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