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Evaluation of segmentation

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Example

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Reference standard & segmentation

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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

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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

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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

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Example

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Reference standard & segmentation

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What region to evaluate over?

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

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False positives

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False negatives

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

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

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

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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)

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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)

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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

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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)

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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

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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?

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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

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

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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

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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’

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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

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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

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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

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

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ROC analysis

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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.

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Reference standard & segmentation

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Reference standard & soft segmentation

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

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

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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

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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)

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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.

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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?

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

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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!

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

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