KPlet And CBFS: A Graph Based Fingerprint Representation And Matching Algorithm

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K-Plet And CBFS A Graph Based Fingerprint
Representation And Matching Algorithm

• Sharat Chikkerur
• Center for Unified Biometrics and Sensors
• University at Buffalo
• www.cubs.buffalo.edu

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Abstract

• Background
• Minutiae are the most widely used representation
  for matching fingerprints
• Matching is based on establishing correspondences
  between point pairs
• Recovering optimal transformation is a hard
  problem
• Challenges
• Global alignment is not robust to non-linear
  distortion
• Local features based matching are more resilient
  to distortion
• However, local evidence has to be validated based
  on global consistency to avoid false positives
  no formal mechanisms in literature
• Contributions
• New graph based matching algorithm robust to non
  linear distortion
• K-Plet A graph based representation to capture
  local geometry
• CBFS A dual graph based technique for
  propagating local matches
• Result Performs better than NIST BOZORTH3
  matcher (FVC DB1) database

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Outline

• Introduction
• Fingerprints 101
• Matching Algorithm
• Prior Related Work
• New Representation K-plet
• Local Matching Dynamic Programming
• Consolidation Coupled BFS
• Experimental Evaluation
• Conclusion

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Fingerprints 101 Fingerprint Classes

• A fingerprint is made up of system of oriented
  friction ridges
• A fingerprint can be classified based on type the
  ridge flow pattern

• Classification helps in narrowing down possible
  matches
• In reality, the class distribution is skewed
  (gt65 are loops)
• Used only in law enforcement applications

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Fingerprints 101 Ridge Characteristics

• Fingerprints can be distinguished based on the
  ridge characteristics
• Ridge characteristics mark local discontinuities
  in the ridge flow
• No two individuals have the same pattern of
  ridge characteristics at the same relative
  locations

Global Features
Local Features
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Outline

• Introduction
• Fingerprints 101
• Matching Algorithm
• Prior Related Work
• New Representation K-plet
• Local Matching Dynamic Programming
• Consolidation Coupled BFS
• Experimental Evaluation
• Conclusion

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Prior Related Work Matching Paradigms

• Manual
• Human experts use a combination of visual,
  textural, minutiae cues and experience for
  verification
• Still used in the final stages of law enforcement
  applications
• Image based
• Utilizes only visual appearance.
• Requires the complete image to be stored (large
  template sizes)
• Texture based
• Treats the fingerprint as an oriented texture
  image
• Less accurate than minutiae based matchers since
  most regions in the fingerprints carry low
  textural content
• Minutiae based
• Uses the relative position of the minutiae points
• The most popular and accurate approach for
  verification
• Resembles manual approach very closely.

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Image Based Matching Optical Correlation

• Advantages
• Image itself is used as the template
• Requires only low resolution images
• Optical correlation makes it extremely fast
  (Choudary and Awwal 99, Lee et al. 99, Roberge
  et al. 99, Baze et al.00)
• Disadvantages
• Image itself is used as the template (template
  size about 30 KB)
• Requires accurate alignment of the two prints
  (unreliable in poor prints)
• Not robust to changes in scale, orientation and
  position.

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Texture Based Matching Filterbanks

• Advantages
• Uses texture information (lost in optical and
  minutiae based schemes)
• Performs well with poor quality prints
• Features are statistically independent from
  minutiae and can be combined with minutiae
  matchers for higher accuracy (Jain et al. 00,
  Jain et al 01)
• Disadvantages
• Requires accurate alignment of the two prints
  (unreliable in poor prints)
• Not invariant to translation, orientation and
  non-linear distortion.
• Less Accurate than minutiae based matchers

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Minutiae Based Matching

• Advantages
• Invariant to translation, rotation and scale
  changes
• Very accurate (Ratha et al 96, Jain et al. 97,
  Jian Yau 00, Bazen and Garez 03)
• Disadvantages
• Minutiae extraction is error prone is low quality
  images
• Not robust to non-linear distortion.
• Does not use visual and textural cues

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Outline

• Introduction
• Matching Algorithm
• Prior Related Work
• New Representation K-plet
• Local Matching Dynamic Programming
• Consolidation Coupled BFS
• Experimental Evaluation
• Conclusion
• Software Demos

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Minutiae Based Matching

• Challenges
• Minutiae extraction is error prone is low quality
  images
• Not robust to non-linear distortion.
• Intra-user variation

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Challenges Non-linear Distortion
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Challenges Quality and Intra-user variance
Variation in quality
Intra-user variation
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Prior Related Work Global Matching

• Global Matching
• Point correspondences not known combinatorial
  problem
• Relaxation approach (Ranade and Rosenfield 93)
• Likelihood of each match is either decreased or
  increased at each iteration based on
  compatibility of rest of the points
• Iterative approach makes it too slow to be
  practical
• Generalized Hough Transform (Ratha et al. 96)
• All possible transformation represented as a
  quantized search space
• Searches for the most optimal transform in the
  search space
• Very fast
• Ridge Alignment (Jain et al. 97)
• Performs explicit alignment before matching
• Each minutiae is associated with its ridge
  (represented by a curve)
• The alignment is based on ridge correspondence
• Global matching is then performed using string
  edit distance

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Prior Related Work Local Matching

• (Jiang and Yau 00)
• 11 dimensional local features derived from
  reference minutiae and two closest neighbors
• Best match is used only for explicit alignment
• (Jea and Govindaraju 04)
• 5 dimesional features Si (ri0, ri1, fi0, fi1, di)
  derived from two closest neighbors
• Alignment is still required
• (Ratha et al. 00)
• Star representation derived from all minutiae
  within a particular radius
• Consolidation by checking consistency
• (Garris et. al 03 BOZORTH3)
• Line features
• Consolidation by linking consisting matches

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Proposed Algorithm

• Representation
• K-Plet
• Features invariant to rotation and translation
• Local relationship formally represented by a
  directed graph
• Local Matching
• Posed as a string alignment problem and solved by
  dynamic programming
• Matches all neighbors simultaneously
• Consolidation
• Coupled Breadth First Search
• Breadth first search is used to propagate the
  matches
• Similar to human verification
• No explicit alignment required at any stage

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Neighborhood Representation K-plet
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K-plet
T
r
F
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The Graphical View
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Local Matching

• All local neighbors have to be matched
  simultaneously. Greedy approach does not work
  when conflicts occur
• These can solved by finding the alignment through
  optimization process such as by solving a string
  alignment problem

• Example of alignment
• S (acbcdb) (ac__bcdb)
• T (cadbd) - (_cadb_d_)
• Trivial solution requires exponential time
• Each match is given a cost. Alignment solved
  through recurrence relation

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Graphical Matching Coupled BFS
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Graphical Matching Coupled BFS
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Coupled BFS
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Graphical Matching Coupled BFS
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Graphical Matching Coupled BFS
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Graphical Matching Coupled BFS
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Overview of the BFS algorithm
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Important Differences w.r.t BFS

• Traditional Breadth First Search
• Traversal Defined only over a single graph
• All neighbors are considered for expanding the
  path
• Coupled Breadth First Search
• Traversal proceeds in two directed graphs
  simultaneously
• Only matched neighbors are considered for
  expanding the path
• Constant number of neighbors provides a bound for
  the traversal complexity

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Complexity Analysis

• The algorithm can be divided into two stages
• Alignment T1
• Pair correspondence T2
• Singular points are not known
• All possible alignments are tried T1O(n2)
• T2
• Complexity of BFS over graph G(V,E) O(VE)
• At each vertex we perform a string alignment
  O(K2)O(1)
• Due to our specialized construction of the K-plet
  E KV
• O(T2)O(n)
• Total complexity O(n2). O(n) O(n3)
• Singular points are known (S.Chikkerur and Ratha,
  AUTOID 05)
• Only c nearest neighbors are tried, T1 O(c2)
  O(1)
• O(T2)O(n), as before
• Total complexity O(1). O(n) O(n)!

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Experimental Evaluation

• 800 prints from FVC2002(DB1)
• 2800 genuine tests,4950 impostor tests
• Compared with BOZORTH 3

Error Rates BOZORTH3 3.6 EER, 5.0
FMR100 Proposed 1.5 EER, 1.65 FMR100
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Software

• CUBS Truthing Tool
• CUBS Minutiae Truthing Tool
• CUBS Fingerprint Verification Demo
• Matlab code for Fingerprint Enhancement
• Matlab Toolbox for Fingerprint Verification
• Download available from
• http//www.mathworks.com/matlabcentral
• http//www.eng.buffalo.edu/ssc5

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Conclusion

• A new matching algorithm based on graph matching
  principles.
• We presented a new representation (K-plet) to
  encode local neighborhood
• We presented CBFS (Coupled BFS), a new dual graph
  traversal algorithm
• The unique advantages of the proposed algorithm
  are as follows
• The proposed algorithm is robust to non-linear
  distortion
• Ambiguities in minutiae pairings are solved by
  employing an optimization approach.
• The coupled BFS algorithm provides a very generic
  way of consolidating local matches.
• We also presented an experimental evaluation of
  the proposed approach and showed that it exceeds
  the performance of the NIST BOZORTH3

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Thank You

• http//www.cubs.buffalo.edu