1. Ch.9 Bayesian Models of Sensory Cue Integration 2008. 12. 29 (Mon) Summarized and Presented by J.W. Ha 1

2. Main Objects Modeling multiple cues on subjects Mainly 3D visual perception Ambiguity, Regularity  Integration Using Bayesian formula Constraints  Prior Estimates  Likelihood Cue Integration  Bayesian approaches 2

3. Introduction Sensory Cues –Uncertain information  ambiguity –Mitigated by factors Factors –Integrating multiple cues –Objects have statistical regularities Bayesian Probability Theory –Provides a framework for modeling to way to combine multiple cue information and prior knowledge –Provides predictive theories how human sensory systems make perceptual inferences 3

4. Basics Fig 9.1 4

5. Basics Bayesian Formula –Posterior is proportional to likelihood function associated with each cue and prior When one cue is less certain than another, the integrated estimate should be biased toward the more reliable cue 5

6. PSYCHOPHYSICAL TESTS OF BAYESIAN CUE INTEGRATION 6

7. The Linear Case Integrated sum of cues –z = f(z 1, z 2 ) = w 1 z 1 + w 2 z 2 + k –w 1 /w 2 = σ 2 2 /σ 1 2 Discrimination thresholds –The difference in the value of z needed by an observer to correctly discriminate stimuli over 75% –For Gaussian model, T is proportional to standard deviation of internal perceptual representations –w 1 /w 2 = σ 2 2 /σ 1 2 = T 2 2 /T 1 2 –By measuring T, predict w 7

8. The Linear Case Fig 9.3 –Relation between texture and slant –Observers will give more weight to texture cues at high slants 8

9. Fig 9.4 –In high slant, low texture thresholds –The gap at b) occurs due to difference single cue from combined cue 9

10. A Nonlinear Case In case that the likelihood function is not a Gaussian –The sensory noise is Gaussian as a result of the nonlinear mapping from sensory feature space to the parameter space being estimated Skew symmetry –Fig 9.5 10

11. A Nonlinear Case Fig 9.7 : Spin-dependent biases 11

12. A Nonlinear Case Fig 9.7 : Subject’s data along with model prediction 12

13. PSYCHOPHYSICAL TESTS OF BAYESIAN PRIORS 13

14. Psychophysical Tests of Bayesian Priors 3D vision problem –An ill-posed problem –Inherent ambiguity of inverting the 3D to 2D perspective projection and in part due to noise in the image –Highly structured  prior knowledge Priori constraints –Prior knowledge –3D shape Motion (rigidity, elastic motion) Surface contours (isotropy, symmetry) 14

15. Psychophysical Tests of Bayesian Priors Fig 9.8 15

16. Psychophysical Tests of Bayesian Priors Fig 9.9 16

17. MIXTURE MODELS, PRIORS AND CUE INTEGRATION 17

18. Model Self-Selection Interpreting 3D cues  Model Selection –Single cue provides the information necessary to determine when a particular prior should be applied –Other cues resolve ambiguities Nuisance parameters 18

19. Model Self-Selection Estimating surface orientation from texture 19

20. Model Self-Selection Fig 9.12 –The result of an experiment designed to test whether and how subjects switch between isotropic and anisotropic models 20