1. Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis

2. Outline Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant Two-cue results: JNDs Conclusions

3. Outline Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant Two-cue results: JNDs Conclusions

4. Sources of Depth Information Motion Parallax Occlusion Stereo Disparity Shading Texture Linear Perspective Etc.

5. Depth Cues Motion Parallax Occlusion Stereo Disparity Shading Texture Linear Perspective Etc.

6. Optimal Cue Combination: Statistical Approach If the goal is to produce an estimate with minimal variance, and the cues are uncorrelated, then the optimal estimate is a weighted average where

7. Optimal Cue Combination: Bayesian Inference Approach From the Bayesian standpoint, the measurements D and T each result in a likelihood function These are combined with a prior distribution

8. Optimal Cue Combination: Bayesian Inference Approach From Bayes rule, and assuming conditional independence of the cues, the posterior distribution satisfies:

9. Optimal Cue Combination: Bayesian Inference Approach where p stands for the prior which acts as if it were an additional cue, and the weights are again proportional to inverse variance. Finally, assuming Gaussian likelihoods and prior, it turns out that the maximum a posteriori (MAP) estimate satisfies:

10. Previous Qualitative Tests that Cue Weights Depend on Reliability Young, Landy & Maloney (1993) Johnston, Cumming & Landy (1994) Rogers and Bradshaw (1995) Frisby, Buckley & Horsman (1995) Backus and Banks (1999) etc.

11. Previous Quantitative Tests that Cue Weights Depend on Reliability Landy & Kojima (2001) – texture cues to location Ernst & Banks (2002) – visual and haptic cues to size Gepshtein & Banks (2003) – visual and haptic cues to size Knill & Saunders (2003) – texture and disparity cues to slant

12. The Current Study Texture and disparity cues to slant Vary reliability by varying base slant (as in Knill & Saunders, 2003) and distance Measure single-cue reliability Compare two-cue weights to predictions Compare two-cue reliability to predictions

13. Outline Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant Two-cue results: JNDs Conclusions

14. Types of Stimuli Disparity-only: sparse random dots Texture: Voronoi textures viewed monocularly Two-cue stimuli: Voronoi texture stereograms, both conflict and no-conflict

15. Stimuli – Disparity-only

16. Stimuli – Voronoi textures

17. Cue Conflict Stimuli

18. Methods Task: 2IFC slant discrimination Single-cue and two-cue blocks Opposite-sign slants mixed across trials in a block to avoid slant adaptation One stimulus fixed, other varied by staircase; several interleaved staircases Analysis: fit psychometric function to estimate PSE and JND

19. Outline Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant Two-cue results: JNDs Conclusions

20. Single-cue JNDs: Texture

21. Single-cue JNDs: Disparity

23. Predicted Cue Weights

24. Outline Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant Two-cue results: JNDs Conclusions

25. Cue Conflict Paradigm

26. Determination of PSEs

27. Determination of Weights

28. Full Two-Cue Dataset ACHJMH

29. Effect of Viewing Distance

30. Effect of Base Slant

31. Outline Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant Two-cue results: JNDs Conclusions

32. Improvement in Reliability with Cue Combination If the optimal weights are used: then the resulting variance is lower than that achieved by either cue alone.

33. Improvement in JND with 2 Cues

34. Conclusion The data are consistent with optimal cue combination Texture weight is increased with increasing distance and increasing base slant, as predicted Two cue JNDs are generally lower than the constituent single-cue JNDs Thus, weights are determined trial-by-trial, based on the current stimulus information and, in particular, the two single-cue slant estimates

36. Are Cue Weights Chosen Locally?