Abstract

The detection performance of a wavelet-based joint transform correlator (JTC) is studied by use of two types of images with different spatial-frequency contents and contrast. The simulation results show that, in comparison with an amplitude-modulated JTC, the performance for intraclass pattern recognition can be optimized by using a single wavelet filter.

© 2007 Optical Society of America

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References

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  1. S. Jutamulia, "Joint transform correlator," in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 984-989.
  2. D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 35, 260-264 (1991).
    [CrossRef]
  3. M. S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlation," Appl. Opt. 32, 4344-4350 (1993).
    [CrossRef] [PubMed]
  4. R. K. Wang, L. Shang, and C. R. Chatwin, "Modified fringe-adjusted joint transform correlation to accommodate noise in the input scene," Appl. Opt. 35, 286-296 (1996).
    [CrossRef] [PubMed]
  5. X. Huang, H. Lai, and Z. Gao, "Multiple-target detection with use of a modified amplitude-modulated joint transform correlator," Appl. Opt. 36, 9198-9204 (1997).
    [CrossRef]
  6. X. J. Lu, A. Katz, E. G. Kanterakis, and N. P. Caviris, "Joint transform correlator that uses wavelet transform," Opt. Lett. 17, 1700-1702 (1992).
    [CrossRef] [PubMed]
  7. P. Kaewkasi, J. Widjaja, and J. Uozumi, "Effects of threshold on single-target detection by using modified amplitude-modulated joint transform correlator," Opt. Commun. 271, 48-58 (2007).
    [CrossRef]
  8. J. Li, Y. Zhang, and J. Hu, "Object recognition with a wavelet-transform-based joint transform correlator," Opt. Eng. 35, 775-777 (1996).
    [CrossRef]
  9. R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 532-538 (1998).
    [CrossRef]
  10. J. Widjaja, "Automatic holographic particle sizing using wavelet-based joint transform correlator," Optik 107, 132-134 (1998).
  11. M. S. Alam and D. Chain, "Efficient multiple target recognition using a joint wavelet transform processor," Opt. Eng. 39, 1203-1210 (2000).
    [CrossRef]
  12. S. Mallat and W. L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inf. Theory 38, 617-643 (1992).
    [CrossRef]
  13. S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Patt. Anal. Machine Intell. 14, 710-732 (1992).
    [CrossRef]
  14. Y. Sheng, D. Roberge, H. Szu, and T. Lu, "Optical wavelet matched filters for shift-invariant pattern recognition," Opt. Lett. 18, 299-301 (1993).
    [CrossRef] [PubMed]
  15. J. M. Combes, A. Grossmann, and Ph. Tchamitchian, eds., Wavelets: Time-Frequency Methods and Phase Space, 1st ed. (Springer-Verlag, 1989).
  16. J. Widjaja, "Wavelet transform correlator," in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 2993-2999.
  17. D. Roberge and Y. Sheng, "Optical composite wavelet-matched filters," Opt. Eng. 33, 2290-2295 (1994).
    [CrossRef]
  18. D. Roberge and Y. Sheng, "Optical wavelet-matched filter," Appl. Opt. 33, 5287-5293 (1994).
    [CrossRef] [PubMed]

2007 (1)

P. Kaewkasi, J. Widjaja, and J. Uozumi, "Effects of threshold on single-target detection by using modified amplitude-modulated joint transform correlator," Opt. Commun. 271, 48-58 (2007).
[CrossRef]

2000 (1)

M. S. Alam and D. Chain, "Efficient multiple target recognition using a joint wavelet transform processor," Opt. Eng. 39, 1203-1210 (2000).
[CrossRef]

1998 (2)

R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 532-538 (1998).
[CrossRef]

J. Widjaja, "Automatic holographic particle sizing using wavelet-based joint transform correlator," Optik 107, 132-134 (1998).

1997 (1)

1996 (2)

J. Li, Y. Zhang, and J. Hu, "Object recognition with a wavelet-transform-based joint transform correlator," Opt. Eng. 35, 775-777 (1996).
[CrossRef]

R. K. Wang, L. Shang, and C. R. Chatwin, "Modified fringe-adjusted joint transform correlation to accommodate noise in the input scene," Appl. Opt. 35, 286-296 (1996).
[CrossRef] [PubMed]

1994 (2)

D. Roberge and Y. Sheng, "Optical composite wavelet-matched filters," Opt. Eng. 33, 2290-2295 (1994).
[CrossRef]

D. Roberge and Y. Sheng, "Optical wavelet-matched filter," Appl. Opt. 33, 5287-5293 (1994).
[CrossRef] [PubMed]

1993 (2)

1992 (3)

X. J. Lu, A. Katz, E. G. Kanterakis, and N. P. Caviris, "Joint transform correlator that uses wavelet transform," Opt. Lett. 17, 1700-1702 (1992).
[CrossRef] [PubMed]

S. Mallat and W. L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inf. Theory 38, 617-643 (1992).
[CrossRef]

S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Patt. Anal. Machine Intell. 14, 710-732 (1992).
[CrossRef]

1991 (1)

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 35, 260-264 (1991).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Inf. Theory (1)

S. Mallat and W. L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inf. Theory 38, 617-643 (1992).
[CrossRef]

IEEE Trans. Patt. Anal. Machine Intell. (1)

S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Patt. Anal. Machine Intell. 14, 710-732 (1992).
[CrossRef]

Opt. Commun. (2)

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 35, 260-264 (1991).
[CrossRef]

P. Kaewkasi, J. Widjaja, and J. Uozumi, "Effects of threshold on single-target detection by using modified amplitude-modulated joint transform correlator," Opt. Commun. 271, 48-58 (2007).
[CrossRef]

Opt. Eng. (4)

J. Li, Y. Zhang, and J. Hu, "Object recognition with a wavelet-transform-based joint transform correlator," Opt. Eng. 35, 775-777 (1996).
[CrossRef]

R. Tripathi and K. Singh, "Pattern discrimination using a bank of wavelet filters in a joint transform correlator," Opt. Eng. 37, 532-538 (1998).
[CrossRef]

D. Roberge and Y. Sheng, "Optical composite wavelet-matched filters," Opt. Eng. 33, 2290-2295 (1994).
[CrossRef]

M. S. Alam and D. Chain, "Efficient multiple target recognition using a joint wavelet transform processor," Opt. Eng. 39, 1203-1210 (2000).
[CrossRef]

Opt. Lett. (2)

Optik (1)

J. Widjaja, "Automatic holographic particle sizing using wavelet-based joint transform correlator," Optik 107, 132-134 (1998).

Other (3)

J. M. Combes, A. Grossmann, and Ph. Tchamitchian, eds., Wavelets: Time-Frequency Methods and Phase Space, 1st ed. (Springer-Verlag, 1989).

J. Widjaja, "Wavelet transform correlator," in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 2993-2999.

S. Jutamulia, "Joint transform correlator," in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 984-989.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of an optical setup for performing wavelet-based JTC.

Fig. 2
Fig. 2

3D autocorrelation outputs of noise-free high-contrast fingerprint detection preprocessed by the wavelet filter dilated at (a) a = 0.5 and (b) a = 4 . Cross-correlation outputs of noisy high-contrast fingerprint target preprocessed by the wavelet filter dilated at (c) a = 0.5 and (d) a = 4 .

Fig. 3
Fig. 3

Normalized PCDs of the fingerprint detections as a function of the dilation factor.

Fig. 4
Fig. 4

3D autocorrelation outputs of noise-free high-contrast human face detection preprocessed by the wavelet filter dilated at (a) a = 0.5 and (b) a = 4 . Cross-correlation outputs of noisy high-contrast human face target preprocessed by the wavelet filter dilated at (c) a = 0.5 and (d) a = 4 .

Fig. 5
Fig. 5

Normalized PCDs of the human face detections as a function of the dilation factor.

Equations (9)

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W f ( a x , a y , b x , b y ) = 1 a x a y + f ( x , y ) h * × ( x b x a x , y b y a y ) d x d y ,
C ( a x , a y , x , y ) = + W t ( a x , a y , b x , b y ) × W r * ( a x , a y , b x x , b y y ) d b x d b y ,
C ( a x , a y , x , y ) = + T ( u , v ) R * ( u , v ) | H ( a x u , a y v ) | 2 × exp [ i 2 π ( x u + y v ) ] d u d v ,
f ( x , y ) = r ( x x 0 , y ) + c T t ( x + x 0 , y ) + n ( x + x 0 , y ) ,
| F ( u , v ) | 2 = | R ( u , v ) | 2 + c T 2 | T ( u , v ) | 2 + | N ( u , v ) | 2 + c T T * ( u , v ) N ( u , v ) + c T T ( u , v ) N * ( u , v ) + c T [ R ( u , v ) T * ( u , v ) exp ( j 4 u x 0 ) + T ( u , v ) R * ( u , v ) exp ( j 4 u x 0 ) ] + R ( u , v ) N * ( u , v ) exp ( j 4 u x 0 ) + N ( u , v ) R * ( u , v ) exp ( j 4 u x 0 ) ,
O ( u , v ) = | H ( a x u , a y v ) | 2 | F ( u , v ) | 2 = | H ( a x u , a y v ) | 2 { | R ( u , v ) | 2 + c T 2 | T ( u , v ) | 2 + | N ( u , v ) | 2 + c T T * ( u , v ) N ( u , v ) + c T T ( u , v ) N * ( u , v ) + c T [ R ( u , v ) T * ( u , v ) exp ( j 4 u x 0 ) + T ( u , v ) R * ( u , v ) exp ( j 4 u x 0 ) ] + R ( u , v ) N * ( u , v ) exp ( j 4 u x 0 ) + N ( u , v ) R * ( u , v ) exp ( j 4 u x 0 ) } .
C ( x , y ) = c T { W r ( a x , a y , x , y ) W t ( a x , a y , x , y ) δ ( x ± 2 x 0 ) } + W r ( a x , a y , x , y ) W n ( a x , a y , x , y ) δ ( x ± 2 x 0 ) ,
h ( x , y ) = 1 σ 2 ( x 2 + y 2 σ 2 2 ) exp ( x 2 + y 2 2 σ 2 ) .
P C D = I ( i , j ) max { 1 M × N i = 0 M 1 j = 0 N 1 [ I ( i , j ) E { I ( i , j ) } ] 2 } 1 / 2 .

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