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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
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Ch.9 Bayesian Models of Sensory Cue Integration
2008. 12. 29 (Mon)Summarized and Presented by J.W.
Ha
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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
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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 com-
bine multiple cue information and prior knowledge– Provides predictive theories how human sensory
systems make perceptual inferences
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Basics
• Fig 9.1
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Basics
• Bayesian Formula
– Posterior is proportional to likelihood function asso-ciated with each cue and prior
• When one cue is less certain than another, the integrated estimate should be biased to-ward the more reliable cue
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PSYCHOPHYSICAL TESTS OF BAYESIAN CUE INTE-GRATION
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The Linear Case
• Integrated sum of cues– z = f(z1, z2) = w1z1 + w2z2 + k – w1/w2 = σ2
2/σ12
• Discrimination thresholds– The difference in the value of z needed by an ob-
server to correctly discriminate stimuli over 75%– For Gaussian model, T is proportional to standard
deviation of internal perceptual representations– w1/w2 = σ2
2/σ12 = T2
2/T12
– By measuring T, predict w
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The Linear Case
• Fig 9.3
– Relation between texture and slant– Observers will give more weight to texture cues at
high slants
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• Fig 9.4
– In high slant, low texture thresholds– The gap at b) occurs due to difference single cue
from combined cue
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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
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A Nonlinear Case
• Fig 9.7 : Spin-dependent biases
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A Nonlinear Case
• Fig 9.7 : Subject’s data along with model pre-diction
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PSYCHOPHYSICAL TESTS OF BAYESIAN PRIORS
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Psychophysical Tests of Bayesian Priors
• 3D vision problem– An ill-posed problem– Inherent ambiguity of inverting the 3D to 2D per-
spective 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)
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Psychophysical Tests of Bayesian Priors• Fig 9.8
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Psychophysical Tests of Bayesian Priors
• Fig 9.9
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MIXTURE MODELS, PRI-ORS AND CUE INTEGRA-TION
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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
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Model Self-Selection
• Estimating surface orientation from texture
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Model Self-Selection
• Fig 9.12
– The result of an experiment designed to test whether and how subjects switch between isotropic and anisotropic models