On the Persistence of Fingerprints

Soweon Yoon and Anil K. Jain

Michigan State University http://biometrics.cse.msu.edu

IBPC 2014

April 3, 2014

Research supported by NSF CITeR

Fundamental Premise for Fingerprint Recognition

Do these two impressions come from the same finger?

• Uniqueness: Ridge patterns on different fingers are distinctive • Persistence: Friction ridge patterns do not change over time

• Traditional perspective: Persistence of fingerprint ridge structure • Galton compared 11 pairs of fingerprints from six different

individuals; only 1 out of 389 minutiae was found to be missing

Persistence of Fingerprints

F. Galton, Finger Prints, Macmillan, 1892

Uniqueness and Persistence

National Research Council, “Strengthening Forensic Science in the United States: A Path Forward”, 2009

“Uniqueness and persistence are necessary conditions for friction ridge identification to be feasible, but those conditions do not imply that anyone can reliably discern whether or not two friction ridge impressions were made by the same person.”

Problem Definition

∆T

Mat

ch S

core

Stable?

Trend of genuine match scores

∆T

Mat

ch S

core

False rejection

occurs

Decision threshold

Trend of matching accuracy

Determine the persistence of fingerprints w.r.t. AFIS accuracy

Data Type: Longitudinal vs. Cross-Sectional

Subject 1

Subject 2

Subject 3

Subject 5

Subject 6

Subject 4

Population

y1

y2

y4

y3

y

y6

5

Subject 1

Subject 2

Subject 3

Subject 5

Subject 6

Subject 4

Population

y11

y21

y41

y31

y51

y61

y12

y32

y33

y42

y62

y43

y44

Longitudinal data Repeated measurements on a collection of

individuals sampled from a population

Cross-sectional data A single measurement is made on each individual

sampled from a population

Longitudinal data are called • Balanced data : Every subject has the same number of measurements • Time-structured data: Repeated measurements follow an identical time schedule across individuals

Longitudinal vs. Cross-Sectional Analysis

∆T

Mat

ch S

core

Short-term comparisons

Long-term comparisons

Cross-sectional Analysis

P. J. Diggle, K-Y. Liang, and S. L. Zeger, Analysis of Longitudinal Data, Oxford Science Publications, 1994

∆T

Mat

ch S

core

Subject 1

Subject 2 Subject 3

Subject 4

Subject 5

Subject 6

Longitudinal Analysis

Match scores decrease w.r.t. ∆T Match scores increase w.r.t. ∆T

• Longitudinal fingerprint data do not satisfy the properties of balanced & time structured required for cross-sectional analysis

Longitudinal Fingerprint Database • Repeat offenders booked by the Michigan State Police • 15,597 subjects with at least 5 tenprint cards, minimum

time span of 5-years (max. time span is 12 years) and demographics (race, gender, age)

• All genuine pairwise comparisons by two COTS matchers • Currently, only right index finger is used in the analysis

June 2001 July 2002 April 2003 Sept. 2007 March 2008 Oct. 2008

Approach

• Fit and evaluate a multilevel statistical model with time gap as covariate to genuine match scores – Null hypothesis: Slope of linear model is 0

• Compare time gap with other possible covariates (i.e., subject’s age, fingerprint quality, race, and gender)

• Fit a multilevel model with time gap as covariate to binary match decisions

• Longitudinal data can be viewed as hierarchical data ˗ j-th measurement (match score) for subject i

• A model in its simplest form

ijijiiij xy εϕϕ ++= 10 ),0(~ 2εσε Nij

ii b0000 += βϕ

ii b1101 += βϕ

2110

0120

1

0 ,00

~σσσσ

Nbb

i

i

Level-1 Model (Within-person change)

Level-2 Model (Between-person change)

j-th measurement for subject i Covariate (or predictor, explanatory variable)

Fixed effects Random effects

Multilevel Statistical Model

ijijiiij xbby εββ ++++= )()( 110000Composite Model

0 2 4 6 8 10 12-1.5

-1

-0.5

0

0.5

1

1.5

∆ T

Gen

uine

Mat

ch S

core

Subject 2 ),( 1202 ϕϕ

0 2 4 6 8 10 12-1.5

-1

-0.5

0

0.5

1

1.5

∆ T

Gen

uine

Mat

ch S

core

Subject 4 ),( 1404 ϕϕ

0 2 4 6 8 10 12-1.5

-1

-0.5

0

0.5

1

1.5

∆ T

Gen

uine

Mat

ch S

core

Subject 3 ),( 1303 ϕϕ

0 2 4 6 8 10 12-1.5

-1

-0.5

0

0.5

1

1.5

∆ T

Gen

uine

Mat

ch S

core

Subject 1 ),(),( 1101 ϕϕ=SlopeIntercept

Level-1 Model ijijiiij xy εϕϕ ++= 10

Level-2 Model ii b0000 += βϕ

ii b1101 += βϕ

i0ϕ

i1ϕ

),( 1000 ββ

Population mean

Parameter space

),( 11100100 bb ++ ββ),( 12100200 bb ++ ββ

),( 13100300 bb ++ ββ

),( 14100400 bb ++ ββ

Subject 1 Subject 2

Subject 3

Subject 4

Part I. Genuine Match Score Modeling

ijiijy εϕ += 0

ijijiiij xy εϕϕ ++= 10

Model A (Unconditional mean model)

Model B

ii b0000 += βϕ

ii b1101 += βϕ

Level-1 Level-2

Model C

ijijiiij Ty εϕϕ +∆+= 10

iii bC 001000 ++= ββϕ

iii bC 111101 ++= ββϕ

ijij Tx ∆=

ijij AGEx =

ijij Qx =

BT: Time interval

BA: Subject’s age

BQ: Max. of NFIQ of fingerprints in comparison

ii bMaleC =

ii bWhiteC =CG: Gender CR: Race

ii b0000 += βϕ

A BA BT BQ CG CR D1

1.02

1.04

1.06

1.08

1.1

1.12x 106

Models

AIC

Model Comparisons • Goodness-of-Fit

– Smaller the value, better the model fit

• AIC (Akaike Information Criterion) • Decrease in AIC observed for

Models BT, BA, BQ vs. Model A • ΔT, AGE & Q explain the variance

in genuine match scores • Q is the best covariate • AIC barely decreases for Model

BT vs. Models CG, CR • Gender and race are not

important covariates • Model D with ΔT, AGE, and Q

explains variance the best

-4 -3 -2 -1 0 1 2 3 4

0.0010.0030.010.020.050.10

0.25

0.50

0.75

0.900.950.980.99

0.9970.999

Standardized Residuals

Prob

abilit

y

-3 -2 -1 0 1 2

0.0010.0030.010.020.050.10

0.25

0.50

0.75

0.900.950.980.99

0.9970.999

Standardized Residuals

Prob

abilit

y

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1

0.0010.0030.010.020.050.10

0.25

0.50

0.75

0.900.950.980.99

0.9970.999

Standardized ResidualsPr

obab

ility

Validation of Model Assumptions • Normal probability plots

– If linear, the distribution is normal

),0(~ 2εσε Nij

2110

0120

1

0 ,00

~σσσσ

Nbb

i

i

Level-2 Level-1

• Departures from normality are observed at tails

0 20 40 60 80

-3

-2

-1

0

1

2

Age [Year]

Mat

ch S

core

Mean95% Confidence Interval

0 2 4 6 8 10 12

-3

-2

-1

0

1

2

Time Interval [Year]

Mat

ch S

core

Mean95% Confidence Interval

Parameter Estimates and Hypothesis Tests

• Genuine match scores decrease w.r.t. time interval, subject’s age, and NFIQ

• Bootstrap to obtain parameter estimates and confidence interval – Resample N (= 15,597) subjects with replacement; 1,000 bootstrap samples

• H0: β10 = 0 (slope of linear model is 0) – H0 is rejected at 0.05 level for Model BT, BA, and BQ

1 2 3 4 5

-3

-2

-1

0

1

2

NFIQ

Mat

ch S

core

Mean95% Confidence Interval

Time Interval Age Quality

Part II. Matching Accuracy Modeling

∆T

Mat

ch S

core

False rejection occurs

Decision threshold

True Acceptance

Prob

abili

ty o

f Tru

e Ac

cept

ance

1

0 ∆T

Multilevel Model for Binary Responses (Generalized Linear Mixed-effects Model)

ijijiiij

ijij

ijij

xgBiny

Thyy

εϕϕπ

π

++=

>

=

10

*

*

)(),1(~

otherwise,0,1

ii b0000 += βϕ

ii b1101 += βϕ

),0(~ 2εσε Nij

2110

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0 ,00

~σσσσ

Nbb

i

i

Level-1

Level-2

functionlogit a is )g(, responsesfor binary

function;link a is )(

⋅

⋅g

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

Time Interval [Year]

Prob

abilit

y of

Tru

e Ac

cept

ance

Mean95% Confidence Interval

Matching Accuracy over Time • 400 bootstrap samples

• Probability of true acceptance remains close to 1 within 12-year time interval

Threshold corresponding to FAR=0.01%

Summary and Conclusions • Statistical analysis with multilevel models for longitudinal

fingerprint data (15,597 subjects with 12-year time span)

• Based on the results of hypothesis test and bootstrap confidence interval, we can make following inferences

– Genuine match score tends to decrease over time

– Matching accuracy tends to remain stable over time with high confidence

• Future work

– Analyze longitudinal data with longer time span

– Explore nonlinear models and interaction terms

Thank you.