Biometric’s Individuality
Dr. Pushkin Kachroo
Introduction
• Individuality: View biometric as a password
• How easy is it to guess a biometric machine
representation
Approaches to Individuality
• For Formulation of the Individuality Problem,
we need
– Representation of the biometric identifier
– A metric of similarity of two biometric identifiers
– Representation of the target population (or their
representative samples)
Fingerprint Example
• Fingerprint features for individuality
–
–
–
–
Location of singular points, core, delta
Ridge count between pair of minutiae
Type, direction, and location of minutiae
Location of sweat pores
• However, latent prints from a crime scene might
not have many features
Defining Individuality
• Given a biometric sample, determine the
probability of finding an arbitrary biometric
sample from the target population sufficiently
similar to it: Probability of False Association.
• Given two fingerprints from two different
fingers, determine the probability that they are
sufficiently similar.
• The theoretical lower bounds on False Accept
and False Reject rates (intrinsic error rates)
• Within-class, and between-class variations.
Calculating Individuality
• Given a representation scheme and a similarity
metric…
• Theoretical method: model all realistic
phenomenon affecting between-class and
within-class pattern variation, and then
theoretically estimate probability
• Empirical method: Data driven
Empirical Individuality Studies
• Iris: 256-byte binary code; use Hamming
distance (http://en.wikipedia.org/wiki/Hamming_distance)
(Dougman study) 10-52 probability of finding similar Iris patterns
• Handwriting study (Srihari): False Accept Rate~5%
Theoretical Individuality Studies:
A Partial Iris Model
• N bit iriscode: R
• N-bit query bit string: Q
• Hamming distance h(Q,R)
• Q and R: Real world irises
• Q=Q(Q), R = R(R) are binary strings
“01000100101” of length N.
• Hypotheses:
– H0: Q~R, Q and R from the same iris
– Ha: Qnot~R, Q and R from different irises
FRR/FAR
FRR (dT )  Prob (h  dT | H 0 )
FAR(dT )  Prob (h  dT | H a )
Qˆ  Q  noise
True bitstring
Measured bitstring
FAR Modeling
FAR(dT )  Prob (h(Qˆ , R)  dT | H a )
Determine the probability that enough bits flip in the sensing process
Qˆ  S (Q)
ˆ , R ) is small
So that the Hamming distance h(Q
h(Qˆ , R)  n  0, n  0,..., N
N
FAR(dT )   [Prob (h(Qˆ , R)  dT | h(Q, R)  n)  Prob (h(Q, R)  n)]
n 1
N
FAR(dT )   Pn (dT )  Gn
n 1
FAR Probability Calculations
N
FAR(dT )   [Prob (h(Qˆ , R)  dT | h(Q, R)  n)  Prob (h(Q, R)  n)]
n 1
N
FAR(dT )   Pn (dT )  Gn
n 1
Assume i bits flip from n non-matching ones and
j flip among (N-n) matching ones
For False Accept:
(n  j  i)  dT
n i
n i


p
(
1

p
)
Probability i bits flip in nonmatching n bits:  
i
 N  n j
 p (1  p) N n  j
Prob j bits flip in nonmatching (N-n) bits: 
 j 
FAR Probability Calculations-2
 N  n j
n i
N n j
 p (1  p)
Pn (dT )   
   p (1  p) n i
j 
( n  j i )  dT 
i
Let g be the prob that individual bit agrees: (for g=1/2)
 N  N n
1 N
n
Gn  Prob (h(Q, R)  n)    g (1  g )  N  
2 n
n
N
FAR(dT )   Pn (dT )  Gn
n 1
FRR Calculation
For False Reject:
h(Qˆ , R)  dT ; h(Q, R)  0
FRR (dT )  Prob (h(Q, R)  dT | h(Q, R)  0)

N
 Prob (h(Q, R)  i | h(Q, R)  0)
i  dT 1
N i
FRR (dT )     p (1  p) N i
i  dT 1  i 
Fingerprint Individuality
R total minutiae, K possible locations, for each location w direction
R
Prob (1) 
Kw
Not desirable to have two minutiae at the same place….
R
Prob ( j ) 
( K  j  1) w
Assume each minutiae has matching probability
R
P  max Prob ( j )  Prob (Q) 
j
( K  Q  1) w
Fingerprint Individuality-2
Chance of matching exactly t of the Q minuiae
PT  P t (1  P)Q t