The Community for Technology Leaders
RSS Icon
Issue No.09 - September (2008 vol.30)
pp: 1507-1519
Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops and whorls are laid out. These models are parametrised by few, geometrically interpretable parameters which are invariant under Euclidean motions. We demonstrate their ability in adapting to given, observed orientation fields, and we compare them to existing models using the fingerprint images of the NIST Special Database 4. We also illustrate that these model allow for extrapolation into unobserved regions. This goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region. Within the framework of quadratic differentials we are able to verify analytically Penrose's formula for the singularities on a palm [L. S. Penrose, "Dermatoglyphics"' Scientific American, vol. 221, no.~6, pp. 73--84, 1969]. Potential applications of these models are the use of their parameters as indices of large fingerprint databases, as well as the definition of intrinsic coordinates for single fingerprint images.
Geometric, Pattern analysis, Applications, Smoothing, Fingerprint recognition, orientation field, fingerprint modelling, quadratic differential, rational functions
Thomas Hotz, Stephan Huckemann, "Global Models for the Orientation Field of Fingerprints: An Approach Based on Quadratic Differentials", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.30, no. 9, pp. 1507-1519, September 2008, doi:10.1109/TPAMI.2007.70826
[1] D. Maltoni, D. Maio, A.K. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition. Springer, 2003.
[2] M. Tico and P. Kuosmanen, “Fingerprint Matching Using an Orientation-Based Minutia Descriptor,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 8, pp. 1009-1014, Aug. 2003.
[3] B. Bhanu and X. Tan, “Fingerprint Indexing Based on Novel Features of Minutiae Triplets,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 5, pp. 616-622, May 2003.
[4] X. Jiang and W. Ser, “Online Fingerprint Template Improvement,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 8, pp. 1121-1126, Aug. 2002.
[5] S. Pankanti, S. Prabhakar, and A.K. Jain, “On the Individuality of Fingerprints,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 8, pp. 1010-1025, Aug. 2002.
[6] Z.M. Kovacs-Vajna, “A Fingerprint Verification System Based on Triangular Matching and Dynamic Time Warping,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1266-1276, Nov. 2000.
[7] A.K. Jain, L. Hong, and R. Bolle, “On-Line Fingerprint Verification,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 4, pp. 302-314, Apr. 1997.
[8] A.K. Jain, L. Hong, S. Pankanti, and R. Bolle, “An Identity-Authentication System Using Fingerprints,” Proc. IEEE, vol. 85, no. 9, pp. 1365-1388, Sept. 1997.
[9] F. Galton, Finger Prints. Macmillan, 1892.
[10] A. Senior, “A Combination Fingerprint Classifier,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 10, pp. 1165-1174, Oct. 2001.
[11] R. Cappelli, A. Lumini, D. Maio, and D. Maltoni, “Fingerprint Classification by Directional Image Partitioning,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 402-421, May 1999.
[12] A.K. Jain, S. Prabhakar, and L. Hong, “A Multichannel Approach to Fingerprint Classification,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 4, pp. 348-359, Apr. 1999.
[13] N.K. Ratha, K. Karu, C. Shaoyun, and A.K. Jain, “A Real-Time Matching System for Large Fingerprint Databases,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 28, pp. 799-813, Aug. 1996.
[14] C.A.B. Smith, “Notes on the Forms of Dermatoglyphic Patterns,” Dermatoglyphics: Fifty Years Later, Birth Defects: Original Article Series, vol. 15, no. 6, pp. 43-52, The Nat'l Foundation, 1979.
[15] K.V. Mardia, Q. Li, and T.J. Hainsworth, “On the Penrose Hypothesis on Fingerprint Patterns,” IMA J. Math. Applied in Medicine and Biology, vol. 9, pp. 289-294, 1992.
[16] B.G. Sherlock and D.M. Monro, “A Model for Interpreting Fingerprint Topology,” Pattern Recognition, vol. 26, no. 7, pp.1047-1055, 1993.
[17] P.R. Vizcaya and L.A. Gerhardt, “A Nonlinear Orientation Model for Global Description of Fingerprints,” Pattern Recognition, vol. 29, no. 7, pp. 1221-1231, 1996.
[18] J. Gu, J. Zhou, and D. Zhang, “A Combination Model for Orientation Field of Fingerprints,” Pattern Recognition, vol. 37, pp. 543-553, 2004.
[19] L.S. Penrose, “Dermatoglyphics,” Scientific Am., vol. 221, no. 6, pp.73-84, 1969.
[20] A.M. Bazen and S.H. Gerez, “An Intrinsic Coordinate System for Fingerprint Matching,” Proc. Third Int'l Conf. Audio- and Video-Based Biometric Person Authentication (AVBPA '01), pp. 198-204, 2001.
[21] C.I. Watson and C.L. Wilson, NIST Special Database 4: Fingerprint Database. Nat'l Inst. Standards and Tech nology, Mar. 1992.
[22] K. Bonnevie, “Studies on Papillary Patterns of Human Fingers,” J.Genetics, vol. 15, no. 1, pp. 1-111, Nov. 1924.
[23] L.S. Penrose and P.T. Ohara, “The Development of Epidermal Ridges,” J. Medical Genetics, vol. 10, no. 3, pp. 201-208, Sept. 1973.
[24] M. Kücken and A.C. Newell, “Fingerprint Formation,” J.Theoretical Biology, vol. 235, no. 1, pp. 71-83, 2005.
[25] H. Grötzsch, “Über die Geometrie der schlichten konformen Abbildung,” Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, Physikalisch-Mathematische Klasse, pp. 654-671, 1933.
[26] O. Teichmüller, Extremale quasikonforme Abbildungen und quadratische differentiale, Abhandlungen der Preußischen Akademie der Wissenschaften, Mathematisch-naturwissenschaftliche Klasse, vol. 22, no. 1939. Verlag der Akademie der Wissenschaften, 1940.
[27] A.L. Kholodenko, “Use of Quadratic Differentials for Description of Defects and Textures in Liquid Crystals and $2 + 1$ Gravity,” J.Geometry and Physics, vol. 33, nos. 1-2, pp. 59-102, 2000.
[28] S. Kerckhoff, H. Masur, and J. Smillie, “Ergodicity of Billiard Flows and Quadratic Differentials,” Annals of Math., second series, vol. 124, no. 2, pp. 293-311, Sept. 1986.
[29] M. Kontsevich and A. Zorich, “Connected Components of the Moduli Spaces of Abelian Differentials with Prescribed Singularities,” Inventiones mathematicae, vol. 153, pp. 631-678, 2003.
[30] G. Jensen, “Quadratic Differentials,” Univalent Functions, chapter8, C. Pommerenke, ed. Vandenhoeck & Ruprecht, 1975.
[31] K. Strebel, Quadratic Differentials. Springer, 1984.
[32] C.L. Wilson, G.T. Candela, and C.I. Watson, “Neural Network Fingerprint Classification,” J. Artificial Neural Networks, vol. 1, no. 2, pp. 203-228, 1994.
[33] J. Zhou and J. Gu, “Modeling Orientation Fields of Fingerprints with Rational Complex Functions,” Pattern Recognition, vol. 37, pp. 389-391, 2004.
[34] D. Maio, D. Maltoni, R. Cappelli, J.L. Wayman, and A.K. Jain, “FVC2000: Fingerprint Verification Competition,” IEEE Trans. Pattern Analysis Machine Intelligence, vol. 24, no. 3, pp. 402-412, Mar. 2002.
[35] A.M. Bazen and S.H. Gerez, “Systematic Methods for the Computation of the Directional Fields and Singular Points of Fingerprints,” IEEE Trans. Pattern Analysis Machine Intelligence, vol. 24, no. 7, pp. 905-919, July 2002.
[36] J.A. Nelder and R. Mead, “A Simplex Algorithm for Function Minimization,” Computer J., vol. 7, pp. 308-313, 1965.
27 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool