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Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information

Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information. James M. Hillis. Michael S. Landy. Martin S. Banks. Outline. Background: Optimal cue combination Methods: slant discrimination Single-cue results Two-cue results: perceived slant

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Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information

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

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

  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. 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

  22. 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 ACH JMH

  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

  35. Are Cue Weights Chosen Locally?

  36. Are Cue Weights Chosen Locally?

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