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Bayesian modeling in the context of robust cue integration

Bayesian modeling in the context of robust cue integration. David C. Knill Center for Visual Science University of Rochester. The Bayesian approach as a framework for psychophysics. David C. Knill Center for Visual Science University of Rochester.

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Bayesian modeling in the context of robust cue integration

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  1. Bayesian modeling in the context of robust cue integration David C. Knill Center for Visual Science University of Rochester

  2. The Bayesian approach as a framework for psychophysics David C. Knill Center for Visual Science University of Rochester

  3. Some properties of a useful psychophysical framework • Support building predictive models of perceptual performance. • Support bridging statements between models and descriptions of behavior. • Explain “why” perception / sensorimotor control works the way it does. • Help guide psychophysical research • Suggests new and interesting theoretical questions. • Supports scaling down perceptual / sensorimotor problems to bring them into the lab. • Scales up naturally

  4. World model

  5. World model Noise Sensory processing Generative model Sensory Features Information

  6. World model Noise Sensory processing Generative model Sensory Features p(S | I) Bayesian Computations

  7. World model Noise Sensory processing Generative model Estimate Sensory Features p(S | I) Bayesian Computations * Task model

  8. World model Noise Sensory processing Generative model Estimate Sensory Features p(S | I) Bayesian Computations * Ideal Observer Task model

  9. World model Noise Sensory processing Generative model Estimate Sensory Features p(S | I) Bayesian Computations * Ideal Observer Task model

  10. Estimate Sensory Features Human Observer

  11. Estimate Sensory Features p(S | I) Bayesian Computations * Task model Rational Observer

  12. World model Generative model Estimate Sensory Features p(S | I) Bayesian Computations * Task model Rational Observer

  13. Ideal observer models Rational observer models The domain of Bayesian models Description of sensorimotor / perceptual behavior

  14. Cue integration:Estimating slant from monocular and binocular cues

  15. Linear process model Texture data (It) Slant from texture St wt Sst Action / Decision + Stereo data (Is) Ss ws Slant from stereo

  16. Normative (ideal observer) model Stereo likelihood

  17. Normative (ideal observer) model Texture likelihood

  18. Normative (ideal observer) model Joint likelihood

  19. Humans weight sensory cues “optimally” • Discrimination thresholds in single cue conditions predict weights measured in multi-cue experiments. • Ernst and Banks, 2002; Knill and Saunders, 2003; Alais and Burr (2004); etc., etc., etc.

  20. Texture information Binocular information Least Reliable Equally reliable Most Reliable

  21. What are cue weights?

  22. What are cue weights? • Summary descriptions of perceptual performance.

  23. What are cue weights? • Summary descriptions of perceptual performance. • Summary descriptions of the information available for a task.

  24. What are cue weights? • Summary descriptions of perceptual performance. • Summary descriptions of the information available for a task. • Support logical links between behavior and rational / normative models of performance.

  25. Robust non-linear cue integration

  26. Robust non-linear cue integration • Classical question • How does the brain interpret multiple sensory cues when they have large “conflicts”

  27. Robust non-linear cue integration • Classical question • How does the brain interpret multiple sensory cues when they have large “conflicts” • For visual depth cues • Re-conceptualize the problem • what normally gives rise to what we call large cue “conflicts?”

  28. Answer • Most depth cues are informative because of statistical regularities in the world

  29. Answer • Most depth cues are informative because of statistical regularities in the world • Examples • Texture - isotropy, homogeneity • Figure shape - isotropy, symmetry • Motion - rigidity

  30. Answer • Most depth cues are informative because of statistical regularities in the world • Examples • Texture - isotropy, homogeneity • Figure shape - isotropy, symmetry • Motion - rigidity • Constraints don’t always apply • True prior model = mixture of constraints

  31. Answer • Most depth cues are informative because of statistical regularities in the world • Examples • Texture - isotropy, homogeneity • Figure shape - isotropy, symmetry • Motion - rigidity • Constraints don’t always apply • True prior model = mixture of constraints • Large “conflicts” arise when strong constraint does not hold.

  32. Compression cue = slant suggested by circle interpretation

  33. Likelihood function - p(circle) + p(ellipse)

  34. Figure shape cue

  35. Disparity cue

  36. Combined cues

  37. Predictions of mixture model All circles Circles + narrow range of ellipses Circles + broad range of ellipses

  38. Stereoscopic slant = 35o

  39. Model fits Stereoscopic slant = 35o

  40. Model fits Stereoscopic slant = 55o

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