Abstract

We present a new method for selecting the optimal spatial light modulator operating curve on which to encode an ideal complex-valued filter function. The method is an extension of the optimization procedure that was used to derive the ideal complex-valued filter. To illustrate the method we consider the selection of a typical operating curve of a commercially available LCD and use this operating curve to encode a filter that was optimized for the task of fingerprint verification. We then extend the method to include the selection of the optimal operating curve from a series of synthetic operating curves.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Roberge, C. Soutar, B. V. K. Vijaya Kumar, “Optimal correlation filter for fingerprint verification,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 15 (1998).
  2. Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak, and Horner efficiency,” Opt. Lett. 16, 829–831 (1991).
    [CrossRef] [PubMed]
  3. C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
    [CrossRef]
  4. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
    [CrossRef] [PubMed]
  5. A. Stoianov, C. Soutar, A. Graham, “High-speed fingerprint verification using an optical correlator,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 29 (1998).
  6. C. Soutar, R. D. Juday, “Method and apparatus for improved spatial light modulation,” U.S. patent applied for.
  7. I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.
  8. A. Skorucak, C. Soutar, “Selection criteria for spatial light modulator operating curves,” in Optical Pattern Recognition VII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2752, 120–131 (1996).
    [CrossRef]
  9. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  10. R. D. Juday, R. S. Barton, J. Kinser, J. L. Alvarez, “Efficient code for optimal realizable filter calculation,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 262–268 (1993).
    [CrossRef]

1994 (1)

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

1993 (1)

1991 (1)

1987 (1)

Alvarez, J. L.

R. D. Juday, R. S. Barton, J. Kinser, J. L. Alvarez, “Efficient code for optimal realizable filter calculation,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 262–268 (1993).
[CrossRef]

Barton, R. S.

R. D. Juday, R. S. Barton, J. Kinser, J. L. Alvarez, “Efficient code for optimal realizable filter calculation,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 262–268 (1993).
[CrossRef]

Casasent, D.

Graham, A.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

A. Stoianov, C. Soutar, A. Graham, “High-speed fingerprint verification using an optical correlator,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 29 (1998).

Isbrucker, V.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

Juday, R. D.

R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
[CrossRef] [PubMed]

R. D. Juday, R. S. Barton, J. Kinser, J. L. Alvarez, “Efficient code for optimal realizable filter calculation,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 262–268 (1993).
[CrossRef]

C. Soutar, R. D. Juday, “Method and apparatus for improved spatial light modulation,” U.S. patent applied for.

Kinser, J.

R. D. Juday, R. S. Barton, J. Kinser, J. L. Alvarez, “Efficient code for optimal realizable filter calculation,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 262–268 (1993).
[CrossRef]

Knopp, J.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Konvalinka, I.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

Lazic, V.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

Mahalanobis, A.

Milkie, T.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

Monroe, S. E.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Pemberton, N.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

Réfrégier, Ph.

Roberge, D.

D. Roberge, C. Soutar, B. V. K. Vijaya Kumar, “Optimal correlation filter for fingerprint verification,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 15 (1998).

Skorucak, A.

A. Skorucak, C. Soutar, “Selection criteria for spatial light modulator operating curves,” in Optical Pattern Recognition VII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2752, 120–131 (1996).
[CrossRef]

Soutar, C.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

D. Roberge, C. Soutar, B. V. K. Vijaya Kumar, “Optimal correlation filter for fingerprint verification,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 15 (1998).

A. Stoianov, C. Soutar, A. Graham, “High-speed fingerprint verification using an optical correlator,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 29 (1998).

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

C. Soutar, R. D. Juday, “Method and apparatus for improved spatial light modulation,” U.S. patent applied for.

A. Skorucak, C. Soutar, “Selection criteria for spatial light modulator operating curves,” in Optical Pattern Recognition VII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2752, 120–131 (1996).
[CrossRef]

Stoianov, A.

A. Stoianov, C. Soutar, A. Graham, “High-speed fingerprint verification using an optical correlator,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 29 (1998).

Vijaya Kumar, B. V. K.

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
[CrossRef] [PubMed]

D. Roberge, C. Soutar, B. V. K. Vijaya Kumar, “Optimal correlation filter for fingerprint verification,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 15 (1998).

Appl. Opt. (2)

Opt. Eng. (1)

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Opt. Lett. (1)

Other (6)

D. Roberge, C. Soutar, B. V. K. Vijaya Kumar, “Optimal correlation filter for fingerprint verification,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 15 (1998).

A. Stoianov, C. Soutar, A. Graham, “High-speed fingerprint verification using an optical correlator,” in Optical Pattern Recognition IX, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3386, paper 29 (1998).

C. Soutar, R. D. Juday, “Method and apparatus for improved spatial light modulation,” U.S. patent applied for.

I. Konvalinka, T. Milkie, V. Lazic, A. Graham, C. Soutar, V. Isbrucker, N. Pemberton, “Touchstone—a DSP based biometric system,” paper presented at the International Conference on Signal Processing Applications and Technology (ICSPAT) ’98, Toronto, Canada, 13–16 September 1998.

A. Skorucak, C. Soutar, “Selection criteria for spatial light modulator operating curves,” in Optical Pattern Recognition VII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2752, 120–131 (1996).
[CrossRef]

R. D. Juday, R. S. Barton, J. Kinser, J. L. Alvarez, “Efficient code for optimal realizable filter calculation,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 262–268 (1993).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Probability of false rejection (Fr) and false acceptance (Fa) as a function of the ratio threshold L. Note that both axes are plotted with a logarithmic scale.

Fig. 2
Fig. 2

Diagram of the eight points that are used from the highly coupled operating curve. Imag., imaginary.

Fig. 3
Fig. 3

Plot of CP against E total + for the highly coupled curve, for different values of g. Open circle, system performance for the ideal complex-valued filter; filled circles, system performance for the value of g specified by the adjacent label.

Fig. 4
Fig. 4

Pictorial representation of the magnitude values for an ideal filter. The zero gray-scale level represents the minimum value of magnitude (0.0), and the 255 gray-scale level represents the maximum value of magnitude (1.0).

Fig. 5
Fig. 5

Histogram of the number of points at each complex value for an ideal complex-valued filter.

Fig. 6
Fig. 6

Mapping of the available nodes in the complex plane for constructing the synthetic operating curve.

Fig. 7
Fig. 7

Plot of the array of rank-ordered E total + for the set of synthetic operating curves. Solid curve, plot of all values for the 33,000 permutations of operating curves; circles, operating curves that represent equally spaced values of E total + .

Fig. 8
Fig. 8

Plot of the operating curves that represent the points in Fig. 7 labeled (top) a, (middle) b, and (bottom) c.

Fig. 9
Fig. 9

A plot of CP against E total + for the synthetic operating curves. Open circle, system performance for the ideal complex-valued filter; filled circles, system performance for the nine operating curves that correspond to the equally spaced values of E total + .

Fig. 10
Fig. 10

Probability of Fr and Fa as a function of the threshold L. Points 1, 2, and 3 represent the CP values obtained with the highly coupled curve, the optimal synthetic operating curve, and full-complex modulation, respectively.

Equations (16)

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

If   f t x = f s x + input t , s x , then   c t x = c s x + output t , s x     for   s ,   t 1 , ,   T , t s .
E noise =   | H u | 2 P u d u ,
P u = 2 T T - 1 t = 1 T - 1 s = t + 1 T   | Fourier   transform of   input t , s x | 2 ,
E similarity = 1 T t = 1 T     | c t x - δ x | 2 d x .
E similarity = 1 T t = 1 T     | C t u - 1 | 2 d u .
E total = α E noise + β E similarity .
E total = α     | H u | 2 P u d u + β   1 T t = 1 T     | C t u - 1 | 2 d u ,
C t u F t u H u .
β   1 T t = 1 T F * t u H * u - 1 F t u + α H * u P u = 0 .
H u = β   1 T t = 1 T   F * t u α P u + β   1 T t = 1 T   | F t u | 2 .
A u = 1 T t = 1 T   F t u ,
D u = 1 T t = 1 T   | F t u | 2 .
H u = β A * u α P u + β D u .
H u = H u max | H u | .
E total = γ 2 α     | H u | 2 d u + 1 - α 2 1 / 2   D u d u 1 T t = 1 T     F t u H u - 1 γ 2 d u ,
  E total + = γ 2 α     | H + u | 2 d u + 1 - α 2 1 / 2   D u d u 1 T t = 1 T     F t u H + u - 1 γ 2 d u .

Metrics