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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References

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  1. D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of fingerprint recognition (Springer, New York, 2003).
  2. N. Ratha and R. Bolle, eds., Automatic Fingerprint Recognition Systems (Springer, New York, 2003).
  3. 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).
  4. 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).
  5. 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.
  6. 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.
  7. C. M. Brislawn, "Fingerprints go digital," Not. Am. Math. Soc. 42, 1278-1283 (1995).
  8. 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]
  9. F. Galton, Finger Prints (Macmillan, London, 1892). http://galton.org/books/finger-prints/index.htm
  10. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A. 336, 165-190 (1974).
    [CrossRef]
  11. 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).
  12. 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]
  13. R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Satellite radar interferometry: two-dimensional phase unwrapping," Radio Science 23, 713-720 (1988).
    [CrossRef]
  14. J. M. Huntley, "Noise-immune phase unwrapping algorithm," Appl. Opt. 28, 3268-3270 (1989).
    [CrossRef] [PubMed]
  15. D. J. Bone, "Fourier fringe analysis: the two-dimensional phase unwrapping problem," Appl. Opt. 30, 3627-3632 (1991).
    [CrossRef] [PubMed]
  16. D. L. Fried and J. L. Vaughn, "Branch cuts in the phase function," Appl. Opt. 31, 2865-2882 (1992).
    [CrossRef] [PubMed]
  17. D. C. Ghiglia, and M. D. Pritt, Two-dimensional phase unwrapping (John Wiley and Sons, New York, 1998).
  18. R. Penrose, "The topology of ridge systems," Ann. Hum. Genet. 42, 435-444 (1979).
    [CrossRef]
  19. M. Kass and A. Witkin, "Analyzing oriented patterns," Computer vision, graphics, and image processing 37, 362-385 (1987).
    [CrossRef]
  20. C. F. Shu and R. C. Jain, "Direct Estimation and Error Analysis for Oriented Patterns," CVGIP-Image Understanding 58, 383-398 (1993).
    [CrossRef]
  21. 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]
  22. B. G. Sherlock and D. M. Monro, "A model for interpreting fingerprint topology," Pattern Recogn. 26, 1047-1055 (1993).
    [CrossRef]
  23. 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]
  24. A. Witkin and M. Kass, "Reaction-diffusion textures," Comput. Graphics 25, 299-308 (1991).
    [CrossRef]
  25. J. P. Crutchfield, ed., Is Anything Ever New? Considering Emergence, in Complexity: Metaphors, Models, and Reality, (Addison-Wesley, Redwood City, 1994). http://www.santafe.edu/research/publications/wpabstract/199403011
  26. 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
  27. D. Gabor, "Microscopy by reconstructed wave-fronts," Proc. R. Soc., London 197, 454-487 (1949).
    [CrossRef]
  28. J. G. Daugman and C. J. Downing, "Demodulation, predictive coding, and spatial vision," J. Opt. Soc. Am. A 12, 641-660 (1995).
    [CrossRef]
  29. 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, D. Mintie, ed., (1999). http://www.ct.gov/dss/cwp/view.asp?A=2349&Q=304724
  30. 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),
  31. 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]
  32. B. Jähne, Practical handbook on Image processing for Scientific applications (CRC Press, Boca Raton, Florida, 1997).
  33. K. G. Larkin, "Uniform estimation of orientation using local and nonlocal 2-D energy operators," Opt. Express 13, 8097 - 8121 (2005).
    [CrossRef] [PubMed]
  34. G. H. Granlund, and H. Knutsson, Signal processing for computer vision (Kluwer, Dordrecht, Netherlands, 1995).
  35. 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).
  36. K. G. Larkin, "Natural demodulation of 2D fringe patterns," in Fringe'01 - The Fourth International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, and W. Osten, eds., (Elsevier, Bremen, Germany, 2001). http://citeseer.ist.psu.edu/458598.html
  37. Y. Tong, S. Lombey, A. N. Hirani, and M. Desbrun, "Discrete multiscale vector field decomposition," ACM Transactions on Graphics 22, 445 - 452 (2003).
    [CrossRef]
  38. NIST Image Group's Fingerprint Research, "Fingerprint Test Data on CD-ROM," (NIST), http://www.itl.nist.gov/iad/894.03/fing/fing.html.
  39. S. Kasaei, M. Deriche, and B. Boashash, "A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization," IEEE Trans. Image Process. 11, 1365-1378 (2002).
    [CrossRef]
  40. P. A. Fletcher and K. G. Larkin, "Direct embedding and detection of RST invariant Watermarks," in IH2002, Fifth International Workshop on Information Hiding, F. A. P. Petitcolas, ed., (Springer Verlag, Noordwijkerhout, The Netherlands, 2002), pp. 129-144.
  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]

2005 (1)

2003 (1)

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 (1)

S. Kasaei, M. Deriche, and B. Boashash, "A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization," IEEE Trans. Image Process. 11, 1365-1378 (2002).
[CrossRef]

2001 (2)

1998 (1)

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]

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 (2)

1993 (2)

B. G. Sherlock and D. M. Monro, "A model for interpreting fingerprint topology," Pattern Recogn. 26, 1047-1055 (1993).
[CrossRef]

C. F. Shu and R. C. Jain, "Direct Estimation and Error Analysis for Oriented Patterns," CVGIP-Image Understanding 58, 383-398 (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]

1979 (1)

R. Penrose, "The topology of ridge systems," Ann. Hum. Genet. 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," Proc. R. Soc., London 197, 454-487 (1949).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A. 336, 165-190 (1974).
[CrossRef]

Boashash, B.

S. Kasaei, M. Deriche, and B. Boashash, "A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization," IEEE Trans. Image Process. 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]

Bone, D.

Bone, D. J.

Brislawn, C. M.

C. M. Brislawn, "Fingerprints go digital," Not. Am. Math. Soc. 42, 1278-1283 (1995).

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 Trans. Image Process. 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]

Fried, D. L.

Gabor, D.

D. Gabor, "Microscopy by reconstructed wave-fronts," Proc. R. Soc., London 197, 454-487 (1949).
[CrossRef]

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]

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.

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]

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 Trans. Image Process. 11, 1365-1378 (2002).
[CrossRef]

Kass, M.

A. Witkin and M. Kass, "Reaction-diffusion textures," Comput. Graphics 25, 299-308 (1991).
[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).

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.

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]

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]

Monro, D. M.

B. G. Sherlock and D. M. Monro, "A model for interpreting fingerprint topology," Pattern Recogn. 26, 1047-1055 (1993).
[CrossRef]

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.

Penrose, R.

R. Penrose, "The topology of ridge systems," Ann. Hum. Genet. 42, 435-444 (1979).
[CrossRef]

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]

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).

Tong, Y.

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

Turing, A. M.

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]

Vaughn, J. L.

Werner, C. L.

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

Witkin, A.

A. Witkin and M. Kass, "Reaction-diffusion textures," Comput. Graphics 25, 299-308 (1991).
[CrossRef]

Zebker, H. A.

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

ACM Transactions on Graphics (1)

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

Ann. Hum. Genet. (1)

R. Penrose, "The topology of ridge systems," Ann. Hum. Genet. 42, 435-444 (1979).
[CrossRef]

Appl. Opt. (3)

Bull. Math. Biol. (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]

Comput. Graphics (1)

A. Witkin and M. Kass, "Reaction-diffusion textures," Comput. Graphics 25, 299-308 (1991).
[CrossRef]

CVGIP-Image Understanding (1)

C. F. Shu and R. C. Jain, "Direct Estimation and Error Analysis for Oriented Patterns," CVGIP-Image Understanding 58, 383-398 (1993).
[CrossRef]

IEEE Trans PAMI (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]

IEEE Trans. Image Process. (1)

S. Kasaei, M. Deriche, and B. Boashash, "A novel fingerprint image compression technique using wavelets packets and pyramid lattice vector quantization," IEEE Trans. Image Process. 11, 1365-1378 (2002).
[CrossRef]

Image Analysis and Signal Processing: Adv. Math. Theory Appl. (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).

J. Opt. Soc. Am. A (3)

London (1)

D. Gabor, "Microscopy by reconstructed wave-fronts," Proc. R. Soc., London 197, 454-487 (1949).
[CrossRef]

Not. Am.Math. Soc. (1)

C. M. Brislawn, "Fingerprints go digital," Not. Am. Math. Soc. 42, 1278-1283 (1995).

Opt. Express (1)

Pattern Recogn. (1)

B. G. Sherlock and D. M. Monro, "A model for interpreting fingerprint topology," Pattern Recogn. 26, 1047-1055 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

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]

Proc. R. Soc. Lond. A. (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A. 336, 165-190 (1974).
[CrossRef]

Radio Science (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]

Other (20)

M. Kass and A. Witkin, "Analyzing oriented patterns," Computer vision, graphics, and image processing 37, 362-385 (1987).
[CrossRef]

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

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).

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

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

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

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).

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).

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.

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.

J. P. Crutchfield, ed., Is Anything Ever New? Considering Emergence, in Complexity: Metaphors, Models, and Reality, (Addison-Wesley, Redwood City, 1994). http://www.santafe.edu/research/publications/wpabstract/199403011

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

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

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

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

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, D. Mintie, ed., (1999). http://www.ct.gov/dss/cwp/view.asp?A=2349&Q=304724

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),

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

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

NIST Image Group's Fingerprint Research, "Fingerprint Test Data on CD-ROM," (NIST), http://www.itl.nist.gov/iad/894.03/fing/fing.html.

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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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