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![Different criteria
Image
restoration
Visual
recognition
Mean square error
E [ s
ˆ
s
2
/N]
Variance of
estimate
Fisher information
E [-
ln P ( r | θ )]
ˆ ] -1
Var [
(Ideal observer)](https://image.slidesharecdn.com/hi-tajima-eb2-131226022707-phpapp02/85/Defining-statistical-perceptions-with-an-empirical-Bayesian-approach-13-320.jpg)
![Different criteria
Image
restoration
Visual
recognition
Mean square error
E [ s
ˆ
s
2
/N]
Signal detection
theory
Fisher information
E [-
ln P ( r | θ )]
(d ' )
(Ideal observer)
2](https://image.slidesharecdn.com/hi-tajima-eb2-131226022707-phpapp02/85/Defining-statistical-perceptions-with-an-empirical-Bayesian-approach-14-320.jpg)
Uploaded bySatohiro Tajima
Defining statistical perceptions with an empirical Bayesian approach.
The document discusses the perception of image statistics using an empirical Bayes estimation approach. It explores various aspects of statistical perception, including the criteria for image restoration and visual recognition, as well as the implications of different receptive field sizes in the context of natural image statistics. The author highlights the roles of statistics in recognition, denoising, and compression, emphasizing the application of empirical Bayes methods in vision science and image engineering.
Defining statistical perceptions with an empirical Bayesian approach.
- 1. Defining statistical perceptions withan empirical Bayes approach Satohiro Tajima
- 2. Perception of imagestatistics is an empirical Bayes estimation.
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- 4. Stimulus statistics =cue for recognition 1 α α=1.284 α=1.122 α=1.201
- 5. Stimulus statistics =cue for recognition Texture (Hansen & Hess, J. Vis., 2006) Blur (Liu et al., CVPR., 2008) Scene category (Torralba & Oliva, Network, 2003)
- 6. We can perceivestatistics!
- 7. Idea Image engineering “Imagerestoration” Empirical Bayes Vision science “Perception of stimulus statistics”
- 8. Problem in perceivingstimulus statistics Statistics (smoothness) Stimulus (image) θ Stochasticity Neural response s “Percepts” r Noise ^ ^ s Estimate θ
- 9. Bayesian framework Statistics StimulusResponse θ θ s s Goal of: r Image restoration r Visual recognition
- 10. Bayesian framework Statistics StimulusResponse “hyperparameter” θ s r Bayes Empirical Bayes θ s r
- 11. Bayesian framework Statistics StimulusResponse θ s r θ s r
- 12. Different goals ofestimation Image restoration Visual recognition Statistics Stimulus for Stimulus Statistics for … But both are mathematically equal manipulations.
- 13. Different criteria Image restoration Visual recognition Mean squareerror E [ s ˆ s 2 /N] Variance of estimate Fisher information E [- ln P ( r | θ )] ˆ ] -1 Var [ (Ideal observer)
- 14. Different criteria Image restoration Visual recognition Mean squareerror E [ s ˆ s 2 /N] Signal detection theory Fisher information E [- ln P ( r | θ )] (d ' ) (Ideal observer) 2
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- 18. Natural image statistics •Smoothness • Contrast Statistics θ Cortex
- 19. Neural response model Receptivefield Statistics θ Cortex
- 20. Estimation of stimulus Receptivefield s As r ^ s (Tajima, Inoue & Okada, J. Phys. Soc. Jpn., 2008)
- 21. Estimation of statistics -ｌｎ P(r|θ) Receptive field (Tajima, Inoue & Okada, J. Phys. Soc. Jpn., 2008)
- 22. Optimal receptive fieldsize? Image restoration Criteria: Visual recognition Mean square error Fisher information of smoothness (Noise level) Receptive field size Receptive field size (Natural image model: Power-law model)
- 23. Receptive field size Optimalreceptive field size? (Natural image model: Power-law model)
- 24. Receptive field size Optimalreceptive field size? Intensity-dependent RF changes: Retina (Barlow et al., 1957) V1 (Polat & Norcia, 1996) MT (Hunter & Born, 2011)
- 25. Receptive field size Optimalreceptive field size? Parasol Bistratified Midget Retinal ganglion cells
- 26. Which cell typeis the best? Receptive field Parasol (Magno) SIZE Midget (Parvo) SHAPE Bistratified (Konio) (Field et al., Nature, 2010)
- 27. Parasol (Magno) Midget (Parvo) Bistratified(Konio) Fisher information Which cell type is the best? - (prediction) (Natural image model: Power-law model)
- 28. Parasol (Magno) Midget (Parvo) Bistratified(Konio) Fisher information Which cell type is the best? - (prediction) (Natural image model: Power-law model)
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- 30. Message Image engineering “Imagerestoration” Empirical Bayes! Vision science “Perception of stimulus statistics”
- 31. Vision science Image engineering What criteria should we use? Purpose: • Mean square error Restoration • Fisher information Human recognition
- 32. Image engineering Vision science What is the function of statistics perception? Rolls of statistics: • Compression Cue for recognition • Denoising Prior for stimulus estimation • Prediction Hidden variables of system
- 33. Perception of imagestatistics is empirical Bayes estimation.
- 34. Satohiro Tajima. Defining statisticalperceptions with an empirical Bayesian approach. Physical Review E, 87(4):042707, (2013). https://sites.google.com/site/satohirotajima/