1. Virginia Image and Video Analysis Pavement conditions, fighter jets, and psychophysics! a.k.a. “Did you hear that???” Andrea Vaccari

2. Virginia Image and Video Analysis Detection theory History: -Introduced in the mid-50s in RADAR field. -It’s a plane! - No, it’s a bird! - No, it’s superman! -Around the same time in psychology. -Mid-60s introduced in psychophysics to deal with sensitivity vs. bias Slide 2

3. Virginia Image and Video Analysis Detection theory Applications: -Detection (It is there, isn’t it?) -Discrimination (Is VIVA coffee sweeter than BoJo?) -Receiver evaluation (You can’t tell the difference, can you?) -Test evaluation (My algorithm rocks!... NOT!) -Product evaluation (You like my webpage, don’t you?) -… you name it! Slide 3

4. Virginia Image and Video Analysis Stimulus-response matrix Binary type experiments: -either correct or incorrect (2 classes) Four options: -Hit -Miss (Type II error) -False alarm (Type I error) -Correct rejection Slide 4 Correct rejection False alarm Type I error Miss Type II error Hit Stimulus Response No Yes Yes No

5. Virginia Image and Video Analysis Can you hear that? Slide 5 Probability Neural activity What’s this noise?? Standard deviation (σ)

6. Virginia Image and Video Analysis Can you hear that? Slide 6 Probability Neural activity D

7. Virginia Image and Video Analysis Can you hear that? Slide 7 Probability Neural activity D

8. Virginia Image and Video Analysis Can you hear that? Slide 8 Probability Neural activity How difficult is it, really? Give me a number! Discriminability, sensitivity (d’)D

9. Virginia Image and Video Analysis You have to choose! Slide 9 Probability Neural activity No! Yes!

10. Virginia Image and Video Analysis You have to choose! Slide 10 Probability Neural activity No! Yes! Stimulus Response No Yes Yes No Correct rejection False alarm Type I error

11. Virginia Image and Video Analysis You have to choose! Slide 11 Probability Neural activity No! Yes! Stimulus Response No Yes Yes No Miss Type II error Hit

12. Virginia Image and Video Analysis I’m Swiss! Neutral bias! Slide 12 Probability Neural activity No! Yes! Stimulus Response No Yes Yes No Miss Type II error Hit Correct rejection False alarm Type I error Correct rejection False alarm Type I error Miss Type II error Hit

13. Virginia Image and Video Analysis Are you liberal or conservative? Slide 13 Liberal bias! Probability Neural activity No! Yes! Conservative bias! How biased are you, really? Give me a number! Criterion, bias (β) Correct rejection False alarm Type I error Miss Type II error Hit

14. Virginia Image and Video Analysis What if? Slide 14 Manipulate biases a.k.a. payoffs! -I give you $10 for each hit! -I give you $5 for each correct rejection! -You pay me $1 for each error! (just because) Now we can actually define an optimum criterion! This also works in real life without artificial payoffs: think RADAR detection of incoming bombers!

15. Virginia Image and Video Analysis Terminology Slide 15 Sensitivity or Recall: TPR = TP/P = TP/(TP + FN) Specificity: SPC = TN/N = TN/(TN + FP) Fall-out, False Positive Rate: FPR = FP/N = FP/(TN + FP) = 1 - SPC Correct rejection False alarm Type I error Miss Type II error Hit Stimulus Response No Yes Yes No True Negatives False Positives False Negatives True Positives Stimulus Response No Yes Yes No

16. Virginia Image and Video Analysis So, how good are you? Slide 16 Receiver Operator Curve: TPR = TP/(TP + FN) FPR = FP/(TN + FP) TPR FPR = 1 - SPC

17. Virginia Image and Video Analysis How do you choose? Slide 17 Probability Neural activity (y) No! Yes! p(y|H 1 ) p(y|H 2 ) p(H 2 |y 0 ) > p(H 1 |y 0 ) Priori: p(H 2 ) = π 2, p(H 1 ) = π 1 p(H i |y 0 ) = p(y 0 |H i )π i / p(y 0 )p(y 0 ) = p(y 0 |H 1 )π 1 + p(y 0 |H 2 )π 2 p(y 0 |H 2 )/p(y 0 |H 1 ) ≥ π 1 /π 2 L(y 0 ) ≥ τ MAP L(y 0 ) => Likelihood ratio τ MAP => Max a posteriori

18. Virginia Image and Video Analysis How do you choose? Slide 18 If you consider payoffs: Correct rejection False alarm Type I error Miss Type II error Hit Stimulus Response No Yes Yes No U 22 U 21 U 12 U 11 Stimulus Response No Yes Yes No L(y 0 ) ≥ π 1 (U 11 – U 21 )/π 2 (U 22 – U 12 ) L(y 0 ) ≥ τ B