effects of viewing geometry on combination of disparity and texture gradient information michael s....
Post on 20-Dec-2015
216 views
TRANSCRIPT
![Page 1: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/1.jpg)
Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information
Michael S. Landy
Martin S. Banks
James M. Hillis
![Page 2: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/2.jpg)
Outline
• Background: Optimal cue combination
• Methods: slant discrimination
• Single-cue results
• Two-cue results: perceived slant
• Two-cue results: JNDs
• Conclusions
![Page 3: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/3.jpg)
Outline
• Background: Optimal cue combination
• Methods: slant discrimination
• Single-cue results
• Two-cue results: perceived slant
• Two-cue results: JNDs
• Conclusions
![Page 4: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/4.jpg)
Sources of Depth Information
• Motion Parallax
• Occlusion
• Stereo Disparity
• Shading
• Texture
• Linear Perspective
• Etc.
![Page 5: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/5.jpg)
Depth Cues
• Motion Parallax
• Occlusion
• Stereo Disparity
• Shading
• Texture
• Linear Perspective
• Etc.
![Page 6: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/6.jpg)
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
ˆ ˆ ˆ ,t t d dS w S w S
2 2
2 2 2 2
1/ 1/and .
1/ 1/ 1/ 1/t d
t dt d t d
w w
![Page 7: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/7.jpg)
Optimal Cue Combination:Bayesian Inference Approach
From the Bayesian standpoint, the measurements D and T each result in a likelihood function
( | ) and ( | ).p T S p D S
These are combined with a prior distribution
( ).p S
![Page 8: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/8.jpg)
Optimal Cue Combination:Bayesian Inference Approach
( | , ) ( | ) ( | ) ( ).p S T D p T S p D S p S
From Bayes rule, and assuming conditional independence of the cues, the posterior distribution satisfies:
![Page 9: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/9.jpg)
Optimal Cue Combination:Bayesian Inference Approach
ˆ ˆ ˆ ,t t d d p pS w S w S w S
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:
![Page 10: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/10.jpg)
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.
![Page 11: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/11.jpg)
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
![Page 12: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/12.jpg)
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
![Page 13: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/13.jpg)
Outline
• Background: Optimal cue combination
• Methods: slant discrimination
• Single-cue results
• Two-cue results: perceived slant
• Two-cue results: JNDs
• Conclusions
![Page 14: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/14.jpg)
Types of Stimuli
• Disparity-only: sparse random dots
• Texture: Voronoi textures viewed monocularly
• Two-cue stimuli: Voronoi texture stereograms, both conflict and no-conflict
![Page 15: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/15.jpg)
Stimuli – Disparity-only
![Page 16: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/16.jpg)
Stimuli – Voronoi textures
![Page 17: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/17.jpg)
Cue Conflict Stimuli
![Page 18: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/18.jpg)
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
![Page 19: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/19.jpg)
Outline
• Background: Optimal cue combination
• Methods: slant discrimination
• Single-cue results
• Two-cue results: perceived slant
• Two-cue results: JNDs
• Conclusions
![Page 20: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/20.jpg)
Single-cue JNDs: Texture
![Page 21: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/21.jpg)
Single-cue JNDs: Disparity
![Page 22: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/22.jpg)
Single-cue JNDs: Disparity
![Page 23: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/23.jpg)
Predicted Cue Weights
![Page 24: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/24.jpg)
Outline
• Background: Optimal cue combination
• Methods: slant discrimination
• Single-cue results
• Two-cue results: perceived slant
• Two-cue results: JNDs
• Conclusions
![Page 25: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/25.jpg)
Cue Conflict Paradigm
![Page 26: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/26.jpg)
Determination of PSEs
![Page 27: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/27.jpg)
Determination of Weights
![Page 28: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/28.jpg)
Full Two-Cue Dataset
ACH JMH
![Page 29: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/29.jpg)
Effect of Viewing Distance
![Page 30: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/30.jpg)
Effect of Base Slant
![Page 31: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/31.jpg)
Outline
• Background: Optimal cue combination
• Methods: slant discrimination
• Single-cue results
• Two-cue results: perceived slant
• Two-cue results: JNDs
• Conclusions
![Page 32: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/32.jpg)
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.
2 2
2 2t d
t d
2 2
2 2 2 2
1/ 1/and
1/ 1/ 1/ 1/t d
t dt d t d
w w
![Page 33: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/33.jpg)
Improvement in JND with 2 Cues
![Page 34: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/34.jpg)
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
![Page 35: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/35.jpg)
![Page 36: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/36.jpg)
Are Cue Weights Chosen Locally?
![Page 37: Effects of Viewing Geometry on Combination of Disparity and Texture Gradient Information Michael S. Landy Martin S. Banks James M. Hillis](https://reader038.vdocuments.us/reader038/viewer/2022110207/56649d4b5503460f94a293aa/html5/thumbnails/37.jpg)
Are Cue Weights Chosen Locally?