Abstract

A new joint wavelet transform correlation-based technique is proposed for feature extraction such as the detection of edges in an unknown input scene. We exploited a modified version of the Roberts and the Sobel wavelet filters as reference images for extracting the edges of an unknown input scene. The performance of the proposed technique with the aforementioned wavelet filters is evaluated and compared by use of numerical simulations. For noise-free input scenes the Roberts wavelet filter was found to yield a superior output compared with that of the Sobel wavelet filter. However, for noisy input scenes the Sobel wavelet filter was found to yield a better output compared with the Roberts wavelet filter.

© 1998 Optical Society of America

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References

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    [CrossRef]
  4. M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
    [CrossRef] [PubMed]
  5. M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
    [CrossRef]
  6. X. J. Lu, A. Katz, E. G. Kanterakis, N. P. Caviris, “Joint transform correlator that uses wavelet transforms,” Opt. Lett. 17, 1700–1702 (1992).
    [CrossRef] [PubMed]
  7. W. Wang, G. Jin, Y. Yan, M. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. 34, 370–376 (1995).
    [CrossRef] [PubMed]
  8. F. Ahmed, M. A. Karim, M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
    [CrossRef]
  9. F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
    [CrossRef]
  10. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Welsey, New York, 1993).
  11. A. K. Cherri, M. A. Karim, “Edge enhancement using optical symbolic substitution,” Opt. Eng. 30, 259–264 (1991).
    [CrossRef]

1995 (3)

W. Wang, G. Jin, Y. Yan, M. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. 34, 370–376 (1995).
[CrossRef] [PubMed]

F. Ahmed, M. A. Karim, M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
[CrossRef]

1993 (1)

1992 (2)

W. B. Hahn, D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

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

1991 (2)

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

A. K. Cherri, M. A. Karim, “Edge enhancement using optical symbolic substitution,” Opt. Eng. 30, 259–264 (1991).
[CrossRef]

1988 (1)

1966 (1)

Ahmed, F.

F. Ahmed, M. A. Karim, M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

Alam, M. S.

F. Ahmed, M. A. Karim, M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
[CrossRef]

M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
[CrossRef] [PubMed]

Barnes, T. H.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Caviris, N. P.

Cherri, A. K.

A. K. Cherri, M. A. Karim, “Edge enhancement using optical symbolic substitution,” Opt. Eng. 30, 259–264 (1991).
[CrossRef]

Eiju, T.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Flannery, D. L.

W. B. Hahn, D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Welsey, New York, 1993).

Goodman, J. W.

Hahn, W. B.

W. B. Hahn, D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

Haskell, T. G.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Javidi, B.

Jin, G.

Johnson, F. T. J.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Kanterakis, E. G.

Karim, M. A.

F. Ahmed, M. A. Karim, M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
[CrossRef] [PubMed]

A. K. Cherri, M. A. Karim, “Edge enhancement using optical symbolic substitution,” Opt. Eng. 30, 259–264 (1991).
[CrossRef]

Katz, A.

Kuo, C. J.

Lu, X. J.

Matsuda, K.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Wang, W.

Weaver, C. S.

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Welsey, New York, 1993).

Wu, M.

Yan, Y.

Appl. Opt. (4)

Opt. Eng. (5)

F. Ahmed, M. A. Karim, M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
[CrossRef]

W. B. Hahn, D. L. Flannery, “Design elements of binary joint transform correlation and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

A. K. Cherri, M. A. Karim, “Edge enhancement using optical symbolic substitution,” Opt. Eng. 30, 259–264 (1991).
[CrossRef]

Opt. Lett. (1)

Other (1)

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Welsey, New York, 1993).

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Figures (5)

Fig. 1
Fig. 1

(a) JTC architecture 1. (b) JTC architecture 2.

Fig. 2
Fig. 2

(a) Input scene consisting of a binary cross (target) and r +(x, y) filter (reference). (b) The output obtained by use of the modified Roberts wavelet filter. (c) The correlator output obtained by use of the modified Sobel wavelet filter.

Fig. 3
Fig. 3

Correlation performance obtained by use of a noise-free gray-level target image: (a) the input scene, (b) the correlator output obtained by use of the r +(x, y) filter, and (c) the correlator output obtained by use of the s +(x, y) filter.

Fig. 4
Fig. 4

Correlation performance obtained by use of a noisy gray-level target object (SNR = 2 dB) in the proposed architecture: (a) the input scene, (b) the correlator output obtained by use of the r +(x, y) filter, and (c) the correlator output obtained by use of the s +(x, y) filter.

Fig. 5
Fig. 5

Graph of the correlation-peak intensity versus the SNR obtained with the modified version of the Roberts and the Sobel wavelet filters.

Equations (16)

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r 1 x ,   y = rect x + 0.5 ,   y - 0.5 - rect x - 0.5 ,   y + 0.5 ,
r 2 x ,   y = rect x - 0.5 ,   y - 0.5 - rect x + 0.5 ,   y + 0.5 .
r + x ,   y = 0.5   rect x + 0.5 ,   y - 0.5 + 0.5   rect x - 0.5 ,   y - 0.5 - 0.5   rect x + 0.5 ,   y + 0.5 - 0.5   rect x - 0.5 ,   y + 0.5 ,
r - x ,   y = 0.5   rect x + 0.5 ,   y - 0.5 + 0.5   rect x + 0.5 ,   y + 0.5 - 0.5   rect x - 0.5 ,   y - 0.5 - 0.5   rect x - 0.5 ,   y + 0.5 .
s 1 x ,   y = rect x + 1 ,   y + 1 + 2   rect x ,   y + 1 + rect x - 1 ,   y + 1 - rect x + 1 ,   y - 1 - 2   rect x ,   y - 1 - rect x - 1 ,   y - 1 ,
s 2 x ,   y = rect x - 1 ,   y - 1 + 2   rect x - 1 ,   y + rect x - 1 ,   y + 1 - rect x + 1 ,   y - 1 - 2   rect x + 1 ,   y - rect x + 1 ,   y + 1 .
s + x ,   y = rect x - 1 ,   y + rect x ,   y + 1 + rect x - 1 ,   y + 1 - rect x + 1 ,   y - 1 - rect x ,   y - 1 - rect x + 1 ,   y ,
s - x ,   y = rect x + 1 ,   y + rect x + 1 ,   y + 1 + rect x ,   y + 1 - rect x ,   y - 1 - rect x - 1 ,   y - 1 - rect x - 1 ,   y .
f x ,   y = t x ,   y + y 1 + r + x ,   y - y 2 + n x ,   y + y 1 = t x ,   y + y 1 + 0.5   rect x + 0.5 ,   y - 0.5 - y 2 + 0.5   rect x - 0.5 ,   y - 0.5 - y 2 - 0.5   rect x + 0.5 ,   y + 0.5 - y 2 - 0.5   rect x - 0.5 ,   y + 0.5 - y 2 + n x ,   y + y 1 ,
F u ,   v = | T u ,   v | exp j 2 π vy 1 - 2 j   sinc u ,   v cos π u sin π v ×   exp - j 2 π vy 2 + | N u ,   v | exp j 2 π vy 1 ,
| F u ,   v | 2 = | T u ,   v | 2 + | N u ,   v | 2 + | 2   sinc u ,   v cos π u sin π v | 2 - 4 | T u ,   v | | sinc u ,   v cos π u sin π v | × cos 2 π v y 2 - y 1 + 1 4 v - 4 | N u ,   v | | sinc u ,   v cos π u sin π v | × cos 2 π v y 2 - y 1 + 1 4 v + 2 | T u ,   v | | N u ,   v | .
g ( x ,   y ) = t ( x ,   y ) t * ( x ,   y ) + n ( x ,   y ) n * ( x ,   y ) + [ 2   rect ( x ,   y ) δ ( x ,   y ) ] [ 2   rect ( x ,   y ) δ ( x ,   y ) ] * - [ ( t ( x ,   y ) * { rect ( x ,   y ) δ [ x ,   y - ( y 2 - y 1 ) ] } ) + ( t ( x ,   y ) { rect ( x ,   y ) δ [ x ,   y + ( y 2 - y 1 ) } ] * ) * ] - [ ( n ( x ,   y ) * { rect ( x ,   y ) δ [ x ,   y - ( y 2 - y 1 ) ] } ) + ( n ( x ,   y ) { rect ( x ,   y ) × δ [ x ,   y + ( y 2 - y 1 ) ] } * ) * ] + 2 [ t ( x ,   y ) n ( x ,   y ) δ ( x ,   y ) ] [ t ( x ,   y ) n ( x ,   y ) δ ( x ,   y ) ] * ,
[ ( n x ,   y * rect x ,   y δ x ,   y - y 2 - y 1 ) + ( n x ,   y rect x ,   y δ x ,   y + y 2 - y 1 * ) * ]
| P ( u ,   v ) | + 2 = | F ( u ,   v ) | 2 - | T ( u ,   v ) | 2 - | N ( u ,   v ) | 2 - | 2   sinc ( u ,   v ) cos ( π u ) cos ( π v ) | 2 - 2 | T ( u ,   v ) | | N ( u ,   v ) | = - 4 | T ( u ,   v ) | | sinc ( u ,   v ) cos ( π u ) sin ( π v ) | cos × 2 π v ( y 2 - y 1 + 1 4 v ) - 4 | N ( u ,   v ) | | × sinc ( u ,   v ) cos ( π u ) sin ( π v ) | cos × 2 π v ( y 2 - y 1 + 1 4 v ) .
| P u ,   v | av 2 = | P u ,   v | + 2 + | P u ,   v | - 2 2 .
g ( x ,   y ) = - [ ( t ( x ,   y ) * { rect ( x ,   y ) δ [ x ,   y - ( y 2 - y 1 ) } ] ) + ( t ( x ,   y ) { rect ( x ,   y ) δ [ x ,   y + ( y 2 - y 1 ) ] } * ) * ] - [ ( n ( x ,   y ) * { rect ( x ,   y ) δ [ x ,   y - ( y 2 - y 1 ) ] } ) + ( n ( x ,   y ) { rect ( x ,   y ) × δ [ x ,   y + ( y 2 - y 1 ) ] } * ) * ] .

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