Abstract

An adaptive phase-input joint transform correlator for pattern recognition is presented. The input of the system is two phase-only images: input scene and reference. The reference image is generated with a new iterative algorithm using phase-only synthetic discriminant functions. The algorithm takes into account calibration lookup tables of all optoelectronics elements used in optodigital experiments. The designed adaptive phase-input joint transform correlator is able to reliably detect a target and its distorted versions embedded into a cluttered background. Computer simulations are provided and compared with those of various existing joint transform correlators in terms of discrimination capability, tolerance to input additive noise, and to small geometric image distortions. Experimental optodigital results are also provided and discussed.

© 2007 Optical Society of America

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  1. C. S. Weaver and J. L. Goodman, "Technique for optically convolving two functions," Appl. Opt. 5, 1248-1249 (1966).
    [CrossRef] [PubMed]
  2. J. Nicolas, J. Campos, C. Iemmi, I. Moreno, and M. J. Yzuel, "Convergent optical correlator alignment based on frequency filtering," Appl. Opt. 41, 1505-1514 (2002).
    [CrossRef] [PubMed]
  3. A. Vanderlugt, "Signal detection by complex filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
  4. B. V. K. Vijaya Kumar and L. Hassebrook, "Performance measures for correlation filters," Appl. Opt. 29, 2997-3006 (1990).
    [CrossRef]
  5. B. Javidi, "Nonlinear joint power spectrum based optical correlator," Appl. Opt. 28, 2358-2366 (1989).
    [CrossRef] [PubMed]
  6. B. Javidi and J. Wang, "Binary nonlinear joint transform correlator with median and subset median thresholding," Appl. Opt. 30, 967-976 (1991).
    [CrossRef] [PubMed]
  7. M. S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlator," Appl. Opt. 32, 4344-4350 (1993).
    [CrossRef] [PubMed]
  8. G. Lu, Z. Zhang, and F. T. S. Yu, "Phase-encoded input joint transform correlator with improved pattern discriminability," Opt. Lett. 20, 1307-1309 (1995).
    [CrossRef] [PubMed]
  9. F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
    [CrossRef]
  10. L. Bigue and P. Ambs, "Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator," Appl. Opt. 38, 4296-4305 (1999).
    [CrossRef]
  11. C. F. Hester and D. Casasent, "Multivariant technique for multiclass pattern recognition," Appl. Opt. 19, 1758-1761 (1980).
    [CrossRef] [PubMed]
  12. D. Casasent, "Unified synthetic discriminant function computational formulation," Appl. Opt. 23, 1620-1627 (1984).
    [CrossRef] [PubMed]
  13. J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 0570051-05700510 (2006).
  14. V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, "Pattern recognition with an adaptive joint transform correlator," Appl. Opt. 45, 5929-5941 (2006).
    [CrossRef] [PubMed]
  15. K. Lu and B. E. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
    [CrossRef]
  16. C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
    [CrossRef]
  17. D. A. Jared and D. J. Ennis, "Inclusion of filter modulation in synthetic-discriminant-function construction," Appl. Opt. 28, 232-239 (1989).
    [CrossRef] [PubMed]
  18. M. Montes-Usategui, I. Juvells, and J. Campos, "Computation of arbitrary constrained synthetic discriminant functions," Appl. Opt. 34, 3904-3914 (1995).
    [CrossRef] [PubMed]
  19. L. P. Yaroslavsky, "The theory of optimal methods for localization of objects in pictures," in Progress in Optics, E. Wolf, ed. (Elsevier, 1993), Vol. XXXII, pp. 145-201.
    [CrossRef]
  20. D. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," J. Soc. Ind. Appl. Math. 11, 431-441 (1963).
    [CrossRef]
  21. D. Knuth, The Art of Computer Programming (Addison-Wesley, 1997), Vol. 3.
  22. A. Mahalanobis, B. V. K. Vijaya Kumar, and D. Casasent, "Minimum average correlation energy filters," Appl. Opt. 26, 3633-3640 (1987).
    [CrossRef] [PubMed]
  23. Z. Bahri and B. V. K. Vijaya Kumar, "Generalized synthetic discriminant functions," J. Opt. Soc. Am. A 5, 562-571 (1988).
    [CrossRef]
  24. R. D. Juday, "Optimal realizable filters and the minimum Euclidean distance principle," Appl. Opt. 32, 5100-5111 (1993).
    [CrossRef] [PubMed]

2006 (2)

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 0570051-05700510 (2006).

V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, "Pattern recognition with an adaptive joint transform correlator," Appl. Opt. 45, 5929-5941 (2006).
[CrossRef] [PubMed]

2002 (1)

1999 (1)

1997 (1)

D. Knuth, The Art of Computer Programming (Addison-Wesley, 1997), Vol. 3.

1995 (3)

1994 (1)

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

1993 (3)

1991 (1)

1990 (2)

B. V. K. Vijaya Kumar and L. Hassebrook, "Performance measures for correlation filters," Appl. Opt. 29, 2997-3006 (1990).
[CrossRef]

K. Lu and B. E. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

1989 (2)

1988 (1)

1987 (1)

1984 (1)

1980 (1)

1966 (1)

1964 (1)

A. Vanderlugt, "Signal detection by complex filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).

1963 (1)

D. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," J. Soc. Ind. Appl. Math. 11, 431-441 (1963).
[CrossRef]

Alam, M. S.

Alvarez-Borrego, J.

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 0570051-05700510 (2006).

V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, "Pattern recognition with an adaptive joint transform correlator," Appl. Opt. 45, 5929-5941 (2006).
[CrossRef] [PubMed]

Ambs, P.

Bahri, Z.

Bigue, L.

Campos, J.

Casasent, D.

Diaz-Ramirez, V. H.

Ennis, D. J.

Gonzalez-Fraga, J. A.

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 0570051-05700510 (2006).

Goodman, J. L.

Hassebrook, L.

Hester, C. F.

Hudson, T. D.

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

Iemmi, C.

Jared, D. A.

Javidi, B.

Juday, R. D.

Juvells, I.

Karim, M. A.

Knuth, D.

D. Knuth, The Art of Computer Programming (Addison-Wesley, 1997), Vol. 3.

Kober, V.

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 0570051-05700510 (2006).

V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, "Pattern recognition with an adaptive joint transform correlator," Appl. Opt. 45, 5929-5941 (2006).
[CrossRef] [PubMed]

Lu, G.

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

G. Lu, Z. Zhang, and F. T. S. Yu, "Phase-encoded input joint transform correlator with improved pattern discriminability," Opt. Lett. 20, 1307-1309 (1995).
[CrossRef] [PubMed]

Lu, K.

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

K. Lu and B. E. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Lu, M.

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

Mahalanobis, A.

Marquardt, D.

D. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," J. Soc. Ind. Appl. Math. 11, 431-441 (1963).
[CrossRef]

McMillen, D. K.

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

Montes-Usategui, M.

Moreno, I.

Nicolas, J.

Saleh, B. E.

K. Lu and B. E. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Soutar, C.

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

Vanderlugt, A.

A. Vanderlugt, "Signal detection by complex filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).

Vijaya Kumar, B. V. K.

Wang, J.

Weaver, C. S.

Yaroslavsky, L. P.

L. P. Yaroslavsky, "The theory of optimal methods for localization of objects in pictures," in Progress in Optics, E. Wolf, ed. (Elsevier, 1993), Vol. XXXII, pp. 145-201.
[CrossRef]

Yin, S.

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

Yu, F. T. S.

G. Lu, Z. Zhang, and F. T. S. Yu, "Phase-encoded input joint transform correlator with improved pattern discriminability," Opt. Lett. 20, 1307-1309 (1995).
[CrossRef] [PubMed]

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

Yzuel, M. J.

Zhang, Z.

Appl. Opt. (14)

B. V. K. Vijaya Kumar and L. Hassebrook, "Performance measures for correlation filters," Appl. Opt. 29, 2997-3006 (1990).
[CrossRef]

B. Javidi, "Nonlinear joint power spectrum based optical correlator," Appl. Opt. 28, 2358-2366 (1989).
[CrossRef] [PubMed]

B. Javidi and J. Wang, "Binary nonlinear joint transform correlator with median and subset median thresholding," Appl. Opt. 30, 967-976 (1991).
[CrossRef] [PubMed]

M. S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlator," Appl. Opt. 32, 4344-4350 (1993).
[CrossRef] [PubMed]

L. Bigue and P. Ambs, "Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator," Appl. Opt. 38, 4296-4305 (1999).
[CrossRef]

C. F. Hester and D. Casasent, "Multivariant technique for multiclass pattern recognition," Appl. Opt. 19, 1758-1761 (1980).
[CrossRef] [PubMed]

D. Casasent, "Unified synthetic discriminant function computational formulation," Appl. Opt. 23, 1620-1627 (1984).
[CrossRef] [PubMed]

C. S. Weaver and J. L. Goodman, "Technique for optically convolving two functions," Appl. Opt. 5, 1248-1249 (1966).
[CrossRef] [PubMed]

J. Nicolas, J. Campos, C. Iemmi, I. Moreno, and M. J. Yzuel, "Convergent optical correlator alignment based on frequency filtering," Appl. Opt. 41, 1505-1514 (2002).
[CrossRef] [PubMed]

V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, "Pattern recognition with an adaptive joint transform correlator," Appl. Opt. 45, 5929-5941 (2006).
[CrossRef] [PubMed]

D. A. Jared and D. J. Ennis, "Inclusion of filter modulation in synthetic-discriminant-function construction," Appl. Opt. 28, 232-239 (1989).
[CrossRef] [PubMed]

M. Montes-Usategui, I. Juvells, and J. Campos, "Computation of arbitrary constrained synthetic discriminant functions," Appl. Opt. 34, 3904-3914 (1995).
[CrossRef] [PubMed]

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

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

IEEE Trans. Inf. Theory (1)

A. Vanderlugt, "Signal detection by complex filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).

J. Opt. Soc. Am. A (1)

J. Soc. Ind. Appl. Math. (1)

D. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," J. Soc. Ind. Appl. Math. 11, 431-441 (1963).
[CrossRef]

Opt. Eng. (4)

K. Lu and B. E. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, "Adaptive synthetic discriminant function filters for pattern recognition," Opt. Eng. 45, 0570051-05700510 (2006).

F. T. S. Yu, M. Lu, G. Lu, S. Yin, T. D. Hudson, and D. K. McMillen, "Optimum target detection using a spatial-domain bipolar composite filter with a joint transform correlator," Opt. Eng. 34, 3200-3207 (1995).
[CrossRef]

Opt. Lett. (1)

Other (2)

D. Knuth, The Art of Computer Programming (Addison-Wesley, 1997), Vol. 3.

L. P. Yaroslavsky, "The theory of optimal methods for localization of objects in pictures," in Progress in Optics, E. Wolf, ed. (Elsevier, 1993), Vol. XXXII, pp. 145-201.
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Block diagram of the classical joint transform correlator.

Fig. 2
Fig. 2

Block diagram of the phase-input JTC.

Fig. 3
Fig. 3

Block diagram of the proposed binary search algorithm.

Fig. 4
Fig. 4

Block diagram of the adaptive phase-input JTC design procedure.

Fig. 5
Fig. 5

Optical setup for implementation of the adaptive phase-input JTC.

Fig. 6
Fig. 6

(a) Phase response of LCD1, (b) intensity response of LCD2.

Fig. 7
Fig. 7

Test images: (a) target, (b) nondesired object, (c) real background.

Fig. 8
Fig. 8

(a) Input scene, (b) adaptive reference image.

Fig. 9
Fig. 9

Computer simulation intensity correlation planes obtained for the scene in Fig. 8(a) with (a) CJTC, (b) BJTC, (c) FAJTC, (d) PIJTC, (e) MACEmap, and (f) SDFproj.

Fig. 10
Fig. 10

Computer simulation intensity correlation plane obtained for the scene in Fig. 8(a) with (a) AJTC and (b) APIJTC.

Fig. 11
Fig. 11

Input scene corrupted by additive white noise with the standard deviation of σ n = 0.31.

Fig. 12
Fig. 12

Adaptive reference image invariant to (a) rotation distortions and (b) scale distortions.

Fig. 13
Fig. 13

Tolerance of the APIJTC to geometric distortions. (a) DC versus rotation degree, (b) DC versus scale factor.

Fig. 14
Fig. 14

Joint input image used for real experiment.

Fig. 15
Fig. 15

Optical intensity correlation plane obtained with the APIJTC.

Tables (2)

Tables Icon

Table 1 Performance of JTCs: 95% Confidence DC

Tables Icon

Table 2 Noise Tolerance: 95% Confidence DC of Tested JTCs for Additive White Gaussian Noise

Equations (35)

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f ( x , y ) = s ˜ ( x + δ x , y ) + r ( x δ x , y ) .
w ( x x 0 , y y 0 ) = { 0 , within   the   object   area 1 , otherwise .
J P S ( μ , v ) = | S ( μ , v ) | 2 + | B ˜ ( μ , v ) | 2 + | R ( μ , v ) | 2 + S ( μ , v ) B ˜ * ( μ , v ) + B ˜ ( μ , v ) S * ( μ , v ) + [ S ( μ , v ) R * ( μ , v ) + B ˜ ( μ , v ) R * ( μ , v ) ] × exp ( i 2 δ x μ ) + [ R ( μ , v ) S * ( μ , v ) + R ( μ , v ) B ˜ * ( μ , v ) ] exp ( i 2 δ x μ ) ,
c ( x , y ) = c s s ( x , y ) + c b ˜ b ˜ ( x , y ) + c r r ( x , y ) + c s b ˜ ( x , y ) + c b ˜ s ( x , y ) + c s r ( x + 2 δ x , y ) + c b ˜ r ( x + 2 δ x , y ) + c r s ( x 2 δ x , y ) + c r b ˜ ( x 2 δ x , y ) .
D C = 1 | C B ( 0 , 0 ) | 2 | C T ( 0 , 0 ) | 2 ,
ϕ z = E X P [ i π z ( x , y ) G min G max G min ] ,
ϕ f ( x , y ) = E X P [ i π s ˜ ( x + δ x , y ) ] + E X P [ i π r ( x δ x , y ) ] ,
c ( τ x , τ y ) = | w r E X P { i π [ s ( x , y ) + b ˜ ( x , y ) r ( x + τ x , y + τ y ) ] } d x d y | 2 ,
c t a r ( x 0 , y 0 ) = | w r d x d y | 2 = | E | 2 ,
c b g ( τ b x , τ b y ) = | w r E X P { i π [ b ˜ ( x , y ) r ( x + τ b x , y + τ b y ) ] } d x d y | 2 .
c i = h ( x , y ) s i ( x , y ) ,
a = ( S + S ) 1 c ,
h = S ( S + S ) 1 c .
c = [ 1 1   …   1 0 0   …   0 ] T .
h p o = E X P { i π S a } .
c = R + h p o ,
R = [ exp ( i π s 11 ) exp ( i π s 12 ) exp ( i π s 1 K ) exp ( i π s 21 ) exp ( i π s 22 ) exp ( i π s 2 K ) exp ( i π s d 1 ) exp ( i π s d 2 ) exp ( i π s d K ) ] .
a = { a i | i = 1 ,  …  ,   K } .
c = [ λ t exp ( i π α 1 ) ,  …  , λ t exp ( i π α N ) , λ f exp ( i π α N + 1 ) ,  … ,  λ f exp ( i π α N + M ) ] T ,
λ t cos ( π α 1 ) = i = 1 d cos [ π ( j = 1 K a j s i j ) s i 1 ] ,
λ t cos ( π α N ) = i = 1 d cos [ π ( j = 1 K a j s i j ) s i N ] ,
λ f cos ( π α ( N + 1 ) ) = i = 1 d cos [ π ( j = 1 K a j s i j ) s i ( N + 1 ) ] ,
λ f cos ( π α ( N + M ) ) = i = 1 d cos [ π ( j = 1 K a j s i j ) s i ( N + M ) ] ,
λ t sin ( π α 1 ) = i = 1 d sin [ π ( j = 1 K a j s i j ) s i 1 ] ,
λ t sin ( π α N ) = i = 1 d sin [ π ( j = 1 K a j s i j ) s i N ] ,
λ f sin ( π α ( N + 1 ) ) = i = 1 d sin [ π ( j = 1 K a j s i j ) s i ( N + 1 ) ] ,
λ f sin ( π α ( N + M ) ) = i = 1 d sin [ π ( j = 1 K a j s i j ) s i ( N + M ) ] .
c r e = R r e + C O S { π S a } + R i m + S I N { π S a } ,
c i m = R i m + C O S { π S a } R r e + S I N { π S a } ,
C P R = | λ f | 2 | λ t | 2 .
h g k = x + [ I d S ( S + S ) 1 S + ] z k 1 ,

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