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

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Presentation transcript:

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

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

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

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

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

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

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

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

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:

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.

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

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

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

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

Stimuli – Disparity-only

Stimuli – Voronoi textures

Cue Conflict Stimuli

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

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

Single-cue JNDs: Texture

Single-cue JNDs: Disparity

Predicted Cue Weights

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

Cue Conflict Paradigm

Determination of PSEs

Determination of Weights

Full Two-Cue Dataset ACHJMH

Effect of Viewing Distance

Effect of Base Slant

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

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.

Improvement in JND with 2 Cues

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

Are Cue Weights Chosen Locally?