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Presented by Ibrahim M Ismail

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Outline Introduction to Project Background to Fingerprint Matching Linear Program Design Results Comparison 2

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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) 3

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Notations 4 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

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Translation 5

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Rotation 6

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Matching 8

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Maximization Function 10

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Score 11 Match: 10.65 Non-match: 7.97

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Threshold Value 12 scorematchnon matchFRR (%)FAR (%)Average 000010050 100010050 200.113938473099.9430349.97152 302.088872009098.8416349.42081 41.2552301264.6714774020.62761595.4614548.04453 51.6736401678.3934675282.0920588.9289845.51051 65.02092050212.799088495.43933178.332741.88602 78.78661087915.2297759212.343164.3182738.33068 810.4602510517.5465248821.9665347.9301234.94832 910.8786610914.4322066132.6359831.9407532.28837 109.6234309629.76072920642.8870319.8442831.36566 1110.0418416.60843144752.7196711.659732.18968 1212.552301264.9373338464.016745.88682134.95178 1310.878661091.86099506375.732222.48765739.10994 1410.878661091.10140524186.610881.00645743.80867 152.9288702930.22787694693.514640.34181546.92823 162.9288702930.15191796496.443510.15191848.29772 171.2552301260.07595898298.535560.03797949.28677 180.836820084099.58159049.79079 1900100050 2000100050

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Threshold value 13

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Other Techniques 14 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 15 FRR: 0.16% FAR: 11.23% Average: 5.70%

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On-Line Fingerprint Matching 16 FRR: 5.46% FAR: 0.84% Average: 3.15%

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Fingerprint Matching combining the global orientation field with Minutia 17 FAR: 3.01% FRR: 12.43% Average: 7.72%

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Comparing 18 Fingerprint Matching Approaches Average Error Rate (%) LP Approach31.36% On-Line Fingerprint Matching5.70% Efficient Algorithm for Fingerprint Matching3.15% Fingerprint Matching Combining the Global Orientation Field with Minutia 7.72%

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Critical Examination 19 Advanced Decision Making Large Increase of Variable Size (loss of time) for accuracy Rows/Inequalities Avg: 7,315 Max: 21,807 O(|M||N|+|M||K|+ |N||K|) Columns/Variables Avg: 14,544 Max: 91,769 O(|M||N||K|)

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Simplex Algorithm 20 George Bernard Dantzig 1947 Simplex Brief outline Exponential Worst Case Binary Integer Programming NP Hard

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Conclusion 21 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 22

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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. 23

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