1. Evaluation of segmentation

2. Example

3. Reference standard & segmentation

4. Segmentation performance Qualitative/subjective evaluation  the easy way out, sometimes the only option Quantitative evaluation preferable in general A wild variety of performance measures exists Many measures are applicable outside the segmentation domain as well Focus here is on two class problems

5. Some terms Ground truth = the real thing Gold standard = the best we can get Bronze standard = gold standard with limitations Reference standard = preferred term for gold standard in the medical community

6. What to evaluate? Without reference standard, subjective or qualitative evaluation is hard to avoid Region/pixel based comparisons Border/surface comparisons (a selection of) Points Global performance measures versus local measures

7. Example

8. Reference standard & segmentation

9. What region to evaluate over?

10. Combination of reference and result masked true positive true negative false negative false positive

11. False positives

12. False negatives

13. Confusion matrix (Contingency table) Segmentation Reference negativepositive negative191152 TN 3813 FP positive9764 FN 19648 TP

14. Do not get confused! False positives are actually negative False negatives are actually positives

15. Confusion matrix (Contingency table) Segmentation Reference negativepositive negative.852 TN.017 FP positive.044 FN.088 TP

16. Accuracy, sensitivity, specificity sensitivity = true positive fraction = 1 – false negative fraction = TP / (TP + FN) specificity = true negative fraction = 1 – false positive fraction = TN / (TN + FP) accuracy = (TP + TN) / (TP + TN + FP + FN)

17. Accuracy Range: from 0 to 1 Useful measure, but: Depends on prior probability (prevalence); in other words: on amount of background Even ‘stupid’ methods can achieve high accuracy (e.g. ‘all background’, or ‘most likely class’ systems)

18. Sensitivity & specificity Are intertwined ‘stupid’ methods can achieve arbitrarily large sensitivity/specificity at the expense of low specificity/sensitivity Do not depend on prior probability Are useful when false positives and false negatives have different consequences

19. NPNNNNNPPPPP PP N N true positives (TP) false positives (FP) false negatives (FN) true negatives (TN) sensitivity = true positive fraction = 1 – false negative fraction = TP / (TP + FN) specificity = true negative fraction = 1 – false positive fraction = TN / (TN + FP) accuracy = (TP+TN) / (TP+TN+FP+FN)

20. NPNNNNNPPPPP PP N N true positives (TP) = 3 false positives (FP) = 3 false negatives (FN) = 2 true negatives (TN) = 4 sensitivity = TP / (TP + FN) = 3 / 5 = 0.6 specificity = TN / (TN + FP) = 4 / 7 = 0.57 accuracy = (TP+TN) / (TP+TN+FP+FN) = 7 / 12 = 0.58

21. NPNNNNNPPPPPP P N N = 3 = 2 = 4 sensitivity = 3 / 5 = 0.6 specificity = 4 / 7 = 0.57 accuracy = 7 / 12 = 0.58 algorithm 1 NPNPPNPPPPPP P P N N = 4 = 5 = 1 = 2 sensitivity = 4 / 5 = 0.8 specificity = 2 / 7 = 0.29 accuracy = 6 / 12 = 0.5 algorithm 2 Which system is better?

22. Back to the retinal image… result reference negativepositive negative.852 TN.017 FP positive.044 FN.088 TP Accuracy: 0.93949 Sensitivity: 0.668027 Specifity: 0.980443

23. Overlap = intersection / union = TP/(TP+FP+FN) TP FN FP TN Reference Segmentation

24. Overlap Overlap ranges from 0 (no overlap) to 1 (complete overlap) The background (TN) is disregarded in the overlap measure Small objects with irregular borders have lower overlap values than big compact objects

25. Kappa Accuracy would not be zero if we used a system that is ‘guessing’ A ‘guessing’ system should get a ‘zero’ mark (remember multiple choice exams…) Kappa is an attempt to measure ‘accuracy in excess of accuracy expected by chance’

26. Kappa Result Reference negativepositive negative 1911523813194965 positive 97641964829412 20091623461224377 System positive rate: 23461/224377 =.105 Total number of positives True positives of a guessing system:.105 * 29412 = 3075 … etc Accuracy guessing system:.792 System accuracy: (191152 + 19648)/ 224377 =.939

27. Kappa accguess = the accuracy of a randomly guessing system with a given positive (or negative) rate kappa = (acc – accguess) / (1 – accguess) In our case: kappa = (.939 -.792)/(1 -.792) =.707

28. Kappa Maximum value is 1, can be negative A ‘guessing’ system has kappa = 0 ‘Stupid systems’ (‘all background’ or ‘most likely class’) have kappa = 0 Systems with negative kappa have ‘worse than chance’ performance

29. Positive/negative predictive value PPV and NPV depend on prevalence, contrary to sensitivity and specificity

30. ROC analysis

31. Evaluating algorithms Most algorithms can produce a continuous instead of a discrete output, monotonically related to the probability that a case is positive. Using a variable threshold on such a continuous output, a user can choose the (sensitivity, specificity) of the system. This is formalized in an ROC (receiver operator characteristic) analysis.

32. Reference standard & segmentation

33. Reference standard & soft segmentation

34. ROC analysis P n (x) P p (x) x true positive fraction true negative fraction false positive fraction

35. ROC curve true positive fraction sensitivity detection rate false positive fraction 1 - specificity chance of false alarm

36. ROC curves Receiver Operating Characteristic curve Originally proposed in radar detection theory Formalizes the trade-off between sensitivity and specificity Makes the discriminability and decision bias explicit Each hard classification is one operating point on the ROC curve

37. ROC curves A single measure for the performance of a system is the area under the ROC curve Az A system that randomly generates a label with probability p has an ROC curve that is a straight line from (0,0) to (1,1), Az = 0.5 A perfect system has Az = 1 Az does not depend on prior probabilities (prevalence)

38. ROC curves If one assumes P n (x) and P p (x) are Gaussian, two parameters determine the curve: the difference between the means and the ratio of the standards deviations. They can be estimated with a maximum-likelihood procedure. There are procedures to obtain confidence intervals for ROC curves and to test if the Az value of two curves are significantly different.

39. Intuitive meaning for Az Is there an intuitive meaning for Az? Consider the two-alternative forced-choice experiment: an observer is confronted with one positive and one negative case, both randomly chosen. The observer must select the positive case. What is the chance that the observer does this correctly?

40. P n (x) P p (x) x true positive fraction width false positive fraction column

41. Az as a segmentation performance measure Ranges from 0.5 to 1 Soft labeling is required (not easy for humans in segmentation) Independent of system threshold (operating point) and prevalence (priors) Depends on ‘amount of background’ though!

42. Summary Various pixel-based measures were considered for two class, hard (binary) classification results: –Accuracy –Sensitivity, specificity –Overlap –Kappa ROC