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 Threshold planes, according to ‘surface’ hypothesis Thresholds should all be the same, according to ‘fronto-parallel’ hypothesis
Prediction L R Threshold planes
Interleaved psychometric functions L R Threshold planes
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 RcycLR L Threshold (arcmin) MDB 12% difference p < (one-tailed t-test) 23% diff. p <
Summary of thresholds RcycLR L Threshold (arcmin) AG 15% difference p < % diff. p < 0.01
Summary Threshold planes 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 which the target was displaced (arcmin) Target column Slanted grid (+0.1) depth judgement Slanted 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 MDBSubject 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: