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Evaluation of segmentation

Evaluation of segmentation . Example. Reference standard & segmentation. 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

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Evaluation of segmentation

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  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

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

  15. Confusion matrix (Contingency table) Segmentation Reference

  16. 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) Accuracy, sensitivity, specificity

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

  20. P N N P P P N N P N N P P true positives (TP) = 3 P false positives (FP) = 3 N false negatives (FN) = 2 N 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. P P N P N P P P P P P P N N N N P P P N N N P P sensitivity = 4 / 5 = 0.8 P N = 4 = 1 algorithm 2 specificity = 2 / 7 = 0.29 P N = 5 = 2 accuracy = 6 / 12 = 0.5 sensitivity = 3 / 5 = 0.6 P N = 3 = 2 algorithm 1 specificity = 4 / 7 = 0.57 P N = 3 = 4 accuracy = 7 / 12 = 0.58 Which system is better?

  22. Back to the retinal image… Accuracy: 0.93949 Sensitivity: 0.668027 Specifity: 0.980443

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

  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 System accuracy: (191152 + 19648)/ 224377 = .939 Total number of positives True positives of a guessing system: .105 * 29412 = 3075 … etc Accuracy guessing system: .792 System positive rate: 23461/224377 = .105

  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 Pp(x) Pn(x) true positive fraction x false positive fraction true negative 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 Pn(x) and Pp(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. Pp(x) Pn(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

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