Biometric Technologies Minutia based Fingerprint Matching using Linear Programming

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Biometric TechnologiesMinutia based Fingerprint
Matching using Linear Programming
Presented by Ibrahim M Ismail
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Outline

• Introduction to Project
• Background to Fingerprint Matching
• Linear Program Design
• Results
• Comparison

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Introduction

• Use Linear Programming (LP) for minutiae based
  fingerprint matching.
• Why LP ?
• Rules for LP
• No multiplication of variables
• Just three things involved
• Data Sets
• Linear Inequalities/Equalities
• Maximization/Minimization Function (also Linear)

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Notations

x coordinates for the template minutiae set
y coordinates for the template minutiae set
angle of orientation for the template minutiae set
x coordinates for the input minutiae set
y coordinates for the input minutiae set
angle of orientation for the input minutiae set
translation amount in the positive x-direction
translation amount in the positive y-direction
Sini holds the sin value
Cosi holds the sin value
0 implies non match and 1 implies match
Set to 2000
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Translation
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Rotation
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Rotation
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Matching
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Matching
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Maximization Function
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Score
Match 10.65 Non-match 7.97
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Threshold Value
score match non match FRR () FAR () Average
0 0 0 0 100 50
1 0 0 0 100 50
2 0 0.113938473 0 99.94303 49.97152
3 0 2.088872009 0 98.84163 49.42081
4 1.255230126 4.671477402 0.627615 95.46145 48.04453
5 1.673640167 8.393467528 2.09205 88.92898 45.51051
6 5.020920502 12.79908849 5.439331 78.3327 41.88602
7 8.786610879 15.22977592 12.3431 64.31827 38.33068
8 10.46025105 17.54652488 21.96653 47.93012 34.94832
9 10.87866109 14.43220661 32.63598 31.94075 32.28837
10 9.623430962 9.760729206 42.88703 19.84428 31.36566
11 10.041841 6.608431447 52.71967 11.6597 32.18968
12 12.55230126 4.93733384 64.01674 5.886821 34.95178
13 10.87866109 1.860995063 75.73222 2.487657 39.10994
14 10.87866109 1.101405241 86.61088 1.006457 43.80867
15 2.928870293 0.227876946 93.51464 0.341815 46.92823
16 2.928870293 0.151917964 96.44351 0.151918 48.29772
17 1.255230126 0.075958982 98.53556 0.037979 49.28677
18 0.836820084 0 99.58159 0 49.79079
19 0 0 100 0 50
20 0 0 100 0 50
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Threshold value
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Other Techniques

• Title On-line fingerprint verification
• Authors A. Jain and L. Hong
• Journal Pattern Analysis and Machine
  Intelligence 1997
• Title An efficient algorithm for fingerprint
  matching
• Authors C. Wang, M. Gavrilova, Y. Luo and J.
  Rokne
• Conference Proceedings of the 18th
  International Conference on Pattern Recognition,
  2006
• Title Fingerprint matching combining the global
  orientation field with minutia
• Authors J. Qi, S. Yang and Y. Wang
• Journal Pattern Recognition Letters 26 (15),
  2005

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On-Line Fingerprint Matching

• FRR 0.16
• FAR 11.23
• Average 5.70

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On-Line Fingerprint Matching

• FRR 5.46
• FAR 0.84
• Average 3.15

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Fingerprint Matching combining the global
orientation field with Minutia

• FAR 3.01
• FRR 12.43
• Average 7.72

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Comparing
Fingerprint Matching Approaches Average Error Rate ()
LP Approach 31.36
On-Line Fingerprint Matching 5.70
Efficient Algorithm for Fingerprint Matching 3.15
Fingerprint Matching Combining the Global Orientation Field with Minutia 7.72
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Critical Examination

• Advanced Decision Making
• Large Increase of Variable Size (loss of time)
  for accuracy
• Rows/Inequalities
• Avg 7,315
• Max 21,807
• O(MNMK
• NK)
• Columns/Variables
• Avg 14,544
• Max 91,769
• O(MNK)

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Simplex Algorithm

• George Bernard Dantzig
• 1947
• Simplex
• Brief outline
• Exponential Worst Case
• Binary Integer Programming
• NP Hard

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Conclusion

• Slow vs. Accurate
• Not Flexible
• To be fair
• Should be judged against algorithms that use the
  similar matching criteria

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References

• 1 Cappelli R., Maio D. and Maltoni D., Modeling
  Plastic Distortion in Fingerprint Images, ICAPR
  2001, LNCS 2013, pp. 369-376, 2001.
• 2 Chengfeng Wang, Marina Gavrilova, Yuan Luo,
  Jon Rokne, An efficient algorithm for fingerprint
  matching, Proceedings of the 18th International
  Conference on Pattern Recognition - Volume 1,
  2006, 1034-1037
• 3 Fornefett M., Rohr K. and Stiehl H.S.,
  Radial basis functions with compact support for
  elastic registration of medical images, Image and
  Vision Computing, no. 19, pp. 87-96, 2001.
• 4 FVC 2004 Fingerprint Verification
  Competition, Retrieved April 13, 2008, from the
  World Wide Web http//bias.csr.unibo.it/fvc2004/
• 5 GLPK (GNU Linear Programming Kit), Retrieved
  13 April, 2008 from the World Wide Web
  www.gnu.org/software/glpk/glpk.html
• 6 GNU MathProg, Retrieved April 13, 2008, from
  the World Wide Web www.lpsolve.sourceforge.net/5.
  5/MathProg.htm

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References

• 7 Greenberg, cites V. Klee and G.J. Minty.
  "How Good is the Simplex Algorithm?" In O.
  Shisha, editor, Inequalities, III, pages 159175.
  Academic Press, New York, NY, 1972
• 8 Jain A.K., Hong L. and Bolle R., On-line
  fingerprint verification, PAMI, vol. 19, no. 4,
  pp. 302-314, 1997.
• 9 Maltoni D., Maio D., Jain A. K., and
  Prabhakar S. Handbook of Fingerprint Recognition.
  Springer-Verlag, New York, 2003.
• 10 The MathWorks, Retrieved April 13, 2008,
  from the World Wide Web www.mathworks.com/
• ref11 Qi J., Yang S., Wang Y., Fingerprint
  matching combining the global orientation field
  with minutia, Pattern Recognition Lett. 26 (15)
  (2005) 24242430.
• 12 Wang C.F. and Hu Z.Y., Image Based
  Rendering under Varying Illumination, the Journal
  of High Technology Letters, vol. 9, no. 3, pp.
  6-11, 2003.

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THANK YOU!

• Questions?