Evaluation of segmentation
This presentation is the property of its rightful owner.
Sponsored Links
1 / 42

Evaluation of segmentation PowerPoint PPT Presentation


  • 58 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Evaluation of segmentation

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Evaluation of segmentation

Evaluation of segmentation


Example

Example


Reference standard segmentation

Reference standard & segmentation


Segmentation performance

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

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

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


Example1

Example


Reference standard segmentation1

Reference standard & segmentation


What region to evaluate over

What region to evaluate over?


Combination of reference and result

Combination of reference and result

masked

true positive

true negative

false negative

false positive


False positives

False positives


False negatives

False negatives


Confusion matrix contingency table

Confusion matrix (Contingency table)

Segmentation

Reference


Do not get confused

Do not get confused!

  • False positives are actually negative

  • False negatives are actually positives


Confusion matrix contingency table1

Confusion matrix (Contingency table)

Segmentation

Reference


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, sensitivity, specificity


Accuracy

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

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


Evaluation of segmentation

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)


Evaluation of segmentation

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


Evaluation of segmentation

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?


Back to the retinal image

Back to the retinal image…

Accuracy: 0.93949

Sensitivity: 0.668027

Specifity: 0.980443


Overlap intersection union tp tp fp fn

Overlap = intersection / union = TP/(TP+FP+FN)

Reference

Segmentation

TP

FN

FP

TN


Overlap

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

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’


Kappa1

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


Kappa2

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


Kappa3

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

Positive/negative predictive value

  • PPV and NPV depend on prevalence, contrary to sensitivity and specificity


Roc analysis

ROC analysis


Evaluating algorithms

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 segmentation2

Reference standard & segmentation


Reference standard soft segmentation

Reference standard & soft segmentation


Roc analysis1

ROC analysis

Pp(x)

Pn(x)

true positive fraction

x

false positive fraction

true negative fraction


Roc curve

ROC curve

true positive fraction

sensitivity

detection rate

false positive fraction

1 - specificity

chance of false alarm


Roc curves

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 curves1

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 curves2

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.


Intuitive meaning for az

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?


Evaluation of segmentation

Pp(x)

Pn(x)

x

true positive fraction

width false positive fraction column


Az as a segmentation performance measure

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

Summary

  • Various pixel-based measures were considered for two class, hard (binary) classification results:

    • Accuracy

    • Sensitivity, specificity

    • Overlap

    • Kappa

  • ROC


  • Login