What determines the reference framework for stereopsis?

Andrew Glennerster, Martin Birch

and Suzanne McKee*

University Laboratory of Physiology, Oxford

*Smith-Kettlewell Eye Research Institute, San Francisco

Viewing geometry

Depth in fronto-parallel coordinates

L R

Fixation plane

Depth relative to a local surface

L R

Mitchison and McKee (85, 87)Mitchison and Westheimer (84)

Reference plane

Depth perpendicular to a local surface

L R

Prediction

L R

Thresholdplanes,accordingto‘surface’hypothesis

Thresholdsshould all bethe same,according to‘fronto-parallel’hypothesis

Prediction

L R

Thresholdplanes

Interleaved psychometric functions

L R

Thresholdplanes

Stimulus details

Target column

4

Task• is central column in front or behind the plane of the grid?

• dot size 2 arcmin• pixel size 0.45 arcmin• anti-aliased• viewing distance 2.65 m• exposure 600 ms• grid disparity gradient +/- 0.1• slant about a vertical axis• modified Wheatstone stereoscope

Stimulus

Psychometric procedure• method of constant stimuli• 7 disparities per psychometric function (at least 1400 trials)• 3 psychometric functions interleaved …

Results: grid disparity gradient -0.1

Subject MDB

Grid disparity gradient +0.1

Subject MDB

Grid disparity gradient -0.1

Subject AG

Grid disparity gradient +0.1

Subject AG

Summary of thresholds

0

0.2

0.4

0.6

0.8

R cyc L R cyc L

Thr

esho

ld (

arcm

in) MDB 12% difference

p < 0.001(one-tailed t-test)

23% diff.p < 0.0001

Summary of thresholds

0

0.2

0.4

0.6

0.8

R cyc L R cyc L

Thr

esho

ld (

arcm

in) AG

15% differencep < 0.0112% diff.

p < 0.01

Summary

Thresholdplanes

• Thresholds for detecting relative disparity depend on the local surface slant

• Thresholds are lowest when the displacement is more orthogonal to the surface

Conclusion

• The visual system may represent depth in a surface-based coordinate frame ...

• … and hence be much less sensitive to rotations and translations of the head

Conclusion

• The visual system may represent depth in a surface-based coordinate frame ...

• … and hence be much less sensitive to rotations and translations of the head

Comparison with lateral displacement thresholds Key:

F-P grid, lateral judgement

Width of grid in the eye in whichthe target was displaced

(arcmin)

Target columnTarget column

Slanted grid (+0.1) depth judgementSlanted grid (-0.1) depth judgement

Subject MDB

Sensitivity to lateral displacement

Subject MDB

… and to disparity + lateral displacement

Subject MDB

… and to disparity + lateral displacement

Subject MDB

Grid gradient 0.1

Subject MDB Subject SPM

Grid gradient +0.1 and -0.1

Subject MDB

Local surface model

Subject MDB

+0.1 gradient -0.1 gradient

Interleaved slants

Subject MDB

+0.4 arcmin disparity -0.4 arcmin disparity

Effect of perceived slant

Subject MDB

Grid perceived as fronto-parallel:

Grid perceived as slanted: