Abstract

A joint transform correlation system based on wavelet transforms is introduced. The selection of wavelets and the optical wavelet transform of images enables this optical correlator to identify the specific features and distinguish similar characters. Preliminary experimental results are given.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  2. J. E. Rao, J. Opt. Soc. Am. 56, 1490 (1966).
    [CrossRef]
  3. F. T. S. Yu, X. J. Lu, Appl. Opt. 23, 3109 (1984).
    [CrossRef] [PubMed]
  4. F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
    [CrossRef]
  5. A. Grossmann, J. Morlet, SIAM J. Appl. Math. 15, 723 (1984).
    [CrossRef]
  6. I. Daubechies, Commun. Pure Appl. Math. 41, 909 (1988).
    [CrossRef]
  7. S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 37, 2091 (1989).
    [CrossRef]
  8. Y. Zhang, Y. Li, E. G. Kanterakis, A. Katz, X. J. Lu, R. Tolimieri, N. P. Caviris, Opt. Lett. 17, 210 (1992).
    [CrossRef] [PubMed]

1992

1989

S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 37, 2091 (1989).
[CrossRef]

1988

I. Daubechies, Commun. Pure Appl. Math. 41, 909 (1988).
[CrossRef]

1984

F. T. S. Yu, X. J. Lu, Appl. Opt. 23, 3109 (1984).
[CrossRef] [PubMed]

F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
[CrossRef]

A. Grossmann, J. Morlet, SIAM J. Appl. Math. 15, 723 (1984).
[CrossRef]

1966

1964

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Caviris, N. P.

Daubechies, I.

I. Daubechies, Commun. Pure Appl. Math. 41, 909 (1988).
[CrossRef]

Grossmann, A.

A. Grossmann, J. Morlet, SIAM J. Appl. Math. 15, 723 (1984).
[CrossRef]

Kanterakis, E. G.

Katz, A.

Li, Y.

Lu, X. J.

Mallat, S. G.

S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 37, 2091 (1989).
[CrossRef]

Morlet, J.

A. Grossmann, J. Morlet, SIAM J. Appl. Math. 15, 723 (1984).
[CrossRef]

Rao, J. E.

Tolimieri, R.

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Yu, F. T. S.

Zhang, Y.

Appl. Opt.

Commun. Pure Appl. Math.

I. Daubechies, Commun. Pure Appl. Math. 41, 909 (1988).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

S. G. Mallat, IEEE Trans. Acoust. Speech Signal Process. 37, 2091 (1989).
[CrossRef]

IEEE Trans. Inf. Theory

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
[CrossRef]

Opt. Lett.

SIAM J. Appl. Math.

A. Grossmann, J. Morlet, SIAM J. Appl. Math. 15, 723 (1984).
[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 (3)

Fig. 1
Fig. 1

Real-time joint transform correlator based on wavelet transform. LCTV, the input device; LCLV, the Fourier plane converter; M, mirror; L1, L2, transform lenses; L3, L4, imaging lenses; F, bandpass (Bp) filters; Rj, correlation of hj and gj.

Fig. 2
Fig. 2

Correlation functions of the letters D and D or D and O. (a) The inputs D, D and D, O. (b) Autocorrelations of D and D (left column) and cross correlation of D and O (right column) at frequency band (0, 0.8 lp/mm); the first row shows the whole output intensity distribution, and the second row is the particular correlation. (c) The correlations at frequency band (0.8, 2.4 lp/mm), (d) The correlations at frequency band (2.4, 7.2 lp/mm).

Fig. 3
Fig. 3

Autocorrelation functions of D and D (left column) and cross correlation of D and O (right column) obtained by scanning the joint transform spectrum with a small aperture (1 mm in diameter). (a) Correlations when the small aperture is centered at (1, 0 mm). (b) Correlations with the small aperture at (2, 0 mm). (c) Correlations when the aperture is at (0, −1 mm).

Equations (11)

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

W ( s , ξ ) = + f ( x ) s ψ [ s ( x ξ ) ] d x , f ( x ) = 1 C Ψ + + W ( s , ξ ) s ψ [ s ( x ξ ) ] d ξ d s ,
W ( 2 j , ξ ) = + F ( u ) Ψ 0 ( u 2 j ) exp ( i 2 π u ξ ) d u ,
f j ( x ) = + W ^ ( 2 j , u ) Ψ 0 ( u 2 j ) exp ( i 2 π u x ) d u ,
f ( x ) = 1 C Ψ j = + f j ( x ) ,
f j ( x ) = + F ( u ) Ψ 0 ( u 2 j ) Ψ 0 ( u 2 j ) exp ( i 2 π u x ) d u .
B 0 ( u ) = j = 0 Ψ 0 ( u 2 j ) Ψ 0 ( u 2 j ) .
B j ( u ) = Ψ 0 ( u 2 j ) Ψ 0 ( u 2 j ) , j = 1 , 2 , , N .
j = 0 Ψ 0 ( u 2 j ) Ψ 0 ( u 2 j ) = 1 .
U j ( u ) = k 0 + k B j ( | H | 2 + | G | 2 ) + k B j H G * exp ( i 4 π u a ) + k B j H * G exp ( i 4 π u a ) ,
R j ( x 2 a ) = b j * h * g * * δ ( x 2 a ) , R j ( x + 2 a ) = b j * h * * g * δ ( x + 2 a ) ,
b j = F 1 { B j } = ψ j * ψ j * .

Metrics