Abstract

We propose a coherent mathematical model for human fingerprint images. Fingerprint structure is represented simply as a hologram – namely a phase modulated fringe pattern. The holographic form unifies analysis, classification, matching, compression, and synthesis of fingerprints in a self-consistent formalism. Hologram phase is at the heart of the method; a phase that uniquely decomposes into two parts via the Helmholtz decomposition theorem. Phase also circumvents the infinite frequency singularities that always occur at minutiae. Reliable analysis is possible using a recently discovered two-dimensional demodulator. The parsimony of this model is demonstrated by the reconstruction of a fingerprint image with an extreme compression factor of 239.

© 2007 Optical Society of America

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    [Crossref]
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    [Crossref]
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  41. K. G. Larkin and P. A. Fletcher, “Extreme compression of fingerprint images: squeezing patterns until the spirals pop out,” in Fifth International Workshop on Information Optics (Toledo, Spain, 2006). http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=860&Issue=1

2007 (1)

A. Ross, J. Shah, and A. K. Jain, “From Template to Image: reconstructing fingerprints from minutiae points,” IEEE Trans PAMI 29, 544–560 (2007).
[Crossref]

2006 (1)

K. G. Larkin and P. A. Fletcher, “Extreme compression of fingerprint images: squeezing patterns until the spirals pop out,” in Fifth International Workshop on Information Optics (Toledo, Spain, 2006). http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=860&Issue=1

2005 (1)

K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Optics Express 13, 8097–8121 (2005).
[Crossref] [PubMed]

2003 (2)

N. Ratha and R. Bolle, eds., Automatic Fingerprint Recognition Systems (Springer, New York, 2003).

Y. Tong, S. Lombey, A. N. Hirani, and M. Desbrun, “Discrete multiscale vector field decomposition,” ACM Transactions on Graphics 22, 445–452 (2003).
[Crossref]

2002 (2)

S. Kasaei, M. Deriche, and B. Boashash, “A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization,” IEEE Transactions On Image Processing 11, 1365–1378 (2002).
[Crossref]

A. W. Senior, R. M. Bolle, N. K. Ratha, and S. Pankanti, “Fingerprint Minutiae: A Constructive Definition,” in Workshop on biometrics, IEEE ECCV, (Copenhagen, Denmark, 2002).

2001 (3)

1998 (2)

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping (John Wiley and Sons, New York, 1998).

D. A. Egolf, I. V. Melnikov, and E. Bodenschatz, “Importance of local pattern properties in spiral defect chaos,” Phys. Rev. Lett. 80, 3228–3231 (1998).
[Crossref]

1997 (1)

B. Jähne, Practical handbook on Image processing for Scientific applications (CRC Press, Boca Raton, Florida, 1997).

1996 (1)

V. A. Soifer, V. V. Kotlyar, S. N. Khonina, and A. G. Khramov, “The method of the directional field in the interpretation and recognition of images with structure redundancy,” Image Analysis and Signal Processing: Adv. Math. Theory Appl. 6, 710–724 (1996).

1995 (3)

C. M. Brislawn, “Fingerprints go digital,” Notices of the AMS  42, 1278–1283 (1995).

J. G. Daugman and C. J. Downing, “Demodulation, predictive coding, and spatial vision,” J. Opt. Soc. Am. A 12, 641–660 (1995).
[Crossref]

G. H. Granlund and H. Knutsson, Signal processing for computer vision (Kluwer, Dordrecht, Netherlands, 1995).

1993 (2)

C. F. Shu and R. C. Jain, “Direct Estimation and Error Analysis For Oriented Patterns,” CVGIP-Image Understanding 58, 383–398 (1993).
[Crossref]

B. G. Sherlock and D. M. Monro, “A model for interpreting fingerprint topology,” Pattern Recogn. 26, 1047–1055 (1993).
[Crossref]

1992 (1)

1991 (2)

1990 (1)

A. M. Turing, “The chemical basis of morphogenesis, reprinted from Philosophical Transactions of the Royal Society (Part B), 237, 37-72 (1953)," Bull. Math. Biol. 52, 153–197 (1990).
[Crossref] [PubMed]

1989 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

1987 (1)

M. Kass and A. Witkin, “Analyzing oriented patterns,” Computer vision, graphics, and image processing 37, 362–385 (1987).
[Crossref]

1979 (1)

R. Penrose, “The topology of ridge systems,” Ann. Hum. Genet.,Lond. 42, 435–444 (1979).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A. 336, 165–190 (1974).
[Crossref]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Pro. R. Soc. London 197, 454–487 (1949).
[Crossref]

1892 (1)

F. Galton, Finger Prints (Macmillan, London, 1892). http://galton.org/books/finger-prints/index.htm

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A. 336, 165–190 (1974).
[Crossref]

Bicz, W.

W. Bicz, “The idea of description (reconstruction) of fingerprints with mathematical algorithms and history of the development of this idea at Optel,” (Optel, 2003), http://www.optel.pl/article/english/idea.htm, (Accessed 9 May 2006),

Bigun, J.

J. Tharna, K. Nilsson, and J. Bigun, “Orientation scanning to improve lossless compression of fingerprint images.,” in Audio and Video based Person Authentication - AVBPA03, J. Kittler and M. S. Nixon, eds. (Springer, Heidelberg, 2003), pp.343–350.

Boashash, B.

S. Kasaei, M. Deriche, and B. Boashash, “A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization,” IEEE Transactions On Image Processing 11, 1365–1378 (2002).
[Crossref]

Bodenschatz, E.

D. A. Egolf, I. V. Melnikov, and E. Bodenschatz, “Importance of local pattern properties in spiral defect chaos,” Phys. Rev. Lett. 80, 3228–3231 (1998).
[Crossref]

Bolle, R. M.

A. W. Senior, R. M. Bolle, N. K. Ratha, and S. Pankanti, “Fingerprint Minutiae: A Constructive Definition,” in Workshop on biometrics, IEEE ECCV, (Copenhagen, Denmark, 2002).

Bone, D.

Bone, D. J.

Brislawn, C. M.

C. M. Brislawn, “Fingerprints go digital,” Notices of the AMS  42, 1278–1283 (1995).

Cartwright, A. N.

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint Image Enhancement using STFT Analysis,” in ICAPR, S. Singh, M. Singh, C. Apte, and P. Perner, eds., (Springer-Verlag, Bath, UK, 2005).

Chikkerur, S.

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint Image Enhancement using STFT Analysis,” in ICAPR, S. Singh, M. Singh, C. Apte, and P. Perner, eds., (Springer-Verlag, Bath, UK, 2005).

Daugman, J. G.

Deriche, M.

S. Kasaei, M. Deriche, and B. Boashash, “A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization,” IEEE Transactions On Image Processing 11, 1365–1378 (2002).
[Crossref]

Desbrun, M.

Y. Tong, S. Lombey, A. N. Hirani, and M. Desbrun, “Discrete multiscale vector field decomposition,” ACM Transactions on Graphics 22, 445–452 (2003).
[Crossref]

Downing, C. J.

Egolf, D. A.

D. A. Egolf, I. V. Melnikov, and E. Bodenschatz, “Importance of local pattern properties in spiral defect chaos,” Phys. Rev. Lett. 80, 3228–3231 (1998).
[Crossref]

Fletcher, P. A.

K. G. Larkin and P. A. Fletcher, “Extreme compression of fingerprint images: squeezing patterns until the spirals pop out,” in Fifth International Workshop on Information Optics (Toledo, Spain, 2006). http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=860&Issue=1

P. A. Fletcher and K. G. Larkin, –Direct embedding and detection of RST invariant Watermarks,” in IH2002, Fifth International Workshop on Information Hiding, Petitcolas F. A. P., ed., (Springer Verlag, Noordwijkerhout, The Netherlands, 2002), pp. 129–144.

Fried, D. L.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Pro. R. Soc. London 197, 454–487 (1949).
[Crossref]

Gaensslen, R. E.

A. K. Jain and S. Pankanti, “Automated Fingerprint Identification and Imaging Systems,” in Advances in Fingerprint Technology, H. C. Lee and R. E. Gaensslen, eds., (CRC Press, 2001).

Galton, F.

F. Galton, Finger Prints (Macmillan, London, 1892). http://galton.org/books/finger-prints/index.htm

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping (John Wiley and Sons, New York, 1998).

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Govindaraju, V.

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint Image Enhancement using STFT Analysis,” in ICAPR, S. Singh, M. Singh, C. Apte, and P. Perner, eds., (Springer-Verlag, Bath, UK, 2005).

Granlund, G. H.

G. H. Granlund and H. Knutsson, Signal processing for computer vision (Kluwer, Dordrecht, Netherlands, 1995).

Grasemann, U.

U. Grasemann and R. Miikkulainen, “Effective image compression using evolved wavelets,” in Genetic And Evolutionary Computation Conference (GECCO-05),(ACM, Washington DC, 2005), pp. 1961–1968.

Hirani, A. N.

Y. Tong, S. Lombey, A. N. Hirani, and M. Desbrun, “Discrete multiscale vector field decomposition,” ACM Transactions on Graphics 22, 445–452 (2003).
[Crossref]

Huntley, J. M.

Jähne, B.

B. Jähne, Practical handbook on Image processing for Scientific applications (CRC Press, Boca Raton, Florida, 1997).

Jain, A. K.

A. Ross, J. Shah, and A. K. Jain, “From Template to Image: reconstructing fingerprints from minutiae points,” IEEE Trans PAMI 29, 544–560 (2007).
[Crossref]

A. K. Jain and S. Pankanti, “Automated Fingerprint Identification and Imaging Systems,” in Advances in Fingerprint Technology, H. C. Lee and R. E. Gaensslen, eds., (CRC Press, 2001).

D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of fingerprint recognition (Springer, New York, 2003).

Jain, R. C.

C. F. Shu and R. C. Jain, “Direct Estimation and Error Analysis For Oriented Patterns,” CVGIP-Image Understanding 58, 383–398 (1993).
[Crossref]

Kasaei, S.

S. Kasaei, M. Deriche, and B. Boashash, “A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization,” IEEE Transactions On Image Processing 11, 1365–1378 (2002).
[Crossref]

Kass, M.

A. Witkin and M. Kass, “Reaction-diffusion textures,” Comput. Graphics 25, 299–308 (1991).
[Crossref]

M. Kass and A. Witkin, “Analyzing oriented patterns,” Computer vision, graphics, and image processing 37, 362–385 (1987).
[Crossref]

Khonina, S. N.

V. A. Soifer, V. V. Kotlyar, S. N. Khonina, and A. G. Khramov, “The method of the directional field in the interpretation and recognition of images with structure redundancy,” Image Analysis and Signal Processing: Adv. Math. Theory Appl. 6, 710–724 (1996).

Khramov, A. G.

V. A. Soifer, V. V. Kotlyar, S. N. Khonina, and A. G. Khramov, “The method of the directional field in the interpretation and recognition of images with structure redundancy,” Image Analysis and Signal Processing: Adv. Math. Theory Appl. 6, 710–724 (1996).

Knutsson, H.

G. H. Granlund and H. Knutsson, Signal processing for computer vision (Kluwer, Dordrecht, Netherlands, 1995).

Kosz, D.

D. Kosz, “New numerical methods of fingerprint recognition based on mathematical description of arrangement of dermatoglyphics and creation of minutiae,” in Biometrics in Human Service User Group Newsletter,Mintie D., ed., (1999). http://www.ct.gov/dss/cwp/view.asp?A=2349&Q=304724

Kotlyar, V. V.

V. A. Soifer, V. V. Kotlyar, S. N. Khonina, and A. G. Khramov, “The method of the directional field in the interpretation and recognition of images with structure redundancy,” Image Analysis and Signal Processing: Adv. Math. Theory Appl. 6, 710–724 (1996).

Larkin, K. G.

K. G. Larkin and P. A. Fletcher, “Extreme compression of fingerprint images: squeezing patterns until the spirals pop out,” in Fifth International Workshop on Information Optics (Toledo, Spain, 2006). http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=860&Issue=1

K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Optics Express 13, 8097–8121 (2005).
[Crossref] [PubMed]

K. G. Larkin, “Natural demodulation of 2D fringe patterns,” in Fringe´01 - The Fourth International Workshop on Automatic Processing of Fringe Patterns, Juptner W. and Osten W., eds., (Elsevier, Bremen, Germany, 2001). http://citeseer.ist.psu.edu/458598.html

K. G. Larkin, D. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns: I. General background to the spiral phase quadrature transform.,” J. Opt. Soc. Am. A 18, 1862–1870 (2001). http://www.opticsinfobase.org/abstract.cfm?URI=josaa-18-8-1862
[Crossref]

K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns: II. Stationary phase analysis of the spiral phase quadrature transform.,” J. Opt. Soc. Am. A 18, 1871–1881 (2001).
[Crossref]

P. A. Fletcher and K. G. Larkin, –Direct embedding and detection of RST invariant Watermarks,” in IH2002, Fifth International Workshop on Information Hiding, Petitcolas F. A. P., ed., (Springer Verlag, Noordwijkerhout, The Netherlands, 2002), pp. 129–144.

Lee, H. C.

A. K. Jain and S. Pankanti, “Automated Fingerprint Identification and Imaging Systems,” in Advances in Fingerprint Technology, H. C. Lee and R. E. Gaensslen, eds., (CRC Press, 2001).

Lombey, S.

Y. Tong, S. Lombey, A. N. Hirani, and M. Desbrun, “Discrete multiscale vector field decomposition,” ACM Transactions on Graphics 22, 445–452 (2003).
[Crossref]

Maio, D.

D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of fingerprint recognition (Springer, New York, 2003).

Maltoni, D.

D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of fingerprint recognition (Springer, New York, 2003).

Melnikov, I. V.

D. A. Egolf, I. V. Melnikov, and E. Bodenschatz, “Importance of local pattern properties in spiral defect chaos,” Phys. Rev. Lett. 80, 3228–3231 (1998).
[Crossref]

Miikkulainen, R.

U. Grasemann and R. Miikkulainen, “Effective image compression using evolved wavelets,” in Genetic And Evolutionary Computation Conference (GECCO-05),(ACM, Washington DC, 2005), pp. 1961–1968.

Monro, D. M.

B. G. Sherlock and D. M. Monro, “A model for interpreting fingerprint topology,” Pattern Recogn. 26, 1047–1055 (1993).
[Crossref]

Myung, J.

J. Myung and M. Pitt, “Model Selection Methods,” in Amsterdam Workshop on Model Selection(Amsterdam, 2004). http://www2.fmg.uva.nl/modelselection/presentation.cfm?presenter=5

Nilsson, K.

J. Tharna, K. Nilsson, and J. Bigun, “Orientation scanning to improve lossless compression of fingerprint images.,” in Audio and Video based Person Authentication - AVBPA03, J. Kittler and M. S. Nixon, eds. (Springer, Heidelberg, 2003), pp.343–350.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A. 336, 165–190 (1974).
[Crossref]

Oldfield, M. A.

Pankanti, S.

A. W. Senior, R. M. Bolle, N. K. Ratha, and S. Pankanti, “Fingerprint Minutiae: A Constructive Definition,” in Workshop on biometrics, IEEE ECCV, (Copenhagen, Denmark, 2002).

A. K. Jain and S. Pankanti, “Automated Fingerprint Identification and Imaging Systems,” in Advances in Fingerprint Technology, H. C. Lee and R. E. Gaensslen, eds., (CRC Press, 2001).

Penrose, R.

R. Penrose, “The topology of ridge systems,” Ann. Hum. Genet.,Lond. 42, 435–444 (1979).
[Crossref]

Pitt, M.

J. Myung and M. Pitt, “Model Selection Methods,” in Amsterdam Workshop on Model Selection(Amsterdam, 2004). http://www2.fmg.uva.nl/modelselection/presentation.cfm?presenter=5

Prabhakar, S.

D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of fingerprint recognition (Springer, New York, 2003).

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping (John Wiley and Sons, New York, 1998).

Ratha, N. K.

A. W. Senior, R. M. Bolle, N. K. Ratha, and S. Pankanti, “Fingerprint Minutiae: A Constructive Definition,” in Workshop on biometrics, IEEE ECCV, (Copenhagen, Denmark, 2002).

Ross, A.

A. Ross, J. Shah, and A. K. Jain, “From Template to Image: reconstructing fingerprints from minutiae points,” IEEE Trans PAMI 29, 544–560 (2007).
[Crossref]

Senior, A. W.

A. W. Senior, R. M. Bolle, N. K. Ratha, and S. Pankanti, “Fingerprint Minutiae: A Constructive Definition,” in Workshop on biometrics, IEEE ECCV, (Copenhagen, Denmark, 2002).

Shah, J.

A. Ross, J. Shah, and A. K. Jain, “From Template to Image: reconstructing fingerprints from minutiae points,” IEEE Trans PAMI 29, 544–560 (2007).
[Crossref]

Sherlock, B. G.

B. G. Sherlock and D. M. Monro, “A model for interpreting fingerprint topology,” Pattern Recogn. 26, 1047–1055 (1993).
[Crossref]

Shu, C. F.

C. F. Shu and R. C. Jain, “Direct Estimation and Error Analysis For Oriented Patterns,” CVGIP-Image Understanding 58, 383–398 (1993).
[Crossref]

Soifer, V. A.

V. A. Soifer, V. V. Kotlyar, S. N. Khonina, and A. G. Khramov, “The method of the directional field in the interpretation and recognition of images with structure redundancy,” Image Analysis and Signal Processing: Adv. Math. Theory Appl. 6, 710–724 (1996).

Tharna, J.

J. Tharna, K. Nilsson, and J. Bigun, “Orientation scanning to improve lossless compression of fingerprint images.,” in Audio and Video based Person Authentication - AVBPA03, J. Kittler and M. S. Nixon, eds. (Springer, Heidelberg, 2003), pp.343–350.

Tong, Y.

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Figures (6)

Fig. 1.
Fig. 1.

Digitized fingerprint image from NIST database (262,144 bytes).

Fig.2.
Fig.2.

Simple synthesized fringe pattern. Note the dominant loop and delta structures as well as the ridge endings and bifurcations.

Fig. 3.
Fig. 3.

Steps in the 2-D demodulation using unwrapped direction map

Fig. 4.
Fig. 4.

Minutiae polarity map

Fig. 5.
Fig. 5.

All four elemental images after decompression (1095 bytes total).

Fig. 6.
Fig. 6.

Decompressed (239×) fingerprint (1095 bytes) on the left, and the original (right).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

f x y = a x y + b x y . cos [ ψ x y ] + n x y .
ψ x y = ψ C x y + ψ S x y .
ψ S x y = n = 1 N p n arctan ( y y n x x n ) .
$ { f x y a x y } = F 1 { exp [ u v ] . F { b x y . cos [ ψ x y ] } } i exp [ x y ] . b x y . sin [ ψ x y ] .
exp [ i β x y ] . $ { f x y a x y } = ib x y . sin [ ψ x y ] .
exp [ i β x y ] . $ { f x y a x y } + f x y a x y = b x y . exp [ x y ] .
f x y a x y + b x y . cos [ ψ C x y + ψ S x y ] .

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