Chapter 5

Basic System Errors

(Alireza Tavakkoli)

2

Outline

• Matching

• The Receiver Operating Curves (ROC)

• Error Conditions Specific to Biometrics

• Negative Authentication

• Trade-offs

3

Matching

• Definition

• Notations:Biometric Uniqueness

4

Matching Scores

• Similarity measure Prob (B=B’)– Higher match score Higher Prob.

• Similarity d(B’,B)– [0,Inf.) [0,1]

5

The Tail of Two Errors

• Hypothesis Test and Errors:

• Two Errors:– False Match (Type I)– Flase Non-match (Type II)

NonMatchHhypothesisAlternate

MatchHhypothesisNullThe

a

:

: 0

6

Score Distributions

Hard Decision

Reliability of s

7

FMR and FNMR

x

y

a

xFNMRdsHspxF

yFMRdsHspyG

0|

1|

T

s m

T

s

T

nTs nTs a

dsspdsHspTFNRM

dsspdsspdsHspFMR

0|)(

1|

8

Estimating Error from Data

• Access to G(y) & F(x)

• Estimation:

• Need to be studied more

N

jjj

i

M

ii

sN

sN

sG

sM

sM

sF

1

1

#11ˆ

#11ˆ

YY

XX

9

Error Rates of Match Engines

• FM and FNM – Accept/Reject Object

• FA and FR– Accept/Reject Null Hypothesis

10

Positive Authentication

• Errors in Pos. Authentication:– False Accept (FA)– False Reject (FR)

• Problems:– FA Security Breach– FR Convenience Problems

11

ROC

T

TTROC

TTT

1,0

0,1

FNMR,FMRROC

- Design vs Application

- Security vs Convenience

FMR ↑ FNMR ↓

12

Variations of ROCs

Semi-log plots

Log-log plot

13

Using the ROC Curve

• Comparing matchers– Tradeoff between FMR & FNMR.– Specific Threshold FMR(T)/FNMR(T)

14

Expressing Quality of ROC

• The Equal Error Rate:

• d-prime:

• Expected Overall Error

• Cost Function

15

Expressing Quality of ROC

• The Equal Error Rate:

16

Expressing Quality of ROC

• d-prime:

22'

nm

nmd

17

Expressing Quality of ROC

• Expected Overall Error

TEE

pp

pTFNMRpTFMRTE

T

GI

GI

min

1

)(

min

18

Expressing Quality of ROC

• Cost Function

GFAGFNM PFMRCPFNMRCCost 1

19

Error Conditions Specific to Biometrics

• FTAFTEFTU Significant Cost.

• FTA:

• FTE:

• Manual vs Automatic Authentication

• CMC or RPM

20

Negative Authentication

• Negative Hypotheses:

• The Two Errors:– Falsely missing B– Incorrectly matching B

and B’.

21

Negative Authentication

• Detection Theory Terminology:– False Negative– False Positive

22

Trade Offs

• Different Errors Different Outcomes– False Accept Security Breach.– False Reject Inconvenience.

• Convenience vs Security• Cost vs Security• Cost of Negative Authentication

23

Convenience vs Security

• Convenience of a Biometric

• Convenience of Implementation

FAR1

FRR1

Security

eConvenienc

24

Cost vs Security in Pos. Auth.

• Why it is important

– FRR ↑ Service denial Exception handling

• Dynamic Authentication Protocol

FRRCost

25

Cost of Negative Authentication

• Screening:

• Higher FPR&FNR Inconvenient to all

FPR

FNR1

Cost

Security

26

Neg. Vs Pos. Authentiocation

27

• Questions?