# Presented by Ibrahim M Ismail. Outline Introduction to Project Background to Fingerprint Matching Linear Program Design Results Comparison 2.

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Presented by Ibrahim M Ismail

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

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

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

Translation 5

Rotation 6

7

Matching 8

9

Maximization Function 10

Score 11 Match: 10.65 Non-match: 7.97

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

Threshold value 13

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

On-Line Fingerprint Matching 15 FRR: 0.16% FAR: 11.23% Average: 5.70%

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

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

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%

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|)

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

Conclusion 21 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 22

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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