Presented byIbrahim M Ismail

OutlineIntroduction to Project

Background to Fingerprint Matching

Linear Program Design

Results

Comparison

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IntroductionUse 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

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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

Sin[i] holds the sin value

Cos[i] holds the sin value

0 implies non match and 1 implies match

Set to 2000

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

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Match:10.65

Non-match:7.97

Threshold Value

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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

Threshold value

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Other Techniques

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Title: On-line fingerprint verification Authors: A. Jain and L. Hong Journal: Pattern Analysis and Machine Intelligence 1997

Title: An efficient algorithm for fingerprint matchingAuthors: C. Wang, M. Gavrilova, Y. Luo and J. RokneConference: Proceedings of the 18th International Conference on Pattern Recognition, 2006

Title: Fingerprint matching combining the global orientation field with minutiaAuthors: J. Qi, S. Yang and Y. WangJournal: Pattern Recognition Letters 26 (15), 2005

On-Line Fingerprint Matching

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FRR: 0.16%FAR: 11.23%Average: 5.70%

On-Line Fingerprint Matching

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FRR: 5.46%FAR: 0.84%Average: 3.15%

Fingerprint Matching combining the global orientation field with Minutia

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FAR: 3.01%FRR: 12.43%Average: 7.72%

Comparing

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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%

Critical Examination

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Advanced Decision MakingLarge Increase of Variable Size (loss of time) for accuracy

Rows/InequalitiesAvg: 7,315Max: 21,807O(|M||N|+|M||K|+

|N||K|)

Columns/VariablesAvg: 14,544Max: 91,769O(|M||N||K|)

Simplex Algorithm

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George Bernard Dantzig1947

Simplex Brief outline Exponential Worst Case Binary Integer Programming

NP Hard

Conclusion

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Slow vs. Accurate

Not Flexible

To be fair…Should be judged against algorithms that use the similar matching criteria

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 159–175. 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) 2424–2430.

[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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Questions?