Abstract

Two coherent optical systems are described that can realize local nonlinear preprocessing operators such as the Sobel edge-enhancement function in parallel on a 2-D input image. By local, we refer to the size of the image region rather than a nonstationary process. Realization of such operators using a multiple-exposure matched spatial filter and a computer-generated hologram is discussed. Experimental results using these techniques for 3 × 3 and 5 × 5 Sobel operators, respectively, are presented. Our techniques can be extended to larger window sizes and other edge-enhancement operators. These new operators are achieved by novel coherent systems using complex arithmetic with magnitude evaluation of the output pattern.

© 1983 Optical Society of America

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References

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  1. W. Pratt, Digital Image Processing (Wiley, New York, 1977).
  2. L. Davis, Comput. Graphics Image Process. 4, 248 (Sept.1975).
    [CrossRef]
  3. G. Robinson, Comput. Graphics Image Process. 6, 492 (1977).
    [CrossRef]
  4. R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  5. G. Robinson, J. Reis, “A Real-Time Edge Processing Unit,” in Proceedings, IEEE Workshop on Picture Data Description and Management, Chicago, Apr. 1977, (IEEE, New York, 1977), pp.155–164.
  6. I. Abdou, W. Pratt, Proc. IEEE 67, 753 (1979).
    [CrossRef]
  7. J. Fram, E. Deutsch, Proc. IEEE C-24, 616 (June1975).
  8. A. Arcese, P. H. Mengert, E. W. Trombini, IEEE Trans. Inf. Theory IT-16, 534 (1970).
    [CrossRef]
  9. C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-14, 44 (1976).
    [CrossRef]
  10. C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-15, 257 (1977).
    [CrossRef]
  11. W. K. Pratt, IEEE Trans. Aerosp. Electron. Syst. AES-10, 353 (1974).
    [CrossRef]
  12. Y. Barniv, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 25 (1981).
  13. Y. Barniv, H. Mostafavi, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 238, 156 (1980).
  14. J. Prewitt, “Object Enhancement and Extraction,” in Picture Processing and Psychopictorics, B. Lipkin, A. Rosenfeld, Eds. (Academic, New York, 1970).
  15. I. Abdou, Report 830, U. Southern California, Image Processing Institute (1973).
  16. J. Chen, D. Casasent, at LIA Conference, International Congress on Applications of Lasers and Electro-Optics, Boston (Laser Institute of America, September1982).
  17. S. K. Yao, S. H. Lee, J. Opt. Soc. Am. 61, 474 (1971).
    [CrossRef]
  18. F. Caimi et al., Appl. Opt. 19, 2653 (1980).
    [CrossRef] [PubMed]
  19. W. H. Lee, “Computer-Generated Holograms: Techniques and Applications,” in Progress in Optics, Vol. 16 (North-Holland, New York, 1978).
    [CrossRef]

1981 (1)

Y. Barniv, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 25 (1981).

1980 (2)

Y. Barniv, H. Mostafavi, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 238, 156 (1980).

F. Caimi et al., Appl. Opt. 19, 2653 (1980).
[CrossRef] [PubMed]

1979 (1)

I. Abdou, W. Pratt, Proc. IEEE 67, 753 (1979).
[CrossRef]

1977 (2)

G. Robinson, Comput. Graphics Image Process. 6, 492 (1977).
[CrossRef]

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-15, 257 (1977).
[CrossRef]

1976 (1)

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-14, 44 (1976).
[CrossRef]

1975 (2)

L. Davis, Comput. Graphics Image Process. 4, 248 (Sept.1975).
[CrossRef]

J. Fram, E. Deutsch, Proc. IEEE C-24, 616 (June1975).

1974 (1)

W. K. Pratt, IEEE Trans. Aerosp. Electron. Syst. AES-10, 353 (1974).
[CrossRef]

1971 (1)

1970 (1)

A. Arcese, P. H. Mengert, E. W. Trombini, IEEE Trans. Inf. Theory IT-16, 534 (1970).
[CrossRef]

Abdou, I.

I. Abdou, W. Pratt, Proc. IEEE 67, 753 (1979).
[CrossRef]

I. Abdou, Report 830, U. Southern California, Image Processing Institute (1973).

Arcese, A.

A. Arcese, P. H. Mengert, E. W. Trombini, IEEE Trans. Inf. Theory IT-16, 534 (1970).
[CrossRef]

Barniv, Y.

Y. Barniv, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 25 (1981).

Y. Barniv, H. Mostafavi, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 238, 156 (1980).

Caimi, F.

Casasent, D.

Y. Barniv, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 25 (1981).

Y. Barniv, H. Mostafavi, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 238, 156 (1980).

J. Chen, D. Casasent, at LIA Conference, International Congress on Applications of Lasers and Electro-Optics, Boston (Laser Institute of America, September1982).

Chen, J.

J. Chen, D. Casasent, at LIA Conference, International Congress on Applications of Lasers and Electro-Optics, Boston (Laser Institute of America, September1982).

Davis, L.

L. Davis, Comput. Graphics Image Process. 4, 248 (Sept.1975).
[CrossRef]

Deutsch, E.

J. Fram, E. Deutsch, Proc. IEEE C-24, 616 (June1975).

Duda, R.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Fram, J.

J. Fram, E. Deutsch, Proc. IEEE C-24, 616 (June1975).

Hart, P.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Lee, S. H.

Lee, W. H.

W. H. Lee, “Computer-Generated Holograms: Techniques and Applications,” in Progress in Optics, Vol. 16 (North-Holland, New York, 1978).
[CrossRef]

McGillem, C. D.

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-15, 257 (1977).
[CrossRef]

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-14, 44 (1976).
[CrossRef]

Mengert, P. H.

A. Arcese, P. H. Mengert, E. W. Trombini, IEEE Trans. Inf. Theory IT-16, 534 (1970).
[CrossRef]

Mostafavi, H.

Y. Barniv, H. Mostafavi, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 238, 156 (1980).

Pratt, W.

I. Abdou, W. Pratt, Proc. IEEE 67, 753 (1979).
[CrossRef]

W. Pratt, Digital Image Processing (Wiley, New York, 1977).

Pratt, W. K.

W. K. Pratt, IEEE Trans. Aerosp. Electron. Syst. AES-10, 353 (1974).
[CrossRef]

Prewitt, J.

J. Prewitt, “Object Enhancement and Extraction,” in Picture Processing and Psychopictorics, B. Lipkin, A. Rosenfeld, Eds. (Academic, New York, 1970).

Reis, J.

G. Robinson, J. Reis, “A Real-Time Edge Processing Unit,” in Proceedings, IEEE Workshop on Picture Data Description and Management, Chicago, Apr. 1977, (IEEE, New York, 1977), pp.155–164.

Robinson, G.

G. Robinson, Comput. Graphics Image Process. 6, 492 (1977).
[CrossRef]

G. Robinson, J. Reis, “A Real-Time Edge Processing Unit,” in Proceedings, IEEE Workshop on Picture Data Description and Management, Chicago, Apr. 1977, (IEEE, New York, 1977), pp.155–164.

Svedlow, M.

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-15, 257 (1977).
[CrossRef]

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-14, 44 (1976).
[CrossRef]

Trombini, E. W.

A. Arcese, P. H. Mengert, E. W. Trombini, IEEE Trans. Inf. Theory IT-16, 534 (1970).
[CrossRef]

Yao, S. K.

Appl. Opt. (1)

Comput. Graphics Image Process. (2)

L. Davis, Comput. Graphics Image Process. 4, 248 (Sept.1975).
[CrossRef]

G. Robinson, Comput. Graphics Image Process. 6, 492 (1977).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

W. K. Pratt, IEEE Trans. Aerosp. Electron. Syst. AES-10, 353 (1974).
[CrossRef]

IEEE Trans. Geosci. Electron. (2)

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-14, 44 (1976).
[CrossRef]

C. D. McGillem, M. Svedlow, IEEE Trans. Geosci. Electron. GE-15, 257 (1977).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. Arcese, P. H. Mengert, E. W. Trombini, IEEE Trans. Inf. Theory IT-16, 534 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (2)

I. Abdou, W. Pratt, Proc. IEEE 67, 753 (1979).
[CrossRef]

J. Fram, E. Deutsch, Proc. IEEE C-24, 616 (June1975).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

Y. Barniv, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 292, 25 (1981).

Y. Barniv, H. Mostafavi, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 238, 156 (1980).

Other (7)

J. Prewitt, “Object Enhancement and Extraction,” in Picture Processing and Psychopictorics, B. Lipkin, A. Rosenfeld, Eds. (Academic, New York, 1970).

I. Abdou, Report 830, U. Southern California, Image Processing Institute (1973).

J. Chen, D. Casasent, at LIA Conference, International Congress on Applications of Lasers and Electro-Optics, Boston (Laser Institute of America, September1982).

W. H. Lee, “Computer-Generated Holograms: Techniques and Applications,” in Progress in Optics, Vol. 16 (North-Holland, New York, 1978).
[CrossRef]

W. Pratt, Digital Image Processing (Wiley, New York, 1977).

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

G. Robinson, J. Reis, “A Real-Time Edge Processing Unit,” in Proceedings, IEEE Workshop on Picture Data Description and Management, Chicago, Apr. 1977, (IEEE, New York, 1977), pp.155–164.

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Figures (6)

Fig. 1
Fig. 1

Block diagram of the Sobel operator as a linear operator function and a nonlinear point operator (after Ref. 6).

Fig. 2
Fig. 2

Multiple-exposure Sobel filter synthesis system: M, mirror; VBS, variable beam splitter; CL, collimation lens system; FT lens, Fourier transform lens; MSF, matched spatial filter.

Fig. 3
Fig. 3

System to produce the Sobel edge-enhanced image from a multiple-exposure matched spatial filter.

Fig. 4
Fig. 4

Input image (a) and Sobel edge-enhanced image (b) using the multiple-exposure matched spatial filter system.

Fig. 5
Fig. 5

System to produce the Sobel edge-enhanced image using computer-generated holograms.

Fig. 6
Fig. 6

Input image (a) and edge-enhanced output images (b) using computer-generated holograms (5 × 5 Sobel) and (c) a multiple-matched filter (3 × 3 Sobel).

Equations (19)

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x = [ 1 + 1 0 0 ] , y = [ 1 0 + 1 0 ] .
x = [ 1 0 + 1 1 0 + 1 1 0 + 1 ] , y = [ 1 1 1 0 0 0 + 1 + 1 + 1 ] .
2 f / x 2 = f ( m 1 , n ) 2 f ( m , n ) + f ( m + 1 , n ) .
2 x 2 = [ 0 0 0 1 2 1 0 0 0 ] .
2 x 2 + 2 y 2 = [ 0 0 0 1 2 1 0 0 0 ] + [ 0 1 0 0 2 0 0 1 0 ] = [ 0 1 0 1 4 1 0 1 0 ]
2 x 2 + 2 y 2 = [ 1 0 0 0 2 0 0 0 1 ] + [ 0 0 1 0 2 0 1 0 0 ] = [ 1 0 1 0 4 0 1 0 1 ] .
a 0 a 1 a 2 a 7 f ( m , n ) a 3 a 6 a 5 a 4 .
g ( m , n ) = ( X 2 + Y 2 ) 1 / 2 ,
X = ( a 2 + 2 a 3 + a 4 ) ( a 0 + 2 a 7 + a 6 ) , Y = ( a 0 + 2 a 1 + a 2 ) ( a 6 + 2 a 5 + a 4 ) .
X = [ 1 0 + 1 2 0 + 2 1 0 + 1 ] , Y = [ + 1 + 2 + 1 0 0 0 1 2 1 ] .
g = [ ( f / x y ) 2 + ( f / y x ) 2 ] 1 / 2 ,
X = [ 1 1 0 + 1 + 1 1 1 0 + 1 + 1 2 2 0 + 2 + 2 1 1 0 + 1 + 1 1 1 0 + 1 + 1 ] , Y = [ + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 2 + 1 + 1 0 0 0 0 0 1 1 2 1 1 1 1 2 1 1 ] .
output = f * h = f ( x , y ) * [ δ ( x + d , y ) δ ( x , y ) ] d f / d x ,
g ( m , n ) = ( X 2 + Y 2 ) 1 / 2 = [ | X + j Y | 2 ] 1 / 2 = | X + j Y | .
X + j Y = [ ( a 2 + 2 a 3 + a 4 ) ( a 0 + 2 a 7 + a 6 ) ] + j [ ( a 0 + 2 a 1 + a 2 ) ( a 6 + 2 a 5 + a 4 ) ] ,
g ( x , y ) = f ( x , y ) * m , n k m , n δ ( x m d , y n d )
= f ( x , y ) * [ ( 1 + j ) δ ( x d , y d ) + 2 δ ( x d , y ) + ( 1 j ) δ ( x d , y + d ) + 2 j δ ( x , y d ) 2 j δ ( x , y + d ) ( 1 j ) δ ( x + d , y d ) 2 δ ( x + d , y ) ( 1 + j ) δ ( x + d , y + d ) ] ,
m n k m n δ ( x m d , y n d ) .
A ( x , y ) exp [ j ϕ ( x , y ) ] ,

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