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An idea for studying human texture perception in a probabilistic framework. Reference: S. Tajima (2013) Defining statistical perceptions with an empirical Bayesian approach. Physical Review E, 87(4):042707. https://sites.google.com/site/satohirotajima/
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Defining statistical perceptionswith an empirical Bayes approach
Satohiro Tajima
Perception of image statistics is an empirical Bayes estimation.
Stimulus statistics?
1
α
α=1.284
α=1.122
α=1.201
Contrast Smoothness
Stimulus statistics = cue for recognition
1
α
α=1.284
α=1.122
α=1.201
Stimulus statistics = cue for recognition
Scene categoryBlurTexture
(Hansen & Hess, J. Vis., 2006) (Liu et al., CVPR., 2008) (Torralba & Oliva, Network, 2003)
We can perceive statistics!
Idea
Image engineering
“Perception of stimulus statistics”
“Image restoration”
Empirical Bayes
Vision science
Problem in perceiving stimulus statistics
θ s r
Statistics(smoothness)
Stimulus(image)
Neural response
θs
EstimateStochasticity Noise
“Percepts”
θ s r
θ s r
Stimulus
Imagerestoration
Visualrecognition
Goal of:Bayesian framework
Statistics Response
Bayesian framework
θ s r
θ s r
“hyperparameter”StimulusStatistics Response
Bayes
Empirical Bayes
Bayesian framework
θ s r
θ s r
StimulusStatistics Response
Different goals of estimation
Imagerestoration
Visualrecognition
… But both are mathematically equal manipulations.
for
StimulusStatistics
for
Stimulus Statistics
Different criteria
Imagerestoration
Visualrecognition
Mean square error
]/ˆ[E2Nss
Fisher information
)]|(ln[E θrP- -1]ˆ[Var
Variance of estimate
(Ideal observer)
Different criteria
Imagerestoration
Visualrecognition
]/ˆ[E2Nss
Mean square error
Fisher information
)]|(ln[E θrP- 2)'( d
Signal detectiontheory
(Ideal observer)
Application
Decoding retinal codes
Decoding retinal codes
θStatistics
Cortex
Estimate (Percept)
θ s r
Natural image statistics
θStatistics
Cortex
• Smoothness• Contrast
Neural response model
θStatistics
Cortex
Receptive field
Estimation of stimulus
Receptive field
(Tajima, Inoue & Okada, J. Phys. Soc. Jpn., 2008)
s As r s^
Estimation of statistics
(Tajima, Inoue & Okada, J. Phys. Soc. Jpn., 2008)
SmoothnessCo
ntra
st
Receptive field
- ｌ
ｎ P
(r|θ
)
Optimal receptive field size?
(Natural image model: Power-law model)
Receptive field size
Mean square error
(Noise level)
Fisher informationof smoothness
Receptive field size
Criteria:
Image restoration Visual recognition
Optimal receptive field size?
(Natural image model: Power-law model)
Rec
eptiv
e fie
ld s
ize
Optimal receptive field size?
Intensity-dependent RF changes:
Retina (Barlow et al., 1957)V1 (Polat & Norcia, 1996)MT (Hunter & Born, 2011)
Rec
eptiv
e fie
ld s
ize
Optimal receptive field size?
Retinal ganglion cells
Midget
Parasol
Bistratified
Rec
eptiv
e fie
ld s
ize
Which cell type is the best?
Midget(Parvo)
Parasol(Magno)
Bistratified(Konio)
Receptive field
(Field et al., Nature, 2010)
SIZE SHAPE
Which cell type is the best? - (prediction)
(Natural image model: Power-law model)
Midget (Parvo)Parasol (Magno)
Bistratified (Konio)
Fis
her
info
rmat
ion
Which cell type is the best? - (prediction)
(Natural image model: Power-law model)
Midget (Parvo)Parasol (Magno)
Bistratified (Konio)
Fis
her
info
rmat
ion
Implementation of empirical Bayes?
Message
Image engineering
“Perception of stimulus statistics”
“Image restoration”
Empirical Bayes!
Vision science
Vision science Image engineering
• Mean square error• Fisher information Human recognition
Restoration
Purpose:
What criteria should we use?
Image engineering Vision science
• Compression• Denoising• Prediction
Prior for stimulus estimation
Hidden variables of system
Cue for recognition
Rolls of statistics:
What is the function of statistics perception?
Perception of image statistics is empirical Bayes estimation.
https://sites.google.com/site/satohirotajima/
Satohiro Tajima.Defining statistical perceptions with an empirical Bayesian approach.Physical Review E, 87(4):042707, (2013).
