1. 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

2. Viewing geometry

6. Depth in fronto-parallel coordinates L R Fixation plane

7. Depth relative to a local surface L R Mitchison and McKee (85, 87) Mitchison and Westheimer (84) Reference plane

8. Depth perpendicular to a local surface L R

9. Prediction L R Threshold planes, according to ‘surface’ hypothesis Thresholds should all be the same, according to ‘fronto-parallel’ hypothesis

10. Prediction L R Threshold planes

11. Interleaved psychometric functions L R Threshold planes

12. 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 …

13. Results: grid disparity gradient -0.1 Subject MDB

14. Grid disparity gradient +0.1 Subject MDB

15. Grid disparity gradient -0.1 Subject AG

16. Grid disparity gradient +0.1 Subject AG

17. Summary of thresholds RcycLR L Threshold (arcmin) MDB 12% difference p < 0.001 (one-tailed t-test) 23% diff. p < 0.0001

18. Summary of thresholds RcycLR L Threshold (arcmin) AG 15% difference p < 0.01 12% diff. p < 0.01

19. 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

20. 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

21. 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

22. 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

23. Sensitivity to lateral displacement Subject MDB

24. … and to disparity + lateral displacement Subject MDB

25. … and to disparity + lateral displacement Subject MDB

27. Grid gradient 0.1 Subject MDBSubject SPM

28. Grid gradient +0.1 and -0.1 Subject MDB

29. Local surface model Subject MDB +0.1 gradient-0.1 gradient

30. Interleaved slants Subject MDB +0.4 arcmin disparity-0.4 arcmin disparity

31. Effect of perceived slant Subject MDB Grid perceived as fronto-parallel: Grid perceived as slanted: