Fingerprint Matching

1
Fingerprint Matching

• Chapter 4.1- 4.3
• On-Line Fingerprint Verification
• Anil Jain, Fellow, IEEE, Lin Hong, and Ruud
  Bolle, Fellow, IEEE
• Presented by Chris Miles

2
Fingerprint Matching

• Compare two given fingerprints T,I
• Return degree of similarity (0-gt1)
• Binary Yes/No
• T -gt template, acquired during enrollment
• I -gt Input
• Either input images, or feature vectors
  (minutiae) extracted from them

3
Issues involved with matching

• extremely difficult problem
• Displacement
• Rotation
• Partial Overlap
• Not completely in image
• Distortion (Non-Linear)
• Stretches when pushed down

4
More issues

• Pressure and Skin condition
• Pressure, dryness, disease, sweat, dirt, grease,
  humidity
• Noise
• Dirt on the sensor
• Feature Extraction Errors

5
State of the Art

• Many algorithms match high quality images
• Challenge is in low-quality and partial matches
• 20 of the problems (low quality) at FVC2000
  caused 80 of the false non-matches
• Many were correctly identified at FVC2002 though

6
Approaches

• Correlation-based matching
• Superimpose images compare pixels
• Minutiae-based matching
• Classical Technique Most popular
• Compare extracted minutiae
• Ridge Feature-based matching
• Compare the structures of the ridges
• Everything else

7
FVC2002
8
Correlation-based Techniques

• T and I are images
• Sum of squared Differences
• SSD(T,I) T-I2 (T-I)T(T-I) T2
  I2 2TTI
• Difference between pixels
• T2 I2 are constant under transformation
• Try to maximize correlation Minimizes
  difference
• CC(T,I) TTI
• Can't be used because of displacement / rotation

9
Maximizing Correlation

• I(?x,?y,?)
• Transformation of I
• Rotation around the origin by ?
• Translation by x,y
• S(T,I) max CC(T,I(?x,?y,?))
• Try them all take max

10
Correlation Results
11
Doesn't Work

• Non-Linear distortion is significant and not
  accounted for
• Skin Condition / Pressure cause brightness /
  contrast and thickness to vary significantly
• Difference correlation
• Check max/min correlation values
• Matches show greater range
• Computationally Expensive (try them all)

12
Divide and Conquer

• Identify local regions in the image
• Pieces of the whole
• Interesting regions
• Match them
• Sum correlations to find global correlation
• Check difference of transforms for each region
• Consolidation

13
Computation Improvements

• Correlation Theorem
• Spatial Correlation point wise mutation in
  fourier domain
• T?I F-1(F (T) x F(I))
• Resultant image has values correlation for
  translating to those points
• No rotation
• Very large computation improvement

14
Computational Improvements

• Multi resolution hierarchical approaches
• Fourier-Mellin
• Gives rotational invariance
• Other steps reduce accuracy
• Divide and Fourier
• Partition into local regions
• Match them against each other
• Border overlap
• Much faster

15
Optical Fingerprint Matching

• Lenses to derive the Fourier transform of the
  images
• Joint transform correlator for matching
• Very expensive
• Complex
• Immature

16
Minutiae-based Methods

• Classical Technique
• T, I are feature vectors of minutiae
• Minutiae (x,y,?)
• Two minutiae match if
• Euclidean distance lt r0
• Difference between angles lt ??
• Tolerance Boxes
• r0
• ??

17
Alignment

• Displacement
• Rotation
• Scale
• Distortion-tolerant transformations
• More transformations
• higher degree of freedom for matcher
• More false matches

18
Formulation

• M''j map(m'j)
• Map applies a geometrical transformation
• mm(m''j, mi) returns 1 if they match
• Matching can be formulated as
• maximize ??mm(map?x, ?y, ?)(m'P(i)), mi)
• P is an unknown function which pairs the minutiae
• Which minutiae in I corresponds to which in T

m
i1
?x, ?y, ?, P
19
P

• Pairs the minutiae
• If P(i) j
• j is i's mate
• Most likely pair
• If P(i) null
• i, from T has no mate in I
• If no i matches a j, that j has no mate
• Each minutiae has a maximum of one mate
• Trivial if alignment is known

20
Point Pattern Matching

• Alignment is rarely known
• Cast as point pattern matching
• Angular component is only a small difference
• Techniques
• Relaxation
• Algebraic and operational research solutions
• Tree search (pruning)
• Search (Energy Minimization)
• Hough Transform

21
Matching
22
(No Transcript)
23
Relaxation

• Maintain confidence levels between all possible
  matchings
• How likely we think Ia matches Tb
• Iteratively
• Calculate the consistencies the transformations
  required for those matches
• Adjust the confidence levels of points that agree
  with other points
• Decrease others
• Iterative -gt slow

24
Algebraic and Operational Research Solutions

• Use algebraic methods
• Requires very restrictive assumptions
• Exactly aligns under affine transformation
• N M
• All minutiae perfectly identified
• Assignment problems
• Bipartite graph matching

25
Tree Search (Pruning)

• Search the tree of possible matches
• If A matches B, then C matches F, then D matches
  K
• More assumptions
• MN
• No outliers -gt All minutiae must match

26
Search (Energy Minimization)

• Cast as a general search problem
• Search towards the optimal set of matches
• Fitness is a function of consistency
• Can use any general search technique
• GA
• Simulated Annealing

27
Hough Transform

• Brute force search over possible Pairings /
  rotations / scalings
• Foreach mi in I
• Foreach mj in T
• Foreach ? in discretized ?'s
• If ?I ?J lt threshold
• Foreach scale in discretized scales
• dx,dy mi map ?,scale (mj)
• Adx,dy,theta,scale
• Whichever A is highest is the closest
  transformation
• Can then find pairings easily

28
Hough Transform
29
Improvements

• Vote on neighboring bins / smooth the bins, to
  get more robust answers
• Parallelize on custom hardware
• Hierarchical discretization
• Chang et al 1997
• Find the principle pair and a course
  transformation with respect to it that matches
  the most points
• Calculate pairing
• Use the pairing to calculate exact alignment

30
Principle Pair

• Brute force for the segment, 2 pts, which can be
  best mapped to a corresponding segment in T
• Foreach mi in I
• Foreach mj in T
• Reset A
• Foreach mi2 in I
• Foreach mj2 in T
• ?,S Transformation required to turn mi1,mi2
  into mj1,mj2
• A?,S
• Remember the mi1and mj1 and ???S?with the highest
  A value
• mi1,mj1 are the principle pair and ???S is the
  course transformation

31
Segment Matching

• Udupa, Garg, Sharma 2001
• Looking for matching segments of similar lengths
• Foreach, determine transforms to match them
• Try to match remaining minutiae
• Check consistencies of best matches
• Final score is a combination of the number of
  mated pairs, the fraction of consistent
  alignments, and the topological correspondence

32
Minutiae match with pre-alignment

• Idea pre-align T before storage in database
• Align each I just once against the global
  orientation
• Reduces computation in identification systems
• Absolute pre-alignment
• Orient everything in a common direction
• No reliable system to do this
• Difficult to detect core, or even basic
  orientation
• Relative pre-alignent
• Align I to for each T seperately
• No computation savings

33
M82 Fbi

• Do course absolute pre-alignment
• Center the image around the core location
• Orient it with ridges to the left/right averaged
  facing up
• Find principal pairs
• Look at minutiae around the center
• Find the best matching pair -gt Principle
• Calculate course transformation, deformation
  tensor

34
Avoiding Alignment

• Ordinary Person - You should go to work
• Philosopher - Why?
• Intrinsic coordinate system
• Instead of using global coordinate system orient
  them with respect to the ridge patterns
• Minutiae are defined with respect to this
• Transformation / rotation does not change their
  relative location
• Problems partitioning the image into the local
  coordinate systems

35
Ridge Relative Pre-alignment

• Jain, Hong, Bolle 1997
• Store minutiae along with information about the
  ridge attached to it
• Oriented along minutiae orientation
• Normalized to ridge frequency
• Compare with other ridges until you find a good
  match
• Take as principle pair

36
Comparing ridges

• Convert minutiae in T,I to polar coordinates with
  respect to the reference minutiae
• Reference minutiae the one with the ridge
• Order them into a list
• Check how many insertions / deletions /
  transformations are necessary to match the lists
• Variant
• Match distances and relative angles of sampled
  points

37
Results
38
Results