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Slant Anisotropy and Tilt-dependent Variations in Stereo Precision

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

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Slant Anisotropy and Tilt-dependent Variations in Stereo Precision

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  1. 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

  2. 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

  5. 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

  6. 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

  8. Cue Combination Multiple depth cues are used to estimate 3D shape

  9. 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:

  10. Cue Combination Estimates can be combined by a weighted average Combined estimate is shifted toward single-cue estimate of lower variance

  11. 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 wDless 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 wDless 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 wDless 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 wDless 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 wDless 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

  18. 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

  19. Cue Combination & Slant Anisotropy With real surfaces: so Thus, we expect variation in wD to have little or no effect on perceived slant.

  20. 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

  25. 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 estimatingsD2andsT2 • and from that we can derive predicted weights wD and wT

  26. Texture threshold Monocular viewing Stimulus

  27. Disparity Threshold Binocular viewing Stimulus

  28. Two-cue Experiment • 2-IFC: which interval has more positive slant? • 2 conflict conditions: STor 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

  29. Two-cue Experiment Conflict stimulus Texture Disparity 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 Texture Disparity specified slant

  30. Texture Dominance wT = 1 wD = 0 SD varied ST varied PSE (deg) Sfixed Svaried in Conflict Stimulus (deg)

  31. Disparity Dominance wT = 0 wD = 1 SD varied ST varied PSE (deg) Sfixed Svaried in Conflict Stimulus (deg)

  32. Two-cue Results 70 60 50 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 70 60 50 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)

  34. Two-cue Results 40 40 30 30 20 20 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)

  35. Predictions 40 40 30 30 20 20 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 10 10 0 0 -10 -10 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)

  37. Predictions 10 10 0 0 -10 -10 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 -20 -20 -30 -30 -40 -40 -40 -30 -20 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)

  39. Predictions -20 -20 -30 -30 -40 -40 -40 -30 -20 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 -50 -50 -60 -60 -70 -70 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)

  41. Predictions -50 -50 -60 -60 -70 -70 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)

  42. Predictions -50 -50 -60 -60 -70 -70 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 -20 -20 -30 -30 -40 -40 -40 -30 -20 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)

  44. Predictions 10 10 0 0 -10 -10 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 40 40 30 30 20 20 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 70 60 50 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)

  47. Conclusions • In the single-cue experiment, disparity thresholds were slightly, but consistently, lower with tilt 90 than with tilt 0. • 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. • Slant anisotropy is thus a byproduct of cue conflict between disparity- and texture-specified slants. • However, the cause of poorer disparity thresholds at tilt = 0 remains mysterious.

  48. Single-cue Experiment 75% % “more slant” threshold 50% slant difference The thresholds were used to determine the variances of the disparity and texture estimators at different tilts and base slants. Single cue thresholds Empirical weights

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

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

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