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 Many measures are applicable outside the segmentation domain as well Focus here is on two class problems

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

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

Example

Reference standard & segmentation

What region to evaluate over?

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

False positives

False negatives

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

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

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

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)

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)

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

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)

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

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?

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

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

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

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’

Kappa Result Reference negativepositive negative positive System positive rate: 23461/ =.105 Total number of positives True positives of a guessing system:.105 * = 3075 … etc Accuracy guessing system:.792 System accuracy: ( )/ =.939

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 = ( )/( ) =.707

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

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

ROC analysis

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.

Reference standard & segmentation

Reference standard & soft segmentation

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

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

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

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)

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.

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?

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

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!

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