Slant Anisotropy and Tilt- dependent Variations in Stereo Precision Tandra Ghose Vision Science Program UC Berkeley 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 Supported 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 horopter Garding 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 horopter Garding 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 horopter Garding 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 : 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 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 w D is small We propose that w D 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 w D is small We propose that w D 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 w D is small We propose that w D 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 w D is small We propose that w D 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 w D is small We propose that w D 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 w D is small We propose that w D is less for tilt 0 than for tilt 90 Cue Combination & Slant Anisotropy

With real surfaces: so Thus, we expect variation in w D to have little or no effect on perceived slant because the weights presumably add to 1

Cue Combination & Slant Anisotropy With real surfaces: so Thus, we expect variation in w D to have little or no effect on perceived slant because the weights presumably add to 1

Cue Combination & Slant Anisotropy With real surfaces: so Thus, we expect variation in w D 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 slant no feedback Standard S = –60,-30,0,30 or 60 deg  S 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  D 2 and  T 2 and from that we can derive predicted weights w D and w T

Texture threshold Monocular viewing Stimulus

Disparity Threshold Binocular viewing Stimulus

Two-cue Experiment 2-IFC: which interval has more positive slant? 2 conflict conditions: S T or S D 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 stimulus DisparityTexture specified slant Conflict stimulus DisparityTexture specified slant For each conflict stimulus, we find the value of the no-conflict stimulus that has the same perceived slant (PSE).

Texture Dominance S D varied S fixed S varied in Conflict Stimulus (deg) PSE (deg) S T varied w T = 1 w D = 0

Disparity Dominance S D varied S fixed S varied in Conflict Stimulus (deg) PSE (deg) S T varied w T = 0 w D = 1

Two-cue Results 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed PSE S varied in Conflict Stimulus (deg) S D varied S T varied

Predictions 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed PSE S varied in Conflict Stimulus (deg) S D varied S T varied

Two-cue Results 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed S varied in Conflict Stimulus (deg)

Predictions 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed S varied in Conflict Stimulus (deg)

Two-cue Results 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed PSE S varied in Conflict Stimulus (deg)

Predictions 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed PSE S varied in Conflict Stimulus (deg)

Two-cue Results 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed S varied in Conflict Stimulus (deg)

Predictions 5060 conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 PSE (deg) S fixed S varied in Conflict Stimulus (deg)

Two-cue Results conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 S varied in Conflict Stimulus (deg) PSE (deg) S fixed

Predictions conflict (deg) Base Slant = conflict (deg) SJW tilt 0tilt 90 S varied in Conflict Stimulus (deg) PSE (deg) S fixed

Predictions conflict (deg) Base Slant = conflict (deg) RM tilt 0tilt 90 S varied in Conflict Stimulus (deg) PSE (deg) S fixed

Predictions 5060 conflict (deg) Base Slant = conflict (deg) tilt 0tilt 90 PSE (deg) S fixed S varied in Conflict Stimulus (deg) RM

Predictions 5060 conflict (deg) Base Slant = conflict (deg) tilt 0tilt 90 PSE (deg) S fixed PSE S varied in Conflict Stimulus (deg) RM

Predictions 5060 conflict (deg) Base Slant = conflict (deg) tilt 0tilt 90 PSE (deg) S fixed S varied in Conflict Stimulus (deg) RM

Predictions 5060 conflict (deg) Base Slant = conflict (deg) tilt 0tilt 90 PSE (deg) S fixed PSE S varied 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. Empirical weightsSingle cue thresholds % “more slant” 50% 75% threshold slant difference

Single-Cue data Disparity thresholdTexture threshold Base-Slant (deg) Log(threshold) Tilt=0 Tilt=90

Single-Cue data Disparity thresholdTexture threshold Base-Slant (deg) Log(threshold) Tilt=0 Tilt=90

With real surfaces: so Thus, we expect variation in w D to have little or no effect on perceived slant. S = w D *S D + (1-w D )*S T S = S T Cue Combination & Slant Anisotropy