SD + (1-wD)*ST

S = ST



ˆ ˆT DS S

Slant Anisotropy and Tilt- dependent Variations in Stereo Precision Tandra Ghose Vision Science...

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