Presentation is loading. Please wait.

Presentation is loading. Please wait.

External noise yields a surprise: What template? Stanley Klein, Dennis Levi, Suko Toyofuku Vision Science University of California, Berkeley.

Published by Modified over 8 years ago

Similar presentations

Presentation on theme: "External noise yields a surprise: What template? Stanley Klein, Dennis Levi, Suko Toyofuku Vision Science University of California, Berkeley."— Presentation transcript:

1 External noise yields a surprise: What template? Stanley Klein, Dennis Levi, Suko Toyofuku Vision Science University of California, Berkeley

2 Overview Detection of patterns in noise Why noise masking is a powerful technique The Lu-Dosher framework: useful black boxes Graham-Nachmias experiment in noise (detect 1 st +3 rd ) Rating scale methods for isolating sources of noise A faster classification image method Double pass and other methods Can the black boxes be unblackened?

3 The Lu-Dosher model Single template Constant power nonlinearity Multiplicative noise Simple decision stage Alternative models Multiple templates More complex nonlinearities Keep multiplicative noise Complex decision stages

4 The Lu-Dosher model Single template Constant power nonlinearity Multiplicative noise Simple decision stage Alternative models Multiple templates More complex nonlinearities Keep multiplicative noise Complex decision stages

5 The Lu-Dosher model Single template Constant power nonlinearity Multiplicative noise Simple decision stage Alternative models Multiple templates More complex nonlinearities Keep multiplicative noise Complex decision stages Ideal Observer

6 The Lu-Dosher model Single template Constant power nonlinearity Multiplicative noise Simple decision stage Alternative models Multiple templates More complex nonlinearities Keep multiplicative noise Complex decision stages

7 Thresholds for 6th Harmonic Thresholds 2nd Harmonic The Graham-Nachmias Experiment Plus Noise 2 nd plus 6 th test pattern 2 nd plus 6 th plus noise the stimulus for this discussion P(x)= c(cos(2x) - cos(6x)) N(x) =  f a f cos(fx)+ b f sin(fx) for f=1 to 7 multiple channels single matched template Our thresholds lie near the curve c 2 2 /th 2 2 + c 6 2 /th 6 2 = 1, compatible with a matched template model. However, the double-pass analysis will raise doubts about the single template hypothesis.

8 Stimulus test external total Trial level contrast noise contrast response T 2 T 6 N 2 N 6 C 2 C 6 pass1 pass2 11 0 0.02 -.03.02 -.03 1 1 22.08 -.08 -.01 -.02.07 -.10 2 1 31 0 0 -.02.06 -.02.06 2 1 44.24 -.24.05 -.03.29 -.27 4 4 51 0 0.06.03.06.03 1 1 etc. Rating scale method of constant stimuli Four stimulus levels (1,2,3,4) were randomly intermixed: The lowest level had zero contrast (before noise) One of four responses (1,2,3,4) was given to each presentation.

9 Stimulus plot C2C2 C6C6 -0.100.10.20.30.4 -0.3 -0.2 -0.1 0 0.1 0.2 1 0.3 -0.4 1 2 1 2 1 4 4 1 1 Stimulus test external total Trial level contrast noise contrast response T 2 T 6 N 2 N 6 C 2 C 6 pass1 pass2 11 0 0.02 -.03.02 -.03 1 1 22.08 -.08 -.01 -.02.07 -.10 2 1 31 0 0 -.02.06 -.02.06 2 1 44.24 -.24.05 -.03.29 -.27 4 4 51 0 0.06.03.06.03 1 1 etc.

10 1 3 Contrast 2 nd Harmonic Contrast 6 th Harmonic 2 nd and 6 th contrasts and responses for levels 1 and 3

11 2 4 Contrast 2 nd Harmonic Contrast 6 th Harmonic 2 nd and 6 th contrasts and responses for levels 2 and 4

12 The Graham-Nachmias Experiment Plus Noise 2 nd plus 6 th test pattern 2 nd plus 6 th plus noise 2 nd – 6 th 2 nd – (1/3)6 th Classification profile The 2 and 6 c/deg components are well matched to the test pattern. Linear regression allows high quality profiles in less than 800 trials.

13 Reverse correlation vs. linear regression Resp(k) = ∑ x’ Template(x’) Pattern(x’, k) + Noise(k) or R(k) = ∑ x’ T (x’) P (x’, k) + N human (k) T rev cor (x) = ∑ k R(k) P(x,k) = ∑ x’ T(x’) ∑ k P(x’,k)P(x,k) + noise = T(x) + ∑ k N human (k) P(x,k) + ∑ x’ N stim (x’,x)T(x’) Where ∑ k P(x’,k)P(x,k) =  (x,x’) + N stim (x,x’) (N stim <<1for white) T lin reg (x) = ∑ k R(k) P PseudoInv (x,k) = T(x) + ∑ k N human (k) P PseudoInv (x,k) In order to calculate P PseudoInv #trials > #stimulus components Web site information to be given at end

14 Reverse correlation vs. linear regression Resp(k) = ∑ x’ Template(x’) Pattern(x’, k) + Noise(k) or R(k) = ∑ x’ T (x’) P (x’, k) + N human (k) T rev cor (x) = ∑ k R(k) P(x,k) = ∑ x’ T(x’) ∑ k P(x’,k)P(x,k) + noise = T(x) + ∑ k N human (k) P(x,k) + ∑ x’ N stim (x’,x)T(x’) Where ∑ k P(x’,k)P(x,k) =  (x,x’) + N stim (x,x’) (N stim <<1for white) T lin reg (x) = ∑ k R(k) P PseudoInv (x,k) = T(x) + ∑ k N human (k) P PseudoInv (x,k) In order to calculate P PseudoInv #trials > #stimulus components For sparse classification images, linear regression with <1/2 the number of trials as reverse correlation can give comparable precision and accuracy.

15 test external total Trial Stimulus contrast noise contrast response T 2 T 6 N 2 N 6 C 2 C 6 pass1 pass2 11 0 0.02 -.03.02 -.03 1 1 22.08 -.08 -.01 -.02.07 -.10 2 1 31 0 0 -.02.06 -.02.06 2 1 44.24 -.24.05 -.03.29 -.27 4 4 51 0 0.06.03.06.03 1 1 etc. Response histogram for stimulus level 1 1 2 3 4 2 1 12341234 Response 1 Response 2 For stimulus level 1 R1 = 1 and R2 = 1 : 2 cases R1 = 2 and R2 = 1 : 1 case

16 2 4 Response-pass 1 Response-pass 2 Stimulus 2Stimulus 4 Contrast 2 nd Harmonic Contrast 6 th Harmonic

17 1 3 Response-pass 1 Response-pass 2 Stimulus 1Stimulus 3 Contrast 2 nd Harmonic Contrast 6 th Harmonic

18 1 3 Response-pass 1 Response-pass 2 Stimulus 1Stimulus 3 Contrast 2 nd Harmonic Contrast 6 th Harmonic Fit a bivariate normal to the response histograms (tricky)

19 1 3 Response-pass 1 Response-pass 2 Stimulus 1Stimulus 3 Contrast 2 nd Harmonic Contrast 6 th Harmonic 1 R The elongation, R, is directly related to the ratio F of internal to external noise.

20 Filters and nonlinearity External noise + Internal Multiplicative and additive noise + Filters and nonlinearity Ideal Decision Stage template Test stimulus Two methods for calculating F=internal noise/External noise observer Double pass method: F= 1/(R 2 – 1) where R is elongation of the double pass response ellipse (preceding slide). d’ (efficiency) method: F = (d’ template /d’ human ) 2 -1 where d’ template is the d’ of an ideal observer who uses the template specified by the classification image.

21 F: Ratio of internal to external noise Normals Amblyopic eyes F (Double-pass) 2 nd – 6 th For detection of 2 nd and 6 th F 2pass <= 1 Very promising. F d’ ~ 2.5 Very interesting. The discrepancy in the two estimates of F indicates incorrect model assumptions. Ahumada and Beard have found similar results. nonlinearities? But our expts. indicate they are too weak. multiple templates? But our expts. indicate a matched filter. inefficient decision stage? uncertainty? non-straight criterion boundaries?

22 Can one see a pattern in the criteria? Can one see a pattern in the double pass agreement? Are the criteria straight as a single template would predict? Contrast 2 nd Harmonic Contrast 6 th Harmonic R 1 = R 2 Triple pass data as well as broader classification tools may help answer these questions.

23 History Lu-Dosher model Summary

24 gain control saturation feedback uncertainty criteria shifts attention NdNd Summary Fancier model complex gain control saturation

25 Acknowledgments Thom Carney– for help with Winvis Alex Tauras – for help with figures NEI – for help with funds This talk will be found at: cornea.berkeley.edu

26

27 Experiment to measure equivalent input noise Input noise

28

29

Download ppt "External noise yields a surprise: What template? Stanley Klein, Dennis Levi, Suko Toyofuku Vision Science University of California, Berkeley."

Similar presentations

Adaptive Methods Research Methods Fall 2008 Tamás Bőhm.

Adaptive Methods Research Methods Fall 2008 Tamás Bőhm.
Assumptions underlying regression analysis

Assumptions underlying regression analysis
Adaptive Methods Research Methods Fall 2010 Tamás Bőhm.

Adaptive Methods Research Methods Fall 2010 Tamás Bőhm.
11-1 Empirical Models Many problems in engineering and science involve exploring the relationships between two or more variables. Regression analysis.

11-1 Empirical Models Many problems in engineering and science involve exploring the relationships between two or more variables. Regression analysis.
Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Curve Fitting ~ Least Squares Regression Chapter.

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 ~ Curve Fitting ~ Least Squares Regression Chapter.
Spatial Filtering (Chapter 3)

Spatial Filtering (Chapter 3)
Introduction Relative weights can be estimated by fitting a linear model using responses from individual trials: where g is the linking function. Relative.

Introduction Relative weights can be estimated by fitting a linear model using responses from individual trials: where g is the linking function. Relative.
Inference for Regression

Inference for Regression
Probability & Statistical Inference Lecture 9

Probability & Statistical Inference Lecture 9
Prediction, Correlation, and Lack of Fit in Regression (§11. 4, 11

Prediction, Correlation, and Lack of Fit in Regression (§11. 4, 11
Tracking Objects with Dynamics Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem 04/21/15 some slides from Amin Sadeghi, Lana Lazebnik,

Tracking Objects with Dynamics Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem 04/21/15 some slides from Amin Sadeghi, Lana Lazebnik,
Class 5: Thurs., Sep. 23 Example of using regression to make predictions and understand the likely errors in the predictions: salaries of teachers and.

Class 5: Thurs., Sep. 23 Example of using regression to make predictions and understand the likely errors in the predictions: salaries of teachers and.
Engineering Data Analysis & Modeling Practical Solutions to Practical Problems Dr. James McNames Biomedical Signal Processing Laboratory Electrical & Computer.

Engineering Data Analysis & Modeling Practical Solutions to Practical Problems Dr. James McNames Biomedical Signal Processing Laboratory Electrical & Computer.
MSU CSE 803 Stockman Linear Operations Using Masks Masks are patterns used to define the weights used in averaging the neighbors of a pixel to compute.

MSU CSE 803 Stockman Linear Operations Using Masks Masks are patterns used to define the weights used in averaging the neighbors of a pixel to compute.
Multivariate Data Analysis Chapter 4 – Multiple Regression.

Multivariate Data Analysis Chapter 4 – Multiple Regression.
Lecture 19: Tues., Nov. 11th R-squared (8.6.1) Review

Lecture 19: Tues., Nov. 11th R-squared (8.6.1) Review
Class 6: Tuesday, Sep. 28 Section 2.4. Checking the assumptions of the simple linear regression model: –Residual plots –Normal quantile plots Outliers.

Class 6: Tuesday, Sep. 28 Section 2.4. Checking the assumptions of the simple linear regression model: –Residual plots –Normal quantile plots Outliers.
Lecture 16 – Thurs, Oct. 30 Inference for Regression (Sections 7.3-7.4): –Hypothesis Tests and Confidence Intervals for Intercept and Slope –Confidence.

Lecture 16 – Thurs, Oct. 30 Inference for Regression (Sections ): –Hypothesis Tests and Confidence Intervals for Intercept and Slope –Confidence.
MSU CSE 803 Linear Operations Using Masks Masks are patterns used to define the weights used in averaging the neighbors of a pixel to compute some result.

MSU CSE 803 Linear Operations Using Masks Masks are patterns used to define the weights used in averaging the neighbors of a pixel to compute some result.
Analysis of Individual Variables Descriptive – –Measures of Central Tendency Mean – Average score of distribution (1 st moment) Median – Middle score (50.

Analysis of Individual Variables Descriptive – –Measures of Central Tendency Mean – Average score of distribution (1 st moment) Median – Middle score (50.

Similar presentations

Ads by Google